Details

analyze18.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
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)

sample2.9s (76.1%)

Results

1.8s	4092×	body	1024	valid
559.0ms	1968×	body	512	valid
227.0ms	451×	body	2048	valid
176.0ms	942×	body	256	valid
84.0ms	803×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 30 to 16 computations (46.7% saved)

preprocess31.0ms (0.8%)

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)

Iter	Nodes	Cost
0	8	22
1	20	22
2	35	22
3	59	22
4	133	22
5	336	22
6	878	22
7	2569	22
0	1	1

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)

simplify22.0ms (0.6%)

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)

Iter	Nodes	Cost
0	8	22
1	20	22
2	35	22
3	59	22
4	133	22
5	336	22
6	878	22
7	2569	22

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)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

57.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	57.8b	(/.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)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	2.0b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	3.6b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series6.0ms (0.1%)

Counts

3 → 32

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	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 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	-inf	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite106.0ms (2.8%)

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)

Iter	Nodes	Cost
0	8	18
1	186	18
2	3690	18
0	6	6
1	130	6
2	2149	6
0	6	6
0	8	3
1	186	3
2	3690	3
0	8	3
0	6	6
1	129	6
2	2129	6
0	6	6

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 exp.f64 (log.f64 (.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 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 exp.f64 (log.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 exp.f64 (log.f64 (.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 expm1.f64 (log1p.f64 (.f64 2 (cosh.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 exp.f64 (log.f64 (*.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 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 exp.f64 (log.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (tanh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 exp.f64 (log.f64 (*.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 expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x))))))))

simplify31.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def_binary64`
513×	`unswap-sqr_binary64`
470×	`associate-l_binary64`
347×	`associate-r_binary64`
238×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	447
1	150	441
2	350	437
3	996	437
4	3086	437

Stop Event

1×	node limit

Counts

69 → 66

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))))
(-.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 (*.f64 -1/3 (pow.f64 x 3)) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
2
(+.f64 2 (pow.f64 x 2))
(+.f64 2 (+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 2 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4)))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 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)))

Outputs
(*.f64 2 x)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (.f64 x 1/3) 2) (.f64 1/60 (pow.f64 x 5)))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/60 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7)))))
(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 (*.f64 -1/3 (pow.f64 x 3)) x)
(fma.f64 -1/3 (pow.f64 x 3) x)
(fma.f64 (pow.f64 x 3) -1/3 x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(fma.f64 -17/315 (pow.f64 x 7) (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x)))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 5) 2/15 x)))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 7) -17/315 x)))
(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.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) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.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) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.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) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.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) (exp.f64 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 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 x) (exp.f64 (.f64 -1 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 x) (exp.f64 (.f64 -1 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 x) (exp.f64 (.f64 -1 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 2 (+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 (+.f64 2 (.f64 x x)) (.f64 1/12 (pow.f64 x 4)))
(+.f64 2 (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x)))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) 2))
(+.f64 2 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))))
(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) 2)))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) 2)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 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)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

prune54.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	4	67

Error

0.0b

Counts

67 → 4

Alt Table

Status	Error	Program
	3.3b	(fma.f64 (pow.f64 x 3) -1/3 x)
▶	0.0b	(tanh.f64 x)
	2.0b	(.f64 (.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
	57.8b	(-.f64 (/.f64 (exp.f64 x) (.f64 2 (cosh.f64 x))) (/.f64 (exp.f64 (neg.f64 x)) (.f64 2 (cosh.f64 x))))

Compiler

Compiled 1036 to 458 computations (55.8% saved)

localize1.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(tanh.f64 x)
1.0ms	x	@	inf	(tanh.f64 x)
0.0ms	x	@	0	(tanh.f64 x)

rewrite30.0ms (0.8%)

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)

Iter	Nodes	Cost
0	3	3
1	75	3
2	1079	3

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

simplify36.0ms (1%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-def_binary64`
624×	`unswap-sqr_binary64`
298×	`associate-l_binary64`
232×	`*-commutative_binary64`
198×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	222
1	65	222
2	140	222
3	334	222
4	688	222
5	1542	222
6	2432	222
7	3940	222

Stop Event

1×	node limit

Counts

43 → 40

Calls

Call 1

Inputs
x
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.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) (/.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 (*.f64 -1/3 (pow.f64 x 3)) x)
(fma.f64 -1/3 (pow.f64 x 3) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(fma.f64 -17/315 (pow.f64 x 7) (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 -17/315 (pow.f64 x 7) (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (fma.f64 -17/315 (pow.f64 x 7) 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))))

prune28.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Error

Counts

44 → 4

Alt Table

Status	Error	Program
▶	1.3b	(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
	56.6b	(*.f64 (-.f64 1 (pow.f64 (exp.f64 -2) x)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 -2) x))))
✓	0.0b	(tanh.f64 x)
	2.0b	(/.f64 (.f64 2 (sinh.f64 x)) (.f64 2 (cosh.f64 x)))

Compiler

Compiled 476 to 341 computations (28.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (pow.f64 (exp.f64 2) x))
✓	0.0b	(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
✓	0.0b	(pow.f64 (exp.f64 2) x)
✓	1.2b	(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))

series9.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
2.0ms	x	@	inf	(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
1.0ms	x	@	inf	(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
1.0ms	x	@	-inf	(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
1.0ms	x	@	-inf	(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))

rewrite54.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

485×	`log-prod_binary64`
187×	`fma-def_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`
168×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	230	44
2	2794	44

Stop Event

1×	node limit

Counts

4 → 127

Calls

Call 1

Inputs
(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
(pow.f64 (exp.f64 2) x)
(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
(+.f64 1 (pow.f64 (exp.f64 2) x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x))))) (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x))))) 1)))) (#(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 (expm1.f64 (+.f64 x 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 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 2)) (/.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) (cbrt.f64 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (+.f64 -1 (neg.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 (+.f64 x x)) (hypot.f64 1 (exp.f64 x))) (hypot.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 (+.f64 x x)) 1) (+.f64 1 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 (+.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) 2)) (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (expm1.f64 (+.f64 x x))) (+.f64 -1 (neg.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (expm1.f64 (+.f64 x x)) -1) (+.f64 -1 (neg.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (hypot.f64 1 (exp.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) (pow.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))) 3) (pow.f64 (expm1.f64 (+.f64 x x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log1p.f64 (pow.f64 (exp.f64 2) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 1 (pow.f64 (exp.f64 2) x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (exp.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 2) x))) (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 2) x))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (exp.f64 2) x)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (exp.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 x) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) (cbrt.f64 (pow.f64 (exp.f64 4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (exp.f64 4) x)) (cbrt.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (exp.f64 2) x)) (sqrt.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 x) (pow.f64 (exp.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 4/3) x) (pow.f64 (exp.f64 2/3) x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 4) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 2) (.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) 2) (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (exp.f64 x)) (hypot.f64 1 (exp.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (exp.f64 2) (.f64 x 3))) (/.f64 1 (fma.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x)) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (exp.f64 4) x)) (/.f64 1 (-.f64 1 (pow.f64 (exp.f64 2) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))) (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)))) (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (hypot.f64 1 (exp.f64 x))) (/.f64 1 (hypot.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (+.f64 -1 (neg.f64 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -1) (pow.f64 (hypot.f64 1 (exp.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) (.f64 x 3)))) (fma.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (-.f64 1 (pow.f64 (exp.f64 4) x))) (-.f64 1 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (hypot.f64 1 (exp.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (pow.f64 (exp.f64 2) 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 4) x) (-.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) 2) (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 1 (exp.f64 x)) (hypot.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 (exp.f64 2) (.f64 x 3))) (/.f64 1 (fma.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (pow.f64 (exp.f64 4) x)) (/.f64 1 (-.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x)) 1) (+.f64 1 (pow.f64 (exp.f64 2) (.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (pow.f64 (exp.f64 4) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) 2) (/.f64 1 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 1 (exp.f64 x)) (/.f64 1 (hypot.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (neg.f64 (pow.f64 (exp.f64 2) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 2) (.f64 x 3))) (fma.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 2) (.f64 x 3))) (+.f64 (pow.f64 (exp.f64 4) x) (-.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (exp.f64 4) x)) (-.f64 1 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (exp.f64 2) (.f64 x 3)))) (neg.f64 (fma.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (exp.f64 4) x))) (neg.f64 (-.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (.f64 x 4)) (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (exp.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (exp.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 2) x) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 x) (exp.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) (cbrt.f64 (pow.f64 (exp.f64 4) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (exp.f64 4) x)) (cbrt.f64 (pow.f64 (exp.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (exp.f64 2) x)) (sqrt.f64 (pow.f64 (exp.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 x) (pow.f64 (exp.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 4/3) x) (pow.f64 (exp.f64 2/3) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (pow.f64 (exp.f64 2) x))))))))

simplify40.0ms (1%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-def_binary64`
454×	`unswap-sqr_binary64`
365×	`*-commutative_binary64`
220×	`associate-l_binary64`
210×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	511
1	133	509
2	325	497
3	943	497
4	2234	497
5	3044	497

Stop Event

1×	node limit

Counts

175 → 162

Calls

Call 1

Inputs
x
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
1
(+.f64 (*.f64 2 x) 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2 x) 1))
(+.f64 (.f64 4/3 (pow.f64 x 3)) (+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2 x) 1)))
(exp.f64 (*.f64 2 x))
(exp.f64 (*.f64 2 x))
(exp.f64 (*.f64 2 x))
(exp.f64 (*.f64 2 x))
(exp.f64 (*.f64 2 x))
(exp.f64 (*.f64 2 x))
(exp.f64 (*.f64 2 x))
(exp.f64 (*.f64 2 x))
1/2
(+.f64 (*.f64 -1/2 x) 1/2)
(+.f64 (.f64 -1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 3)) 1/2))
(+.f64 (.f64 -1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 1/2 (*.f64 -1/15 (pow.f64 x 5)))))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
2
(+.f64 (*.f64 2 x) 2)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2 x) 2))
(+.f64 (.f64 4/3 (pow.f64 x 3)) (+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2 x) 2)))
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 1 (exp.f64 (*.f64 2 x)))

Outputs
x
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(fma.f64 -1/3 (pow.f64 x 3) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(fma.f64 -17/315 (pow.f64 x 7) (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 -17/315 (pow.f64 x 7) (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (fma.f64 -17/315 (pow.f64 x 7) x)))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 (expm1.f64 (*.f64 x 2)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 (expm1.f64 (*.f64 x 2)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 (expm1.f64 (*.f64 x 2)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 (expm1.f64 (*.f64 x 2)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 (expm1.f64 (*.f64 x 2)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 (expm1.f64 (*.f64 x 2)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 (expm1.f64 (*.f64 x 2)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(/.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 (expm1.f64 (*.f64 x 2)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
1
(+.f64 (*.f64 2 x) 1)
(fma.f64 2 x 1)
(fma.f64 x 2 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2 x) 1))
(fma.f64 2 (*.f64 x x) (fma.f64 2 x 1))
(fma.f64 2 (*.f64 x x) (fma.f64 x 2 1))
(fma.f64 2 (fma.f64 x x x) 1)
(fma.f64 x (fma.f64 x 2 2) 1)
(+.f64 (.f64 4/3 (pow.f64 x 3)) (+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2 x) 1)))
(fma.f64 4/3 (pow.f64 x 3) (fma.f64 2 (*.f64 x x) (fma.f64 2 x 1)))
(fma.f64 (pow.f64 x 3) 4/3 (fma.f64 2 (*.f64 x x) (fma.f64 x 2 1)))
(fma.f64 (pow.f64 x 3) 4/3 (fma.f64 2 (fma.f64 x x x) 1))
(fma.f64 (pow.f64 x 3) 4/3 (fma.f64 x (fma.f64 x 2 2) 1))
(fma.f64 x 2 (fma.f64 (*.f64 x x) (fma.f64 x 4/3 2) 1))
(exp.f64 (*.f64 2 x))
(pow.f64 (exp.f64 2) x)
(pow.f64 (exp.f64 x) 2)
(exp.f64 (*.f64 2 x))
(pow.f64 (exp.f64 2) x)
(pow.f64 (exp.f64 x) 2)
(exp.f64 (*.f64 2 x))
(pow.f64 (exp.f64 2) x)
(pow.f64 (exp.f64 x) 2)
(exp.f64 (*.f64 2 x))
(pow.f64 (exp.f64 2) x)
(pow.f64 (exp.f64 x) 2)
(exp.f64 (*.f64 2 x))
(pow.f64 (exp.f64 2) x)
(pow.f64 (exp.f64 x) 2)
(exp.f64 (*.f64 2 x))
(pow.f64 (exp.f64 2) x)
(pow.f64 (exp.f64 x) 2)
(exp.f64 (*.f64 2 x))
(pow.f64 (exp.f64 2) x)
(pow.f64 (exp.f64 x) 2)
(exp.f64 (*.f64 2 x))
(pow.f64 (exp.f64 2) x)
(pow.f64 (exp.f64 x) 2)
1/2
(+.f64 (*.f64 -1/2 x) 1/2)
(fma.f64 -1/2 x 1/2)
(fma.f64 x -1/2 1/2)
(+.f64 (.f64 -1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 3)) 1/2))
(fma.f64 -1/2 x (fma.f64 1/6 (pow.f64 x 3) 1/2))
(fma.f64 x -1/2 (fma.f64 (pow.f64 x 3) 1/6 1/2))
(fma.f64 (pow.f64 x 3) 1/6 (fma.f64 x -1/2 1/2))
(fma.f64 x (fma.f64 (*.f64 x x) 1/6 -1/2) 1/2)
(fma.f64 x (fma.f64 x (*.f64 x 1/6) -1/2) 1/2)
(+.f64 (.f64 -1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 1/2 (*.f64 -1/15 (pow.f64 x 5)))))
(fma.f64 -1/2 x (fma.f64 1/6 (pow.f64 x 3) (+.f64 1/2 (*.f64 (pow.f64 x 5) -1/15))))
(fma.f64 x -1/2 (fma.f64 (pow.f64 x 3) 1/6 (fma.f64 (pow.f64 x 5) -1/15 1/2)))
(fma.f64 (pow.f64 x 5) -1/15 (fma.f64 x (fma.f64 (*.f64 x x) 1/6 -1/2) 1/2))
(fma.f64 x (fma.f64 x (*.f64 x 1/6) -1/2) (fma.f64 (pow.f64 x 5) -1/15 1/2))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 1 (+.f64 1 (exp.f64 (*.f64 2 x))))
(/.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
2
(+.f64 (*.f64 2 x) 2)
(fma.f64 2 x 2)
(fma.f64 x 2 2)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2 x) 2))
(fma.f64 2 (*.f64 x x) (fma.f64 2 x 2))
(fma.f64 2 (*.f64 x x) (fma.f64 x 2 2))
(fma.f64 2 (fma.f64 x x x) 2)
(fma.f64 x (fma.f64 x 2 2) 2)
(+.f64 (.f64 4/3 (pow.f64 x 3)) (+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2 x) 2)))
(fma.f64 4/3 (pow.f64 x 3) (fma.f64 2 (*.f64 x x) (fma.f64 2 x 2)))
(fma.f64 (pow.f64 x 3) 4/3 (fma.f64 2 (*.f64 x x) (fma.f64 x 2 2)))
(fma.f64 (pow.f64 x 3) 4/3 (fma.f64 2 (fma.f64 x x x) 2))
(fma.f64 x 2 (fma.f64 (*.f64 x x) (fma.f64 x 4/3 2) 2))
(fma.f64 (pow.f64 x 3) 4/3 (fma.f64 x (fma.f64 x 2 2) 2))
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 (pow.f64 (exp.f64 2) x) 1)
(fma.f64 (exp.f64 x) (exp.f64 x) 1)
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 (pow.f64 (exp.f64 2) x) 1)
(fma.f64 (exp.f64 x) (exp.f64 x) 1)
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 (pow.f64 (exp.f64 2) x) 1)
(fma.f64 (exp.f64 x) (exp.f64 x) 1)
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 (pow.f64 (exp.f64 2) x) 1)
(fma.f64 (exp.f64 x) (exp.f64 x) 1)
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 (pow.f64 (exp.f64 2) x) 1)
(fma.f64 (exp.f64 x) (exp.f64 x) 1)
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 (pow.f64 (exp.f64 2) x) 1)
(fma.f64 (exp.f64 x) (exp.f64 x) 1)
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 (pow.f64 (exp.f64 2) x) 1)
(fma.f64 (exp.f64 x) (exp.f64 x) 1)
(+.f64 1 (exp.f64 (*.f64 2 x)))
(+.f64 (pow.f64 (exp.f64 2) x) 1)
(fma.f64 (exp.f64 x) (exp.f64 x) 1)

prune123.0ms (3.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	164	2	166

Error

Counts

166 → 2

Alt Table

Status	Error	Program
▶	1.3b	(.f64 (expm1.f64 (.f64 x 2)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
✓	0.0b	(tanh.f64 x)

Compiler

Compiled 2802 to 2231 computations (20.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))
	0.0b	(pow.f64 (exp.f64 2) x)
✓	1.2b	(log1p.f64 (pow.f64 (exp.f64 2) x))
✓	1.2b	(.f64 (expm1.f64 (.f64 x 2)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))

series55.0ms (1.4%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
28.0ms	x	@	inf	(.f64 (expm1.f64 (.f64 x 2)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
21.0ms	x	@	-inf	(.f64 (expm1.f64 (.f64 x 2)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
4.0ms	x	@	0	(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))
1.0ms	x	@	0	(.f64 (expm1.f64 (.f64 x 2)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
0.0ms	x	@	0	(log1p.f64 (pow.f64 (exp.f64 2) x))

rewrite52.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`expm1-log1p-u_binary64`
783×	`log1p-expm1-u_binary64`
103×	`add-sqr-sqrt_binary64`
100×	`pow1_binary64`
99×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	216	34
2	2479	34

Stop Event

1×	node limit

Counts

3 → 75

Calls

Call 1

Inputs
(.f64 (expm1.f64 (.f64 x 2)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
(log1p.f64 (pow.f64 (exp.f64 2) x))
(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (expm1.f64 (*.f64 x 2))) (+.f64 (pow.f64 (exp.f64 2) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (expm1.f64 (*.f64 x 2)) 3) (pow.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1) 3) (pow.f64 (expm1.f64 (*.f64 x 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) (log.f64 (expm1.f64 (*.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) (log.f64 (expm1.f64 (*.f64 x 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (expm1.f64 (*.f64 x 2)) (+.f64 (pow.f64 (exp.f64 2) x) 1))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1))) (log.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)) 2)) (log.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) (pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 2) (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 2) (neg.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) (neg.f64 (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 2)) (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))) (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 2)) (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))) (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (pow.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 3)) (+.f64 0 (+.f64 (pow.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 2) (*.f64 0 (log1p.f64 (pow.f64 (exp.f64 2) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (pow.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 2)) (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (exp.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (pow.f64 (exp.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)) 2) (cbrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)) (sqrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 2) x) 3)) (+.f64 1 (-.f64 (pow.f64 (exp.f64 4) x) (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (exp.f64 4) x)) (-.f64 1 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))) (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 -1) (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 2)) (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (pow.f64 (exp.f64 2) x) 1)))))))

simplify28.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

709×	`distribute-rgt-in_binary64`
696×	`distribute-lft-in_binary64`
328×	`fma-def_binary64`
185×	`distribute-rgt-out_binary64`
170×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	596
1	173	443
2	545	393
3	2010	393

Stop Event

1×	node limit

Counts

111 → 101

Calls

Call 1

Inputs
(.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x))
(+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (.f64 (+.f64 (.f64 -2 (exp.f64 (neg.f64 (log.f64 2)))) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 2)))
(+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (+.f64 (.f64 (+.f64 (.f64 4/3 (exp.f64 (neg.f64 (log.f64 2)))) (.f64 -2 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 3)) (.f64 (+.f64 (.f64 -2 (exp.f64 (neg.f64 (log.f64 2)))) (.f64 2 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 2))))
(+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (+.f64 (.f64 (+.f64 (.f64 4/3 (exp.f64 (neg.f64 (log.f64 2)))) (.f64 -4/3 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 4)) (+.f64 (.f64 (+.f64 (.f64 4/3 (exp.f64 (neg.f64 (log.f64 2)))) (.f64 -2 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 3)) (.f64 (+.f64 (.f64 -2 (exp.f64 (neg.f64 (log.f64 2)))) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 2)))))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(log.f64 2)
(+.f64 (log.f64 2) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (log.f64 2) x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/12 (pow.f64 x 4)) x)))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(exp.f64 (neg.f64 (log.f64 2)))
(+.f64 (exp.f64 (neg.f64 (log.f64 2))) (.f64 -1 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)))
(+.f64 (.f64 1/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3))) (+.f64 (exp.f64 (neg.f64 (log.f64 2))) (.f64 -1 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x))))
(+.f64 (.f64 -2/15 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 5))) (+.f64 (.f64 1/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3))) (+.f64 (exp.f64 (neg.f64 (log.f64 2))) (.f64 -1 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)))))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))

Outputs
(.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x))
(*.f64 x 1)
x
(+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (.f64 (+.f64 (.f64 -2 (exp.f64 (neg.f64 (log.f64 2)))) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 2)))
(.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x))
(*.f64 x 1)
x
(+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (+.f64 (.f64 (+.f64 (.f64 4/3 (exp.f64 (neg.f64 (log.f64 2)))) (.f64 -2 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 3)) (.f64 (+.f64 (.f64 -2 (exp.f64 (neg.f64 (log.f64 2)))) (.f64 2 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 2))))
(fma.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x) (fma.f64 (.f64 (exp.f64 (neg.f64 (log.f64 2))) -2/3) (pow.f64 x 3) (.f64 (.f64 x x) (*.f64 (exp.f64 (neg.f64 (log.f64 2))) 0))))
(fma.f64 1 x (fma.f64 (.f64 x x) 0 (.f64 -1/3 (pow.f64 x 3))))
(fma.f64 -1/3 (pow.f64 x 3) x)
(+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (+.f64 (.f64 (+.f64 (.f64 4/3 (exp.f64 (neg.f64 (log.f64 2)))) (.f64 -4/3 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 4)) (+.f64 (.f64 (+.f64 (.f64 4/3 (exp.f64 (neg.f64 (log.f64 2)))) (.f64 -2 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 3)) (.f64 (+.f64 (.f64 -2 (exp.f64 (neg.f64 (log.f64 2)))) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2))))) (pow.f64 x 2)))))
(fma.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x) (fma.f64 (.f64 (exp.f64 (neg.f64 (log.f64 2))) -2/3) (pow.f64 x 3) (.f64 (.f64 x x) (*.f64 (exp.f64 (neg.f64 (log.f64 2))) 0))))
(fma.f64 1 x (fma.f64 (.f64 x x) 0 (.f64 -1/3 (pow.f64 x 3))))
(fma.f64 -1/3 (pow.f64 x 3) x)
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (expm1.f64 (.f64 2 x)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
(.f64 (expm1.f64 (.f64 2 x)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (expm1.f64 (.f64 2 x)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
(.f64 (expm1.f64 (.f64 2 x)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (expm1.f64 (.f64 2 x)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
(.f64 (expm1.f64 (.f64 2 x)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (expm1.f64 (.f64 2 x)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
(.f64 (expm1.f64 (.f64 2 x)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (expm1.f64 (.f64 2 x)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
(.f64 (expm1.f64 (.f64 2 x)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (expm1.f64 (.f64 2 x)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
(.f64 (expm1.f64 (.f64 2 x)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (expm1.f64 (.f64 2 x)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
(.f64 (expm1.f64 (.f64 2 x)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x)))))))
(.f64 (expm1.f64 (.f64 2 x)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
(.f64 (expm1.f64 (.f64 2 x)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(log.f64 2)
(+.f64 (log.f64 2) x)
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (log.f64 2) x))
(fma.f64 1/2 (*.f64 x x) (+.f64 (log.f64 2) x))
(+.f64 (log.f64 2) (fma.f64 1/2 (*.f64 x x) x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/12 (pow.f64 x 4)) x)))
(fma.f64 1/2 (*.f64 x x) (+.f64 (log.f64 2) (fma.f64 -1/12 (pow.f64 x 4) x)))
(+.f64 (fma.f64 (pow.f64 x 4) -1/12 x) (fma.f64 1/2 (*.f64 x x) (log.f64 2)))
(+.f64 (fma.f64 (pow.f64 x 4) -1/12 (log.f64 2)) (fma.f64 1/2 (*.f64 x x) x))
(+.f64 (log.f64 2) (fma.f64 1/2 (*.f64 x x) (fma.f64 (pow.f64 x 4) -1/12 x)))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log1p.f64 (pow.f64 (exp.f64 2) x))
(log1p.f64 (pow.f64 (exp.f64 x) 2))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log1p.f64 (pow.f64 (exp.f64 2) x))
(log1p.f64 (pow.f64 (exp.f64 x) 2))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log1p.f64 (pow.f64 (exp.f64 2) x))
(log1p.f64 (pow.f64 (exp.f64 x) 2))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log1p.f64 (pow.f64 (exp.f64 2) x))
(log1p.f64 (pow.f64 (exp.f64 x) 2))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log1p.f64 (pow.f64 (exp.f64 2) x))
(log1p.f64 (pow.f64 (exp.f64 x) 2))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log1p.f64 (pow.f64 (exp.f64 2) x))
(log1p.f64 (pow.f64 (exp.f64 x) 2))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log1p.f64 (pow.f64 (exp.f64 2) x))
(log1p.f64 (pow.f64 (exp.f64 x) 2))
(log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))
(log1p.f64 (pow.f64 (exp.f64 2) x))
(log1p.f64 (pow.f64 (exp.f64 x) 2))
(exp.f64 (neg.f64 (log.f64 2)))
1/2
(+.f64 (exp.f64 (neg.f64 (log.f64 2))) (.f64 -1 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)))
(+.f64 (exp.f64 (neg.f64 (log.f64 2))) (neg.f64 (*.f64 (exp.f64 (neg.f64 (log.f64 2))) x)))
(fma.f64 -1/2 x 1/2)
(fma.f64 x -1/2 1/2)
(+.f64 (.f64 1/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3))) (+.f64 (exp.f64 (neg.f64 (log.f64 2))) (.f64 -1 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x))))
(fma.f64 1/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3)) (+.f64 (exp.f64 (neg.f64 (log.f64 2))) (neg.f64 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x))))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 -1/2 x 1/2))
(fma.f64 (pow.f64 x 3) 1/6 (fma.f64 x -1/2 1/2))
(fma.f64 x -1/2 (fma.f64 (pow.f64 x 3) 1/6 1/2))
(+.f64 (.f64 -2/15 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 5))) (+.f64 (.f64 1/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3))) (+.f64 (exp.f64 (neg.f64 (log.f64 2))) (.f64 -1 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)))))
(fma.f64 -2/15 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 5)) (fma.f64 1/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3)) (+.f64 (exp.f64 (neg.f64 (log.f64 2))) (neg.f64 (*.f64 (exp.f64 (neg.f64 (log.f64 2))) x)))))
(fma.f64 -1/15 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 -1/2 x 1/2)))
(fma.f64 (pow.f64 x 5) -1/15 (fma.f64 (pow.f64 x 3) 1/6 (fma.f64 x -1/2 1/2)))
(fma.f64 (pow.f64 x 3) 1/6 (fma.f64 (pow.f64 x 5) -1/15 (fma.f64 x -1/2 1/2)))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))
(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))
(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))
(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))
(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))
(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))
(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))
(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))
(exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (*.f64 2 x))))))
(exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))
(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
(/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1))

prune86.0ms (2.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	137	2	139

Error

Counts

139 → 2

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (expm1.f64 (.f64 x 2)) (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))
✓	0.0b	(tanh.f64 x)

Compiler

Compiled 2324 to 1973 computations (15.1% saved)

regimes33.0ms (0.9%)

Accuracy

Total 0.0b remaining (38.9%)

Threshold costs 0.0b (38.9%)

Counts

38 → 1

Compiler

Compiled 447 to 269 computations (39.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tanh.f64 x)

Outputs
(tanh.f64 x)

end38.0ms (1%)

Stop Event

1×

done

Compiler

Compiled 22 to 17 computations (22.7% saved)

Details

analyze18.0ms (0.5%)

sample2.9s (76.1%)

preprocess31.0ms (0.8%)

simplify22.0ms (0.6%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series6.0ms (0.1%)

rewrite106.0ms (2.8%)

simplify31.0ms (0.8%)

prune54.0ms (1.4%)

localize1.0ms (0%)

series3.0ms (0.1%)

rewrite30.0ms (0.8%)

simplify36.0ms (1%)

prune28.0ms (0.7%)

localize8.0ms (0.2%)

series9.0ms (0.2%)

rewrite54.0ms (1.4%)

simplify40.0ms (1%)

prune123.0ms (3.2%)

localize11.0ms (0.3%)

series55.0ms (1.4%)

rewrite52.0ms (1.3%)

simplify28.0ms (0.7%)

prune86.0ms (2.3%)

regimes33.0ms (0.9%)

simplify2.0ms (0%)

end38.0ms (1%)

Profiling