Details

analyze7.0ms (0.2%)

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

Compiler

Compiled 15 to 8 computations (46.7% saved)

sample2.6s (59.5%)

Results

1.7s	4097×	body	1024	valid
476.0ms	2025×	body	512	valid
222.0ms	1766×	body	256	valid
190.0ms	368×	body	2048	valid
0.0ms	4×	body	256	invalid

preprocess69.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

720×	`fma-def_binary64`
478×	`fma-neg_binary64`
463×	`times-frac_binary64`
381×	`associate-/r/_binary64`
306×	`associate-/l/_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	891	22
7	2601	22
8	6641	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 15 to 8 computations (46.7% saved)

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
478×	`fma-neg_binary64`
463×	`times-frac_binary64`
381×	`associate-/r/_binary64`
306×	`associate-/l/_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	891	22
7	2601	22
8	6641	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))))

eval0.0ms (0%)

Compiler: Compiled 14 to 7 computations (50% saved)

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

57.3b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	57.3b	(/.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)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	2.2b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	5.6b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 34 to 7 computations (79.4% saved)

series5.0ms (0.1%)

Counts

3 → 32

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	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)))

rewrite143.0ms (3.2%)

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	3652	18
0	6	6
1	130	6
2	2188	6
0	6	6
0	8	3
1	186	3
2	3652	3
0	8	3
0	6	6
1	129	6
2	2150	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 expm1.f64 (log1p.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 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 expm1.f64 (log1p.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 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 expm1.f64 (log1p.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 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 expm1.f64 (log1p.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 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 expm1.f64 (log1p.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 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 expm1.f64 (log1p.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 exp.f64 (log.f64 (*.f64 2 (cosh.f64 x))))))))

simplify79.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def_binary64`
528×	`fma-neg_binary64`
514×	`unswap-sqr_binary64`
469×	`associate-l_binary64`
380×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	447
1	150	441
2	350	437
3	995	437
4	3266	437
5	5399	437
6	7520	437

Stop Event

1×	node limit

Counts

69 → 67

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 x 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))
(fma.f64 1/3 (pow.f64 x 3) (+.f64 x 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)))
(fma.f64 x (fma.f64 1/3 (.f64 x x) 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 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/2520 (pow.f64 x 7) (*.f64 2 x))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/2520 (pow.f64 x 7) (+.f64 x 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)))
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 2 (+.f64 (.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 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x 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)))

eval16.0ms (0.4%)

Compiler: Compiled 968 to 399 computations (58.8% saved)

prune10.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	3	68

Error

0.0b

Counts

68 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	2.3b	(.f64 (.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
	3.7b	x
▶	0.0b	(tanh.f64 x)

Compiler

Compiled 17 to 13 computations (23.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 x)

Compiler

Compiled 4 to 2 computations (50% saved)

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)

rewrite49.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

465×	`pow1_binary64`
459×	`add-sqr-sqrt_binary64`
450×	`*-un-lft-identity_binary64`
437×	`add-log-exp_binary64`
435×	`log1p-expm1-u_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 (exp.f64 (.f64 x -2)))) (/.f64 (exp.f64 (.f64 x -2)) (+.f64 1 (exp.f64 (.f64 x -2)))))))) (#(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 (exp.f64 (.f64 x -2))) (/.f64 1 (+.f64 1 (exp.f64 (.f64 x -2)))))))) (#(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 (exp.f64 (.f64 x -2))) (-.f64 1 (exp.f64 (.f64 x -2)))))))) (#(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 (exp.f64 (.f64 x -2))) (+.f64 1 (exp.f64 (.f64 x -2))))))) (#(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 (exp.f64 (.f64 x -2)))) (neg.f64 (+.f64 1 (exp.f64 (.f64 x -2)))))))) (#(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 expm1.f64 (log1p.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 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 (exp.f64 (*.f64 x -2)))) (/.f64 (exp.f64 (*.f64 x -2)) (+.f64 1 (exp.f64 (*.f64 x -2)))))))) (#(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 (exp.f64 (*.f64 x -2))) (/.f64 1 (+.f64 1 (exp.f64 (*.f64 x -2)))))))) (#(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 (exp.f64 (*.f64 x -2))) (-.f64 1 (exp.f64 (*.f64 x -2)))))))) (#(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 (exp.f64 (*.f64 x -2))) (+.f64 1 (exp.f64 (*.f64 x -2))))))) (#(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 (exp.f64 (*.f64 x -2)))) (neg.f64 (+.f64 1 (exp.f64 (*.f64 x -2)))))))) (#(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 expm1.f64 (log1p.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 exp.f64 (log.f64 (tanh.f64 x)))))))

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

871×	`div-sub_binary64`
830×	`fma-def_binary64`
624×	`unswap-sqr_binary64`
590×	`fma-neg_binary64`
303×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	222
1	65	222
2	140	222
3	333	222
4	688	222
5	1579	222
6	2473	222
7	3981	222
8	6252	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))))

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sinh.f64 x)
✓	0.0b	(/.f64 1 (*.f64 2 (cosh.f64 x)))
✓	2.2b	(.f64 (.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))

Compiler

Compiled 33 to 20 computations (39.4% saved)

series7.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(.f64 (.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
2.0ms	x	@	inf	(.f64 (.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
1.0ms	x	@	inf	(/.f64 1 (*.f64 2 (cosh.f64 x)))
1.0ms	x	@	-inf	(/.f64 1 (*.f64 2 (cosh.f64 x)))
1.0ms	x	@	0	(.f64 (.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))

rewrite71.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

977×	`pow1_binary64`
904×	`add-log-exp_binary64`
903×	`log1p-expm1-u_binary64`
903×	`expm1-log1p-u_binary64`
103×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	211	17
2	2628	17

Stop Event

1×	node limit

Counts

3 → 76

Calls

Call 1

Inputs
(.f64 (.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
(/.f64 1 (*.f64 2 (cosh.f64 x)))
(sinh.f64 x)

Outputs

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

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

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

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

723×	`distribute-lft-out_binary64`
677×	`fma-def_binary64`
508×	`unswap-sqr_binary64`
466×	`associate-l_binary64`
386×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	528
1	134	526
2	330	514
3	975	514
4	3199	514
5	5113	514
6	7238	514

Stop Event

1×	node limit

Counts

112 → 102

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)))
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 5/48 (pow.f64 x 4))))
(+.f64 (.f64 -61/1440 (pow.f64 x 6)) (+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 5/48 (pow.f64 x 4)))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
x
(+.f64 (*.f64 1/6 (pow.f64 x 3)) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/120 (pow.f64 x 5)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))

Outputs
x
(+.f64 (*.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))))
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (.f64 -1/4 (.f64 x x)))
(fma.f64 -1/4 (*.f64 x x) 1/2)
(fma.f64 x (*.f64 x -1/4) 1/2)
(+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 5/48 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4))))
(fma.f64 x (*.f64 x -1/4) (fma.f64 5/48 (pow.f64 x 4) 1/2))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/48 -1/4) 1/2)
(+.f64 (.f64 -61/1440 (pow.f64 x 6)) (+.f64 1/2 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (*.f64 5/48 (pow.f64 x 4)))))
(fma.f64 -61/1440 (pow.f64 x 6) (+.f64 1/2 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/4 (.f64 x x) (.f64 5/48 (pow.f64 x 4))) (fma.f64 -61/1440 (pow.f64 x 6) 1/2))
(fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 x (*.f64 x -1/4) (fma.f64 5/48 (pow.f64 x 4) 1/2)))
(fma.f64 x (*.f64 x -1/4) (fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 5/48 (pow.f64 x 4) 1/2)))
(fma.f64 -61/1440 (pow.f64 x 6) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/48 -1/4) 1/2))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
x
(+.f64 (*.f64 1/6 (pow.f64 x 3)) x)
(fma.f64 1/6 (pow.f64 x 3) x)
(fma.f64 (pow.f64 x 3) 1/6 x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/120 (pow.f64 x 5)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) x))
(fma.f64 (pow.f64 x 3) 1/6 (fma.f64 (pow.f64 x 5) 1/120 x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/5040 (pow.f64 x 7) (fma.f64 1/120 (pow.f64 x 5) x)))
(fma.f64 (pow.f64 x 3) 1/6 (fma.f64 (pow.f64 x 7) 1/5040 (fma.f64 (pow.f64 x 5) 1/120 x)))
(fma.f64 (pow.f64 x 3) 1/6 (fma.f64 (pow.f64 x 5) 1/120 (fma.f64 (pow.f64 x 7) 1/5040 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 -1/2 (exp.f64 x)))

eval41.0ms (0.9%)

Compiler: Compiled 1743 to 1138 computations (34.7% saved)

prune18.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	141	4	145

Error

Counts

145 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	2.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))
▶	1.0b	(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
	3.7b	x
✓	0.0b	(tanh.f64 x)

Compiler

Compiled 25 to 19 computations (24% saved)

localize27.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 2) x)
✓	0.0b	(/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x)))
✓	1.0b	(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))

Compiler

Compiled 44 to 36 computations (18.2% saved)

series9.0ms (0.2%)

Counts

3 → 36

Calls

9 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	@	0	(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)))

rewrite72.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

487×	`log-prod_binary64`
383×	`exp-prod_binary64`
290×	`pow-prod-down_binary64`
265×	`pow2_binary64`
231×	`pow-unpow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	230	35
2	2801	32

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (exp.f64 2) x) (fma.f64 (exp.f64 x) (exp.f64 x) 1)) (pow.f64 (hypot.f64 1 (exp.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1) (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 2)) (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1) (cbrt.f64 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1) (sqrt.f64 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1)))))) (#(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) (fma.f64 (exp.f64 x) (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 (+.f64 x x)) (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) 4))) (cbrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (expm1.f64 (+.f64 x x))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (expm1.f64 (+.f64 x x)) -1) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (hypot.f64 1 (exp.f64 x))) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (hypot.f64 1 (exp.f64 x))) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))) 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 pow.f64 (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) (pow.f64 (hypot.f64 1 (exp.f64 x)) 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1) (expm1.f64 (+.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log1p.f64 (pow.f64 (exp.f64 2) x)))) 2)) (cbrt.f64 (-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log1p.f64 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log1p.f64 (pow.f64 (exp.f64 2) x))))) (sqrt.f64 (-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log1p.f64 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (hypot.f64 1 (exp.f64 x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (hypot.f64 1 (exp.f64 x))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) (pow.f64 (hypot.f64 1 (exp.f64 x)) 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))))))) (#(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 exp.f64 (*.f64 (*.f64 3 (-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log1p.f64 (pow.f64 (exp.f64 2) x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log1p.f64 (pow.f64 (exp.f64 2) x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (hypot.f64 1 (exp.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log1p.f64 (pow.f64 (exp.f64 2) x))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)) (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -4)) (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(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 (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1)) -2) (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 6) x))) (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 (fma.f64 (exp.f64 x) (exp.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) 4) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) 6) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))) (#(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 pow.f64 (exp.f64 -1) (log1p.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))) 2)) (cbrt.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))))) (sqrt.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(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 exp.f64 (*.f64 (*.f64 3 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (hypot.f64 1 (exp.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (pow.f64 (exp.f64 2) x)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 2) x))) 1) 1))))))

((#(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 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 2) x))) 2)) (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 (fma.f64 (exp.f64 x) (exp.f64 x) 1) 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 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (pow.f64 (exp.f64 4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (exp.f64 4) x)) (pow.f64 (cbrt.f64 (exp.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 x) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 4/3) x) (exp.f64 (*.f64 2/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (*.f64 2 (*.f64 1/3 (+.f64 x x)))) (pow.f64 (E.f64) (*.f64 1/3 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (exp.f64 2) (exp.f64 (log1p.f64 x))) (exp.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (E.f64) (exp.f64 (log1p.f64 (+.f64 x x)))) (E.f64))))) (#(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 6) x))))) (#(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 log1p.f64 (expm1.f64 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (*.f64 2 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 4 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (+.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (+.f64 x x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 2) (cbrt.f64 (*.f64 x x)))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 2) (sqrt.f64 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (+.f64 x x) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1)) (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) 4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) 4)) (cbrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1)) -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 6) x)) (/.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)))))

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-/l/_binary64`
564×	`fma-def_binary64`
514×	`associate-/r/_binary64`
455×	`unswap-sqr_binary64`
361×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	402
1	122	400
2	291	394
3	841	394
4	2055	394
5	2880	394
6	4877	394

Stop Event

1×	node limit

Counts

152 → 142

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))))
1/2
(+.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))))
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))

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 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 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 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 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 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 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 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 x)) (fma.f64 (exp.f64 x) (exp.f64 x) 1))
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 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 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))
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 x 2 (fma.f64 x (*.f64 x (fma.f64 x 4/3 2)) 1))
(fma.f64 x (fma.f64 x 2 2) (fma.f64 (pow.f64 x 3) 4/3 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)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(sinh.f64 x)
✓	2.2b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/.f64 (sinh.f64 x) (cosh.f64 x))
0.0ms	x	@	0	(/.f64 (sinh.f64 x) (cosh.f64 x))
0.0ms	x	@	-inf	(/.f64 (sinh.f64 x) (cosh.f64 x))

rewrite48.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`pow1_binary64`
581×	`add-log-exp_binary64`
580×	`log1p-expm1-u_binary64`
580×	`expm1-log1p-u_binary64`
568×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	110	8
2	1519	8

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

Inputs
(/.f64 (sinh.f64 x) (cosh.f64 x))

Outputs

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

simplify69.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

871×	`div-sub_binary64`
830×	`fma-def_binary64`
624×	`unswap-sqr_binary64`
590×	`fma-neg_binary64`
303×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	222
1	65	222
2	140	222
3	333	222
4	688	222
5	1579	222
6	2473	222
7	3981	222
8	6252	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))))

eval102.0ms (2.3%)

Compiler: Compiled 3001 to 1947 computations (35.1% saved)

prune49.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	1	0	1
Picked	0	1	1
Done	1	1	2
Total	212	4	216

Error

Counts

216 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	56.0b	(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
✓	2.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))
	3.7b	x
✓	0.0b	(tanh.f64 x)

Compiler

Compiled 25 to 19 computations (24% saved)

localize34.0ms (0.8%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
✓	5.6b	(-.f64 (exp.f64 (*.f64 2 x)) 1)

Compiler

Compiled 36 to 29 computations (19.4% saved)

series6.0ms (0.1%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
2.0ms	x	@	-inf	(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
1.0ms	x	@	inf	(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
1.0ms	x	@	0	(-.f64 (exp.f64 (*.f64 2 x)) 1)
0.0ms	x	@	inf	(-.f64 (exp.f64 (*.f64 2 x)) 1)

rewrite126.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

441×	`log-prod_binary64`
346×	`exp-prod_binary64`
303×	`prod-diff_binary64`
263×	`pow-prod-down_binary64`
235×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	198	23
2	2633	23

Stop Event

1×	node limit

Counts

2 → 177

Calls

Call 1

Inputs
(-.f64 (exp.f64 (*.f64 2 x)) 1)
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (exp.f64 2) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (pow.f64 (exp.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 (+.f64 x x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (+.f64 x x))))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (cbrt.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (exp.f64 x) 6) -1) (/.f64 1 (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1) (pow.f64 (exp.f64 x) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (exp.f64 x) 4) -1) (pow.f64 (hypot.f64 1 (exp.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (exp.f64 x) 1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 4) -1) (+.f64 1 (pow.f64 (exp.f64 x) 6))) (fma.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 4) -1) (-.f64 1 (pow.f64 (exp.f64 x) 4))) (-.f64 1 (pow.f64 (exp.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) 1) (pow.f64 (exp.f64 x) 4)) (+.f64 (pow.f64 (exp.f64 x) 6) -1)))))) 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1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 2) x) (pow.f64 (hypot.f64 1 (exp.f64 x)) -2) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (/.f64 (exp.f64 x) (hypot.f64 1 (exp.f64 x))) 2) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (hypot.f64 1 (exp.f64 x))) 2)) 2) (cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (hypot.f64 1 (exp.f64 x))) 2)) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (/.f64 (exp.f64 x) (hypot.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (pow.f64 (/.f64 (exp.f64 x) (hypot.f64 1 (exp.f64 x))) 2)) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (exp.f64 x))) 2) -2) (/.f64 (pow.f64 (exp.f64 2) x) (pow.f64 (cbrt.f64 (hypot.f64 1 (exp.f64 x))) 2)) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (hypot.f64 1 (exp.f64 x))) (/.f64 (pow.f64 (exp.f64 2) x) (hypot.f64 1 (exp.f64 x))) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) 1) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (fma.f64 (exp.f64 x) (exp.f64 x) 1)) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (exp.f64 x) 1) (/.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) 1)) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) 4))) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (pow.f64 (cbrt.f64 (hypot.f64 1 (exp.f64 x))) 2)) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) 4))) (/.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (hypot.f64 1 (exp.f64 x))) 2)) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) (hypot.f64 1 (exp.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (hypot.f64 1 (exp.f64 x))) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (exp.f64 x) (hypot.f64 1 (exp.f64 x))) (/.f64 (exp.f64 x) (hypot.f64 1 (exp.f64 x))) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (pow.f64 (exp.f64 x) 6))) (fma.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x)) 1) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (exp.f64 2) x) (-.f64 1 (pow.f64 (exp.f64 x) 4))) (-.f64 1 (pow.f64 (exp.f64 2) x)) (neg.f64 (pow.f64 (hypot.f64 1 (exp.f64 x)) -2)))))))

simplify156.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

624×	`distribute-lft-out_binary64`
579×	`*-commutative_binary64`
565×	`sqr-pow_binary64`
522×	`fma-def_binary64`
481×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	103
1	92	99
2	230	95
3	682	93
4	2041	93
5	3291	93
6	3954	93
7	4364	93
8	5024	93
9	6286	93
10	6790	93
11	7399	93
12	7961	93

Stop Event

1×	node limit

Counts

185 → 191

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 4/3 (pow.f64 x 3)) (*.f64 2 x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 (.f64 4/3 (pow.f64 x 3)) (.f64 2 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)))

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

eval201.0ms (4.5%)

Compiler: Compiled 6192 to 4131 computations (33.3% saved)

prune24.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	191	4	195

Error

Counts

195 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	56.0b	(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
✓	2.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))
	3.7b	x
✓	0.0b	(tanh.f64 x)

Compiler

Compiled 25 to 19 computations (24% saved)

regimes11.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

Inputs
x
x
x
x
(tanh.f64 x)
(/.f64 (sinh.f64 x) (cosh.f64 x))
(.f64 (.f64 2 (sinh.f64 x)) (/.f64 1 (*.f64 2 (cosh.f64 x))))
(/.f64 (-.f64 (exp.f64 (.f64 2 x)) 1) (+.f64 1 (exp.f64 (.f64 2 x))))
(.f64 (expm1.f64 (.f64 x 2)) (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 2) x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(tanh.f64 x)

Calls

2 calls:

6.0ms	x
2.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 78 to 48 computations (38.5% saved)

regimes6.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

4 → 1

Calls

Call 1

Inputs
x
x
x
x

Outputs
x

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
3.7b	1	`x`

Compiler

Compiled 7 to 2 computations (71.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(tanh.f64 x)
x

Outputs
(tanh.f64 x)
x

Compiler

Compiled 5 to 3 computations (40% saved)

soundness0.0ms (0%)

end15.0ms (0.3%)

Compiler: Compiled 4 to 2 computations (50% saved)

Details

analyze7.0ms (0.2%)

sample2.6s (59.5%)

preprocess69.0ms (1.6%)

simplify55.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize11.0ms (0.3%)

series5.0ms (0.1%)

rewrite143.0ms (3.2%)

simplify79.0ms (1.8%)

eval16.0ms (0.4%)

prune10.0ms (0.2%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite49.0ms (1.1%)

simplify68.0ms (1.5%)

localize15.0ms (0.3%)

series7.0ms (0.2%)

rewrite71.0ms (1.6%)

simplify85.0ms (1.9%)

eval41.0ms (0.9%)

prune18.0ms (0.4%)

localize27.0ms (0.6%)

series9.0ms (0.2%)

rewrite72.0ms (1.6%)

simplify69.0ms (1.5%)

localize6.0ms (0.1%)

series1.0ms (0%)

rewrite48.0ms (1.1%)

simplify69.0ms (1.6%)

eval102.0ms (2.3%)

prune49.0ms (1.1%)

localize34.0ms (0.8%)

series6.0ms (0.1%)

rewrite126.0ms (2.9%)

simplify156.0ms (3.5%)

eval201.0ms (4.5%)

prune24.0ms (0.6%)

regimes11.0ms (0.2%)

regimes6.0ms (0.1%)

simplify3.0ms (0.1%)

soundness0.0ms (0%)

end15.0ms (0.3%)

Profiling