Details

analyze35.0ms (0.9%)

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)

sample3.1s (82.9%)

Results

1.9s	4094×	body	1024	valid
579.0ms	1969×	body	512	valid
220.0ms	410×	body	2048	valid
219.0ms	977×	body	256	valid
98.0ms	806×	body	128	valid
0.0ms	3×	body	128	invalid

preprocess34.0ms (0.9%)

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)

simplify23.0ms (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))))

prune2.0ms (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

58.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	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)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	1.7b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	4.4b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series5.0ms (0.1%)

Counts

3 → 32

Calls

9 calls:

Time	Variable		Point	Expression
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))))
1.0ms	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))))
0.0ms	x	@	0	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite111.0ms (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)

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

prune51.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	2	67

Error

Counts

67 → 2

Alt Table

Status	Error	Program
▶	0.0b	(tanh.f64 x)
	1.8b	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))

Compiler

Compiled 988 to 422 computations (57.3% saved)

localize1.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 x)

series4.0ms (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)
1.0ms	x	@	0	(tanh.f64 x)

rewrite34.0ms (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)

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 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 exp.f64 (log.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 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 exp.f64 (log.f64 (tanh.f64 x)))))))

simplify38.0ms (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))))

prune24.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	40	2	42

Error

Counts

42 → 2

Alt Table

Status	Error	Program
✓	0.0b	(tanh.f64 x)
▶	1.8b	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))

Compiler

Compiled 420 to 291 computations (30.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))
✓	0.0b	(fma.f64 (pow.f64 x 3) -1/3 x)

series19.0ms (0.5%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
15.0ms	x	@	inf	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))
1.0ms	x	@	-inf	(fma.f64 (pow.f64 x 3) -1/3 x)
1.0ms	x	@	inf	(fma.f64 (pow.f64 x 3) -1/3 x)
1.0ms	x	@	-inf	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))
1.0ms	x	@	0	(fma.f64 (pow.f64 x 3) -1/3 x)

rewrite46.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

835×	`log1p-expm1-u_binary64`
835×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
97×	`add-log-exp_binary64`
95×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	218	23
2	2258	23

Stop Event

1×	node limit

Counts

2 → 47

Calls

Call 1

Inputs
(fma.f64 (pow.f64 x 3) -1/3 x)
(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x 3) -1/3 x) (*.f64 (pow.f64 x 5) 2/15))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 5) 2/15) (fma.f64 (pow.f64 x 3) -1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (pow.f64 x 5) 2/15) 1) (fma.f64 (pow.f64 x 3) -1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (pow.f64 x 5) 2/15) (*.f64 (pow.f64 x 3) -1/3)) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))) 2) (cbrt.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))) (sqrt.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (pow.f64 x 5) 2/15) 3) (pow.f64 (fma.f64 (pow.f64 x 3) -1/3 x) 3)) (+.f64 (*.f64 (*.f64 (pow.f64 x 5) 2/15) (*.f64 (pow.f64 x 5) 2/15)) (-.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -1/3 x) 2) (*.f64 (*.f64 (pow.f64 x 5) 2/15) (fma.f64 (pow.f64 x 3) -1/3 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (pow.f64 x 5) 2/15) (*.f64 (pow.f64 x 5) 2/15)) (pow.f64 (fma.f64 (pow.f64 x 3) -1/3 x) 2)) (-.f64 (*.f64 (pow.f64 x 5) 2/15) (fma.f64 (pow.f64 x 3) -1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))) 1))))))

simplify68.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

828×	`sqr-pow_binary64`
416×	`unswap-sqr_binary64`
388×	`pow-sqr_binary64`
334×	`cube-prod_binary64`
246×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	228
1	41	228
2	75	228
3	163	228
4	307	228
5	749	228
6	1137	228
7	1783	228
8	1891	228
9	2053	228
10	2266	228
11	2596	228
12	3052	228
13	3649	228
14	4398	228

Stop Event

1×	node limit

Counts

71 → 57

Calls

Call 1

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

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

prune41.0ms (1.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	57	2	59

Error

Counts

59 → 2

Alt Table

Status	Error	Program
✓	0.0b	(tanh.f64 x)
✓	1.8b	(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))

Compiler

Compiled 915 to 709 computations (22.5% saved)

regimes21.0ms (0.6%)

Accuracy

Total -1.7b remaining (-11829.1%)

Threshold costs -1.7b (-11829.1%)

Counts

18 → 1

Compiler

Compiled 189 to 103 computations (45.5% 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)

end31.0ms (0.8%)

Stop Event

1×

done

Compiler

Compiled 19 to 12 computations (36.8% saved)

Details

analyze35.0ms (0.9%)

sample3.1s (82.9%)

preprocess34.0ms (0.9%)

simplify23.0ms (0.6%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series5.0ms (0.1%)

rewrite111.0ms (3%)

simplify31.0ms (0.8%)

prune51.0ms (1.4%)

localize1.0ms (0%)

series4.0ms (0.1%)

rewrite34.0ms (0.9%)

simplify38.0ms (1%)

prune24.0ms (0.6%)

localize7.0ms (0.2%)

series19.0ms (0.5%)

rewrite46.0ms (1.2%)

simplify68.0ms (1.8%)

prune41.0ms (1.1%)

regimes21.0ms (0.6%)

simplify2.0ms (0%)

end31.0ms (0.8%)

Profiling