sqrtexp (problem 3.4.4)

Time bar (total: 3.8s)

analyze178.0ms (4.6%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
50%50%50%0%0%0%0%3
50%50%50%0%0%0%0%4
50%50%50%0%0%0%0%5
53.1%53.1%46.9%0%0%0%0%6
54.7%54.7%45.3%0%0%0%0%7
55.5%55.4%44.5%0%0%0%0%8
55.9%55.8%44.1%0%0%0%0%9
56.1%56%43.9%0%0%0%0%10
56.2%56.1%43.8%0%0%0%0%11
56.2%56.2%43.8%0%0%0%0%12
Compiler

Compiled 14 to 12 computations (14.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 93.0ms
ival-exp: 38.0ms (40.8% of total)
ival-sub: 18.0ms (19.3% of total)
ival-mult: 17.0ms (18.2% of total)
ival-sqrt: 11.0ms (11.8% of total)
ival-div: 6.0ms (6.4% of total)
const: 3.0ms (3.2% of total)

sample2.8s (74.4%)

Results
1.7s5058×1valid
380.0ms3149×0valid
204.0ms2766×0unsamplable
5.0ms49×0infinite
Precisions
Click to see histograms. Total time spent on operations: 1.7s
ival-exp: 788.0ms (47.1% of total)
ival-sub: 309.0ms (18.5% of total)
ival-mult: 158.0ms (9.4% of total)
backward-pass: 145.0ms (8.7% of total)
ival-sqrt: 131.0ms (7.8% of total)
ival-div: 104.0ms (6.2% of total)
const: 38.0ms (2.3% of total)
Bogosity

preprocess90.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
612×div-sub
326×associate--r+
307×associate-+l-
283×fma-define
257×associate--l+
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
024144
156136
282136
3128136
422196
540184
680384
7295984
Stop Event
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x))) #s(literal 1 binary64)) (-.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64))))
(neg.f64 (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x))) #s(literal 1 binary64)) (-.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64)))))
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x))) #s(literal 1 binary64)) (-.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x))) (expm1.f64 (neg.f64 x))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal -2 binary64))) (expm1.f64 (neg.f64 x))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x))))
(neg.f64 (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x))) #s(literal 1 binary64)) (-.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64)))))
(neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x))) (expm1.f64 (neg.f64 x)))))
(neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal -2 binary64))) (expm1.f64 (neg.f64 x)))))
(neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))))

explain382.0ms (10%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1790-1(0.013553827685649502)(-.f64 (exp.f64 x) #s(literal 1 binary64))
1780-0-(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
00-0-x
00-0-(exp.f64 x)
00-0-(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
00-0-#s(literal 2 binary64)
00-0-(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
00-0-(*.f64 #s(literal 2 binary64) x)
00-0-#s(literal 1 binary64)
01(215.45917748643674)0-(exp.f64 (*.f64 #s(literal 2 binary64) x))
Results
50.0ms210×256valid
180.0ms200×1024valid
44.0ms86×512valid
19.0ms16×2048valid
Compiler

Compiled 107 to 79 computations (26.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 222.0ms
ival-exp: 118.0ms (53.2% of total)
ival-mult: 41.0ms (18.5% of total)
ival-sub: 35.0ms (15.8% of total)
ival-div: 13.0ms (5.9% of total)
ival-sqrt: 8.0ms (3.6% of total)
const: 7.0ms (3.2% of total)

eval1.0ms (0%)

Compiler

Compiled 21 to 16 computations (23.8% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
Compiler

Compiled 6 to 5 computations (16.7% saved)

localize147.0ms (3.9%)

Results
139.0ms256×256valid
Compiler

Compiled 15 to 9 computations (40% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-add: 3.0ms (40.6% of total)
ival-exp: 2.0ms (27% of total)
ival-sqrt: 2.0ms (27% of total)
const: 1.0ms (13.5% of total)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done000
Total011
Accuracy
100.0%
Counts
1 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
Compiler

Compiled 24 to 19 computations (20.8% saved)

regimes3.0ms (0.1%)

Accuracy

Total -43.0b remaining (-∞%)

Threshold costs -43b (-∞%)

Counts
2 → 1
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Outputs
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
Calls

3 calls:

1.0ms
x
1.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
1.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
100.0%1(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
3×1-exp
1×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11618
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
Outputs
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

soundness140.0ms (3.7%)

Rules
612×div-sub
326×associate--r+
307×associate-+l-
283×fma-define
257×associate--l+
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
024144
156136
282136
3128136
422196
540184
680384
7295984
Stop Event
1×done
1×node limit
Compiler

Compiled 91 to 61 computations (33% saved)

preprocess32.0ms (0.8%)

Compiler

Compiled 38 to 32 computations (15.8% saved)

end0.0ms (0%)

Profiling

Loading profile data...