Details

Time bar (total: 2.5s)

analyze509.0ms (20%)

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 (63.8%)

Results
851.0ms2757×body1024valid
298.0ms1370×body512valid
270.0ms3251×body128valid
97.0ms616×body256valid
94.0ms262×body2048valid
1.0ms2×body2048invalid

preprocess13.0ms (0.5%)

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))

prune5.0ms (0.2%)

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))

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite30.0ms (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 log1p.f64 (expm1.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 expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))))

simplify67.0ms (2.6%)

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))

prune21.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New39140
Fresh000
Picked011
Done000
Total39241
Error
0b
Counts
41 → 2
Alt Table
StatusErrorProgram
✓0.0b
(/.f64 (exp.f64 x) (expm1.f64 x))
▶21.3b
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2))
Compiler

Compiled 423 to 189 computations (55.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2))
✓0.0b
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
✓0.0b
(fma.f64 x (*.f64 x -1/720) 1/12)
✓0.2b
(*.f64 x -1/720)

series6.0ms (0.2%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@0
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
1.0ms
x
@inf
(*.f64 x -1/720)
1.0ms
x
@-inf
(fma.f64 x (*.f64 x -1/720) 1/12)
1.0ms
x
@inf
(fma.f64 x (*.f64 x -1/720) 1/12)
0.0ms
x
@0
(*.f64 x -1/720)

rewrite53.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
565×prod-diff_binary64
241×fma-def_binary64
197×expm1-udef_binary64
197×log1p-udef_binary64
137×fma-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01142
123442
2284442
Stop Event
1×node limit
Counts
4 → 111
Calls
Call 1
Inputs
(*.f64 x -1/720)
(fma.f64 x (*.f64 x -1/720) 1/12)
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x -1/720))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x -1/720) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x -1/720) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x -1/720)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x -1/720)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 1/518400))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) -1/720))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x -1/720))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x -1/720) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x -1/720)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x -1/720)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x -1/720)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x -1/720)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/12 (*.f64 (*.f64 x x) -1/720))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) -1/720) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (*.f64 x x) -1/720) 1) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x (*.f64 x -1/720) 1/12))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 x -1/720) 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (*.f64 x -1/720) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)) 2) (cbrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)) (sqrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) -1/720) 3) 1/1728) (fma.f64 (*.f64 (*.f64 x x) -1/720) (*.f64 (*.f64 x x) -1/720) (-.f64 1/144 (*.f64 (*.f64 (*.f64 x x) -1/720) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (*.f64 (*.f64 x x) -1/720) (*.f64 (*.f64 x x) -1/720) -1/144) (fma.f64 x (*.f64 x -1/720) -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (*.f64 x -1/720) 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x -1/720) 1/12) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (*.f64 x -1/720) 1/12) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (*.f64 x -1/720) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x (*.f64 x -1/720) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x -1/720) 1/12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (*.f64 x -1/720) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (*.f64 x -1/720) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x (*.f64 x -1/720) 1/12)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (*.f64 x -1/720) 1/12)))))))
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(sqrt.f64 x) (sqrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12))) (*.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12))) (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)) 2)) (cbrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)) (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12))) (sqrt.f64 (fma.f64 x (*.f64 x -1/720) 1/12)) (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2) (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2) (/.f64 1 x))))))))

simplify57.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
561×fma-def_binary64
536×unswap-sqr_binary64
509×associate-/r*_binary64
411×associate-*l*_binary64
298×*-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
027421
167401
2122385
3246385
4521385
51616385
63257385
73613385
84079385
94894385
Stop Event
1×node limit
Counts
159 → 132
Calls
Call 1
Inputs
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
1/12
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(*.f64 -1/720 (pow.f64 x 2))
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(*.f64 -1/720 (pow.f64 x 2))
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
1/2
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (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 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3)))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3)))))
Outputs
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
(*.f64 -1/720 x)
1/12
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (*.f64 x x)))
(fma.f64 -1/720 (*.f64 x x) 1/12)
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (*.f64 x x)))
(fma.f64 -1/720 (*.f64 x x) 1/12)
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (*.f64 x x)))
(fma.f64 -1/720 (*.f64 x x) 1/12)
(*.f64 -1/720 (pow.f64 x 2))
(*.f64 -1/720 (*.f64 x x))
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (*.f64 x x)))
(fma.f64 -1/720 (*.f64 x x) 1/12)
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (*.f64 x x)))
(fma.f64 -1/720 (*.f64 x x) 1/12)
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (*.f64 x x)))
(fma.f64 -1/720 (*.f64 x x) 1/12)
(*.f64 -1/720 (pow.f64 x 2))
(*.f64 -1/720 (*.f64 x x))
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (*.f64 x x)))
(fma.f64 -1/720 (*.f64 x x) 1/12)
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (*.f64 x x)))
(fma.f64 -1/720 (*.f64 x x) 1/12)
(+.f64 1/12 (*.f64 -1/720 (pow.f64 x 2)))
(+.f64 1/12 (*.f64 -1/720 (*.f64 x x)))
(fma.f64 -1/720 (*.f64 x x) 1/12)
1/2
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 x 1/12))
(fma.f64 x 1/12 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 (fma.f64 x 1/12 1/2) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 (fma.f64 x 1/12 1/2) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))
(fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3)))
(*.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 (fma.f64 x 1/12 1/2) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 (fma.f64 x 1/12 1/2) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))
(fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3)))
(*.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 (fma.f64 x 1/12 1/2) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 (fma.f64 x 1/12 1/2) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 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 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))
(+.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 (fma.f64 x 1/12 1/2) (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2)))
(+.f64 1/2 (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x)))
(fma.f64 -1/720 (pow.f64 x 3) (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))
(fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3)))
(*.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 (fma.f64 x 1/12 1/2) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3)))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 1/2) (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2)))
(+.f64 1/2 (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x)))
(fma.f64 -1/720 (pow.f64 x 3) (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))
(fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3)))
(*.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 (fma.f64 x 1/12 1/2) (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3)))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 1/2) (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2)))
(+.f64 1/2 (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x)))
(fma.f64 -1/720 (pow.f64 x 3) (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))

prune81.0ms (3.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1320132
Fresh000
Picked011
Done011
Total1322134
Error
0b
Counts
134 → 2
Alt Table
StatusErrorProgram
✓0.0b
(/.f64 (exp.f64 x) (expm1.f64 x))
✓21.3b
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2))
Compiler

Compiled 2487 to 1806 computations (27.4% saved)

regimes22.0ms (0.9%)

Accuracy

Total 0.0b remaining (4.9%)

Threshold costs 0.0b (4.9%)

Counts
20 → 1
Compiler

Compiled 183 to 114 computations (37.7% 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))

end38.0ms (1.5%)

Stop Event
1×done
Compiler

Compiled 36 to 26 computations (27.8% saved)

Profiling

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