Details

Time bar (total: 2.6s)

analyze484.0ms (18.4%)

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 (61.8%)

Results
876.0ms2795×body1024valid
300.0ms1410×body512valid
240.0ms3125×body128valid
102.0ms271×body2048valid
98.0ms655×body256valid
0.0ms1×body2048invalid
Compiler

Compiled 18 to 12 computations (33.3% saved)

preprocess16.0ms (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)

simplify5.0ms (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
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.0b
(/.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
✓0.0b
(/.f64 (exp.f64 x) (expm1.f64 x))

series7.0ms (0.3%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
3.0ms
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))

rewrite31.0ms (1.2%)

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))))))))

simplify65.0ms (2.4%)

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))

prune18.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New38240
Fresh000
Picked011
Done000
Total38341
Error
0b
Counts
41 → 3
Alt Table
StatusErrorProgram
✓0.0b
(/.f64 (exp.f64 x) (expm1.f64 x))
▶0.0b
(*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
23.6b
(+.f64 1/2 (/.f64 1 x))
Compiler

Compiled 433 to 195 computations (55% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series12.0ms (0.5%)

Counts
4 → 40
Calls

12 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
4.0ms
x
@inf
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
1.0ms
x
@0
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
0.0ms
x
@-inf
(*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
0.0ms
x
@0
(/.f64 1 (expm1.f64 x))

rewrite45.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
773×pow1_binary64
713×log1p-expm1-u_binary64
713×expm1-log1p-u_binary64
83×add-sqr-sqrt_binary64
80×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0932
117629
2208029
Stop Event
1×node limit
Counts
4 → 92
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 1 (expm1.f64 x))
(sqrt.f64 (exp.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.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)) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (cbrt.f64 (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (exp.f64 x) 1/4) (/.f64 (expm1.f64 x) (pow.f64 (exp.f64 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (exp.f64 x))) (neg.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (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)) (cbrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (sqrt.f64 (exp.f64 x))) (neg.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (exp.f64 x)) -1) (neg.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 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 cbrt.f64 (*.f64 (pow.f64 (exp.f64 x) 3/2) (pow.f64 (/.f64 1 (expm1.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (expm1.f64 x)) 3) (pow.f64 (exp.f64 x) 3/2)))))) (#(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 1 (expm1.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (expm1.f64 x))) (cbrt.f64 (pow.f64 (expm1.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) -2)) (cbrt.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (expm1.f64 x) -1/2) (pow.f64 (expm1.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (expm1.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) -1) (pow.f64 (sqrt.f64 (expm1.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (expm1.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1 (expm1.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 x) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (expm1.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (expm1.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (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 (exp.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) 1))))) (#(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 (pow.f64 (exp.f64 x) 1/4) (*.f64 (pow.f64 (exp.f64 x) 1/4) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (exp.f64 (+.f64 x x)))) (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 (cbrt.f64 (exp.f64 (+.f64 x x))) 1/2) (pow.f64 (cbrt.f64 (exp.f64 x)) 1/2))))) (#(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 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))))))))
((#(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 (*.f64 (exp.f64 x) -1) (neg.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 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 log.f64 (+.f64 1 (expm1.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 (/.f64 1 (expm1.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 x) 3/2) (pow.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)) 3) (pow.f64 (exp.f64 x) 3/2)))))) (#(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 (neg.f64 (log.f64 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 x (neg.f64 (log.f64 (expm1.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))))

simplify44.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
733×fma-neg_binary64
555×fma-def_binary64
400×unswap-sqr_binary64
329×*-commutative_binary64
263×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
051394
1129364
2304359
3876352
42002352
52960352
64868352
Stop Event
1×node limit
Counts
132 → 122
Calls
Call 1
Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (*.f64 7/5760 (pow.f64 x 3)) (+.f64 (/.f64 1 x) (*.f64 -1/24 x)))
(+.f64 (*.f64 7/5760 (pow.f64 x 3)) (+.f64 (/.f64 1 x) (+.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 (/.f64 1 x) 1/2)
(-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2)
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 1/2)
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.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)))))
(/.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 (/.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 7/5760 (pow.f64 x 3)) (+.f64 (/.f64 1 x) (*.f64 -1/24 x)))
(fma.f64 7/5760 (pow.f64 x 3) (+.f64 (/.f64 1 x) (*.f64 x -1/24)))
(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 x) (+.f64 (*.f64 -31/967680 (pow.f64 x 5)) (*.f64 -1/24 x))))
(fma.f64 7/5760 (pow.f64 x 3) (+.f64 (/.f64 1 x) (fma.f64 -31/967680 (pow.f64 x 5) (*.f64 x -1/24))))
(+.f64 (fma.f64 -31/967680 (pow.f64 x 5) (*.f64 x -1/24)) (fma.f64 7/5760 (pow.f64 x 3) (/.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 -1/24 (fma.f64 -31/967680 (pow.f64 x 5) (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 -31/967680 (pow.f64 x 5) (fma.f64 x -1/24 (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 (/.f64 1 x) 1/2)
(+.f64 (/.f64 1 x) -1/2)
(-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2)
(+.f64 (fma.f64 1/12 x (/.f64 1 x)) -1/2)
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) -1/2)
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 -1/2))
(-.f64 (+.f64 (*.f64 -1/720 (pow.f64 x 3)) (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 1/2)
(+.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))) -1/2)
(+.f64 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 (/.f64 1 x))) -1/2)
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 (pow.f64 x 3) -1/720 -1/2))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 -1/2)))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (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 1 (fma.f64 x 1/2 (*.f64 1/8 (*.f64 x x))))
(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 (*.f64 x 1/8) 1/2)) (fma.f64 (pow.f64 x 3) 1/48 1))
(fma.f64 x (*.f64 x (fma.f64 x 1/48 1/8)) (fma.f64 x 1/2 1))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x (fma.f64 x 1/48 1/8)) 1))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) (fma.f64 x 1/48 1/8) 1))
(/.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 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 (pow.f64 x 3) -1/720 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))

prune77.0ms (2.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1531154
Fresh101
Picked101
Done011
Total1552157
Error
0b
Counts
157 → 2
Alt Table
StatusErrorProgram
✓0.0b
(/.f64 (exp.f64 x) (expm1.f64 x))
▶0.2b
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
Compiler

Compiled 2216 to 1018 computations (54.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (exp.f64 x))
✓0.0b
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
✓0.1b
(fma.f64 x -1/24 (/.f64 1 x))

series6.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
1.0ms
x
@-inf
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
1.0ms
x
@0
(fma.f64 x -1/24 (/.f64 1 x))
1.0ms
x
@-inf
(fma.f64 x -1/24 (/.f64 1 x))
0.0ms
x
@0
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))

rewrite36.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
758×pow1_binary64
703×log1p-expm1-u_binary64
703×expm1-log1p-u_binary64
84×add-sqr-sqrt_binary64
79×*-un-lft-identity_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0923
117623
2197223
Stop Event
1×node limit
Counts
2 → 40
Calls
Call 1
Inputs
(fma.f64 x -1/24 (/.f64 1 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) (*.f64 x -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x -1/24) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x -1/24) 1) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x -1/24 (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x -1/24 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x -1/24 (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x -1/24 (/.f64 1 x))) (pow.f64 (cbrt.f64 (fma.f64 x -1/24 (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/24 (/.f64 1 x))) 2) (cbrt.f64 (fma.f64 x -1/24 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x -1/24 (/.f64 1 x))) (sqrt.f64 (fma.f64 x -1/24 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x -1/24) 3) (/.f64 (pow.f64 x -2) x)) (+.f64 (*.f64 (*.f64 x -1/24) (*.f64 x -1/24)) (-.f64 (pow.f64 x -2) (*.f64 (*.f64 x -1/24) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x -1/24) (*.f64 x -1/24)) (pow.f64 x -2)) (-.f64 (*.f64 x -1/24) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x -1/24 (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x -1/24 (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x -1/24 (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x -1/24 (/.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x -1/24 (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x -1/24 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x -1/24 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x -1/24 (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x -1/24 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x -1/24 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x -1/24 (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x -1/24 (/.f64 1 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x -1/24) (sqrt.f64 (exp.f64 x))) (*.f64 (/.f64 1 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (exp.f64 x) (pow.f64 (fma.f64 x -1/24 (/.f64 1 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 (exp.f64 x))) (fma.f64 x -1/24 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 x -1/24 (/.f64 1 x)) 3) (pow.f64 (exp.f64 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 x) 3/2) (pow.f64 (fma.f64 x -1/24 (/.f64 1 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 1/2 x) (log.f64 (fma.f64 x -1/24 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 (*.f64 1/2 x) (log.f64 (fma.f64 x -1/24 (/.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))))))))

simplify41.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
679×fma-def_binary64
493×associate-*l*_binary64
362×unswap-sqr_binary64
307×associate-/l/_binary64
285×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
026296
163260
2123236
3244236
4398236
5779236
62427236
74858236
Stop Event
1×node limit
Counts
64 → 55
Calls
Call 1
Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(*.f64 -1/24 x)
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(*.f64 -1/24 x)
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 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 (*.f64 -1/384 (pow.f64 x 3)) (/.f64 1 x))))
(*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
Outputs
(/.f64 1 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 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/24))
(fma.f64 x -1/24 (/.f64 1 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 -1/24 x)
(*.f64 x -1/24)
(+.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 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/24))
(fma.f64 x -1/24 (/.f64 1 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 -1/24 x)
(*.f64 x -1/24)
(+.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 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/24))
(fma.f64 x -1/24 (/.f64 1 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 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 1/12 x) (+.f64 (*.f64 -1/384 (pow.f64 x 3)) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 1/12 x (fma.f64 -1/384 (pow.f64 x 3) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 -1/384 (pow.f64 x 3) (/.f64 1 x))))
(+.f64 (/.f64 1 x) (fma.f64 -1/384 (pow.f64 x 3) (fma.f64 x 1/12 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 -1/384 (*.f64 x x) 1/12) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/384 (pow.f64 x 3) 1/2)))
(*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))))
(*.f64 (*.f64 x -1/24) (sqrt.f64 (exp.f64 x)))
(*.f64 x (/.f64 (sqrt.f64 (exp.f64 x)) -24))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (*.f64 (/.f64 1 x) (sqrt.f64 (exp.f64 x))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (*.f64 (/.f64 1 x) (sqrt.f64 (exp.f64 x))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (*.f64 (/.f64 1 x) (sqrt.f64 (exp.f64 x))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))))
(*.f64 (*.f64 x -1/24) (sqrt.f64 (exp.f64 x)))
(*.f64 x (/.f64 (sqrt.f64 (exp.f64 x)) -24))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (*.f64 (/.f64 1 x) (sqrt.f64 (exp.f64 x))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (*.f64 (/.f64 1 x) (sqrt.f64 (exp.f64 x))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(+.f64 (*.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (*.f64 (/.f64 1 x) (sqrt.f64 (exp.f64 x))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))

prune47.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New87087
Fresh000
Picked011
Done011
Total87289
Error
0b
Counts
89 → 2
Alt Table
StatusErrorProgram
✓0.0b
(/.f64 (exp.f64 x) (expm1.f64 x))
✓0.2b
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
Compiler

Compiled 1172 to 734 computations (37.4% saved)

regimes15.0ms (0.6%)

Accuracy

Total 0.0b remaining (1.4%)

Threshold costs 0.0b (1.4%)

Counts
13 → 1
Compiler

Compiled 118 to 67 computations (43.2% saved)

simplify2.0ms (0.1%)

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))

end38.0ms (1.4%)

Stop Event
1×done
Compiler

Compiled 29 to 20 computations (31% saved)

Profiling

Loading profile data...