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sa pa
APPROX 2014 Adrian Sampson
Two Approximate- Programmability Birds, One Statistical- Inference Stone
University of Washington
Two Approximate- Programmability Birds, One Statistical- Inference - - PowerPoint PPT Presentation
Two Approximate- Programmability Birds, One Statistical- Inference - - PowerPoint PPT Presentation
Two Approximate- Programmability Birds, One Statistical- Inference Stone Adrian Sampson University of Washington sa pa APPROX 2014 Assisted approximate programming Statistical inference Cheap check generation 1 Assisted approximate
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Assisted approximate programming Cheap check generation Statistical inference
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Assisted approximate programming Cheap check generation Statistical inference
1 2 3 4
Next steps
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Expressing quality
Pr[d(f(x), f 0(x)) ≤ b] ≥ p
- riginal program
relaxed version distance metric input bounding parameters
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Assisted approximate programming
f f 0
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Assisted approximate programming
f f 0
int p = 5; @Approx int a = 7; for (int x = 0..) { a += func(2); @Approx int z; z = p * 2; p += 4; } a /= 9; func2(p); a += func(2); @Approx int y; z = p * 22 + z; p += 10; int p = 5; int a = 7; for (int x = 0..) { a += func(2); int z; z = p * 2; p += 4; } a /= 9; func2(p); a += func(2); int y; z = p * 22 + z; p += 10;
Manual
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Assisted approximate programming
f f 0
+
Pr[d(f(x), f 0(x)) ≤ b] ≥ p
ExpAX [Esmaeilzadeh+] Syndy [Misailovic and Rinard, WACAS] Optimization in Rely [Misailovic+] ⋮
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Assisted approximate programming Cheap check generation Statistical inference
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Quality: the fantasy
Correctness Probability
Inputs average probability
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Quality: the reality
Correctness Probability
Inputs average probability
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Cheap checks to fall back to precise execution
Correctness Probability
Inputs average probability
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Cheap checks
f f 0
Pr[d(f(x), f 0(x)) ≤ b] ≥ p
x s.t.
Pr[d(f(x), f 0(x)) ≤ b] ≥ p
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Assisted approximate programming Cheap check generation Statistical inference
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Approximate program
def dist(x1, y1, x2, y2): return sqrt((x1 − x2) ∗∗ 2 + (y1 − y2) ∗∗ 2)
approximate operations
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Approximate program → probabilistic program
def dist(x1, y1, x2, y2): return sqrt((x1 − x2 + error()) ∗∗ 2 + (y1 − y2 + error()) ∗∗ 2) + error()
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Assisted approximate programming as statistical inference
def dist(x1, y1, x2, y2): return sqrt((x1 − x2 + error(?)) ∗∗ 2 + (y1 − y2 + error(?)) ∗∗ 2) + error(?)
s.t.
Pr[d(f(x), f 0(x)) ≤ b] ≥ p
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Cheap check generation as statistical inference
def dist(x1, y1, x2, y2): return sqrt((x1 − x2 + error()) ∗∗ 2 + (y1 − y2 + error()) ∗∗ 2) + error()
s.t.
Pr[d(f(x), f 0(x)) ≤ b] ≥ p
x1 = dist(?) y1 = dist(?) x2 = dist(?) y2 = dist(?)
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First steps
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First steps: translate to a probability distribution
int p = 5; int a = 7; for (int x = 0..) { a += func(2); int z; z = p * 2; p += 4; } a /= 9; func2(p); a += func(2); int y; z = p * 22 + z; p += 10;
? ? ?
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First steps: statistical inference with constraints?
? ? ?
Pr[d(f(x), f 0(x)) ≤ b] ≥ p
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First steps: statistical inference with constraints and objectives?
? ? ?
Pr[d(f(x), f 0(x)) ≤ b] ≥ p
minimize
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First steps: statistical inference with constraints and objectives scalably?
? ? ?
Pr[d(f(x), f 0(x)) ≤ b] ≥ p
minimize
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Assisted approximate programming Cheap check generation Statistical inference
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