Details

Time bar (total: 4.5s)

analyze17.0ms (0.4%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%25%25%4
50%12.5%37.5%5
50%6.2%43.8%6
50%3.1%46.9%7
50%1.6%48.5%8
50%1.6%48.5%9
50.4%1.2%48.5%10
50.4%1.2%48.5%11
50.4%1.1%48.6%12
50.4%1%48.6%13
50.5%0.9%48.6%14
Compiler

Compiled 15 to 8 computations (46.7% saved)

sample4.0s (87%)

Results
1.8s3910×body1024valid
1.7s2029×body512valid
220.0ms434×body2048valid
195.0ms1037×body256valid
91.0ms846×body128valid
0.0ms1×body128invalid
Compiler

Compiled 30 to 16 computations (46.7% saved)

preprocess32.0ms (0.7%)

Algorithm
2×egg-herbie
Rules
720×fma-def_binary64
478×fma-neg_binary64
464×times-frac_binary64
264×associate-*l*_binary64
226×associate-*r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0822
12022
23522
35922
413322
533622
687822
7256922
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 14 to 7 computations (50% saved)

simplify24.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
720×fma-def_binary64
478×fma-neg_binary64
464×times-frac_binary64
264×associate-*l*_binary64
226×associate-*r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0822
12022
23522
35922
413322
533622
687822
7256922
Stop Event
1×node limit
Counts
1 → 1
Calls
Call 1
Inputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
58.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶58.7b
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 42 to 21 computations (50% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓1.5b
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓5.3b
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series5.0ms (0.1%)

Counts
3 → 24
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@0
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
1.0ms
x
@inf
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms
x
@-inf
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms
x
@0
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0ms
x
@0
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

rewrite103.0ms (2.3%)

Algorithm
3×egg-rewrite-iter-limit
3×egg-rewrite
1×batch-egg-rewrite
Rules
99×add-sqr-sqrt_binary64
99×add-sqr-sqrt_binary64
95×*-un-lft-identity_binary64
95×pow1_binary64
95×*-un-lft-identity_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0818
118618
2369018
066
11306
221496
066
083
11863
236903
083
066
11296
221296
066
Stop Event
1×iter limit
1×unsound
1×iter limit
1×unsound
1×iter limit
1×unsound
1×unsound
Counts
3 → 37
Calls
Call 1
Inputs
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) (neg.f64 (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 2 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (sinh.f64 x))) (cbrt.f64 (*.f64 2 (sinh.f64 x)))) (cbrt.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (sinh.f64 x))) (sqrt.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (sinh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (*.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (*.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (exp.f64 x) (exp.f64 x)) (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (sinh.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (*.f64 2 (sinh.f64 x)) (*.f64 2 (sinh.f64 x))) (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (sinh.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) (*.f64 2 (cosh.f64 x))) (/.f64 (exp.f64 (neg.f64 x)) (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (tanh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (tanh.f64 x)) (cbrt.f64 (tanh.f64 x))) (cbrt.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tanh.f64 x)) (sqrt.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (tanh.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (tanh.f64 x) (tanh.f64 x)) (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x tanh.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (tanh.f64 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 2 (cosh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (cosh.f64 x))) (cbrt.f64 (*.f64 2 (cosh.f64 x)))) (cbrt.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x))) (sqrt.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (cosh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (*.f64 (exp.f64 x) (exp.f64 x)) (-.f64 (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (*.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (exp.f64 x) (exp.f64 x)) (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))) (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (cosh.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (*.f64 2 (cosh.f64 x)) (*.f64 2 (cosh.f64 x))) (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x))))))))

simplify33.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
783×fma-def_binary64
695×fma-neg_binary64
507×unswap-sqr_binary64
471×associate-*l*_binary64
377×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
050321
1138317
2352311
31114309
43894309
Stop Event
1×node limit
Counts
61 → 64
Calls
Call 1
Inputs
(*.f64 2 x)
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x))
(+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))
(+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)))
2
(+.f64 2 (pow.f64 x 2))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (+.f64 2 (pow.f64 x 2)))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (+.f64 2 (+.f64 (*.f64 1/360 (pow.f64 x 6)) (pow.f64 x 2))))
(+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x))
(+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x))
(+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x))
(+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x))
Outputs
(*.f64 2 x)
(+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x)))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
(+.f64 (*.f64 1/60 (pow.f64 x 5)) (+.f64 (*.f64 1/2520 (pow.f64 x 7)) (+.f64 (*.f64 1/3 (pow.f64 x 3)) (*.f64 2 x))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (fma.f64 2 x (*.f64 1/2520 (pow.f64 x 7)))))
(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))))
(fma.f64 x (fma.f64 x (*.f64 x 1/3) 2) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 (pow.f64 x 5) 2/15 x) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 17/315 (pow.f64 x 7) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (fma.f64 (pow.f64 x 5) 2/15 x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 17/315)))
(+.f64 (fma.f64 (pow.f64 x 5) 2/15 x) (fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 7) -17/315)))
(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2
(+.f64 2 (pow.f64 x 2))
(+.f64 2 (*.f64 x x))
(fma.f64 x x 2)
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (+.f64 2 (pow.f64 x 2)))
(fma.f64 1/12 (pow.f64 x 4) (+.f64 2 (*.f64 x x)))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x 2))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) 2))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (+.f64 2 (+.f64 (*.f64 1/360 (pow.f64 x 6)) (pow.f64 x 2))))
(fma.f64 1/12 (pow.f64 x 4) (+.f64 2 (fma.f64 1/360 (pow.f64 x 6) (*.f64 x x))))
(+.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 x x)) (fma.f64 1/12 (pow.f64 x 4) 2))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) 2)))
(fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x 2)))
(+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

prune37.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New62264
Fresh000
Picked101
Done000
Total63265
Error
0b
Counts
65 → 2
Alt Table
StatusErrorProgram
1.5b
(*.f64 (*.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
▶0.0b
(tanh.f64 x)
Compiler

Compiled 962 to 423 computations (56% saved)

localize1.0ms (0%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(tanh.f64 x)

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(tanh.f64 x)
1.0ms
x
@inf
(tanh.f64 x)
0.0ms
x
@0
(tanh.f64 x)

rewrite41.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
465×pow1_binary64
437×add-log-exp_binary64
435×log1p-expm1-u_binary64
435×expm1-log1p-u_binary64
428×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033
1753
210793
Stop Event
1×node limit
Counts
1 → 31
Calls
Call 1
Inputs
(tanh.f64 x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (tanh.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 -2) x))) (/.f64 (pow.f64 (exp.f64 -2) x) (+.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (pow.f64 (exp.f64 2) x))) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) (*.f64 2 (cosh.f64 x))) (/.f64 (exp.f64 (neg.f64 x)) (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tanh.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (tanh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (tanh.f64 x)) (pow.f64 (cbrt.f64 (tanh.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (tanh.f64 x)) 2) (cbrt.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tanh.f64 x)) (sqrt.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (exp.f64 -2) x)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (*.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) (-.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) (expm1.f64 (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 2 (cosh.f64 x)) (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (exp.f64 -2) x)) (+.f64 1 (pow.f64 (exp.f64 -2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 x 2)) (+.f64 1 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (sinh.f64 x)) (*.f64 2 (cosh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (exp.f64 -2) x))) (neg.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (*.f64 x 2))) (neg.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (sinh.f64 x))) (neg.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (tanh.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (tanh.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (tanh.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (tanh.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (tanh.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (tanh.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (tanh.f64 x)))))))

simplify39.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
490×fma-neg_binary64
404×distribute-rgt-neg-in_binary64
367×cancel-sign-sub-inv_binary64
299×distribute-lft-neg-in_binary64
281×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
025228
173228
2179224
3535222
41589222
53314222
64744222
Stop Event
1×node limit
Counts
43 → 40
Calls
Call 1
Inputs
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
Outputs
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(fma.f64 (pow.f64 x 3) -1/3 x)
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 -1/3 (pow.f64 x 3)))
(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 17/315 (pow.f64 x 7) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))
(+.f64 x (fma.f64 2/15 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 7) -17/315))))
(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

prune18.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New40040
Fresh011
Picked011
Done000
Total40242
Error
0b
Counts
42 → 2
Alt Table
StatusErrorProgram
▶1.5b
(*.f64 (*.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
✓0.0b
(tanh.f64 x)
Compiler

Compiled 420 to 293 computations (30.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(sinh.f64 x)
✓0.0b
(/.f64 1 (*.f64 2 (cosh.f64 x)))
✓1.5b
(*.f64 (*.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))

series8.0ms (0.2%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(/.f64 1 (*.f64 2 (cosh.f64 x)))
2.0ms
x
@inf
(*.f64 (*.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
1.0ms
x
@-inf
(*.f64 (*.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
1.0ms
x
@-inf
(/.f64 1 (*.f64 2 (cosh.f64 x)))
1.0ms
x
@0
(*.f64 (*.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))

rewrite53.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
903×log1p-expm1-u_binary64
903×expm1-log1p-u_binary64
103×add-sqr-sqrt_binary64
98×*-un-lft-identity_binary64
98×pow1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01023
121117
2262817
Stop Event
1×node limit
Counts
3 → 80
Calls
Call 1
Inputs
(*.f64 (*.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
(/.f64 1 (*.f64 2 (cosh.f64 x)))
(sinh.f64 x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (/.f64 (*.f64 2 (cosh.f64 x)) (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sinh.f64 x) (cosh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (sinh.f64 x)) (*.f64 2 (cosh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 2 (cosh.f64 x)) (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 4 (pow.f64 (sinh.f64 x) 2))) (/.f64 (*.f64 2 (cosh.f64 x)) (cbrt.f64 (*.f64 2 (sinh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (sinh.f64 x))) (/.f64 (*.f64 2 (cosh.f64 x)) (sqrt.f64 (*.f64 2 (sinh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (sinh.f64 x))) (*.f64 (cosh.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (sinh.f64 x)) -1) (*.f64 (cosh.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (sinh.f64 x)) (cosh.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (sinh.f64 x)) (sqrt.f64 (*.f64 2 (cosh.f64 x)))) (sqrt.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (sinh.f64 x)) 1) (*.f64 2 (cosh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (sinh.f64 x)) (cbrt.f64 (*.f64 4 (pow.f64 (cosh.f64 x) 2)))) (cbrt.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (*.f64 2 (sinh.f64 x))) (*.f64 (cosh.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 (*.f64 2 (sinh.f64 x))) (cosh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sinh.f64 x) (cosh.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sinh.f64 x) (cosh.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sinh.f64 x) (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (sinh.f64 x)) 3) (pow.f64 (*.f64 2 (cosh.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (sinh.f64 x)) 3) (pow.f64 (/.f64 1/2 (cosh.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1/2 (cosh.f64 x)) 3) (pow.f64 (*.f64 2 (sinh.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sinh.f64 x) (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sinh.f64 x) (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sinh.f64 x) (cosh.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sinh.f64 x) (cosh.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (cosh.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/2 (cosh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (cosh.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/2 (cosh.f64 x))) (pow.f64 (cbrt.f64 (/.f64 1/2 (cosh.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (cosh.f64 x))) 2) (cbrt.f64 (/.f64 1/2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/2 (cosh.f64 x))) (sqrt.f64 (/.f64 1/2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (*.f64 (cosh.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (pow.f64 (cosh.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 1 (cosh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cosh.f64 x) -1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 (cosh.f64 x) 2))) -1) (pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x))) -1) (pow.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (*.f64 2 (cosh.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (cosh.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (cosh.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/2 (cosh.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (cosh.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/2 (cosh.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (pow.f64 (cosh.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/2 (cosh.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (cosh.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/2 (cosh.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (cosh.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sinh.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) 2) (/.f64 (exp.f64 (neg.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sinh.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sinh.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sinh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sinh.f64 x)) (pow.f64 (cbrt.f64 (sinh.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sinh.f64 x)) 2) (cbrt.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sinh.f64 x)) (sqrt.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (sinh.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (sinh.f64 x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sinh.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sinh.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sinh.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sinh.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sinh.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sinh.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sinh.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sinh.f64 x)))))))

simplify38.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
728×fma-def_binary64
611×associate-*l*_binary64
436×cancel-sign-sub-inv_binary64
245×fma-neg_binary64
212×sub-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
055534
1150534
2406518
31347514
44701514
Stop Event
1×node limit
Counts
116 → 106
Calls
Call 1
Inputs
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
1/2
(-.f64 1/2 (*.f64 1/4 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 5/48 (pow.f64 x 4)) 1/2) (*.f64 1/4 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 5/48 (pow.f64 x 4)) 1/2) (+.f64 (*.f64 61/1440 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 2))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
x
(+.f64 (*.f64 1/6 (pow.f64 x 3)) x)
(+.f64 (*.f64 1/120 (pow.f64 x 5)) (+.f64 (*.f64 1/6 (pow.f64 x 3)) x))
(+.f64 (*.f64 1/120 (pow.f64 x 5)) (+.f64 (*.f64 1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/6 (pow.f64 x 3)) x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
Outputs
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 17/315 (pow.f64 x 7) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 7) -17/315)))
(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1/2
(-.f64 1/2 (*.f64 1/4 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 -1/4 (*.f64 x x)))
(+.f64 1/2 (*.f64 (*.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 1/2)
(fma.f64 x (*.f64 x -1/4) 1/2)
(-.f64 (+.f64 (*.f64 5/48 (pow.f64 x 4)) 1/2) (*.f64 1/4 (pow.f64 x 2)))
(+.f64 (fma.f64 5/48 (pow.f64 x 4) 1/2) (*.f64 -1/4 (*.f64 x x)))
(+.f64 (fma.f64 5/48 (pow.f64 x 4) 1/2) (*.f64 (*.f64 x x) -1/4))
(fma.f64 5/48 (pow.f64 x 4) (fma.f64 (*.f64 x x) -1/4 1/2))
(fma.f64 x (*.f64 x -1/4) (fma.f64 5/48 (pow.f64 x 4) 1/2))
(-.f64 (+.f64 (*.f64 5/48 (pow.f64 x 4)) 1/2) (+.f64 (*.f64 61/1440 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 2))))
(-.f64 (fma.f64 5/48 (pow.f64 x 4) 1/2) (fma.f64 61/1440 (pow.f64 x 6) (*.f64 1/4 (*.f64 x x))))
(-.f64 (fma.f64 5/48 (pow.f64 x 4) 1/2) (fma.f64 1/4 (*.f64 x x) (*.f64 61/1440 (pow.f64 x 6))))
(+.f64 1/2 (fma.f64 5/48 (pow.f64 x 4) (fma.f64 (*.f64 x x) -1/4 (*.f64 (pow.f64 x 6) -61/1440))))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 6) -61/1440 (fma.f64 5/48 (pow.f64 x 4) 1/2)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
x
(+.f64 (*.f64 1/6 (pow.f64 x 3)) x)
(fma.f64 1/6 (pow.f64 x 3) x)
(fma.f64 (pow.f64 x 3) 1/6 x)
(+.f64 (*.f64 1/120 (pow.f64 x 5)) (+.f64 (*.f64 1/6 (pow.f64 x 3)) x))
(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))
(fma.f64 (pow.f64 x 5) 1/120 (fma.f64 (pow.f64 x 3) 1/6 x))
(fma.f64 (pow.f64 x 3) 1/6 (fma.f64 (pow.f64 x 5) 1/120 x))
(+.f64 (*.f64 1/120 (pow.f64 x 5)) (+.f64 (*.f64 1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/6 (pow.f64 x 3)) x)))
(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/5040 (pow.f64 x 7) (fma.f64 1/6 (pow.f64 x 3) x)))
(fma.f64 (pow.f64 x 5) 1/120 (fma.f64 (pow.f64 x 7) 1/5040 (fma.f64 (pow.f64 x 3) 1/6 x)))
(fma.f64 (pow.f64 x 7) 1/5040 (fma.f64 (pow.f64 x 3) 1/6 (fma.f64 (pow.f64 x 5) 1/120 x)))
(fma.f64 (pow.f64 x 3) 1/6 (fma.f64 (pow.f64 x 5) 1/120 (fma.f64 (pow.f64 x 7) 1/5040 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))

prune54.0ms (1.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1060106
Fresh000
Picked011
Done011
Total1062108
Error
0b
Counts
108 → 2
Alt Table
StatusErrorProgram
✓1.5b
(*.f64 (*.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
✓0.0b
(tanh.f64 x)
Compiler

Compiled 1416 to 924 computations (34.7% saved)

regimes32.0ms (0.7%)

Accuracy

Total 0.0b remaining (68.7%)

Threshold costs 0.0b (68.7%)

Counts
39 → 1
Compiler

Compiled 420 to 198 computations (52.9% saved)

simplify1.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033
Stop Event
1×saturated
Calls
Call 1
Inputs
(tanh.f64 x)
Outputs
(tanh.f64 x)

end33.0ms (0.7%)

Stop Event
1×done
Compiler

Compiled 21 to 16 computations (23.8% saved)

Profiling

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