Details

Time bar (total: 3.8s)

analyze515.0ms (13.4%)

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)

sample1.6s (42.3%)

Results
849.0ms2709×body1024valid
287.0ms1318×body512valid
254.0ms3249×body128valid
118.0ms320×body2048valid
99.0ms660×body256valid
1.0ms2×body2048invalid

preprocess14.0ms (0.4%)

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))

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.3b
(/.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
✓0.3b
(/.f64 (exp.f64 x) (expm1.f64 x))

series5.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite30.0ms (0.8%)

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 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 log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))))

simplify64.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
567×sqr-pow_binary64
438×associate-*l*_binary64
362×unswap-sqr_binary64
313×pow-sqr_binary64
311×fma-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
019104
148104
294104
3215104
4331104
5568104
61456104
72283104
82369104
92502104
102660104
112890104
123212104
133633104
144133104
154728104
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 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(/.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 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 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))

prune41.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New37340
Fresh000
Picked011
Done000
Total37441
Error
0.2b
Counts
41 → 4
Alt Table
StatusErrorProgram
23.7b
(+.f64 1/2 (/.f64 1 x))
✓0.3b
(/.f64 (exp.f64 x) (expm1.f64 x))
▶0.3b
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
23.5b
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
Compiler

Compiled 451 to 209 computations (53.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (exp.f64 x))
✓0.3b
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
✓0.3b
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))

series5.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

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

rewrite47.0ms (1.2%)

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 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 log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))))))))
((#(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 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 log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))))
((#(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 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))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (exp.f64 x))))))))

simplify49.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
1004×fma-def_binary64
400×unswap-sqr_binary64
301×*-commutative_binary64
193×associate-*l*_binary64
179×associate-/l/_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
047296
1120270
2278270
3777264
41735263
52859263
63858263
74920263
Stop Event
1×node limit
Counts
140 → 135
Calls
Call 1
Inputs
(/.f64 1 x)
(+.f64 (*.f64 -1/24 x) (/.f64 1 x))
(+.f64 (*.f64 7/5760 (pow.f64 x 3)) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))
(+.f64 (*.f64 7/5760 (pow.f64 x 3)) (+.f64 (*.f64 -1/24 x) (+.f64 (*.f64 -31/967680 (pow.f64 x 5)) (/.f64 1 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 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(/.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 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/48 (pow.f64 x 3)))))
Outputs
(/.f64 1 x)
(+.f64 (*.f64 -1/24 x) (/.f64 1 x))
(fma.f64 -1/24 x (/.f64 1 x))
(fma.f64 x -1/24 (/.f64 1 x))
(+.f64 (*.f64 7/5760 (pow.f64 x 3)) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 -1/24 x (/.f64 1 x)))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 x -1/24 (/.f64 1 x)))
(fma.f64 x -1/24 (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (*.f64 7/5760 (pow.f64 x 3)) (+.f64 (*.f64 -1/24 x) (+.f64 (*.f64 -31/967680 (pow.f64 x 5)) (/.f64 1 x))))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 -1/24 x (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 x -1/24 (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 x -1/24 (fma.f64 7/5760 (pow.f64 x 3) (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 x (fma.f64 x (*.f64 x 7/5760) -1/24) (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x)))
(fma.f64 x (fma.f64 7/5760 (*.f64 x x) -1/24) (fma.f64 -31/967680 (pow.f64 x 5) (/.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 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 (/.f64 1 x))))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 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 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(fma.f64 x 1/2 1)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/8 (*.f64 x x) (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 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/48 (pow.f64 x 3)))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (+.f64 1 (*.f64 (pow.f64 x 3) 1/48))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 x 1/2 (fma.f64 (pow.f64 x 3) 1/48 1)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 3) 1/48 1)))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) (fma.f64 x 1/48 1/8) 1))
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/48 1/8))) 1)

prune1.3s (32.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1750175
Fresh022
Picked011
Done011
Total1754179
Error
0.2b
Counts
179 → 4
Alt Table
StatusErrorProgram
23.7b
(+.f64 1/2 (/.f64 1 x))
✓0.3b
(/.f64 (exp.f64 x) (expm1.f64 x))
✓0.3b
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
▶23.5b
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
Compiler

Compiled 2582 to 1120 computations (56.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
✓0.1b
(fma.f64 x 1/12 1/2)

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(fma.f64 x 1/12 1/2)
0.0ms
x
@0
(fma.f64 x 1/12 1/2)
0.0ms
x
@inf
(fma.f64 x 1/12 1/2)
0.0ms
x
@-inf
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
0.0ms
x
@0
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))

rewrite41.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
842×pow1_binary64
790×log1p-expm1-u_binary64
790×expm1-log1p-u_binary64
85×add-sqr-sqrt_binary64
80×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0816
117216
2212716
Stop Event
1×node limit
Counts
2 → 58
Calls
Call 1
Inputs
(fma.f64 x 1/12 1/2)
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/12) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 1/12) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 1/12 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/12 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2) (cbrt.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) (sqrt.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x 1/12) 3) 1/8) (+.f64 (*.f64 (*.f64 x 1/12) (*.f64 x 1/12)) (-.f64 1/4 (*.f64 (*.f64 x 1/12) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x 1/12) (*.f64 x 1/12)) 1/4) (-.f64 (*.f64 x 1/12) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/12 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/12 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/12 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x 1/12 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/12 1/2)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x -2) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) (/.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) 2) (cbrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) (sqrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3)) (/.f64 1 (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (/.f64 (fma.f64 x 1/12 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2)) (/.f64 1 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (/.f64 (fma.f64 x 1/12 1/2) x))) (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3)) (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (/.f64 (fma.f64 x 1/12 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3)) (+.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (-.f64 (pow.f64 x -2) (/.f64 (fma.f64 x 1/12 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2)) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3))) (neg.f64 (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (/.f64 (fma.f64 x 1/12 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2))) (neg.f64 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (pow.f64 x -2)) (-.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 1/12 1/2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2) (cbrt.f64 (fma.f64 x 1/12 1/2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (/.f64 1 x)) (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) (sqrt.f64 (fma.f64 x 1/12 1/2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))))

simplify10.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
6×fma-def_binary64
5×+-commutative_binary64
2×associate-+r+_binary64
2×associate-+l+_binary64
1×*-commutative_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
013171
123149
228149
330149
Stop Event
1×saturated
Counts
82 → 67
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
Outputs
1/2
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))

prune85.0ms (2.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New67067
Fresh011
Picked011
Done022
Total67471
Error
0.2b
Counts
71 → 4
Alt Table
StatusErrorProgram
▶23.7b
(+.f64 1/2 (/.f64 1 x))
✓0.3b
(/.f64 (exp.f64 x) (expm1.f64 x))
✓0.3b
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
✓23.5b
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
Compiler

Compiled 960 to 766 computations (20.2% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done033
Total044
Error
0.2b
Counts
4 → 4
Alt Table
StatusErrorProgram
✓23.7b
(+.f64 1/2 (/.f64 1 x))
✓0.3b
(/.f64 (exp.f64 x) (expm1.f64 x))
✓0.3b
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
✓23.5b
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
Compiler

Compiled 35 to 25 computations (28.6% saved)

regimes10.0ms (0.3%)

Accuracy

Total -61.8b remaining (-22912%)

Threshold costs -61.8b (-22912%)

Counts
5 → 1
Calls
Call 1
Inputs
(+.f64 1/2 (/.f64 1 x))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))
Results
4.0ms0.3bx
2.0ms0.3b(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.0ms0.3b(exp.f64 x)
Compiler

Compiled 51 to 30 computations (41.2% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))

end15.0ms (0.4%)

Stop Event
1×done
Compiler

Compiled 12 to 8 computations (33.3% saved)

Profiling

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