sqrt D (should all be same)

Time bar (total: 2.0s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample811.0ms (40.4%)

Memory
14.5MiB live, 773.3MiB allocated; 192ms collecting garbage
Samples
528.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 254.0ms
ival-pow2: 118.0ms (46.5% of total)
ival-mult: 61.0ms (24% of total)
ival-sqrt: 60.0ms (23.6% of total)
ival-true: 6.0ms (2.4% of total)
exact: 5.0ms (2% of total)
ival-assert: 3.0ms (1.2% of total)
adjust: 2.0ms (0.8% of total)
Bogosity

explain108.0ms (5.4%)

Memory
-8.2MiB live, 84.9MiB allocated; 17ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1310-5(-1.8327966563181942e-162)(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
00-0-(pow.f64 x #s(literal 2 binary64))
00-0-#s(literal 2 binary64)
00-0-(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))uflow-rescue710
↳(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))underflow71
↳(pow.f64 x #s(literal 2 binary64))underflow71
sqrt.f64(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))oflow-rescue550
↳(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))overflow55
↳(pow.f64 x #s(literal 2 binary64))overflow55
Confusion
Predicted +Predicted -
+1265
-0125
Precision
1.0
Recall
0.9618320610687023
Confusion?
Predicted +Predicted MaybePredicted -
+12605
-00125
Precision?
1.0
Recall?
0.9618320610687023
Freqs
test
numberfreq
0130
1126
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
24.0ms512×0valid
Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-pow2: 6.0ms (45.4% of total)
ival-mult: 3.0ms (22.7% of total)
ival-sqrt: 3.0ms (22.7% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess18.0ms (0.9%)

Memory
20.8MiB live, 20.8MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
11213
23213
39913
415313
524713
627313
729313
056
086
1136
2276
3646
41326
52046
62406
72636
82786
02783
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(hypot.f64 x x)
Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶52.9%
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.4%)

Memory
3.6MiB live, 3.6MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(pow.f64 x #s(literal 2 binary64))
cost-diff0
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
cost-diff3
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0516
0816
11316
22716
36416
413216
520416
624016
726316
827816
027813
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
x
Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(hypot.f64 x x)
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
x

localize17.0ms (0.8%)

Memory
12.3MiB live, 12.3MiB allocated; 0ms collecting garbage
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(pow.f64 x #s(literal 2 binary64))
accuracy0.0234375
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
accuracy30.113187198110104
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
Samples
12.0ms256×0valid
Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-pow2: 3.0ms (46.4% of total)
ival-mult: 2.0ms (30.9% of total)
ival-sqrt: 2.0ms (30.9% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series3.0ms (0.2%)

Memory
2.7MiB live, 2.7MiB allocated; 0ms collecting garbage
Counts
3 → 4
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
Outputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(* -1 (* x (sqrt 2)))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2))
1.0ms
x
@0
((sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2))
1.0ms
x
@-inf
((sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2))

simplify10.0ms (0.5%)

Memory
4.4MiB live, 4.4MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
11817
24317
39217
422817
543717
648517
048517
Stop Event
1×iter limit
1×saturated
Counts
4 → 4
Calls
Call 1
Inputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(* -1 (* x (sqrt 2)))
Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
(*.f64 (*.f64 #s(literal 2 binary64) x) x)
(pow x 2)
(*.f64 x x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))

rewrite66.0ms (3.3%)

Memory
-27.8MiB live, 69.7MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0514
0814
12412
28010
04889
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
3 → 96
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
Outputs
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (neg.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x #s(literal 2 binary64))))
(*.f64 (sqrt.f64 x) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (exp.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 (neg.f64 x)) x)
(hypot.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (neg.f64 (neg.f64 x)))
(hypot.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(hypot.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (neg.f64 x))
(hypot.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) x)
(hypot.f64 (neg.f64 x) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 x) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (neg.f64 (neg.f64 x)))
(hypot.f64 x (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64))))
(*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 x #s(literal 2 binary64)) x)
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(*.f64 (neg.f64 x) (+.f64 (neg.f64 x) (neg.f64 x)))
(*.f64 (neg.f64 x) (-.f64 (neg.f64 x) x))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x (*.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (*.f64 (neg.f64 x) x) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) (*.f64 (neg.f64 x) x)))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x x))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 x x))
(fma.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) x) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) x) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64) (*.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(fma.f64 x x (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 x x (*.f64 x x))
(fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 x) x))
(+.f64 (fma.f64 x x (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(+.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(+.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (-.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (*.f64 (neg.f64 x) x)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (+.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (*.f64 x x)))
(+.f64 (*.f64 x x) (*.f64 (neg.f64 (neg.f64 x)) x))
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))) (*.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))) (-.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (-.f64 (*.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))) (*.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))))))
(neg.f64 (*.f64 (neg.f64 x) x))
(fma.f64 #s(literal 2 binary64) (*.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x))) (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))

eval9.0ms (0.5%)

Memory
17.6MiB live, 17.7MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 024 to 269 computations (73.7% saved)

prune31.0ms (1.5%)

Memory
-30.7MiB live, 14.1MiB allocated; 6ms collecting garbage
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New946100
Fresh000
Picked101
Done000
Total956101
Accuracy
100.0%
Counts
101 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(hypot.f64 x x)
50.3%
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
▶50.5%
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶51.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶52.9%
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
▶50.0%
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
Compiler

Compiled 80 to 66 computations (17.5% saved)

simplify9.0ms (0.4%)

Memory
10.5MiB live, 10.5MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 x)
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
cost-diff0
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 (*.f64 x x) #s(literal 2 binary64))
cost-diff3
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(neg.f64 x)
cost-diff0
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff0
(hypot.f64 x x)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01869
03163
14763
28963
315763
423463
527563
630363
731863
031863
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(hypot.f64 x x)
x
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(sqrt.f64 x)
Outputs
(hypot.f64 x x)
x
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(hypot.f64 x x)
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
x
#s(literal 2 binary64)
(sqrt.f64 x)

localize59.0ms (3%)

Memory
18.6MiB live, 63.7MiB allocated; 6ms collecting garbage
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x #s(literal 2 binary64))
accuracy0.0
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
accuracy0.0
(sqrt.f64 x)
accuracy0.203125
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
accuracy0.0
(*.f64 x x)
accuracy0.00390625
(*.f64 (*.f64 x x) #s(literal 2 binary64))
accuracy15.81717889353128
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
accuracy0.0
(sqrt.f64 #s(literal 2 binary64))
accuracy0.0
(neg.f64 x)
accuracy0.1953125
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy31.841399140595644
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
accuracy0.0
(sqrt.f64 #s(literal 2 binary64))
accuracy0.1953125
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy0.0
(hypot.f64 x x)
Samples
29.0ms130×0valid
19.0ms126×0invalid
Compiler

Compiled 70 to 19 computations (72.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-mult: 20.0ms (54.9% of total)
ival-sqrt: 8.0ms (22% of total)
ival-hypot: 5.0ms (13.7% of total)
ival-pow2: 2.0ms (5.5% of total)
ival-neg: 1.0ms (2.7% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series7.0ms (0.3%)

Memory
10.2MiB live, 10.2MiB allocated; 0ms collecting garbage
Counts
13 → 11
Calls
Call 1
Inputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(sqrt.f64 x)
Outputs
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 x)
(* 2 (pow x 2))
(pow x 2)
(* (sqrt x) (sqrt 2))
(* 2 x)
(sqrt x)
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
Calls

3 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x))
2.0ms
x
@inf
((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x))
2.0ms
x
@0
((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (* x x) 2)) (* (* x x) 2) (* x x) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x))

simplify307.0ms (15.3%)

Memory
-37.8MiB live, 253.5MiB allocated; 40ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02348
15648
214548
330748
463648
598948
6107448
7109448
8109448
9121448
10127048
11127048
12138648
13160048
14193648
15230448
16275548
17362448
18502248
19712848
0805248
Stop Event
1×iter limit
1×node limit
Counts
11 → 11
Calls
Call 1
Inputs
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 x)
(* 2 (pow x 2))
(pow x 2)
(* (sqrt x) (sqrt 2))
(* 2 x)
(sqrt x)
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 x)
(neg.f64 x)
(* 2 (pow x 2))
(*.f64 (*.f64 #s(literal 2 binary64) x) x)
(pow x 2)
(*.f64 x x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 x))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)

rewrite32.0ms (1.6%)

Memory
6.4MiB live, 53.6MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01858
03147
17643
030143
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
13 → 175
Calls
Call 1
Inputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(sqrt.f64 x)
Outputs
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 (neg.f64 x)) x)
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 (neg.f64 x) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (neg.f64 (neg.f64 x)))
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 (neg.f64 x)) x)
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 (neg.f64 x) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (neg.f64 (neg.f64 x)))
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (hypot.f64 x x)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (hypot.f64 x x))
(neg.f64 x)
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 (neg.f64 x)) x)
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 (neg.f64 x) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (neg.f64 (neg.f64 x)))
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 #s(literal 2 binary64) x) x)
(*.f64 (*.f64 x x) #s(literal 2 binary64))
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(*.f64 (neg.f64 x) (+.f64 (neg.f64 x) (neg.f64 x)))
(*.f64 (neg.f64 x) (-.f64 (neg.f64 x) x))
(*.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 x (-.f64 x (neg.f64 x)))
(*.f64 x (*.f64 #s(literal 2 binary64) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (*.f64 (neg.f64 x) x) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (*.f64 x x) (*.f64 (neg.f64 x) x)))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 x x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 x x (*.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(-.f64 (*.f64 x x) (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (*.f64 x x) (*.f64 (neg.f64 (neg.f64 x)) x))
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (neg.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 (neg.f64 x)) x)
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 (neg.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 (neg.f64 x) (neg.f64 (neg.f64 x)))
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (neg.f64 (neg.f64 x)))
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(hypot.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))
(hypot.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 x))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 (neg.f64 x)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) (-.f64 x x))
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(+.f64 x x)
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))

eval10.0ms (0.5%)

Memory
14.8MiB live, 14.8MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 026 to 283 computations (72.4% saved)

prune4.0ms (0.2%)

Memory
8.0MiB live, 8.0MiB allocated; 0ms collecting garbage
Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New1083111
Fresh101
Picked145
Done000
Total1107117
Accuracy
100.0%
Counts
117 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
▶50.3%
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
▶50.5%
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓51.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓52.9%
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
✓50.0%
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
▶49.8%
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
Compiler

Compiled 55 to 45 computations (18.2% saved)

simplify122.0ms (6.1%)

Memory
-28.1MiB live, 161.3MiB allocated; 23ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(sqrt.f64 x)
cost-diff0
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
cost-diff4
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
cost-diff0
(sqrt.f64 x)
cost-diff0
(+.f64 x x)
cost-diff0
(sqrt.f64 (+.f64 x x))
cost-diff0
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
cost-diff0
(neg.f64 x)
cost-diff0
(*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
cost-diff0
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
cost-diff3
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01975
03170
15166
210262
322862
476662
5417462
0878059
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(neg.f64 x)
x
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
x
(sqrt.f64 x)
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 x)
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
Outputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(neg.f64 x)
x
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x #s(literal 2 binary64))))
(sqrt.f64 (+.f64 x x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(+.f64 x x)
(*.f64 x #s(literal 2 binary64))
x
(sqrt.f64 x)
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 x)
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

localize49.0ms (2.4%)

Memory
36.8MiB live, 82.9MiB allocated; 3ms collecting garbage
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(sqrt.f64 x)
accuracy0.0
(sqrt.f64 #s(literal 2 binary64))
accuracy0.203125
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
accuracy0.23113251953688402
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy0.0
(+.f64 x x)
accuracy0.0
(sqrt.f64 (+.f64 x x))
accuracy0.0
(sqrt.f64 x)
accuracy0.203125
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
accuracy0.0
(log.f64 #s(literal 2 binary64))
accuracy0.1953125
(*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
accuracy0.5078125
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
accuracy31.841399140595644
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
Samples
19.0ms126×0invalid
18.0ms130×0valid
Compiler

Compiled 68 to 20 computations (70.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 26.0ms
ival-mult: 8.0ms (30.3% of total)
ival-sqrt: 7.0ms (26.5% of total)
ival-exp: 3.0ms (11.4% of total)
ival-log: 3.0ms (11.4% of total)
ival-pow2: 3.0ms (11.4% of total)
ival-add: 1.0ms (3.8% of total)
ival-neg: 1.0ms (3.8% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series8.0ms (0.4%)

Memory
-45.5MiB live, 9.4MiB allocated; 8ms collecting garbage
Counts
12 → 11
Calls
Call 1
Inputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(neg.f64 x)
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(sqrt.f64 x)
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(log.f64 #s(literal 2 binary64))
Outputs
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(sqrt x)
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2))))
Calls

3 calls:

TimeVariablePointExpression
6.0ms
x
@-inf
((exp (* (log 2) 1/2)) (sqrt (* 2 (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (+ x x) (sqrt x) (* (* (sqrt x) (sqrt 2)) (sqrt x)) (* (sqrt x) (sqrt 2)) (sqrt 2) (log 2))
1.0ms
x
@inf
((exp (* (log 2) 1/2)) (sqrt (* 2 (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (+ x x) (sqrt x) (* (* (sqrt x) (sqrt 2)) (sqrt x)) (* (sqrt x) (sqrt 2)) (sqrt 2) (log 2))
1.0ms
x
@0
((exp (* (log 2) 1/2)) (sqrt (* 2 (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (+ x x) (sqrt x) (* (* (sqrt x) (sqrt 2)) (sqrt x)) (* (sqrt x) (sqrt 2)) (sqrt 2) (log 2))

simplify59.0ms (3%)

Memory
22.9MiB live, 66.4MiB allocated; 6ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02649
16849
221049
343049
494049
5136949
6141649
7142049
8142049
9142049
10149649
11162949
0162949
Stop Event
1×iter limit
1×saturated
Counts
11 → 11
Calls
Call 1
Inputs
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(sqrt x)
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2))))
Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 x)
(neg.f64 x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 x))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))

rewrite45.0ms (2.2%)

Memory
17.3MiB live, 60.0MiB allocated; 11ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01963
03150
17844
026839
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
12 → 110
Calls
Call 1
Inputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(neg.f64 x)
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(sqrt.f64 x)
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(log.f64 #s(literal 2 binary64))
Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (-.f64 (*.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (hypot.f64 x x)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x)))
(fma.f64 (neg.f64 x) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (neg.f64 x) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (*.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x)) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x)))
(+.f64 (*.f64 (neg.f64 x) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (neg.f64 x) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(neg.f64 x)
(*.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x))
(fma.f64 x (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x))
(+.f64 (*.f64 x (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 x (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 x) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 x) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 x) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 x)) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 x)))
(+.f64 (*.f64 (sqrt.f64 x) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 x) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(-.f64 (/.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 x x)
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(pow.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x))
(fma.f64 x (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) x))
(+.f64 (*.f64 x (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 x (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
(fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 x) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 x) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 x) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 x)) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 x)))
(+.f64 (*.f64 (sqrt.f64 x) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 x) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (-.f64 (*.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (*.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(log.f64 #s(literal 2 binary64))

eval8.0ms (0.4%)

Memory
11.0MiB live, 11.0MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 073 to 238 computations (77.8% saved)

prune32.0ms (1.6%)

Memory
-32.8MiB live, 12.0MiB allocated; 6ms collecting garbage
Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New87087
Fresh000
Picked033
Done044
Total87794
Accuracy
100.0%
Counts
94 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
✓50.3%
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
✓50.5%
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓51.8%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓52.9%
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
✓50.0%
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓49.8%
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
Compiler

Compiled 131 to 80 computations (38.9% saved)

regimes12.0ms (0.6%)

Memory
15.3MiB live, 15.3MiB allocated; 0ms collecting garbage
Counts
10 → 1
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
(hypot.f64 x x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
Outputs
(hypot.f64 x x)
Calls

4 calls:

3.0ms
x
3.0ms
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
3.0ms
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
3.0ms
(pow.f64 x #s(literal 2 binary64))
Results
AccuracySegmentsBranch
100.0%1(pow.f64 x #s(literal 2 binary64))
100.0%1(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
100.0%1(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
100.0%1x
Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes10.0ms (0.5%)

Memory
12.9MiB live, 12.9MiB allocated; 0ms collecting garbage
Counts
7 → 2
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (*.f64 x x) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
Outputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
Calls

4 calls:

2.0ms
x
2.0ms
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
2.0ms
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
2.0ms
(pow.f64 x #s(literal 2 binary64))
Results
AccuracySegmentsBranch
79.7%3(pow.f64 x #s(literal 2 binary64))
79.7%3(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
79.7%3(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
99.4%2x
Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes4.0ms (0.2%)

Memory
7.5MiB live, 7.5MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

4 calls:

1.0ms
x
1.0ms
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
1.0ms
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
1.0ms
(pow.f64 x #s(literal 2 binary64))
Results
AccuracySegmentsBranch
51.8%1(pow.f64 x #s(literal 2 binary64))
51.8%1(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
51.8%1(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
51.8%1x
Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch34.0ms (1.7%)

Memory
-27.7MiB live, 21.3MiB allocated; 21ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
33.0ms
-1.6972017374163516e-303
4.456461617020411e-299
Samples
7.0ms160×0valid
Compiler

Compiled 169 to 169 computations (0% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-pow2: 2.0ms (48.2% of total)
ival-mult: 1.0ms (24.1% of total)
ival-sqrt: 1.0ms (24.1% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify45.0ms (2.2%)

Memory
3.7MiB live, 48.0MiB allocated; 9ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01427
12627
24427
38927
416727
526127
645927
7217127
8381827
Stop Event
1×node limit
Calls
Call 1
Inputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
Outputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

derivations52.0ms (2.6%)

Memory
5.1MiB live, 51.0MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
11817
24317
39217
422817
543717
648517
048517
0514
0814
12412
28010
04889
Stop Event
1×done
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
1×iter limit
1×saturated
Compiler

Compiled 27 to 15 computations (44.4% saved)

preprocess20.0ms (1%)

Memory
24.9MiB live, 24.9MiB allocated; 0ms collecting garbage
Compiler

Compiled 66 to 40 computations (39.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

Loading profile data...