Details

Time bar (total: 2.9s)

analyze463.0ms (16.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%62.5%12.5%4
25%56.2%18.8%5
28.1%50%21.9%6
29.7%46.9%23.5%7
30.5%45.3%24.3%8
30.8%44.9%24.3%9
31.2%44.5%24.3%10
31.3%44.4%24.3%11
31.4%44.3%24.3%12
31.4%44.2%24.3%13
31.5%44.2%24.3%14
Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.7s (58.2%)

Results
878.0ms2761×body1024valid
303.0ms1336×body512valid
253.0ms3204×body128valid
121.0ms662×body256valid
104.0ms293×body2048valid
0.0ms1×body128invalid
Compiler

Compiled 18 to 12 computations (33.3% saved)

preprocess17.0ms (0.6%)

Algorithm
2×egg-herbie
Rules
1×+-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
1×expm1-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1128
2138
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
1×expm1-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1128
2138
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.8b
(/.f64 (exp.f64 x) (expm1.f64 x))
Compiler

Compiled 25 to 15 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.8b
(/.f64 (exp.f64 x) (expm1.f64 x))

series8.0ms (0.3%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(/.f64 (exp.f64 x) (expm1.f64 x))
3.0ms
x
@-inf
(/.f64 (exp.f64 x) (expm1.f64 x))
1.0ms
x
@0
(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite32.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
516×pow1_binary64
477×add-log-exp_binary64
477×log1p-expm1-u_binary64
477×expm1-log1p-u_binary64
465×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058
1998
212878
Stop Event
1×node limit
Counts
1 → 31
Calls
Call 1
Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (*.f64 (cbrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (exp.f64 x)) (/.f64 1 (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1) (/.f64 (cbrt.f64 (exp.f64 x)) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (exp.f64 x)) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (exp.f64 x) (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))))))

simplify31.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
1089×fma-neg_binary64
754×fma-def_binary64
260×cancel-sign-sub-inv_binary64
211×associate-*l*_binary64
208×unswap-sqr_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
018110
146106
2101104
3306104
4830104
51782104
63144104
74892104
Stop Event
1×node limit
Counts
43 → 40
Calls
Call 1
Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x))) (*.f64 1/720 (pow.f64 x 3)))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 x 1/12)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x))) (*.f64 1/720 (pow.f64 x 3)))
(+.f64 1/2 (-.f64 (+.f64 (/.f64 1 x) (*.f64 x 1/12)) (*.f64 1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (*.f64 (pow.f64 x 3) -1/720)))
(fma.f64 (pow.f64 x 3) -1/720 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2)))
(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

prune32.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New37340
Fresh000
Picked011
Done000
Total37441
Error
0.6b
Counts
41 → 4
Alt Table
StatusErrorProgram
✓0.8b
(/.f64 (exp.f64 x) (expm1.f64 x))
22.1b
(+.f64 1/2 (/.f64 1 x))
27.6b
(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))
▶0.8b
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
Compiler

Compiled 455 to 214 computations (53% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(sqrt.f64 (exp.f64 x))
✓0.5b
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
✓0.8b
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))

series20.0ms (0.7%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
4.0ms
x
@-inf
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
4.0ms
x
@-inf
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
4.0ms
x
@inf
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
1.0ms
x
@0
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))

rewrite47.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
769×pow1_binary64
713×log1p-expm1-u_binary64
713×expm1-log1p-u_binary64
76×add-sqr-sqrt_binary64
73×*-un-lft-identity_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0923
118423
2203723
Stop Event
1×node limit
Counts
3 → 112
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
(sqrt.f64 (exp.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))) (cbrt.f64 (/.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) 2))) (cbrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))) (sqrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) 1/4) (/.f64 (pow.f64 (exp.f64 x) 1/4) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) 1/4) (*.f64 (pow.f64 (exp.f64 x) 1/4) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (exp.f64 x))) (/.f64 1 (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 x)) (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 1 (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (exp.f64 x)) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (exp.f64 x)) 1) (/.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (exp.f64 x) 1/4) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (pow.f64 (exp.f64 x) 1/4) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (exp.f64 x) (pow.f64 (expm1.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3/2) (pow.f64 (expm1.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 1/2 x) (log.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (*.f64 1/2 x) (log.f64 (expm1.f64 x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 x) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (exp.f64 x)) (*.f64 (pow.f64 (exp.f64 x) -1/2) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)) (pow.f64 (exp.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (pow.f64 (exp.f64 x) -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))) (pow.f64 (exp.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (expm1.f64 x) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x))))))) 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(#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 x (log.f64 (expm1.f64 x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) 1/4) (pow.f64 (exp.f64 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (exp.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1/2) (pow.f64 (cbrt.f64 (exp.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (exp.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (exp.f64 x)) (/.f64 1 (cbrt.f64 (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (exp.f64 x) 1/4) (/.f64 1 (pow.f64 (exp.f64 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (exp.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (pow.f64 (exp.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (sqrt.f64 (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) -1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (exp.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 x) 1))))))

simplify29.0ms (1%)

Algorithm
1×egg-herbie
Rules
703×fma-neg_binary64
633×fma-def_binary64
559×cancel-sign-sub-inv_binary64
259×associate-*l*_binary64
211×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
047316
1123282
2310273
31016264
42946264
Stop Event
1×node limit
Counts
140 → 135
Calls
Call 1
Inputs
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/24 x))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 7/5760 (pow.f64 x 3))) (*.f64 1/24 x))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 7/5760 (pow.f64 x 3))) (+.f64 (*.f64 31/967680 (pow.f64 x 5)) (*.f64 1/24 x)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x))) (*.f64 1/720 (pow.f64 x 3)))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/48 (pow.f64 x 3)))))
Outputs
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/24))
(fma.f64 x -1/24 (/.f64 1 x))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 7/5760 (pow.f64 x 3))) (*.f64 1/24 x))
(+.f64 (/.f64 1 x) (-.f64 (*.f64 7/5760 (pow.f64 x 3)) (*.f64 x 1/24)))
(+.f64 (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x)) (*.f64 x -1/24))
(fma.f64 x -1/24 (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x)))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 7/5760 (pow.f64 x 3))) (+.f64 (*.f64 31/967680 (pow.f64 x 5)) (*.f64 1/24 x)))
(+.f64 (/.f64 1 x) (-.f64 (*.f64 7/5760 (pow.f64 x 3)) (fma.f64 31/967680 (pow.f64 x 5) (*.f64 x 1/24))))
(-.f64 (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x)) (fma.f64 x 1/24 (*.f64 31/967680 (pow.f64 x 5))))
(-.f64 (fma.f64 x -1/24 (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x))) (*.f64 31/967680 (pow.f64 x 5)))
(fma.f64 x -1/24 (fma.f64 (pow.f64 x 5) -31/967680 (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x))))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 x 1/12)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(-.f64 (+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x))) (*.f64 1/720 (pow.f64 x 3)))
(+.f64 1/2 (-.f64 (+.f64 (/.f64 1 x) (*.f64 x 1/12)) (*.f64 (pow.f64 x 3) 1/720)))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (+.f64 1/2 (*.f64 (pow.f64 x 3) -1/720)))
(fma.f64 (pow.f64 x 3) -1/720 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2)))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 x 1/2))
(fma.f64 x 1/2 1)
(+.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/8 (*.f64 x x) (*.f64 x 1/2)))
(+.f64 (*.f64 x (*.f64 x 1/8)) (fma.f64 x 1/2 1))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/8) 1))
(fma.f64 x (fma.f64 x 1/8 1/2) 1)
(+.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/48 (pow.f64 x 3)))))
(+.f64 1 (fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 (pow.f64 x 3) 1/48))))
(+.f64 1 (fma.f64 1/8 (*.f64 x x) (fma.f64 x 1/2 (*.f64 (pow.f64 x 3) 1/48))))
(+.f64 (*.f64 x (+.f64 1/2 (*.f64 x 1/8))) (fma.f64 (pow.f64 x 3) 1/48 1))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x (fma.f64 x 1/48 1/8)) 1))

prune103.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1750175
Fresh022
Picked011
Done011
Total1754179
Error
0.6b
Counts
179 → 4
Alt Table
StatusErrorProgram
✓0.8b
(/.f64 (exp.f64 x) (expm1.f64 x))
▶22.1b
(+.f64 1/2 (/.f64 1 x))
27.6b
(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))
✓0.8b
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
Compiler

Compiled 2588 to 1126 computations (56.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1/2 (/.f64 1 x))

series1.0ms (0%)

Counts
1 → 3
Calls

3 calls:

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

rewrite34.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
628×pow1_binary64
588×add-log-exp_binary64
588×log1p-expm1-u_binary64
588×expm1-log1p-u_binary64
64×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11307
215897
Stop Event
1×node limit
Counts
1 → 31
Calls
Call 1
Inputs
(+.f64 1/2 (/.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (-.f64 1/2 (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/2 (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 2)) (cbrt.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (pow.f64 x -2)) (/.f64 1 (-.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x))) (+.f64 1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/2 (/.f64 1 x)) (-.f64 1/4 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 1/4 (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (pow.f64 x -3))) (neg.f64 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (pow.f64 x -2))) (neg.f64 (-.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) 1/4) (-.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/2 (/.f64 1 x))))))))

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
176
Stop Event
1×saturated
Counts
34 → 33
Calls
Call 1
Inputs
(/.f64 1 x)
1/2
1/2
Outputs
(/.f64 1 x)
1/2
1/2

prune20.0ms (0.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New30333
Fresh011
Picked011
Done022
Total30737
Error
0.6b
Counts
37 → 7
Alt Table
StatusErrorProgram
▶22.9b
(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)
✓22.1b
(+.f64 1/2 (/.f64 1 x))
✓0.8b
(/.f64 (exp.f64 x) (expm1.f64 x))
44.2b
(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)
43.1b
(*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 2)))
27.6b
(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))
✓0.8b
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
Compiler

Compiled 454 to 380 computations (16.3% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1/2 (/.f64 1 x))
✓0.3b
(cbrt.f64 (+.f64 1/2 (/.f64 1 x)))
✓0.8b
(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)

series38.0ms (1.3%)

Counts
2 → 16
Calls

6 calls:

TimeVariablePointExpression
13.0ms
x
@inf
(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)
12.0ms
x
@-inf
(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)
4.0ms
x
@-inf
(cbrt.f64 (+.f64 1/2 (/.f64 1 x)))
4.0ms
x
@inf
(cbrt.f64 (+.f64 1/2 (/.f64 1 x)))
3.0ms
x
@0
(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)

rewrite38.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
787×pow1_binary64
743×log1p-expm1-u_binary64
743×expm1-log1p-u_binary64
84×add-sqr-sqrt_binary64
80×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
119716
2207116
Stop Event
1×node limit
Counts
2 → 61
Calls
Call 1
Inputs
(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)
(cbrt.f64 (+.f64 1/2 (/.f64 1 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (-.f64 1/2 (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/2 (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2) (cbrt.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)) (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 1/6) (*.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 1/6) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (pow.f64 x -2)) (/.f64 1 (-.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)) 3) (cbrt.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 1/6) 3) (pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2) 1) (cbrt.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2))) (cbrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2) (pow.f64 (+.f64 1/2 (/.f64 1 x)) 1/6)) (pow.f64 (+.f64 1/2 (/.f64 1 x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x))) (+.f64 1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/2 (/.f64 1 x)) (-.f64 1/4 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 1/4 (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (pow.f64 x -3))) (neg.f64 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (pow.f64 x -2))) (neg.f64 (-.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) 1/4) (-.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/2 (/.f64 1 x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))) (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)) (cbrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 1/6) (pow.f64 (+.f64 1/2 (/.f64 1 x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (+.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) 1/3) (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 1/8 (pow.f64 x -3))) (cbrt.f64 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (-.f64 1/4 (pow.f64 x -2))) (cbrt.f64 (-.f64 1/2 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 1 x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1 x)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/2 (/.f64 1 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))) 1))))))

simplify29.0ms (1%)

Algorithm
1×egg-herbie
Rules
592×associate-/l*_binary64
409×fma-neg_binary64
294×associate-/l/_binary64
287×associate-/r/_binary64
178×associate-/r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
064602
1190530
2605516
32615516
Stop Event
1×node limit
Counts
77 → 75
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3))) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)))) (*.f64 4/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 2) (pow.f64 x 3)))))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3))) (+.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)) (*.f64 8/243 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 (pow.f64 x 4))))))) (+.f64 (*.f64 4/243 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11)) 1/3) (/.f64 1 (pow.f64 x 4)))) (*.f64 4/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 2) (pow.f64 x 3))))))
1/2
(+.f64 1/2 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3))) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)))) (*.f64 4/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 2) (pow.f64 x 3)))))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3))) (+.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)) (*.f64 8/243 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 (pow.f64 x 4))))))) (+.f64 (*.f64 4/243 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11)) 1/3) (/.f64 1 (pow.f64 x 4)))) (*.f64 4/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 2) (pow.f64 x 3))))))
(cbrt.f64 1/2)
(+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x))))
(-.f64 (+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x)))) (*.f64 1/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 5/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 4) (pow.f64 x 3)))) (+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x))))) (*.f64 1/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))))
(cbrt.f64 1/2)
(+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x))))
(-.f64 (+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x)))) (*.f64 1/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 5/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 4) (pow.f64 x 3)))) (+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x))))) (*.f64 1/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))))
Outputs
1/2
(+.f64 1/2 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)))
(+.f64 1/2 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) (/.f64 1 x)))
(+.f64 1/2 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) x))
(+.f64 1/2 (/.f64 (cbrt.f64 (*.f64 1/2 (cbrt.f64 1/2))) x))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3))) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)))) (*.f64 4/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 2) (pow.f64 x 3)))))
(+.f64 1/2 (-.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) (/.f64 1 x))) (/.f64 4/81 (*.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 1/2) 2)))))
(+.f64 1/2 (+.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) x)) (/.f64 -4/81 (*.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 1/2) 2)))))
(+.f64 1/2 (+.f64 (/.f64 (cbrt.f64 (*.f64 1/2 (cbrt.f64 1/2))) x) (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (/.f64 (/.f64 -4/81 (pow.f64 x 3)) (pow.f64 (cbrt.f64 1/2) 2)))))
(-.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (/.f64 (cbrt.f64 (*.f64 1/2 (cbrt.f64 1/2))) x)) (+.f64 (/.f64 (/.f64 4/81 (pow.f64 (cbrt.f64 1/2) 2)) (pow.f64 x 3)) -1/2))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3))) (+.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)) (*.f64 8/243 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 (pow.f64 x 4))))))) (+.f64 (*.f64 4/243 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11)) 1/3) (/.f64 1 (pow.f64 x 4)))) (*.f64 4/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 2) (pow.f64 x 3))))))
(+.f64 1/2 (-.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (fma.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) (/.f64 1 x) (*.f64 8/243 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1 (pow.f64 x 4)))))) (fma.f64 4/243 (*.f64 (/.f64 1 (pow.f64 x 4)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11)))) (/.f64 4/81 (*.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 1/2) 2))))))
(+.f64 1/2 (-.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (fma.f64 8/243 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (pow.f64 x 4)) (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) x))) (fma.f64 4/243 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11))) (pow.f64 x 4)) (/.f64 4/81 (*.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 1/2) 2))))))
(+.f64 1/2 (-.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 8/243 (pow.f64 x 4)) (/.f64 (cbrt.f64 (*.f64 1/2 (cbrt.f64 1/2))) x))) (fma.f64 4/243 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11))) (pow.f64 x 4)) (/.f64 4/81 (*.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 1/2) 2))))))
(+.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (/.f64 (cbrt.f64 (*.f64 1/2 (cbrt.f64 1/2))) x)) (+.f64 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 8/243 (pow.f64 x 4)) 1/2) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11))) (/.f64 -4/243 (pow.f64 x 4)) (/.f64 (/.f64 -4/81 (pow.f64 (cbrt.f64 1/2) 2)) (pow.f64 x 3)))))
1/2
(+.f64 1/2 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)))
(+.f64 1/2 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) (/.f64 1 x)))
(+.f64 1/2 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) x))
(+.f64 1/2 (/.f64 (cbrt.f64 (*.f64 1/2 (cbrt.f64 1/2))) x))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3))) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)))) (*.f64 4/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 2) (pow.f64 x 3)))))
(+.f64 1/2 (-.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) (/.f64 1 x))) (/.f64 4/81 (*.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 1/2) 2)))))
(+.f64 1/2 (+.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) x)) (/.f64 -4/81 (*.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 1/2) 2)))))
(+.f64 1/2 (+.f64 (/.f64 (cbrt.f64 (*.f64 1/2 (cbrt.f64 1/2))) x) (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (/.f64 (/.f64 -4/81 (pow.f64 x 3)) (pow.f64 (cbrt.f64 1/2) 2)))))
(-.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (/.f64 (cbrt.f64 (*.f64 1/2 (cbrt.f64 1/2))) x)) (+.f64 (/.f64 (/.f64 4/81 (pow.f64 (cbrt.f64 1/2) 2)) (pow.f64 x 3)) -1/2))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3))) (+.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 1/2) 4) 1/3) (/.f64 1 x)) (*.f64 8/243 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 (pow.f64 x 4))))))) (+.f64 (*.f64 4/243 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11)) 1/3) (/.f64 1 (pow.f64 x 4)))) (*.f64 4/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 2) (pow.f64 x 3))))))
(+.f64 1/2 (-.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (fma.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) (/.f64 1 x) (*.f64 8/243 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1 (pow.f64 x 4)))))) (fma.f64 4/243 (*.f64 (/.f64 1 (pow.f64 x 4)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11)))) (/.f64 4/81 (*.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 1/2) 2))))))
(+.f64 1/2 (-.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (fma.f64 8/243 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (pow.f64 x 4)) (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 1/2) 4)) x))) (fma.f64 4/243 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11))) (pow.f64 x 4)) (/.f64 4/81 (*.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 1/2) 2))))))
(+.f64 1/2 (-.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 8/243 (pow.f64 x 4)) (/.f64 (cbrt.f64 (*.f64 1/2 (cbrt.f64 1/2))) x))) (fma.f64 4/243 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11))) (pow.f64 x 4)) (/.f64 4/81 (*.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 1/2) 2))))))
(+.f64 (fma.f64 8/81 (/.f64 (cbrt.f64 1/2) (pow.f64 x 3)) (/.f64 (cbrt.f64 (*.f64 1/2 (cbrt.f64 1/2))) x)) (+.f64 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 8/243 (pow.f64 x 4)) 1/2) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 11))) (/.f64 -4/243 (pow.f64 x 4)) (/.f64 (/.f64 -4/81 (pow.f64 (cbrt.f64 1/2) 2)) (pow.f64 x 3)))))
(cbrt.f64 1/2)
(+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x))))
(+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (/.f64 1 x) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))))))
(fma.f64 1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) x) (cbrt.f64 1/2))
(fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1/3 x) (cbrt.f64 1/2))
(-.f64 (+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x)))) (*.f64 1/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))))
(+.f64 (cbrt.f64 1/2) (-.f64 (*.f64 1/3 (*.f64 (/.f64 1 x) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))))) (*.f64 1/9 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (/.f64 1 (*.f64 x x))))))
(+.f64 (cbrt.f64 1/2) (fma.f64 1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) x) (/.f64 (*.f64 -1/9 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)))) (*.f64 x x))))
(fma.f64 (/.f64 -1/9 (*.f64 x x)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1/3 x) (cbrt.f64 1/2)))
(fma.f64 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (*.f64 x x)) -1/9 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1/3 x) (cbrt.f64 1/2)))
(-.f64 (+.f64 (*.f64 5/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 4) (pow.f64 x 3)))) (+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x))))) (*.f64 1/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 5/81 (*.f64 (pow.f64 (cbrt.f64 1/2) 4) (pow.f64 x 3))) (+.f64 (cbrt.f64 1/2) (-.f64 (*.f64 1/3 (*.f64 (/.f64 1 x) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))))) (*.f64 1/9 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (/.f64 1 (*.f64 x x)))))))
(+.f64 (fma.f64 1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) x) (cbrt.f64 1/2)) (+.f64 (/.f64 5/81 (*.f64 (pow.f64 (cbrt.f64 1/2) 4) (pow.f64 x 3))) (/.f64 (*.f64 -1/9 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)))) (*.f64 x x))))
(+.f64 (/.f64 (/.f64 10/81 (cbrt.f64 1/2)) (pow.f64 x 3)) (fma.f64 (/.f64 -1/9 (*.f64 x x)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1/3 x) (cbrt.f64 1/2))))
(+.f64 (/.f64 (/.f64 10/81 (cbrt.f64 1/2)) (pow.f64 x 3)) (fma.f64 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (*.f64 x x)) -1/9 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1/3 x) (cbrt.f64 1/2))))
(cbrt.f64 1/2)
(+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x))))
(+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (/.f64 1 x) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))))))
(fma.f64 1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) x) (cbrt.f64 1/2))
(fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1/3 x) (cbrt.f64 1/2))
(-.f64 (+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x)))) (*.f64 1/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))))
(+.f64 (cbrt.f64 1/2) (-.f64 (*.f64 1/3 (*.f64 (/.f64 1 x) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))))) (*.f64 1/9 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (/.f64 1 (*.f64 x x))))))
(+.f64 (cbrt.f64 1/2) (fma.f64 1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) x) (/.f64 (*.f64 -1/9 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)))) (*.f64 x x))))
(fma.f64 (/.f64 -1/9 (*.f64 x x)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1/3 x) (cbrt.f64 1/2)))
(fma.f64 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (*.f64 x x)) -1/9 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1/3 x) (cbrt.f64 1/2)))
(-.f64 (+.f64 (*.f64 5/81 (/.f64 1 (*.f64 (pow.f64 (cbrt.f64 1/2) 4) (pow.f64 x 3)))) (+.f64 (cbrt.f64 1/2) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2)) 1/3) (/.f64 1 x))))) (*.f64 1/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)) 1/3) (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 5/81 (*.f64 (pow.f64 (cbrt.f64 1/2) 4) (pow.f64 x 3))) (+.f64 (cbrt.f64 1/2) (-.f64 (*.f64 1/3 (*.f64 (/.f64 1 x) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))))) (*.f64 1/9 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (/.f64 1 (*.f64 x x)))))))
(+.f64 (fma.f64 1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) x) (cbrt.f64 1/2)) (+.f64 (/.f64 5/81 (*.f64 (pow.f64 (cbrt.f64 1/2) 4) (pow.f64 x 3))) (/.f64 (*.f64 -1/9 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7)))) (*.f64 x x))))
(+.f64 (/.f64 (/.f64 10/81 (cbrt.f64 1/2)) (pow.f64 x 3)) (fma.f64 (/.f64 -1/9 (*.f64 x x)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1/3 x) (cbrt.f64 1/2))))
(+.f64 (/.f64 (/.f64 10/81 (cbrt.f64 1/2)) (pow.f64 x 3)) (fma.f64 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 7))) (*.f64 x x)) -1/9 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 1/2) 2))) (/.f64 1/3 x) (cbrt.f64 1/2))))

prune59.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1053108
Fresh213
Picked101
Done033
Total1087115
Error
0.6b
Counts
115 → 7
Alt Table
StatusErrorProgram
✓0.8b
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
62.7b
(pow.f64 (cbrt.f64 (log.f64 (exp.f64 (+.f64 1/2 (/.f64 1 x))))) 3)
✓0.8b
(/.f64 (exp.f64 x) (expm1.f64 x))
23.6b
(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))) 3) 3)
49.2b
(pow.f64 (/.f64 (cbrt.f64 (+.f64 1/8 (pow.f64 x -3))) (cbrt.f64 (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x))))) 3)
✓22.1b
(+.f64 1/2 (/.f64 1 x))
27.6b
(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))
Compiler

Compiled 1705 to 1499 computations (12.1% saved)

regimes67.0ms (2.3%)

Accuracy

Total 0.1b remaining (20.6%)

Threshold costs 0.1b (20.6%)

Counts
29 → 1
Compiler

Compiled 968 to 787 computations (18.7% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11011
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
Outputs
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))

end101.0ms (3.5%)

Stop Event
1×fuel
Compiler

Compiled 95 to 76 computations (20% saved)

Profiling

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