Details

Time bar (total: 2.9s)

analyze493.0ms (17.2%)

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

Compiled 9 to 6 computations (33.3% saved)

sample1.7s (58.7%)

Results
905.0ms2777×body1024valid
289.0ms1319×body512valid
254.0ms3168×body128valid
115.0ms315×body2048valid
105.0ms677×body256valid
0.0ms1×body2048invalid

preprocess15.0ms (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))

prune2.0ms (0.1%)

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))

series3.0ms (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))

rewrite33.0ms (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 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))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))))

simplify65.0ms (2.2%)

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))

prune42.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New38240
Fresh000
Picked011
Done000
Total38341
Error
0.2b
Counts
41 → 3
Alt Table
StatusErrorProgram
✓0.3b
(/.f64 (exp.f64 x) (expm1.f64 x))
22.9b
(+.f64 (/.f64 1 x) 1/2)
▶0.3b
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
Compiler

Compiled 423 to 191 computations (54.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
✓0.3b
(/.f64 (expm1.f64 x) (exp.f64 x))

series4.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

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

rewrite42.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
672×pow1_binary64
625×add-log-exp_binary64
625×log1p-expm1-u_binary64
625×expm1-log1p-u_binary64
69×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0719
114116
2174216
Stop Event
1×node limit
Counts
2 → 74
Calls
Call 1
Inputs
(/.f64 (expm1.f64 x) (exp.f64 x))
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 x) (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) (exp.f64 x)) (exp.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (exp.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) 2) (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (exp.f64 x))) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 (exp.f64 x))) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) 1)))) (#(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 (expm1.f64 x) (exp.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 x) (neg.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 x) (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 (exp.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) (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) (/.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 (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 (/.f64 (exp.f64 x) (expm1.f64 x))) (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (expm1.f64 x) -1) (pow.f64 (exp.f64 (neg.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) -1))))) (#(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)) (/.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (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 *.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (expm1.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) (sqrt.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 1 (neg.f64 (expm1.f64 x))) (neg.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 x) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 (expm1.f64 x) (exp.f64 x))))))) (#(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 (/.f64 (expm1.f64 x) (exp.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (/.f64 (expm1.f64 x) (cbrt.f64 (exp.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 (neg.f64 (exp.f64 x)) (neg.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (exp.f64 x) 1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.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 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) (exp.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 (expm1.f64 x) 3)))))) (#(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))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))))

simplify29.0ms (1%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
493×distribute-lft-out_binary64
413×*-commutative_binary64
384×fma-def_binary64
232×distribute-rgt-out_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
035214
190214
2205214
3594208
41600200
52745200
Stop Event
1×node limit
Counts
98 → 91
Calls
Call 1
Inputs
x
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 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 -1/720 (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
x
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)
(fma.f64 -1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x -1/2) x)
(*.f64 x (fma.f64 x -1/2 1))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 -1/2 (*.f64 x x) x))
(fma.f64 x (*.f64 x -1/2) (fma.f64 1/6 (pow.f64 x 3) x))
(fma.f64 x (*.f64 x (fma.f64 x 1/6 -1/2)) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 -1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x (fma.f64 x 1/6 -1/2)) (fma.f64 -1/24 (pow.f64 x 4) x))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 -1/2) (fma.f64 -1/24 (pow.f64 x 4) x))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) (exp.f64 x))
(/.f64 (expm1.f64 x) (exp.f64 x))
(-.f64 1 (exp.f64 (neg.f64 x)))
(neg.f64 (expm1.f64 (neg.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 (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 (/.f64 1 x) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 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))

prune151.0ms (5.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New89291
Fresh101
Picked101
Done101
Total92294
Error
0b
Counts
94 → 2
Alt Table
StatusErrorProgram
0.3b
(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
▶0.0b
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
Compiler

Compiled 1034 to 460 computations (55.5% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
1.0ms
x
@inf
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
1.0ms
x
@0
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)

rewrite31.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
457×pow1_binary64
428×add-log-exp_binary64
426×log1p-expm1-u_binary64
426×expm1-log1p-u_binary64
418×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0710
11426
216926
Stop Event
1×node limit
Counts
1 → 20
Calls
Call 1
Inputs
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.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 1 (/.f64 -1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (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)) (/.f64 1 (cbrt.f64 (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 (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 /.f64 -1 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (expm1.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (expm1.f64 x) -1/2) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))))) (#(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 cbrt.f64 (pow.f64 (/.f64 -1 (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 -1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 -1 (expm1.f64 x))))))))

simplify32.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
756×fma-def_binary64
604×associate-*l*_binary64
429×unswap-sqr_binary64
324×*-commutative_binary64
209×fma-neg_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
025128
160128
2115128
3262120
4450120
5930104
62320104
74602104
Stop Event
1×node limit
Counts
32 → 30
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 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
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 1/2 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.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 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2))
(+.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 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (neg.f64 (expm1.f64 (neg.f64 x))))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (neg.f64 (expm1.f64 (neg.f64 x))))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (neg.f64 (expm1.f64 (neg.f64 x))))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (neg.f64 (expm1.f64 (neg.f64 x))))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (neg.f64 (expm1.f64 (neg.f64 x))))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (neg.f64 (expm1.f64 (neg.f64 x))))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (neg.f64 (expm1.f64 (neg.f64 x))))
(/.f64 -1 (expm1.f64 (neg.f64 x)))
(/.f64 1 (-.f64 1 (exp.f64 (*.f64 -1 x))))
(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 1 (neg.f64 (expm1.f64 (neg.f64 x))))
(/.f64 -1 (expm1.f64 (neg.f64 x)))

prune18.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New30030
Fresh011
Picked011
Done000
Total30232
Error
0b
Counts
32 → 2
Alt Table
StatusErrorProgram
▶0.3b
(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
✓0.0b
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
Compiler

Compiled 251 to 169 computations (32.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

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

rewrite36.0ms (1.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
113514
2158314
Stop Event
1×node limit
Counts
2 → 46
Calls
Call 1
Inputs
(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
(/.f64 1 (expm1.f64 x))
Outputs
((#(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 1 (/.f64 (expm1.f64 x) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (/.f64 (expm1.f64 x) (cbrt.f64 (exp.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 (neg.f64 (exp.f64 x)) (neg.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (exp.f64 x) 1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.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 (exp.f64 x)) (neg.f64 (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 (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 (/.f64 1 (expm1.f64 x)) 3) (pow.f64 (exp.f64 x) 3)))))) (#(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))))))) (#(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 -.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 (/.f64 1 (cbrt.f64 (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)) (/.f64 1 (cbrt.f64 (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 (/.f64 1 (cbrt.f64 (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 exp.f64 (neg.f64 (log.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (expm1.f64 x))))))))

simplify44.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
512×fma-neg_binary64
411×distribute-rgt-neg-in_binary64
321×fma-def_binary64
281×distribute-lft-neg-in_binary64
221×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
023192
159192
2123192
3307192
4517192
51048192
62130192
73948192
84881192
Stop Event
1×node limit
Counts
70 → 62
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))
(/.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))
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))))
(fma.f64 -1/720 (pow.f64 x 3) (+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (+.f64 (/.f64 1 x) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.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 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)
(fma.f64 -1/720 (pow.f64 x 3) (+.f64 (fma.f64 x 1/12 (/.f64 1 x)) -1/2))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) -1/2))
(fma.f64 x 1/12 (+.f64 (/.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 -1/720 (*.f64 x x) 1/12) -1/2))
(fma.f64 -1/720 (pow.f64 x 3) (-.f64 (/.f64 1 x) (fma.f64 x -1/12 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))

prune86.0ms (3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New62062
Fresh000
Picked011
Done011
Total62264
Error
0b
Counts
64 → 2
Alt Table
StatusErrorProgram
✓0.3b
(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
✓0.0b
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
Compiler

Compiled 602 to 323 computations (46.3% saved)

regimes15.0ms (0.5%)

Accuracy

Total -62.0b remaining (-528733.2%)

Threshold costs -62.0b (-528733.2%)

Counts
6 → 1
Calls
Call 1
Inputs
(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
(+.f64 (/.f64 1 x) 1/2)
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
Outputs
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
Results
9.0ms0.0bx
2.0ms0.0b(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.0ms0.0b(exp.f64 x)
Compiler

Compiled 51 to 30 computations (41.2% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×+-commutative_binary64
2×*-commutative_binary64
2×sub-neg_binary64
2×neg-sub0_binary64
2×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11210
21610
31810
Stop Event
1×saturated
Calls
Call 1
Inputs
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)
Outputs
(pow.f64 (neg.f64 (expm1.f64 (neg.f64 x))) -1)

end13.0ms (0.5%)

Stop Event
1×done
Compiler

Compiled 14 to 12 computations (14.3% saved)

Profiling

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