Hyperbolic tangent

Time bar (total: 4.8s)

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 15 to 8 computations (46.7% saved)

sample2.7s (56.2%)

Results
571.0ms7864×256unsamplable
1.4s3990×1024valid
406.0ms2022×512valid
222.0ms2010×256valid
88.0ms234×2048valid
Bogosity

preprocess285.0ms (5.9%)

Algorithm
1×egg-herbie
Rules
1566×div-sub
1010×fma-neg
638×cancel-sign-sub-inv
606×sub-neg
578×neg-mul-1
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2460-0-(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
40-0-(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
00-0-x
01(302.00811970172754)0-(exp.f64 (neg.f64 x))
00-0-(neg.f64 x)
00-0-(exp.f64 x)
00-0-(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
018220
149220
297220
3196220
4544220
52344220
66420220
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(neg.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Symmetry

(negabs x)

Compiler

Compiled 84 to 23 computations (72.6% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶11.9%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 14 to 7 computations (50% saved)

localize80.0ms (1.7%)

Localize:

Found 3 expressions with local error:

NewAccuracyProgram
✓100.0%
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓98.4%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓13.4%
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Compiler

Compiled 35 to 8 computations (77.1% saved)

series4.0ms (0.1%)

Counts
3 → 24
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@0
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
1.0ms
x
@inf
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms
x
@-inf
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms
x
@0
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms
x
@-inf
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite139.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
110×associate-*r*
108×times-frac
80×add-exp-log
80×add-log-exp
80×add-cube-cbrt
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01242
117442
2342442
Stop Event
1×unsound
Counts
3 → 30
Calls
Call 1
Inputs
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Outputs
-2
-1
0
1/2
1
3/2
2
3
4
5
-2
-1
0
1/2
1
3/2
2
3
4
5
-2
-1
0
1/2
1
3/2
2
3
4
5

simplify105.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
1396×fma-def
1008×unswap-sqr
912×associate-*r*
740×associate-*l*
520×distribute-rgt-out
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
061822
1142817
2334811
3964807
43187807
55283807
67064807
Stop Event
1×node limit
Counts
54 → 53
Calls
Call 1
Inputs
(*.f64 2 x)
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x))
(+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))
(+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
2
(+.f64 2 (pow.f64 x 2))
(+.f64 2 (+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2)))
(+.f64 2 (+.f64 (*.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
-2
-1
0
1/2
1
3/2
2
3
4
5
-2
-1
0
1/2
1
3/2
2
3
4
5
-2
-1
0
1/2
1
3/2
2
3
4
5
Outputs
(*.f64 2 x)
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x)))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))
(+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x))))
(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))))
(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7)))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (*.f64 2 x))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 5) 2/15)))
(+.f64 (fma.f64 (pow.f64 x 3) -1/3 x) (*.f64 (pow.f64 x 5) 2/15))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 -17/315 (pow.f64 x 7) (*.f64 (pow.f64 x 5) 2/15))))
(+.f64 (fma.f64 (pow.f64 x 3) -1/3 x) (fma.f64 (pow.f64 x 5) 2/15 (*.f64 (pow.f64 x 7) -17/315)))
(+.f64 x (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 (*.f64 (pow.f64 x 7) -17/315))))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 7) -17/315 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2
(+.f64 2 (pow.f64 x 2))
(fma.f64 x x 2)
(+.f64 2 (+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2)))
(+.f64 2 (fma.f64 1/12 (pow.f64 x 4) (pow.f64 x 2)))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) 2))
(+.f64 2 (+.f64 (*.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))))
(+.f64 2 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (pow.f64 x 2))))
(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) 2)))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) 2)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
-2
-1
0
1/2
1
3/2
2
3
4
5
-2
-1
0
1/2
1
3/2
2
3
4
5
-2
-1
0
1/2
1
3/2
2
3
4
5

eval15.0ms (0.3%)

Compiler

Compiled 782 to 418 computations (46.5% saved)

prune14.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New48553
Fresh000
Picked011
Done000
Total48654
Accuracy
98.6%
Counts
54 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓11.9%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶97.3%
(/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶97.1%
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
▶97.1%
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
▶96.6%
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
▶95.4%
x
Compiler

Compiled 160 to 121 computations (24.4% saved)

localize377.0ms (7.8%)

Localize:

Found 12 expressions with local error:

NewAccuracyProgram
✓100.0%
(+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))
✓99.9%
(*.f64 2/15 (pow.f64 x 5))
✓99.9%
(*.f64 -17/315 (pow.f64 x 7))
✓99.7%
(*.f64 -1/3 (pow.f64 x 3))
✓100.0%
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5)))
✓99.9%
(*.f64 2/15 (pow.f64 x 5))
✓99.7%
(*.f64 -1/3 (pow.f64 x 3))
✓99.7%
(*.f64 (pow.f64 x 3) -1/3)
✓99.9%
(*.f64 1/60 (pow.f64 x 5))
✓99.9%
(*.f64 1/2520 (pow.f64 x 7))
✓99.9%
(/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓99.7%
(*.f64 1/3 (pow.f64 x 3))
Compiler

Compiled 265 to 197 computations (25.7% saved)

series96.0ms (2%)

Counts
12 → 30
Calls

36 calls:

TimeVariablePointExpression
84.0ms
x
@inf
(*.f64 -17/315 (pow.f64 x 7))
2.0ms
x
@inf
(/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms
x
@0
(*.f64 -17/315 (pow.f64 x 7))
1.0ms
x
@-inf
(/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms
x
@0
(*.f64 1/3 (pow.f64 x 3))

rewrite58.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
408×associate-*r*
264×associate-*l*
252×prod-diff
243×log1p-expm1-u
243×expm1-log1p-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037192
1546192
Stop Event
1×node limit
Counts
12 → 480
Calls
Call 1
Inputs
(*.f64 1/3 (pow.f64 x 3))
(/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 1/2520 (pow.f64 x 7))
(*.f64 1/60 (pow.f64 x 5))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 2/15 (pow.f64 x 5))
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5)))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -17/315 (pow.f64 x 7))
(*.f64 2/15 (pow.f64 x 5))
(+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))
Outputs
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14

simplify132.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
1894×times-frac
1530×fma-neg
1294×fma-def
1190×associate-*r*
866×associate-/r/
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
0931818
12041814
23451810
36941806
413511760
536461760
651991754
763851754
Stop Event
1×node limit
Counts
510 → 84
Calls
Call 1
Inputs
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (+.f64 (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (+.f64 (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (+.f64 (*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (+.f64 (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (+.f64 (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (+.f64 (*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))))))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 -17/315 (pow.f64 x 7))
(*.f64 -17/315 (pow.f64 x 7))
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
Outputs
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(fma.f64 -1/3 (pow.f64 x 3) x)
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (*.f64 2/15 (pow.f64 x 5))))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) (*.f64 2/15 (pow.f64 x 5)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 -17/315 (pow.f64 x 7) (*.f64 2/15 (pow.f64 x 5)))))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) (fma.f64 -17/315 (pow.f64 x 7) (*.f64 2/15 (pow.f64 x 5))))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (fma.f64 -17/315 (pow.f64 x 7) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 -17/315 (pow.f64 x 7) (fma.f64 2/15 (pow.f64 x 5) x)))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
(*.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 1/2520 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (pow.f64 x 7)))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520)))
(fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1/2520 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (pow.f64 x 7))))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (+.f64 (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 (pow.f64 x 3) 1/3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (/.f64 1/3 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (pow.f64 x 3))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (pow.f64 x 3) (/.f64 1/3 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))))
(fma.f64 (pow.f64 x 3) (/.f64 1/3 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))))
(fma.f64 (pow.f64 x 3) (/.f64 1/3 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1/2520 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (pow.f64 x 7)))))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (+.f64 (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (+.f64 (*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 2 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 x 2) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))))
(fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (+.f64 (*.f64 1/3 (*.f64 x x)) 2))))
(fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (+.f64 2 (*.f64 1/3 (*.f64 x x))))))
(fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (+.f64 (*.f64 x 2) (*.f64 (pow.f64 x 3) 1/3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))
(/.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
(*.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 1/2520 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (pow.f64 x 7)))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520)))
(fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1/2520 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (pow.f64 x 7))))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (+.f64 (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 (pow.f64 x 3) 1/3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (/.f64 1/3 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (pow.f64 x 3))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (pow.f64 x 3) (/.f64 1/3 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))))
(fma.f64 (pow.f64 x 3) (/.f64 1/3 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))))
(fma.f64 (pow.f64 x 3) (/.f64 1/3 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1/2520 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (pow.f64 x 7)))))
(+.f64 (*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (+.f64 (*.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (+.f64 (*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))) (*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 2 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))))
(fma.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/60 (/.f64 (pow.f64 x 5) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 x 2) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))))
(fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (+.f64 (*.f64 1/3 (*.f64 x x)) 2))))
(fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (+.f64 2 (*.f64 1/3 (*.f64 x x))))))
(fma.f64 (pow.f64 x 5) (/.f64 1/60 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 (pow.f64 x 7) (/.f64 1/2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (+.f64 (*.f64 x 2) (*.f64 (pow.f64 x 3) 1/3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 -17/315 (pow.f64 x 7))
(*.f64 -17/315 (pow.f64 x 7))
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/16003008000
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14

eval42.0ms (0.9%)

Compiler

Compiled 2001 to 1133 computations (43.4% saved)

prune18.0ms (0.4%)

Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New83184
Fresh000
Picked055
Done011
Total83790
Accuracy
98.6%
Counts
90 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶5.9%
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
✓11.9%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓97.3%
(/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓97.1%
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
✓97.1%
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
✓96.6%
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
✓95.4%
x
Compiler

Compiled 100 to 74 computations (26% saved)

localize49.0ms (1%)

Localize:

Found 3 expressions with local error:

NewAccuracyProgram
100.0%
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓99.9%
(/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520)
✓99.9%
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
Compiler

Compiled 41 to 17 computations (58.5% saved)

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
1.0ms
x
@-inf
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
0.0ms
x
@0
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
0.0ms
x
@inf
(/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520)
0.0ms
x
@0
(/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520)

rewrite36.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
128×associate-*r*
86×log1p-expm1-u
86×expm1-log1p-u
85×add-exp-log
85×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01570
120070
2348170
Stop Event
1×unsound
Counts
2 → 72
Calls
Call 1
Inputs
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
(/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520)
Outputs
-128024064000
-10080
-5040
-2520
-4
-2
-1
-1/2
-1/2520
-1/5040
-1/6350400
-1/12700800
0
1/128024064000
1/25401600
1/12700800
1/6350400
1/5040
1/2520
1/2
1
3/2
7/4
2
3
7/2
4
7
14
2520
5040
5041
10080
6350400
12700800
25401600
-128024064000
-10080
-5040
-2520
-4
-2
-1
-1/2
-1/2520
-1/5040
-1/6350400
-1/12700800
0
1/128024064000
1/25401600
1/12700800
1/6350400
1/5040
1/2520
1/2
1
3/2
7/4
2
3
7/2
4
7
14
2520
5040
5041
10080
6350400
12700800
25401600

simplify94.0ms (2%)

Algorithm
1×egg-herbie
Rules
2070×fma-def
1074×associate-*r/
886×distribute-lft-out
848×associate-/l*
682×*-commutative
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
087972
1176952
2330944
3778944
42134944
54571944
67016944
Stop Event
1×node limit
Counts
96 → 69
Calls
Call 1
Inputs
(*.f64 1/5040 (pow.f64 x 7))
(+.f64 (*.f64 -1/10080 (pow.f64 x 9)) (*.f64 1/5040 (pow.f64 x 7)))
(+.f64 (*.f64 -1/10080 (pow.f64 x 9)) (+.f64 (*.f64 1/24192 (pow.f64 x 11)) (*.f64 1/5040 (pow.f64 x 7))))
(+.f64 (*.f64 -1/10080 (pow.f64 x 9)) (+.f64 (*.f64 -61/3628800 (pow.f64 x 13)) (+.f64 (*.f64 1/24192 (pow.f64 x 11)) (*.f64 1/5040 (pow.f64 x 7)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))
5040
(+.f64 5040 (*.f64 2520 (pow.f64 x 2)))
(+.f64 5040 (+.f64 (*.f64 210 (pow.f64 x 4)) (*.f64 2520 (pow.f64 x 2))))
(+.f64 5040 (+.f64 (*.f64 7 (pow.f64 x 6)) (+.f64 (*.f64 210 (pow.f64 x 4)) (*.f64 2520 (pow.f64 x 2)))))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
-128024064000
-10080
-5040
-2520
-4
-2
-1
-1/2
-1/2520
-1/5040
-1/6350400
-1/12700800
0
1/128024064000
1/25401600
1/12700800
1/6350400
1/5040
1/2520
1/2
1
3/2
7/4
2
3
7/2
4
7
14
2520
5040
5041
10080
6350400
12700800
25401600
-128024064000
-10080
-5040
-2520
-4
-2
-1
-1/2
-1/2520
-1/5040
-1/6350400
-1/12700800
0
1/128024064000
1/25401600
1/12700800
1/6350400
1/5040
1/2520
1/2
1
3/2
7/4
2
3
7/2
4
7
14
2520
5040
5041
10080
6350400
12700800
25401600
Outputs
(*.f64 1/5040 (pow.f64 x 7))
(+.f64 (*.f64 -1/10080 (pow.f64 x 9)) (*.f64 1/5040 (pow.f64 x 7)))
(fma.f64 -1/10080 (pow.f64 x 9) (*.f64 1/5040 (pow.f64 x 7)))
(fma.f64 1/5040 (pow.f64 x 7) (*.f64 -1/10080 (pow.f64 x 9)))
(+.f64 (*.f64 -1/10080 (pow.f64 x 9)) (+.f64 (*.f64 1/24192 (pow.f64 x 11)) (*.f64 1/5040 (pow.f64 x 7))))
(fma.f64 -1/10080 (pow.f64 x 9) (fma.f64 1/24192 (pow.f64 x 11) (*.f64 1/5040 (pow.f64 x 7))))
(fma.f64 -1/10080 (pow.f64 x 9) (fma.f64 1/5040 (pow.f64 x 7) (*.f64 1/24192 (pow.f64 x 11))))
(fma.f64 1/5040 (pow.f64 x 7) (fma.f64 -1/10080 (pow.f64 x 9) (*.f64 1/24192 (pow.f64 x 11))))
(+.f64 (*.f64 -1/10080 (pow.f64 x 9)) (+.f64 (*.f64 -61/3628800 (pow.f64 x 13)) (+.f64 (*.f64 1/24192 (pow.f64 x 11)) (*.f64 1/5040 (pow.f64 x 7)))))
(fma.f64 -1/10080 (pow.f64 x 9) (fma.f64 -61/3628800 (pow.f64 x 13) (fma.f64 1/24192 (pow.f64 x 11) (*.f64 1/5040 (pow.f64 x 7)))))
(fma.f64 -1/10080 (pow.f64 x 9) (fma.f64 -61/3628800 (pow.f64 x 13) (fma.f64 1/5040 (pow.f64 x 7) (*.f64 1/24192 (pow.f64 x 11)))))
(fma.f64 -1/10080 (pow.f64 x 9) (fma.f64 1/5040 (pow.f64 x 7) (fma.f64 1/24192 (pow.f64 x 11) (*.f64 -61/3628800 (pow.f64 x 13)))))
(fma.f64 1/5040 (pow.f64 x 7) (fma.f64 -61/3628800 (pow.f64 x 13) (fma.f64 -1/10080 (pow.f64 x 9) (*.f64 1/24192 (pow.f64 x 11)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))
(/.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))
(/.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))
(/.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))))
(/.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 (pow.f64 x 7) 1/2520) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 1/2520 (/.f64 (pow.f64 x 7) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
5040
(+.f64 5040 (*.f64 2520 (pow.f64 x 2)))
(fma.f64 2520 (pow.f64 x 2) 5040)
(+.f64 5040 (+.f64 (*.f64 210 (pow.f64 x 4)) (*.f64 2520 (pow.f64 x 2))))
(+.f64 5040 (fma.f64 210 (pow.f64 x 4) (*.f64 2520 (pow.f64 x 2))))
(+.f64 (fma.f64 2520 (pow.f64 x 2) 5040) (*.f64 210 (pow.f64 x 4)))
(fma.f64 2520 (pow.f64 x 2) (fma.f64 210 (pow.f64 x 4) 5040))
(fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 210 2520) 5040)
(+.f64 5040 (+.f64 (*.f64 7 (pow.f64 x 6)) (+.f64 (*.f64 210 (pow.f64 x 4)) (*.f64 2520 (pow.f64 x 2)))))
(+.f64 5040 (fma.f64 7 (pow.f64 x 6) (fma.f64 210 (pow.f64 x 4) (*.f64 2520 (pow.f64 x 2)))))
(+.f64 (fma.f64 7 (pow.f64 x 6) (*.f64 210 (pow.f64 x 4))) (fma.f64 2520 (pow.f64 x 2) 5040))
(fma.f64 7 (pow.f64 x 6) (fma.f64 2520 (pow.f64 x 2) (fma.f64 210 (pow.f64 x 4) 5040)))
(fma.f64 7 (pow.f64 x 6) (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 210 2520) 5040))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2520)
(fma.f64 (exp.f64 x) 2520 (/.f64 2520 (exp.f64 x)))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2520)
(fma.f64 (exp.f64 x) 2520 (/.f64 2520 (exp.f64 x)))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2520)
(fma.f64 (exp.f64 x) 2520 (/.f64 2520 (exp.f64 x)))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2520)
(fma.f64 (exp.f64 x) 2520 (/.f64 2520 (exp.f64 x)))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2520)
(fma.f64 (exp.f64 x) 2520 (/.f64 2520 (exp.f64 x)))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2520)
(fma.f64 (exp.f64 x) 2520 (/.f64 2520 (exp.f64 x)))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2520)
(fma.f64 (exp.f64 x) 2520 (/.f64 2520 (exp.f64 x)))
(*.f64 2520 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2520)
(fma.f64 (exp.f64 x) 2520 (/.f64 2520 (exp.f64 x)))
-128024064000
-10080
-5040
-2520
-4
-2
-1
-1/2
-1/2520
-1/5040
-1/6350400
-1/12700800
0
1/128024064000
1/25401600
1/12700800
1/6350400
1/5040
1/2520
1/2
1
3/2
7/4
2
3
7/2
4
7
14
2520
5040
5041
10080
6350400
12700800
25401600
-128024064000
-10080
-5040
-2520
-4
-2
-1
-1/2
-1/2520
-1/5040
-1/6350400
-1/12700800
0
1/128024064000
1/25401600
1/12700800
1/6350400
1/5040
1/2520
1/2
1
3/2
7/4
2
3
7/2
4
7
14
2520
5040
5041
10080
6350400
12700800
25401600

eval23.0ms (0.5%)

Compiler

Compiled 730 to 562 computations (23% saved)

prune16.0ms (0.3%)

Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New80181
Fresh000
Picked101
Done066
Total81788
Accuracy
100.0%
Counts
88 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓11.9%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓97.3%
(/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓97.1%
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
✓97.1%
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
✓96.6%
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
✓95.4%
x
▶8.0%
1
Compiler

Compiled 89 to 66 computations (25.8% saved)

localize10.0ms (0.2%)

Compiler

Compiled 3 to 3 computations (0% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune7.0ms (0.1%)

Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done066
Total077
Accuracy
100.0%
Counts
7 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓11.9%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓97.3%
(/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓97.1%
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
✓97.1%
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
✓96.6%
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
✓95.4%
x
✓8.0%
1
Compiler

Compiled 184 to 127 computations (31% saved)

regimes12.0ms (0.2%)

Counts
8 → 2
Calls
Call 1
Inputs
1
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Outputs
(/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1
Calls

2 calls:

8.0ms
x
3.0ms
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Results
AccuracySegmentsBranch
99.7%2x
99.7%2(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 16 to 8 computations (50% saved)

regimes12.0ms (0.2%)

Counts
7 → 2
Calls
Call 1
Inputs
1
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Outputs
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
1
Calls

2 calls:

8.0ms
x
3.0ms
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Results
AccuracySegmentsBranch
99.6%2x
99.6%2(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 16 to 8 computations (50% saved)

regimes7.0ms (0.1%)

Counts
5 → 2
Calls
Call 1
Inputs
1
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(/.f64 (pow.f64 x 7) (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2520))
Outputs
(+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
1
Calls

1 calls:

7.0ms
x
Results
AccuracySegmentsBranch
99.4%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.1%)

Counts
3 → 2
Calls
Call 1
Inputs
1
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
Outputs
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
1
Calls

1 calls:

5.0ms
x
Results
AccuracySegmentsBranch
99.1%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

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

1 calls:

5.0ms
x
Results
AccuracySegmentsBranch
97.6%2x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes11.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
1
Outputs
1
Calls

1 calls:

11.0ms
x
Results
AccuracySegmentsBranch
8.0%1x
Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.20560215945927174
0.9999999845883912
Compiler

Compiled 18 to 10 computations (44.4% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.20560215945927174
0.9999999845883912
Compiler

Compiled 18 to 10 computations (44.4% saved)

bsearch14.0ms (0.3%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
14.0ms
0.20857502206323758
9.340645984289777
Results
13.0ms112×256valid
Compiler

Compiled 144 to 115 computations (20.1% saved)

bsearch14.0ms (0.3%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
14.0ms
0.20857502206323758
9.340645984289777
Results
13.0ms112×256valid
Compiler

Compiled 102 to 80 computations (21.6% saved)

bsearch15.0ms (0.3%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
15.0ms
0.20857502206323758
9.340645984289777
Results
14.0ms112×256valid
Compiler

Compiled 60 to 45 computations (25% saved)

simplify10.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
26×+-commutative
18×*-commutative
6×sub-neg
4×neg-mul-1
4×neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
059413
187413
292413
395413
496413
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3602879701896397/9007199254740992) (/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 1)
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3602879701896397/9007199254740992) (+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5))))) 1)
(if (<=.f64 x 5494391545392005/4503599627370496) (+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5)))) 1)
(if (<=.f64 x 2589569785738035/2251799813685248) (+.f64 x (*.f64 (pow.f64 x 3) -1/3)) 1)
(if (<=.f64 x 1) x 1)
1
Outputs
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3602879701896397/9007199254740992) (/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 1)
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3602879701896397/9007199254740992) (/.f64 (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 x 2)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 1)
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3602879701896397/9007199254740992) (+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5))))) 1)
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3602879701896397/9007199254740992) (+.f64 x (+.f64 (*.f64 (pow.f64 x 3) -1/3) (+.f64 (*.f64 (pow.f64 x 7) -17/315) (*.f64 (pow.f64 x 5) 2/15)))) 1)
(if (<=.f64 x 5494391545392005/4503599627370496) (+.f64 x (+.f64 (*.f64 -1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5)))) 1)
(if (<=.f64 x 5494391545392005/4503599627370496) (+.f64 x (+.f64 (*.f64 (pow.f64 x 3) -1/3) (*.f64 (pow.f64 x 5) 2/15))) 1)
(if (<=.f64 x 2589569785738035/2251799813685248) (+.f64 x (*.f64 (pow.f64 x 3) -1/3)) 1)
(if (<=.f64 x 1) x 1)
1
Compiler

Compiled 124 to 87 computations (29.8% saved)

soundness325.0ms (6.7%)

Rules
1894×times-frac
1530×fma-neg
1396×fma-def
1294×fma-def
1190×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0931818
12041814
23451810
36941806
413511760
536461760
651991754
763851754
01570
120070
2348170
061822
1142817
2334811
3964807
43187807
55283807
67064807
Stop Event
1×node limit
1×unsound
1×node limit
Compiler

Compiled 52 to 31 computations (40.4% saved)

end0.0ms (0%)

preprocess79.0ms (1.6%)

Compiler

Compiled 450 to 282 computations (37.3% saved)

Profiling

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