Details

Time bar (total: 3.0s)

analyze4.0ms (0.1%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
25%25%75%0%0%0%0%3
62.5%62.5%37.5%0%0%0%0%4
78.6%68.7%18.7%0%12.5%0%0%5
88.5%71.8%9.4%0%18.7%0%0%6
94%73.4%4.7%0%21.9%0%0%7
96.9%74.2%2.3%0%23.4%0%0%8
98.5%74.6%1.2%0%24.2%0%0%9
99.2%75%0.6%0%24.4%0%0%10
99.6%75.1%0.3%0%24.6%0%0%11
99.8%75.1%0.1%0%24.7%0%0%12
Compiler

Compiled 8 to 6 computations (25% saved)

sample2.2s (71.1%)

Results
1.2s2816×body1024valid
413.0ms1381×body512valid
354.0ms3778×body256valid
154.0ms281×body2048valid
0.0ms4×body256infinite
Bogosity

preprocess21.0ms (0.7%)

Algorithm
2×egg-herbie
Rules
186×fma-def
78×associate-*r*
78×associate--r+
70×*-commutative
66×associate-+l-
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11711
22011
32411
43311
54311
66211
711811
817911
926311
1040011
1158911
1266711
1370911
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
Outputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
Compiler

Compiled 8 to 6 computations (25% saved)

simplify27.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
186×fma-def
78×associate-*r*
78×associate--r+
70×*-commutative
66×associate-+l-
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11711
22011
32411
43311
54311
66211
711811
817911
926311
1040011
1158911
1266711
1370911
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
Outputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)

eval0.0ms (0%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
100.0%
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶100.0%
(/.f64 (expm1.f64 x) x)
Compiler

Compiled 5 to 3 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
Compiler

Compiled 8 to 3 computations (62.5% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(/.f64 (expm1.f64 x) x)
0.0ms
x
@inf
(/.f64 (expm1.f64 x) x)
0.0ms
x
@0
(/.f64 (expm1.f64 x) x)

rewrite58.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
1258×add-sqr-sqrt
1246×*-un-lft-identity
1158×add-cube-cbrt
1142×add-cbrt-cube
1130×add-exp-log
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
112011
2153811
Stop Event
1×node limit
Counts
1 → 31
Calls
Call 1
Inputs
(/.f64 (expm1.f64 x) x)
Outputs
((((-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1) (2))) (((-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x)) (2))) (((*.f64 (expm1.f64 x) (/.f64 1 x)) (2))) (((*.f64 (/.f64 (expm1.f64 x) x) 1) (2))) (((*.f64 1 (/.f64 (expm1.f64 x) x)) (2))) (((*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x))) (2))) (((*.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x))) (2))) (((*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2)) (2))) (((*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x))) (2))) (((*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x))) (2))) (((*.f64 (/.f64 1 x) (expm1.f64 x)) (2))) (((*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x))) (2))) (((*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x))) (2))) (((*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x))) (2))) (((*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x)) (2))) (((*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x))) (2))) (((*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x)) (2))) (((*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x))) (2))) (((*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x))) (2))) (((pow.f64 (/.f64 (expm1.f64 x) x) 1) (2))) (((pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2) (2))) (((pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) (2))) (((pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3) (2))) (((pow.f64 (/.f64 x (expm1.f64 x)) -1) (2))) (((neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x))) (2))) (((sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) (2))) (((log.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (2))) (((cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (2))) (((expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) (2))) (((exp.f64 (log.f64 (/.f64 (expm1.f64 x) x))) (2))) (((log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x))) (2))))

simplify52.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
1044×associate-+r+
848×associate-+l+
802×*-commutative
596×associate-*r/
416×associate-+l-
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
097595
1240579
2990579
34388579
Stop Event
1×node limit
Counts
43 → 48
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x 1/6) (fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) 1)))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(/.f64 (expm1.f64 x) x)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (expm1.f64 x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(/.f64 (expm1.f64 x) x)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 x) (expm1.f64 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2))
(/.f64 (expm1.f64 x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) (*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2))
(/.f64 (expm1.f64 x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) (*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(/.f64 (expm1.f64 x) x)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(/.f64 (expm1.f64 x) x)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(/.f64 (expm1.f64 x) x)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(/.f64 (expm1.f64 x) x)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(/.f64 (expm1.f64 x) x)
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(/.f64 (expm1.f64 x) x)
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(/.f64 (expm1.f64 x) x)
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(/.f64 (expm1.f64 x) x)
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)

eval10.0ms (0.3%)

Compiler

Compiled 449 to 217 computations (51.7% saved)

prune7.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New45348
Fresh000
Picked011
Done000
Total45449
Error
100.0%
Counts
49 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶100.0%
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
✓100.0%
(/.f64 (expm1.f64 x) x)
▶63.5%
(+.f64 (*.f64 1/2 x) 1)
64.5%
1
Compiler

Compiled 20 to 15 computations (25% saved)

localize5.0ms (0.2%)

Compiler

Compiled 12 to 9 computations (25% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓100.0%
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
✓100.0%
(/.f64 x (expm1.f64 x))
Compiler

Compiled 15 to 6 computations (60% saved)

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 x (expm1.f64 x))
0.0ms
x
@-inf
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
0.0ms
x
@-inf
(/.f64 x (expm1.f64 x))
0.0ms
x
@inf
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
0.0ms
x
@0
(/.f64 x (expm1.f64 x))

rewrite60.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
1580×add-sqr-sqrt
1558×*-un-lft-identity
1456×add-cube-cbrt
1438×add-cbrt-cube
1424×add-exp-log
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0828
116522
2200722
Stop Event
1×node limit
Counts
2 → 73
Calls
Call 1
Inputs
(/.f64 x (expm1.f64 x))
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Outputs
((((-.f64 (+.f64 1 (/.f64 x (expm1.f64 x))) 1) (2))) (((*.f64 x (/.f64 1 (expm1.f64 x))) (2))) (((*.f64 (/.f64 x (expm1.f64 x)) 1) (2))) (((*.f64 1 (/.f64 x (expm1.f64 x))) (2))) (((*.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) (sqrt.f64 (/.f64 x (expm1.f64 x)))) (2))) (((*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 x)))) (2))) (((*.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2)) (2))) (((*.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) (cbrt.f64 (/.f64 x (expm1.f64 x)))) (2))) (((*.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 x)))) (2))) (((*.f64 (/.f64 1 (expm1.f64 x)) x) (2))) (((*.f64 (neg.f64 x) (/.f64 1 (neg.f64 (expm1.f64 x)))) (2))) (((*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 x (sqrt.f64 (expm1.f64 x)))) (2))) (((*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 x (cbrt.f64 (expm1.f64 x)))) (2))) (((*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (expm1.f64 x))) (2))) (((*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x)))) (2))) (((*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) 1) (/.f64 (cbrt.f64 x) (expm1.f64 x))) (2))) (((*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 x)))) (2))) (((*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x)))) (2))) (((pow.f64 (/.f64 x (expm1.f64 x)) 1) (2))) (((pow.f64 (/.f64 (expm1.f64 x) x) -1) (2))) (((pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) 2) (2))) (((pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 3) (2))) (((pow.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 3) 1/3) (2))) (((neg.f64 (/.f64 x (neg.f64 (expm1.f64 x)))) (2))) (((sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2)) (2))) (((log.f64 (exp.f64 (/.f64 x (expm1.f64 x)))) (2))) (((cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 3)) (2))) (((expm1.f64 (log1p.f64 (/.f64 x (expm1.f64 x)))) (2))) (((exp.f64 (log.f64 (/.f64 x (expm1.f64 x)))) (2))) (((exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) 1)) (2))) (((log1p.f64 (expm1.f64 (/.f64 x (expm1.f64 x)))) (2))))
((((-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1) (2))) (((-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x)) (2))) (((*.f64 (expm1.f64 x) (/.f64 1 x)) (2))) (((*.f64 (/.f64 (expm1.f64 x) x) 1) (2))) (((*.f64 1 (/.f64 (expm1.f64 x) x)) (2))) (((*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x))) (2))) (((*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2))) (2))) (((*.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)) (cbrt.f64 (/.f64 (expm1.f64 x) x))) (2))) (((*.f64 (/.f64 1 x) (expm1.f64 x)) (2))) (((*.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x))) (2))) (((*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x))) (2))) (((*.f64 (/.f64 1 (cbrt.f64 (*.f64 x x))) (/.f64 (expm1.f64 x) (cbrt.f64 x))) (2))) (((*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x)) (2))) (((*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x))) (2))) (((*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (*.f64 x x))) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x))) (2))) (((*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x)) (2))) (((*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x))) (2))) (((*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x))) (2))) (((*.f64 (pow.f64 x -1) (pow.f64 (/.f64 1 (expm1.f64 x)) -1)) (2))) (((*.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1)) (2))) (((*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1)) (2))) (((/.f64 (expm1.f64 x) x) (2))) (((/.f64 -1 (neg.f64 (/.f64 x (expm1.f64 x)))) (2))) (((/.f64 1 (/.f64 x (expm1.f64 x))) (2))) (((/.f64 1 (/.f64 (/.f64 x (expm1.f64 x)) 1)) (2))) (((/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x)))) (2))) (((/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x)))) (2))) (((/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x)))) (2))) (((/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x)) (2))) (((/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x))) (2))) (((/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x)))) (2))) (((/.f64 (/.f64 (expm1.f64 x) 1) x) (2))) (((/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x)) (2))) (((/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x)) (2))) (((sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)) (2))) (((log.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (2))) (((cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (2))) (((expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) (2))) (((exp.f64 (log.f64 (/.f64 (expm1.f64 x) x))) (2))) (((exp.f64 (-.f64 (log.f64 (expm1.f64 x)) (log.f64 x))) (2))) (((exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1)) (2))) (((log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x))) (2))))

simplify77.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
1532×associate-*r/
1020×associate-+r-
980×associate-/r*
788×associate-/l*
684×unswap-sqr
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01951437
14571383
217491383
376001383
Stop Event
1×node limit
Counts
97 → 103
Calls
Call 1
Inputs
1
(+.f64 (*.f64 -1/2 x) 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2))))
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(-.f64 (+.f64 1 (/.f64 x (expm1.f64 x))) 1)
(*.f64 x (/.f64 1 (expm1.f64 x)))
(*.f64 (/.f64 x (expm1.f64 x)) 1)
(*.f64 1 (/.f64 x (expm1.f64 x)))
(*.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) (sqrt.f64 (/.f64 x (expm1.f64 x))))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) (cbrt.f64 (/.f64 x (expm1.f64 x))))
(*.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 x))))
(*.f64 (/.f64 1 (expm1.f64 x)) x)
(*.f64 (neg.f64 x) (/.f64 1 (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) 1) (/.f64 (cbrt.f64 x) (expm1.f64 x)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x))))
(pow.f64 (/.f64 x (expm1.f64 x)) 1)
(pow.f64 (/.f64 (expm1.f64 x) x) -1)
(pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) 2)
(pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 3) 1/3)
(neg.f64 (/.f64 x (neg.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2))
(log.f64 (exp.f64 (/.f64 x (expm1.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 3))
(expm1.f64 (log1p.f64 (/.f64 x (expm1.f64 x))))
(exp.f64 (log.f64 (/.f64 x (expm1.f64 x))))
(exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) 1))
(log1p.f64 (expm1.f64 (/.f64 x (expm1.f64 x))))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (/.f64 1 (cbrt.f64 (*.f64 x x))) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (*.f64 x x))) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (pow.f64 x -1) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1))
(/.f64 (expm1.f64 x) x)
(/.f64 -1 (neg.f64 (/.f64 x (expm1.f64 x))))
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 1 (/.f64 (/.f64 x (expm1.f64 x)) 1))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x)))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (/.f64 (expm1.f64 x) 1) x)
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))
(sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (-.f64 (log.f64 (expm1.f64 x)) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
Outputs
1
(+.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2))))
(fma.f64 -1/2 x (+.f64 1 (*.f64 1/12 (*.f64 x x))))
(fma.f64 -1/2 x (fma.f64 1/12 (*.f64 x x) 1))
(fma.f64 -1/2 x (fma.f64 x (*.f64 x 1/12) 1))
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))))
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (+.f64 1 (*.f64 1/12 (*.f64 x x)))))
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (fma.f64 1/12 (*.f64 x x) 1)))
(fma.f64 -1/2 x (fma.f64 -1/720 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/12) 1)))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(fma.f64 x 1/2 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) 1/6 1))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/6) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) 1/6 (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(-.f64 (+.f64 1 (/.f64 x (expm1.f64 x))) 1)
(/.f64 x (expm1.f64 x))
(*.f64 x (/.f64 1 (expm1.f64 x)))
(/.f64 x (expm1.f64 x))
(*.f64 (/.f64 x (expm1.f64 x)) 1)
(/.f64 x (expm1.f64 x))
(*.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 x (expm1.f64 x))
(*.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) (sqrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(*.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2))
(/.f64 x (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) (cbrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(*.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 x))))
(*.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (/.f64 1 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (cbrt.f64 (*.f64 x x)) (/.f64 (cbrt.f64 x) (expm1.f64 x)))
(*.f64 (/.f64 1 (expm1.f64 x)) x)
(/.f64 x (expm1.f64 x))
(*.f64 (neg.f64 x) (/.f64 1 (neg.f64 (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (expm1.f64 x)))
(/.f64 x (expm1.f64 x))
(*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) 1) (/.f64 (cbrt.f64 x) (expm1.f64 x)))
(*.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (/.f64 1 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (cbrt.f64 (*.f64 x x)) (/.f64 (cbrt.f64 x) (expm1.f64 x)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (/.f64 1 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (cbrt.f64 (*.f64 x x)) (/.f64 (cbrt.f64 x) (expm1.f64 x)))
(*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) (/.f64 (cbrt.f64 (*.f64 x x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(pow.f64 (/.f64 x (expm1.f64 x)) 1)
(/.f64 x (expm1.f64 x))
(pow.f64 (/.f64 (expm1.f64 x) x) -1)
(/.f64 x (expm1.f64 x))
(pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) 2)
(/.f64 x (expm1.f64 x))
(pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 3)
(/.f64 x (expm1.f64 x))
(pow.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 3) 1/3)
(/.f64 x (expm1.f64 x))
(neg.f64 (/.f64 x (neg.f64 (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2))
(/.f64 x (expm1.f64 x))
(log.f64 (exp.f64 (/.f64 x (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 3))
(/.f64 x (expm1.f64 x))
(expm1.f64 (log1p.f64 (/.f64 x (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(exp.f64 (log.f64 (/.f64 x (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) 1))
(/.f64 x (expm1.f64 x))
(log1p.f64 (expm1.f64 (/.f64 x (expm1.f64 x))))
(/.f64 x (expm1.f64 x))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(/.f64 (expm1.f64 x) x)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (expm1.f64 x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(/.f64 (expm1.f64 x) x)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (cbrt.f64 (*.f64 x x))) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) (*.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 x)) (cbrt.f64 (*.f64 x x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (*.f64 x x))) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 1 (cbrt.f64 (*.f64 x x))) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) (*.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 x)) (cbrt.f64 (*.f64 x x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (*.f64 x x))) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 1 (cbrt.f64 (*.f64 x x))) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) (*.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 x)) (cbrt.f64 (*.f64 x x)))
(*.f64 (pow.f64 x -1) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1))
(/.f64 (expm1.f64 x) x)
(/.f64 (expm1.f64 x) x)
(/.f64 -1 (neg.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (/.f64 (/.f64 x (expm1.f64 x)) 1))
(/.f64 (expm1.f64 x) x)
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (/.f64 (expm1.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))
(*.f64 (/.f64 1 (cbrt.f64 (*.f64 x x))) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) (*.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 x)) (cbrt.f64 (*.f64 x x)))
(sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2))
(/.f64 (expm1.f64 x) x)
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(/.f64 (expm1.f64 x) x)
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (-.f64 (log.f64 (expm1.f64 x)) (log.f64 x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(/.f64 (expm1.f64 x) x)
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)

eval19.0ms (0.6%)

Compiler

Compiled 1061 to 511 computations (51.8% saved)

prune15.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1021103
Fresh011
Picked101
Done022
Total1034107
Error
100.0%
Counts
107 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
▶100.0%
(/.f64 1 (/.f64 x (expm1.f64 x)))
✓63.5%
(+.f64 (*.f64 1/2 x) 1)
64.5%
1
Compiler

Compiled 20 to 15 computations (25% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓100.0%
(/.f64 1 (/.f64 x (expm1.f64 x)))
100.0%
(/.f64 x (expm1.f64 x))
Compiler

Compiled 15 to 6 computations (60% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 1 (/.f64 x (expm1.f64 x)))
0.0ms
x
@inf
(/.f64 1 (/.f64 x (expm1.f64 x)))
0.0ms
x
@-inf
(/.f64 1 (/.f64 x (expm1.f64 x)))

rewrite87.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
1578×add-sqr-sqrt
1562×*-un-lft-identity
1454×add-cube-cbrt
1436×add-cbrt-cube
1420×add-exp-log
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0817
116111
2201011
Stop Event
1×node limit
Counts
1 → 39
Calls
Call 1
Inputs
(/.f64 1 (/.f64 x (expm1.f64 x)))
Outputs
((((-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1) (2))) (((-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x)) (2))) (((*.f64 1 (/.f64 (expm1.f64 x) x)) (2))) (((*.f64 (expm1.f64 x) (/.f64 1 x)) (2))) (((*.f64 (/.f64 (expm1.f64 x) x) 1) (2))) (((*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x))) (2))) (((*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2)) (2))) (((*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x))) (2))) (((*.f64 (/.f64 1 x) (expm1.f64 x)) (2))) (((*.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1)) (2))) (((*.f64 -1 (/.f64 1 (/.f64 (neg.f64 x) (expm1.f64 x)))) (2))) (((*.f64 (*.f64 (/.f64 1 x) 1) (expm1.f64 x)) (2))) (((*.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x))) (2))) (((*.f64 (*.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x))) (2))) (((*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x))) (2))) (((*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x))) (2))) (((*.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x))) (2))) (((*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x)) (2))) (((*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x))) (2))) (((*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x))) (2))) (((*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x)) (2))) (((*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x))) (2))) (((*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x))) (2))) (((*.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1)) (2))) (((*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1)) (2))) (((pow.f64 (/.f64 x (expm1.f64 x)) -1) (2))) (((pow.f64 (/.f64 (expm1.f64 x) x) 1) (2))) (((pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2) (2))) (((pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3) (2))) (((pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3) (2))) (((sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)) (2))) (((log.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (2))) (((cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (2))) (((expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) (2))) (((exp.f64 (log.f64 (/.f64 (expm1.f64 x) x))) (2))) (((exp.f64 (-.f64 (log.f64 (expm1.f64 x)) (log.f64 x))) (2))) (((exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1)) (2))) (((exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1)) (2))) (((log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x))) (2))))

simplify59.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
1136×associate-+r+
938×associate-+l+
614×associate-*r/
558×associate-/l*
464×unswap-sqr
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0124721
1306699
21199675
34881675
Stop Event
1×node limit
Counts
51 → 56
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))
(*.f64 -1 (/.f64 1 (/.f64 (neg.f64 x) (expm1.f64 x))))
(*.f64 (*.f64 (/.f64 1 x) 1) (expm1.f64 x))
(*.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (*.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1))
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (-.f64 (log.f64 (expm1.f64 x)) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(/.f64 (expm1.f64 x) x)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (expm1.f64 x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(/.f64 (expm1.f64 x) x)
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 x) (expm1.f64 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))
(/.f64 (expm1.f64 x) x)
(*.f64 -1 (/.f64 1 (/.f64 (neg.f64 x) (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(*.f64 (*.f64 (/.f64 1 x) 1) (expm1.f64 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (*.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2))
(pow.f64 (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)) 3)
(*.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2))
(pow.f64 (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)) 3)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2))
(pow.f64 (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)) 3)
(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1))
(pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -2)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2)) (/.f64 1 (cbrt.f64 (/.f64 x (expm1.f64 x)))))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x))))
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(/.f64 (expm1.f64 x) x)
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(/.f64 (expm1.f64 x) x)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(/.f64 (expm1.f64 x) x)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(/.f64 (expm1.f64 x) x)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(/.f64 (expm1.f64 x) x)
(sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2))
(/.f64 (expm1.f64 x) x)
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(/.f64 (expm1.f64 x) x)
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (-.f64 (log.f64 (expm1.f64 x)) (log.f64 x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1))
(/.f64 (expm1.f64 x) x)
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(/.f64 (expm1.f64 x) x)
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)

eval18.0ms (0.6%)

Compiler

Compiled 1064 to 528 computations (50.4% saved)

prune14.0ms (0.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1021103
Fresh011
Picked011
Done022
Total1025107
Error
100.0%
Counts
107 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
✓100.0%
(/.f64 1 (/.f64 x (expm1.f64 x)))
▶69.6%
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
✓63.5%
(+.f64 (*.f64 1/2 x) 1)
64.5%
1
Compiler

Compiled 28 to 22 computations (21.4% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓100.0%
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
Compiler

Compiled 19 to 15 computations (21.1% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
0.0ms
x
@0
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
0.0ms
x
@-inf
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))

rewrite57.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
1616×add-sqr-sqrt
1592×*-un-lft-identity
1490×add-cube-cbrt
1478×add-cbrt-cube
162×pow1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
117215
2207015
Stop Event
1×node limit
Counts
1 → 25
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
Outputs
((((-.f64 (exp.f64 (log1p.f64 (/.f64 1 (fma.f64 -1/2 x 1)))) 1) (2))) (((*.f64 1 (/.f64 1 (fma.f64 -1/2 x 1))) (2))) (((*.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 1) (2))) (((*.f64 (pow.f64 (fma.f64 -1/2 x 1) -1/2) (pow.f64 (fma.f64 -1/2 x 1) -1/2)) (2))) (((*.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2))) (2))) (((*.f64 (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1)))) (2))) (((*.f64 -1 (/.f64 1 (neg.f64 (fma.f64 -1/2 x 1)))) (2))) (((*.f64 (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 1/4) -1)) (fma.f64 -1/2 x -1)) (2))) (((*.f64 (/.f64 1 (+.f64 1 (*.f64 (pow.f64 x 3) -1/8))) (+.f64 (*.f64 (*.f64 x x) 1/4) (-.f64 1 (*.f64 -1/2 x)))) (2))) (((*.f64 (pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -1) (pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -1)) (2))) (((*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/2 x 1)) 2) -1) (pow.f64 (cbrt.f64 (fma.f64 -1/2 x 1)) -1)) (2))) (((pow.f64 (fma.f64 -1/2 x 1) -1) (2))) (((pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 1) (2))) (((pow.f64 (pow.f64 (fma.f64 -1/2 x 1) -1/2) 2) (2))) (((pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) 3) (2))) (((pow.f64 (pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 3) 1/3) (2))) (((sqrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)) (2))) (((log.f64 (exp.f64 (/.f64 1 (fma.f64 -1/2 x 1)))) (2))) (((log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (fma.f64 -1/2 x 1))))) (2))) (((cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 3)) (2))) (((expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 -1/2 x 1)))) (2))) (((exp.f64 (neg.f64 (log1p.f64 (*.f64 -1/2 x)))) (2))) (((exp.f64 (*.f64 (log1p.f64 (*.f64 -1/2 x)) -1)) (2))) (((exp.f64 (*.f64 (neg.f64 (log1p.f64 (*.f64 -1/2 x))) 1)) (2))) (((log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 -1/2 x 1)))) (2))))

simplify55.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
1078×distribute-lft-in
1032×distribute-rgt-in
850×associate-/l/
810×associate-*r*
698×associate-*l*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0108875
1287823
2893819
33814819
Stop Event
1×node limit
Counts
37 → 62
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/4 (pow.f64 x 2))))
(+.f64 (*.f64 1/2 x) (+.f64 1 (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 1/8 (pow.f64 x 3)))))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (fma.f64 -1/2 x 1)))) 1)
(*.f64 1 (/.f64 1 (fma.f64 -1/2 x 1)))
(*.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 1)
(*.f64 (pow.f64 (fma.f64 -1/2 x 1) -1/2) (pow.f64 (fma.f64 -1/2 x 1) -1/2))
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))))
(*.f64 -1 (/.f64 1 (neg.f64 (fma.f64 -1/2 x 1))))
(*.f64 (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 1/4) -1)) (fma.f64 -1/2 x -1))
(*.f64 (/.f64 1 (+.f64 1 (*.f64 (pow.f64 x 3) -1/8))) (+.f64 (*.f64 (*.f64 x x) 1/4) (-.f64 1 (*.f64 -1/2 x))))
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -1) (pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/2 x 1)) 2) -1) (pow.f64 (cbrt.f64 (fma.f64 -1/2 x 1)) -1))
(pow.f64 (fma.f64 -1/2 x 1) -1)
(pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 1)
(pow.f64 (pow.f64 (fma.f64 -1/2 x 1) -1/2) 2)
(pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) 3)
(pow.f64 (pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 3) 1/3)
(sqrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2))
(log.f64 (exp.f64 (/.f64 1 (fma.f64 -1/2 x 1))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (fma.f64 -1/2 x 1)))))
(cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 3))
(expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 -1/2 x 1))))
(exp.f64 (neg.f64 (log1p.f64 (*.f64 -1/2 x))))
(exp.f64 (*.f64 (log1p.f64 (*.f64 -1/2 x)) -1))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (*.f64 -1/2 x))) 1))
(log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 -1/2 x 1))))
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/4 (pow.f64 x 2))))
(fma.f64 (*.f64 x x) 1/4 (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/4) 1))
(fma.f64 x (*.f64 x 1/4) (fma.f64 1/2 x 1))
(+.f64 (*.f64 1/2 x) (+.f64 1 (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 1/8 (pow.f64 x 3)))))
(+.f64 (fma.f64 1/2 x 1) (fma.f64 1/4 (*.f64 x x) (*.f64 1/8 (pow.f64 x 3))))
(+.f64 (fma.f64 x (*.f64 x 1/4) (*.f64 1/8 (pow.f64 x 3))) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/4) (fma.f64 1/8 (pow.f64 x 3) 1)))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/4 (*.f64 x 1/8))))))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x)))
(-.f64 (/.f64 -4 (*.f64 x x)) (/.f64 2 x))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x)) (/.f64 8 (pow.f64 x 3))))
(+.f64 (-.f64 (/.f64 -4 (*.f64 x x)) (/.f64 2 x)) (/.f64 -8 (pow.f64 x 3)))
(+.f64 (/.f64 -4 (*.f64 x x)) (-.f64 (/.f64 -2 x) (/.f64 8 (pow.f64 x 3))))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))))
(neg.f64 (+.f64 (/.f64 8 (pow.f64 x 3)) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4))))))
(-.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4)))))
(+.f64 (-.f64 (/.f64 -4 (*.f64 x x)) (/.f64 2 x)) (+.f64 (/.f64 -16 (pow.f64 x 4)) (/.f64 -8 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) (+.f64 (/.f64 -8 (pow.f64 x 3)) (/.f64 -16 (pow.f64 x 4))))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x)))
(-.f64 (/.f64 -4 (*.f64 x x)) (/.f64 2 x))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x)) (/.f64 8 (pow.f64 x 3))))
(+.f64 (-.f64 (/.f64 -4 (*.f64 x x)) (/.f64 2 x)) (/.f64 -8 (pow.f64 x 3)))
(+.f64 (/.f64 -4 (*.f64 x x)) (-.f64 (/.f64 -2 x) (/.f64 8 (pow.f64 x 3))))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))))
(neg.f64 (+.f64 (/.f64 8 (pow.f64 x 3)) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4))))))
(-.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4)))))
(+.f64 (-.f64 (/.f64 -4 (*.f64 x x)) (/.f64 2 x)) (+.f64 (/.f64 -16 (pow.f64 x 4)) (/.f64 -8 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) (+.f64 (/.f64 -8 (pow.f64 x 3)) (/.f64 -16 (pow.f64 x 4))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (fma.f64 -1/2 x 1)))) 1)
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 1 (/.f64 1 (fma.f64 -1/2 x 1)))
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 1)
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 (pow.f64 (fma.f64 -1/2 x 1) -1/2) (pow.f64 (fma.f64 -1/2 x 1) -1/2))
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)))
(/.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)) (cbrt.f64 (fma.f64 x -1/2 1)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))))
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)))
(/.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/2 1) -2)) (cbrt.f64 (fma.f64 x -1/2 1)))
(*.f64 -1 (/.f64 1 (neg.f64 (fma.f64 -1/2 x 1))))
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(*.f64 (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 1/4) -1)) (fma.f64 -1/2 x -1))
(*.f64 (/.f64 1 (fma.f64 (*.f64 x x) 1/4 -1)) (fma.f64 -1/2 x -1))
(/.f64 (fma.f64 x -1/2 -1) (fma.f64 x (*.f64 x 1/4) -1))
(*.f64 (/.f64 1 (+.f64 1 (*.f64 (pow.f64 x 3) -1/8))) (+.f64 (*.f64 (*.f64 x x) 1/4) (-.f64 1 (*.f64 -1/2 x))))
(*.f64 (/.f64 1 (+.f64 1 (*.f64 (pow.f64 x 3) -1/8))) (fma.f64 (*.f64 x x) 1/4 (fma.f64 1/2 x 1)))
(/.f64 (fma.f64 1/2 x (fma.f64 x (*.f64 x 1/4) 1)) (fma.f64 (pow.f64 x 3) -1/8 1))
(/.f64 (fma.f64 x (*.f64 x 1/4) (fma.f64 1/2 x 1)) (fma.f64 (pow.f64 x 3) -1/8 1))
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -1) (pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -1))
(pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -2)
(pow.f64 (sqrt.f64 (fma.f64 x -1/2 1)) -2)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/2 x 1)) 2) -1) (pow.f64 (cbrt.f64 (fma.f64 -1/2 x 1)) -1))
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(pow.f64 (fma.f64 -1/2 x 1) -1)
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 1)
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(pow.f64 (pow.f64 (fma.f64 -1/2 x 1) -1/2) 2)
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) 3)
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(pow.f64 (pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 3) 1/3)
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(sqrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2))
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(log.f64 (exp.f64 (/.f64 1 (fma.f64 -1/2 x 1))))
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (fma.f64 -1/2 x 1)))))
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 3))
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 -1/2 x 1))))
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))
(exp.f64 (neg.f64 (log1p.f64 (*.f64 -1/2 x))))
(exp.f64 (neg.f64 (log1p.f64 (*.f64 x -1/2))))
(exp.f64 (*.f64 (log1p.f64 (*.f64 -1/2 x)) -1))
(exp.f64 (neg.f64 (log1p.f64 (*.f64 x -1/2))))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (*.f64 -1/2 x))) 1))
(exp.f64 (neg.f64 (log1p.f64 (*.f64 x -1/2))))
(log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 -1/2 x 1))))
(/.f64 1 (fma.f64 -1/2 x 1))
(/.f64 1 (fma.f64 x -1/2 1))

eval29.0ms (1%)

Compiler

Compiled 728 to 571 computations (21.6% saved)

prune13.0ms (0.4%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New59362
Fresh011
Picked011
Done033
Total59867
Error
100.0%
Counts
67 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
✓100.0%
(/.f64 (expm1.f64 x) x)
✓100.0%
(/.f64 1 (/.f64 x (expm1.f64 x)))
✓69.6%
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
8.7%
(/.f64 -2 x)
7.0%
(-.f64 (/.f64 -4 (*.f64 x x)) (/.f64 2 x))
✓63.5%
(+.f64 (*.f64 1/2 x) 1)
63.2%
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/4 (*.f64 x 1/8))))))
64.5%
1
Compiler

Compiled 56 to 43 computations (23.2% saved)

regimes15.0ms (0.5%)

Counts
10 → 1
Calls
Call 1
Inputs
1
(/.f64 -2 x)
(+.f64 (*.f64 1/2 x) 1)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 -4 (*.f64 x x)) (/.f64 2 x))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/4 (*.f64 x 1/8))))))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Outputs
(/.f64 1 (/.f64 x (expm1.f64 x)))
Calls

2 calls:

7.0ms
x
6.0ms
(/.f64 (-.f64 (exp.f64 x) 1) x)
Results
ErrorSegmentsBranch
100.0%1x
100.0%1(/.f64 (-.f64 (exp.f64 x) 1) x)
Compiler

Compiled 70 to 47 computations (32.9% saved)

regimes6.0ms (0.2%)

Counts
7 → 1
Calls
Call 1
Inputs
1
(/.f64 -2 x)
(+.f64 (*.f64 1/2 x) 1)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 -4 (*.f64 x x)) (/.f64 2 x))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/4 (*.f64 x 1/8))))))
(/.f64 (expm1.f64 x) x)
Outputs
(/.f64 (expm1.f64 x) x)
Calls

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
100.0%1x
Compiler

Compiled 45 to 33 computations (26.7% saved)

regimes9.0ms (0.3%)

Counts
6 → 1
Calls
Call 1
Inputs
1
(/.f64 -2 x)
(+.f64 (*.f64 1/2 x) 1)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 -4 (*.f64 x x)) (/.f64 2 x))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/4 (*.f64 x 1/8))))))
Outputs
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
Calls

1 calls:

7.0ms
x
Results
ErrorSegmentsBranch
69.6%1x
Compiler

Compiled 41 to 31 computations (24.4% saved)

regimes8.0ms (0.2%)

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

1 calls:

6.0ms
x
Results
ErrorSegmentsBranch
69.6%2x
Compiler

Compiled 12 to 9 computations (25% saved)

bsearch12.0ms (0.4%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
11.0ms
-7.826965380114274
-0.4596228601588127
Results
10.0ms112×body256valid
Compiler

Compiled 95 to 78 computations (17.9% saved)

regimes9.0ms (0.3%)

Accuracy

Total -41.8b remaining (-211.8%)

Threshold costs -41.80b (-211.8%)

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

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
69.2%2x
Compiler

Compiled 7 to 5 computations (28.6% saved)

bsearch11.0ms (0.4%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
11.0ms
-7.826965380114274
-0.4596228601588127
Results
10.0ms112×body256valid
Compiler

Compiled 67 to 57 computations (14.9% saved)

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
4×+-commutative
4×*-commutative
2×1-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02694
13294
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(if (<=.f64 x -6980579422424269/4503599627370496) (/.f64 -2 x) (+.f64 (*.f64 1/2 x) 1))
(if (<=.f64 x -2) (/.f64 -2 x) 1)
1
Outputs
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
(if (<=.f64 x -6980579422424269/4503599627370496) (/.f64 -2 x) (+.f64 (*.f64 1/2 x) 1))
(if (<=.f64 x -6980579422424269/4503599627370496) (/.f64 -2 x) (+.f64 1 (*.f64 x 1/2)))
(if (<=.f64 x -2) (/.f64 -2 x) 1)
1
Compiler

Compiled 44 to 34 computations (22.7% saved)

soundness38.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
186×fma-def
78×associate-*r*
78×associate--r+
70×*-commutative
66×associate-+l-
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11711
22011
32411
43311
54311
66211
711811
817911
926311
1040011
1158911
1266711
1370911
Stop Event
1×saturated
Compiler

Compiled 11 to 7 computations (36.4% saved)

end43.0ms (1.4%)

Compiler

Compiled 39 to 28 computations (28.2% saved)

Profiling

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