sqrt A (should all be same)

Time bar (total: 1.5s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
100%100%0%0%0%0%0%2
Compiler

Compiled 10 to 5 computations (50% saved)

sample821.0ms (54.8%)

Results
810.0ms8256×body256valid
Bogosity

preprocess21.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
174×fma-def
40×associate-*r*
28×distribute-lft-neg-in
22×distribute-lft-in
22×neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
13114
27514
318314
428414
534114
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(sqrt.f64 (+.f64 (*.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (neg.f64 x) (neg.f64 x))))
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (*.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (neg.f64 x) (neg.f64 x))))
(hypot.f64 x x)
Symmetry

(abs x)

Compiler

Compiled 10 to 5 computations (50% saved)

simplify3.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
4×*-commutative
4×associate-*r*
4×count-2
2×fma-def
2×hypot-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
1147
2177
3207
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(hypot.f64 x x)

eval0.0ms (0%)

Compiler

Compiled 12 to 5 computations (58.3% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Accurracy
100.0%
Counts
3 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(hypot.f64 x x)
▶54.4%
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
▶100.0%
(hypot.f64 x x)
▶54.4%
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Compiler

Compiled 26 to 12 computations (53.8% saved)

localize34.0ms (2.3%)

Local Accuracy

Found 2 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(hypot.f64 x x)
✓54.4%
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Compiler

Compiled 25 to 6 computations (76% saved)

series3.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(hypot.f64 x x)
1.0ms
x
@-inf
(hypot.f64 x x)
1.0ms
x
@0
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
0.0ms
x
@0
(hypot.f64 x x)
0.0ms
x
@inf
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))

rewrite61.0ms (4%)

Algorithm
1×batch-egg-rewrite
Rules
1210×pow1
1128×add-exp-log
1126×log1p-expm1-u
1126×expm1-log1p-u
1100×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
116914
2203914
Stop Event
1×node limit
Counts
2 → 126
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
(hypot.f64 x x)
Outputs
(+.f64 (*.f64 x x) (*.f64 x x))
(+.f64 (*.f64 (/.f64 0 0) (*.f64 x x)) (*.f64 (/.f64 0 0) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 x x) (/.f64 0 0)) (*.f64 (*.f64 x x) (/.f64 0 0)))
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(*.f64 x (+.f64 x x))
(*.f64 x (*.f64 (+.f64 x x) (/.f64 0 0)))
(*.f64 (*.f64 x x) 2)
(*.f64 (*.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) 1)
(*.f64 1 (/.f64 0 0))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (pow.f64 x 4))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x x)))
(*.f64 (cbrt.f64 (pow.f64 x 4)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x x)))
(*.f64 2 (*.f64 x x))
(*.f64 2 (*.f64 (*.f64 x x) (/.f64 0 0)))
(*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) 0)))
(*.f64 0 (/.f64 1 0))
(*.f64 (+.f64 x x) x)
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 4 (pow.f64 x 4))
(*.f64 (sqrt.f64 2) x)
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (*.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (*.f64 (/.f64 0 0) x) (+.f64 x x))
(*.f64 (*.f64 (/.f64 0 0) 2) (*.f64 x x))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) 0) (*.f64 2 (pow.f64 x 6))))
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) 0))
(/.f64 0 0)
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 (pow.f64 x 4) 0) (+.f64 (pow.f64 x 4) 0)))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 (pow.f64 x 4) 0) 0))
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 (pow.f64 x 4) 0))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 (pow.f64 x 4) 0))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 1/3)
(fabs.f64 (/.f64 0 0))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(hypot.f64 x x)
(exp.f64 (log.f64 (/.f64 0 0)))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(fma.f64 x x (*.f64 x x))
(fma.f64 1 (*.f64 x x) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x x))
(+.f64 (*.f64 x x) (*.f64 x x))
(+.f64 (*.f64 (/.f64 0 0) (*.f64 x x)) (*.f64 (/.f64 0 0) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 x x) (/.f64 0 0)) (*.f64 (*.f64 x x) (/.f64 0 0)))
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(*.f64 x (+.f64 x x))
(*.f64 x (*.f64 (+.f64 x x) (/.f64 0 0)))
(*.f64 (*.f64 x x) 2)
(*.f64 (*.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) 1)
(*.f64 1 (/.f64 0 0))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (pow.f64 x 4))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x x)))
(*.f64 (cbrt.f64 (pow.f64 x 4)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x x)))
(*.f64 2 (*.f64 x x))
(*.f64 2 (*.f64 (*.f64 x x) (/.f64 0 0)))
(*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) 0)))
(*.f64 0 (/.f64 1 0))
(*.f64 (+.f64 x x) x)
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 4 (pow.f64 x 4))
(*.f64 (sqrt.f64 2) x)
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (*.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (*.f64 (/.f64 0 0) x) (+.f64 x x))
(*.f64 (*.f64 (/.f64 0 0) 2) (*.f64 x x))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) 0) (*.f64 2 (pow.f64 x 6))))
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) 0))
(/.f64 0 0)
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 (pow.f64 x 4) 0) (+.f64 (pow.f64 x 4) 0)))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 (pow.f64 x 4) 0) 0))
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 (pow.f64 x 4) 0))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 (pow.f64 x 4) 0))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 1/3)
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(exp.f64 (log.f64 (/.f64 0 0)))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(fma.f64 x x (*.f64 x x))
(fma.f64 1 (*.f64 x x) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x x))

simplify26.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
52×*-commutative
22×sqr-pow
20×associate-*r*
18×distribute-lft-in
16×associate-*l*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01341304
13761304
Stop Event
1×unsound
Counts
150 → 77
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(+.f64 (*.f64 x x) (*.f64 x x))
(+.f64 (*.f64 (/.f64 0 0) (*.f64 x x)) (*.f64 (/.f64 0 0) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 x x) (/.f64 0 0)) (*.f64 (*.f64 x x) (/.f64 0 0)))
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(*.f64 x (+.f64 x x))
(*.f64 x (*.f64 (+.f64 x x) (/.f64 0 0)))
(*.f64 (*.f64 x x) 2)
(*.f64 (*.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) 1)
(*.f64 1 (/.f64 0 0))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (pow.f64 x 4))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x x)))
(*.f64 (cbrt.f64 (pow.f64 x 4)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x x)))
(*.f64 2 (*.f64 x x))
(*.f64 2 (*.f64 (*.f64 x x) (/.f64 0 0)))
(*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) 0)))
(*.f64 0 (/.f64 1 0))
(*.f64 (+.f64 x x) x)
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 4 (pow.f64 x 4))
(*.f64 (sqrt.f64 2) x)
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (*.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (*.f64 (/.f64 0 0) x) (+.f64 x x))
(*.f64 (*.f64 (/.f64 0 0) 2) (*.f64 x x))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) 0) (*.f64 2 (pow.f64 x 6))))
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) 0))
(/.f64 0 0)
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 (pow.f64 x 4) 0) (+.f64 (pow.f64 x 4) 0)))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 (pow.f64 x 4) 0) 0))
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 (pow.f64 x 4) 0))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 (pow.f64 x 4) 0))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 1/3)
(fabs.f64 (/.f64 0 0))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(hypot.f64 x x)
(exp.f64 (log.f64 (/.f64 0 0)))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(fma.f64 x x (*.f64 x x))
(fma.f64 1 (*.f64 x x) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x x))
(+.f64 (*.f64 x x) (*.f64 x x))
(+.f64 (*.f64 (/.f64 0 0) (*.f64 x x)) (*.f64 (/.f64 0 0) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 x x) (/.f64 0 0)) (*.f64 (*.f64 x x) (/.f64 0 0)))
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(*.f64 x (+.f64 x x))
(*.f64 x (*.f64 (+.f64 x x) (/.f64 0 0)))
(*.f64 (*.f64 x x) 2)
(*.f64 (*.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) 1)
(*.f64 1 (/.f64 0 0))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (pow.f64 x 4))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x x)))
(*.f64 (cbrt.f64 (pow.f64 x 4)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x x)))
(*.f64 2 (*.f64 x x))
(*.f64 2 (*.f64 (*.f64 x x) (/.f64 0 0)))
(*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) 0)))
(*.f64 0 (/.f64 1 0))
(*.f64 (+.f64 x x) x)
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 4 (pow.f64 x 4))
(*.f64 (sqrt.f64 2) x)
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (*.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (*.f64 (/.f64 0 0) x) (+.f64 x x))
(*.f64 (*.f64 (/.f64 0 0) 2) (*.f64 x x))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) 0) (*.f64 2 (pow.f64 x 6))))
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) 0))
(/.f64 0 0)
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 (pow.f64 x 4) 0) (+.f64 (pow.f64 x 4) 0)))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 (pow.f64 x 4) 0) 0))
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 (pow.f64 x 4) 0))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 (pow.f64 x 4) 0))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 1/3)
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(exp.f64 (log.f64 (/.f64 0 0)))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(fma.f64 x x (*.f64 x x))
(fma.f64 1 (*.f64 x x) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x x))
Outputs
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(+.f64 x x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(+.f64 x x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(+.f64 x x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(+.f64 x x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(+.f64 x x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(+.f64 x x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(+.f64 x x)
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 x (+.f64 x x))
(+.f64 (*.f64 (/.f64 0 0) (*.f64 x x)) (*.f64 (/.f64 0 0) (*.f64 x x)))
(*.f64 x (+.f64 x x))
(+.f64 (*.f64 (*.f64 x x) (/.f64 0 0)) (*.f64 (*.f64 x x) (/.f64 0 0)))
(*.f64 x (+.f64 x x))
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
-2
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
-2
(*.f64 x (+.f64 x x))
(*.f64 x (*.f64 (+.f64 x x) (/.f64 0 0)))
(*.f64 x (+.f64 x x))
(*.f64 (*.f64 x x) 2)
(*.f64 x (+.f64 x x))
(*.f64 (*.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))
(*.f64 x (*.f64 x (*.f64 x (+.f64 x x))))
(*.f64 (/.f64 0 0) (/.f64 0 0))
-2
(*.f64 (/.f64 0 0) 1)
-2
(*.f64 1 (/.f64 0 0))
-2
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (pow.f64 x 4))))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (*.f64 -2 (cbrt.f64 (pow.f64 x -2))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x x)))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (*.f64 (+.f64 x x) (cbrt.f64 x)))
(*.f64 (cbrt.f64 (pow.f64 x 4)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (*.f64 -2 (cbrt.f64 (pow.f64 x -2))))
(*.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x x)))
(*.f64 (sqrt.f64 x) (*.f64 (+.f64 x x) (sqrt.f64 x)))
(*.f64 2 (*.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (*.f64 (*.f64 x x) (/.f64 0 0)))
(*.f64 x (+.f64 x x))
(*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) 0)))
-2
(*.f64 0 (/.f64 1 0))
-2
(*.f64 (+.f64 x x) x)
(*.f64 x (+.f64 x x))
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 4 (pow.f64 x 4))
-2
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
-2
(*.f64 (pow.f64 2 1/2) x)
(+.f64 x x)
(*.f64 (*.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (*.f64 -2 (cbrt.f64 (pow.f64 x -2))))
(*.f64 (*.f64 (/.f64 0 0) x) (+.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 (*.f64 (/.f64 0 0) 2) (*.f64 x x))
(*.f64 x (+.f64 x x))
(/.f64 1 (/.f64 0 0))
-2
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) 0) (*.f64 2 (pow.f64 x 6))))
-2
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) 0))
-2
(/.f64 0 0)
-2
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 -2 (cbrt.f64 (pow.f64 x -2)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 (pow.f64 x 4) 0) (+.f64 (pow.f64 x 4) 0)))
-2
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 -2 (sqrt.f64 (pow.f64 x -2)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
-2
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 (pow.f64 x 4) 0) 0))
-2
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 (pow.f64 x 4) 0)))
-2
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) 0)))
-2
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 (pow.f64 x 4) 0))
-2
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 (pow.f64 x 4) 0))
-2
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
-2
(pow.f64 (/.f64 0 0) 1)
-2
(pow.f64 (/.f64 0 0) 1/2)
-2
(pow.f64 (/.f64 0 0) 2)
-2
(pow.f64 (/.f64 0 0) 3)
-2
(pow.f64 (/.f64 0 0) 1/4)
-2
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 -2 3/2)
(pow.f64 (/.f64 0 0) 1/3)
-2
(fabs.f64 (/.f64 0 0))
-2
(log.f64 (exp.f64 (/.f64 0 0)))
-2
(cbrt.f64 (/.f64 0 0))
-2
(expm1.f64 (log1p.f64 (/.f64 0 0)))
-2
(hypot.f64 x x)
(exp.f64 (log.f64 (/.f64 0 0)))
-2
(log1p.f64 (expm1.f64 (/.f64 0 0)))
-2
(fma.f64 x x (*.f64 x x))
(*.f64 x (+.f64 x x))
(fma.f64 1 (*.f64 x x) (*.f64 x x))
(fma.f64 -2 (*.f64 x x) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (pow.f64 (cbrt.f64 x) -2) (*.f64 x x))
(+.f64 (*.f64 x x) (*.f64 x x))
(*.f64 x (+.f64 x x))
(+.f64 (*.f64 (/.f64 0 0) (*.f64 x x)) (*.f64 (/.f64 0 0) (*.f64 x x)))
(*.f64 x (+.f64 x x))
(+.f64 (*.f64 (*.f64 x x) (/.f64 0 0)) (*.f64 (*.f64 x x) (/.f64 0 0)))
(*.f64 x (+.f64 x x))
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
-2
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
-2
(*.f64 x (+.f64 x x))
(*.f64 x (*.f64 (+.f64 x x) (/.f64 0 0)))
(*.f64 x (+.f64 x x))
(*.f64 (*.f64 x x) 2)
(*.f64 x (+.f64 x x))
(*.f64 (*.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))
(*.f64 x (*.f64 x (*.f64 x (+.f64 x x))))
(*.f64 (/.f64 0 0) (/.f64 0 0))
-2
(*.f64 (/.f64 0 0) 1)
-2
(*.f64 1 (/.f64 0 0))
-2
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (pow.f64 x 4))))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (*.f64 -2 (cbrt.f64 (pow.f64 x -2))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x x)))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (*.f64 (+.f64 x x) (cbrt.f64 x)))
(*.f64 (cbrt.f64 (pow.f64 x 4)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (*.f64 -2 (cbrt.f64 (pow.f64 x -2))))
(*.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x x)))
(*.f64 (sqrt.f64 x) (*.f64 (+.f64 x x) (sqrt.f64 x)))
(*.f64 2 (*.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (*.f64 (*.f64 x x) (/.f64 0 0)))
(*.f64 x (+.f64 x x))
(*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) 0)))
-2
(*.f64 0 (/.f64 1 0))
-2
(*.f64 (+.f64 x x) x)
(*.f64 x (+.f64 x x))
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 4 (pow.f64 x 4))
-2
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
-2
(*.f64 (pow.f64 2 1/2) x)
(+.f64 x x)
(*.f64 (*.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (*.f64 -2 (cbrt.f64 (pow.f64 x -2))))
(*.f64 (*.f64 (/.f64 0 0) x) (+.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 (*.f64 (/.f64 0 0) 2) (*.f64 x x))
(*.f64 x (+.f64 x x))
(/.f64 1 (/.f64 0 0))
-2
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) 0) (*.f64 2 (pow.f64 x 6))))
-2
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) 0))
-2
(/.f64 0 0)
-2
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 -2 (cbrt.f64 (pow.f64 x -2)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 (pow.f64 x 4) 0) (+.f64 (pow.f64 x 4) 0)))
-2
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 -2 (sqrt.f64 (pow.f64 x -2)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
-2
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 (pow.f64 x 4) 0) 0))
-2
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 (pow.f64 x 4) 0)))
-2
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) 0)))
-2
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 (pow.f64 x 4) 0))
-2
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 (pow.f64 x 4) 0))
-2
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
-2
(pow.f64 (/.f64 0 0) 1)
-2
(pow.f64 (/.f64 0 0) 1/2)
-2
(pow.f64 (/.f64 0 0) 2)
-2
(pow.f64 (/.f64 0 0) 3)
-2
(pow.f64 (/.f64 0 0) 1/4)
-2
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 -2 3/2)
(pow.f64 (/.f64 0 0) 1/3)
-2
(sqrt.f64 (/.f64 0 0))
-2
(fabs.f64 (/.f64 0 0))
-2
(log.f64 (exp.f64 (/.f64 0 0)))
-2
(cbrt.f64 (/.f64 0 0))
-2
(expm1.f64 (log1p.f64 (/.f64 0 0)))
-2
(exp.f64 (log.f64 (/.f64 0 0)))
-2
(log1p.f64 (expm1.f64 (/.f64 0 0)))
-2
(fma.f64 x x (*.f64 x x))
(*.f64 x (+.f64 x x))
(fma.f64 1 (*.f64 x x) (*.f64 x x))
(fma.f64 -2 (*.f64 x x) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (pow.f64 (cbrt.f64 x) -2) (*.f64 x x))

eval20.0ms (1.3%)

Compiler

Compiled 620 to 434 computations (30% saved)

prune12.0ms (0.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New74377
Fresh000
Picked022
Done000
Total74579
Accurracy
100.0%
Counts
79 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
▶20.3%
(+.f64 x x)
▶99.3%
(*.f64 (sqrt.f64 2) x)
✓54.4%
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
1.7%
-2
✓100.0%
(hypot.f64 x x)
▶20.3%
(+.f64 x x)
▶99.3%
(*.f64 (sqrt.f64 2) x)
✓54.4%
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
1.7%
-2
Compiler

Compiled 48 to 28 computations (41.7% saved)

localize26.0ms (1.8%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓99.3%
(*.f64 (sqrt.f64 2) x)
Compiler

Compiled 14 to 9 computations (35.7% saved)

series0.0ms (0%)

Counts
1 → 0
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
(*.f64 (sqrt.f64 2) x)
0.0ms
x
@0
(*.f64 (sqrt.f64 2) x)
0.0ms
x
@inf
(*.f64 (sqrt.f64 2) x)

rewrite50.0ms (3.3%)

Algorithm
1×batch-egg-rewrite
Rules
1182×pow1
1084×add-exp-log
1084×log1p-expm1-u
1084×expm1-log1p-u
1058×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
113811
2150811
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) x)
Outputs
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(sqrt.f64 (*.f64 2 (*.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))

simplify61.0ms (4%)

Algorithm
1×egg-herbie
Rules
1896×log-prod
954×fma-neg
806×*-commutative
676×distribute-lft-out
640×distribute-rgt-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032253
179187
2271121
31535121
44437121
56814121
Stop Event
1×node limit
Counts
11 → 14
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(sqrt.f64 (*.f64 2 (*.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
Outputs
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (*.f64 2 (*.f64 x x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)

eval3.0ms (0.2%)

Compiler

Compiled 92 to 77 computations (16.3% saved)

prune4.0ms (0.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New13114
Fresh011
Picked022
Done112
Total14519
Accurracy
100.0%
Counts
19 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
✓20.3%
(+.f64 x x)
✓99.3%
(*.f64 (sqrt.f64 2) x)
▶54.4%
(sqrt.f64 (*.f64 2 (*.f64 x x)))
1.7%
-2
✓100.0%
(hypot.f64 x x)
✓20.3%
(+.f64 x x)
✓99.3%
(*.f64 (sqrt.f64 2) x)
▶54.4%
(sqrt.f64 (*.f64 2 (*.f64 x x)))
1.7%
-2
Compiler

Compiled 44 to 30 computations (31.8% saved)

localize24.0ms (1.6%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓54.4%
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Compiler

Compiled 18 to 9 computations (50% saved)

series0.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(sqrt.f64 (*.f64 2 (*.f64 x x)))
0.0ms
x
@inf
(sqrt.f64 (*.f64 2 (*.f64 x x)))
0.0ms
x
@-inf
(sqrt.f64 (*.f64 2 (*.f64 x x)))

rewrite56.0ms (3.7%)

Algorithm
1×batch-egg-rewrite
Rules
1354×pow1
1244×add-exp-log
1244×log1p-expm1-u
1244×expm1-log1p-u
1214×add-log-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0817
116011
2181011
Stop Event
1×node limit
Counts
1 → 24
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Outputs
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(*.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 1 (*.f64 x (sqrt.f64 2)))
(*.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (*.f64 x x))))
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))
(*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))
(*.f64 (pow.f64 1 1/2) (*.f64 x (sqrt.f64 2)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1/2))
(*.f64 (pow.f64 (*.f64 2 x) 1/2) (sqrt.f64 x))
(pow.f64 (*.f64 2 (*.f64 x x)) 1/2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))

simplify55.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
1366×log-prod
812×associate-*r*
808×distribute-rgt-in
776×distribute-lft-in
714×associate-*l*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061504
1138504
2486504
32721504
46903504
Stop Event
1×node limit
Counts
36 → 29
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(*.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 1 (*.f64 x (sqrt.f64 2)))
(*.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (*.f64 x x))))
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))
(*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))
(*.f64 (pow.f64 1 1/2) (*.f64 x (sqrt.f64 2)))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1/2))
(*.f64 (pow.f64 (*.f64 2 x) 1/2) (sqrt.f64 x))
(pow.f64 (*.f64 2 (*.f64 x x)) 1/2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 -1 (*.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 (sqrt.f64 2) x)
(*.f64 1 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (*.f64 x x))))
(*.f64 (sqrt.f64 2) x)
(*.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))
(*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 2 x)))
(*.f64 (pow.f64 1 1/2) (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 1/2))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 x x)))))
(*.f64 (pow.f64 (*.f64 2 x) 1/2) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 2 x)))
(pow.f64 (*.f64 2 (*.f64 x x)) 1/2)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 (sqrt.f64 2) x)
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) x)
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(*.f64 (sqrt.f64 2) x)
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)

eval6.0ms (0.4%)

Compiler

Compiled 228 to 177 computations (22.4% saved)

prune7.0ms (0.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New29029
Fresh011
Picked011
Done033
Total29534
Accurracy
100.0%
Counts
34 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
✓20.3%
(+.f64 x x)
✓99.3%
(*.f64 (sqrt.f64 2) x)
✓54.4%
(sqrt.f64 (*.f64 2 (*.f64 x x)))
1.7%
-2
✓100.0%
(hypot.f64 x x)
✓20.3%
(+.f64 x x)
✓99.3%
(*.f64 (sqrt.f64 2) x)
✓54.4%
(sqrt.f64 (*.f64 2 (*.f64 x x)))
1.7%
-2
Compiler

Compiled 44 to 30 computations (31.8% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done044
Total055
Accurracy
100.0%
Counts
5 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 x x)
✓20.3%
(+.f64 x x)
✓99.3%
(*.f64 (sqrt.f64 2) x)
✓54.4%
(sqrt.f64 (*.f64 2 (*.f64 x x)))
1.7%
-2
Compiler

Compiled 48 to 28 computations (41.7% saved)

regimes26.0ms (1.7%)

Counts
6 → 1
Calls
Call 1
Inputs
-2
(+.f64 x x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (*.f64 2 (*.f64 x x)))
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Outputs
(hypot.f64 x x)
Calls

4 calls:

15.0ms
x
3.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
3.0ms
(*.f64 x x)
3.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
100.0%1(+.f64 (*.f64 x x) (*.f64 x x))
100.0%1(*.f64 x x)
Compiler

Compiled 49 to 23 computations (53.1% saved)

regimes3.0ms (0.2%)

Counts
2 → 1
Calls
Call 1
Inputs
-2
(+.f64 x x)
Outputs
(+.f64 x x)
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
20.3%1x
Compiler

Compiled 7 to 4 computations (42.9% saved)

regimes3.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
-2
Outputs
-2
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
1.7%1x
Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(hypot.f64 x x)
(+.f64 x x)
-2
Outputs
(hypot.f64 x x)
(+.f64 x x)
-2
Compiler

Compiled 10 to 6 computations (40% saved)

soundness140.0ms (9.3%)

Rules
1210×pow1
1128×add-exp-log
1126×log1p-expm1-u
1126×expm1-log1p-u
1100×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
1147
2177
3207
0814
116914
2203914
01341304
13761304
01341304
13761304
Stop Event
1×unsound
1×unsound
1×node limit
1×saturated
Compiler

Compiled 203 to 34 computations (83.3% saved)

end0.0ms (0%)

preprocess23.0ms (1.6%)

Remove

(abs x)

Compiler

Compiled 42 to 20 computations (52.4% saved)

Profiling

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