Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample696.0ms (23.4%)

Results

684.0ms

8256×

body

256

valid

Bogosity

preprocess69.0ms (2.3%)

Algorithm

2×	egg-herbie

Rules

702×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`
290×	`exp-prod_binary64`
264×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	21	13
3	28	13
4	47	13
5	87	13
6	184	13
7	434	13
8	1195	13
9	3176	13
10	4367	13
11	5548	13
12	7298	13
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify61.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

702×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`
290×	`exp-prod_binary64`
264×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	21	13
3	28	13
4	47	13
5	87	13
6	184	13
7	434	13
8	1195	13
9	3176	13
10	4367	13
11	5548	13
12	7298	13

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% 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

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 24 to 8 computations (66.7% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite46.0ms (1.6%)

Algorithm

2×	egg-rewrite-iter-limit
2×	egg-rewrite
1×	batch-egg-rewrite

Rules

91×	`add-sqr-sqrt_binary64`
91×	`add-sqr-sqrt_binary64`
87×	`add-log-exp_binary64`
87×	`add-log-exp_binary64`
85×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	176	18
2	2839	18
0	8	9
1	176	9
2	2839	9
0	8	9
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×	unsound

Counts

2 → 22

Calls

Call 1

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

simplify44.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-def_binary64`
488×	`associate-l_binary64`
407×	`associate-/l*_binary64`
394×	`distribute-rgt-in_binary64`
393×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	566
1	223	550
2	836	413
3	4593	335

Stop Event

1×	node limit

Counts

46 → 55

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.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)))
(.f64 2 (/.f64 1 (.f64 2 (cosh.f64 x))))
(.f64 1 (/.f64 2 (.f64 2 (cosh.f64 x))))
(.f64 (.f64 (cbrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (cbrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x))))) (cbrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(pow.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))) 1)
(log.f64 (exp.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(cbrt.f64 (.f64 (.f64 (/.f64 2 (.f64 2 (cosh.f64 x))) (/.f64 2 (.f64 2 (cosh.f64 x)))) (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(log1p.f64 (expm1.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(exp.f64 (log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(.f64 1 (.f64 2 (cosh.f64 x)))
(.f64 (.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) (cbrt.f64 (.f64 2 (cosh.f64 x)))) (cbrt.f64 (*.f64 2 (cosh.f64 x))))
(.f64 (sqrt.f64 (.f64 2 (cosh.f64 x))) (sqrt.f64 (*.f64 2 (cosh.f64 x))))
(*.f64 2 (cosh.f64 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))))))
(/.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))))
(pow.f64 (*.f64 2 (cosh.f64 x)) 1)
(log.f64 (exp.f64 (*.f64 2 (cosh.f64 x))))
(cbrt.f64 (.f64 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x))) (*.f64 2 (cosh.f64 x))))
(expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x))))
(log1p.f64 (expm1.f64 (*.f64 2 (cosh.f64 x))))
(exp.f64 (log.f64 (*.f64 2 (cosh.f64 x))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 5/24) -1/2) (fma.f64 -61/720 (pow.f64 x 6) 1))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.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 (pow.f64 x 4) 1/12))
(+.f64 2 (fma.f64 x x (*.f64 (pow.f64 x 4) 1/12)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 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 (pow.f64 x 4) 1/12))))
(+.f64 2 (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (*.f64 (pow.f64 x 4) 1/12))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 2)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 2)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(.f64 2 (/.f64 1 (.f64 2 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(.f64 1 (/.f64 2 (.f64 2 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(.f64 (.f64 (cbrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (cbrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x))))) (cbrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))) 1)
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(log.f64 (exp.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (.f64 (.f64 (/.f64 2 (.f64 2 (cosh.f64 x))) (/.f64 2 (.f64 2 (cosh.f64 x)))) (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(log1p.f64 (expm1.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(exp.f64 (log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 1 (cosh.f64 x))
(.f64 1 (.f64 2 (cosh.f64 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(.f64 (.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) (cbrt.f64 (.f64 2 (cosh.f64 x)))) (cbrt.f64 (*.f64 2 (cosh.f64 x))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(.f64 (sqrt.f64 (.f64 2 (cosh.f64 x))) (sqrt.f64 (*.f64 2 (cosh.f64 x))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(*.f64 2 (cosh.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 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))))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (exp.f64 (+.f64 x x)) (*.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 -1 (exp.f64 (*.f64 x -2)))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (exp.f64 (.f64 x -3))) (+.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (.f64 x -2))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (exp.f64 x) -3)) (+.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 (*.f64 x -2))))
(/.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))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(pow.f64 (*.f64 2 (cosh.f64 x)) 1)
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(log.f64 (exp.f64 (*.f64 2 (cosh.f64 x))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(cbrt.f64 (.f64 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x))) (*.f64 2 (cosh.f64 x))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(log1p.f64 (expm1.f64 (*.f64 2 (cosh.f64 x))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))
(exp.f64 (log.f64 (*.f64 2 (cosh.f64 x))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(*.f64 2 (cosh.f64 x))

eval14.0ms (0.5%)

Compiler: Compiled 690 to 468 computations (32.2% saved)

prune10.0ms (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	49	6	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	6	56

Error

0.0b

Counts

56 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	16.3b	(/.f64 2 (+.f64 2 (*.f64 x x)))
▶	0.0b	(/.f64 1 (cosh.f64 x))
▶	31.0b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
▶	0.0b	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
▶	0.0b	(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
	30.5b	1

Compiler

Compiled 94 to 76 computations (19.1% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (cosh.f64 x))

Compiler

Compiled 9 to 5 computations (44.4% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/.f64 1 (cosh.f64 x))
1.0ms	x	@	inf	(/.f64 1 (cosh.f64 x))
0.0ms	x	@	0	(/.f64 1 (cosh.f64 x))

rewrite36.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

461×	`pow1_binary64`
448×	`add-sqr-sqrt_binary64`
438×	`*-un-lft-identity_binary64`
428×	`add-log-exp_binary64`
426×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	102	6
2	1198	6

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(/.f64 1 (cosh.f64 x))

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

Outputs

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

simplify34.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-/l/_binary64`
377×	`fma-def_binary64`
306×	`associate-/r/_binary64`
281×	`associate-l_binary64`
257×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	439
1	182	431
2	488	240
3	2901	238

Stop Event

1×	node limit

Counts

33 → 39

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))
(*.f64 -1 (/.f64 1 (neg.f64 (cosh.f64 x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1))
(.f64 (/.f64 1 (.f64 2 (cosh.f64 x))) 2)
(pow.f64 (cosh.f64 x) -1)
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) 1))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/24 -1/2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (fma.f64 5/24 (pow.f64 x 4) 1)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(/.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (cosh.f64 x)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(/.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (cosh.f64 x)))
(*.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 -1 (/.f64 1 (neg.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(.f64 (/.f64 1 (.f64 2 (cosh.f64 x))) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (cosh.f64 x) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -1/2 (.f64 x x))

Compiler

Compiled 19 to 10 computations (47.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite36.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`pow1_binary64`
420×	`add-sqr-sqrt_binary64`
411×	`*-un-lft-identity_binary64`
401×	`add-log-exp_binary64`
401×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1148	7

Stop Event

1×	node limit

Counts

1 → 14

Calls

Call 1

Inputs
(.f64 -1/2 (.f64 x x))

Outputs

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

simplify39.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1079×	`log-prod_binary64`
420×	`associate-l_binary64`
379×	`associate-r_binary64`
325×	`associate-+l+_binary64`
306×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	216
1	102	206
2	359	191
3	3009	191
4	6280	191

Stop Event

1×	node limit

Counts

26 → 18

Calls

Call 1

Inputs
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 0 (.f64 -1/2 (.f64 x x)))
(+.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x))) (cbrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x)))))
(-.f64 (+.f64 1 (.f64 -1/2 (.f64 x x))) 1)
(pow.f64 (.f64 -1/2 (.f64 x x)) 1)
(pow.f64 (pow.f64 (.f64 -1/2 (.f64 x x)) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 -1/2 (.f64 x x))) 3)
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))
(cbrt.f64 (pow.f64 (.f64 -1/2 (.f64 x x)) 3))
(expm1.f64 (log1p.f64 (.f64 -1/2 (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 -1/2 (.f64 x x))))
(exp.f64 (log.f64 (.f64 -1/2 (.f64 x x))))

Outputs
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(+.f64 0 (.f64 -1/2 (.f64 x x)))
(.f64 -1/2 (.f64 x x))
(+.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x))) (cbrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x)))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))
(.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 x x)))))
(.f64 -1/2 (.f64 x x))
(-.f64 (+.f64 1 (.f64 -1/2 (.f64 x x))) 1)
(.f64 -1/2 (.f64 x x))
(pow.f64 (.f64 -1/2 (.f64 x x)) 1)
(.f64 -1/2 (.f64 x x))
(pow.f64 (pow.f64 (.f64 -1/2 (.f64 x x)) 3) 1/3)
(.f64 -1/2 (.f64 x x))
(pow.f64 (cbrt.f64 (.f64 -1/2 (.f64 x x))) 3)
(.f64 -1/2 (.f64 x x))
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(.f64 -1/2 (.f64 x x))
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(.f64 -1/2 (.f64 x x))
(log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))
(.f64 -1/2 (.f64 x x))
(cbrt.f64 (pow.f64 (.f64 -1/2 (.f64 x x)) 3))
(.f64 -1/2 (.f64 x x))
(expm1.f64 (log1p.f64 (.f64 -1/2 (.f64 x x))))
(.f64 -1/2 (.f64 x x))
(log1p.f64 (expm1.f64 (.f64 -1/2 (.f64 x x))))
(.f64 -1/2 (.f64 x x))
(exp.f64 (log.f64 (.f64 -1/2 (.f64 x x))))
(.f64 -1/2 (.f64 x x))

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 2 (+.f64 2 (*.f64 x x)))

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite41.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`pow1_binary64`
657×	`add-log-exp_binary64`
656×	`log1p-expm1-u_binary64`
656×	`expm1-log1p-u_binary64`
644×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	137	8
2	1784	8

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(/.f64 2 (+.f64 2 (*.f64 x x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 2 (fma.f64 x x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 1 (fma.f64 x x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (fma.f64 x x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 2 (fma.f64 x x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 (/.f64 2 (fma.f64 x x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (/.f64 1 (neg.f64 (fma.f64 x x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x x 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (+.f64 8 (pow.f64 x 6))) (+.f64 4 (+.f64 (pow.f64 x 4) (*.f64 -2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (-.f64 4 (pow.f64 x 4))) (-.f64 2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (fma.f64 x x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 4 (pow.f64 (fma.f64 x x 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 2 (fma.f64 x x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))))))

simplify37.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-def_binary64`
617×	`associate-/l*_binary64`
429×	`log-prod_binary64`
387×	`associate-l_binary64`
354×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	542
1	228	481
2	733	418
3	3659	413

Stop Event

1×	node limit

Counts

34 → 56

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 -1/2 (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 1/4 (pow.f64 x 4)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 6)))))
(/.f64 2 (pow.f64 x 2))
(-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 4))) (.f64 16 (/.f64 1 (pow.f64 x 8)))))
(/.f64 2 (pow.f64 x 2))
(-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 4))) (.f64 16 (/.f64 1 (pow.f64 x 8)))))
(-.f64 (+.f64 1 (/.f64 2 (fma.f64 x x 2))) 1)
(*.f64 2 (/.f64 1 (fma.f64 x x 2)))
(*.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(*.f64 1 (/.f64 2 (fma.f64 x x 2)))
(*.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 (/.f64 2 (fma.f64 x x 2))))
(*.f64 -2 (/.f64 1 (neg.f64 (fma.f64 x x 2))))
(*.f64 (/.f64 1 (fma.f64 x x 2)) 2)
(.f64 (/.f64 2 (+.f64 8 (pow.f64 x 6))) (+.f64 4 (+.f64 (pow.f64 x 4) (.f64 -2 (*.f64 x x)))))
(.f64 (/.f64 2 (-.f64 4 (pow.f64 x 4))) (-.f64 2 (.f64 x x)))
(pow.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 3)
(pow.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)
(pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -1)
(sqrt.f64 (/.f64 4 (pow.f64 (fma.f64 x x 2) 2)))
(log.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))
(cbrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3))
(expm1.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2))))
(log1p.f64 (expm1.f64 (/.f64 2 (fma.f64 x x 2))))
(exp.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 -1/2 (pow.f64 x 2))))
(+.f64 1 (fma.f64 1/4 (pow.f64 x 4) (.f64 -1/2 (.f64 x x))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 1/4 (pow.f64 x 4))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 1/4 (pow.f64 x 4) 1))
(fma.f64 (.f64 x x) (fma.f64 (.f64 1/4 x) x -1/2) 1)
(+.f64 1 (+.f64 (.f64 1/4 (pow.f64 x 4)) (+.f64 (.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 1/4 (pow.f64 x 4) (fma.f64 -1/2 (.f64 x x) (.f64 -1/8 (pow.f64 x 6)))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 1/4 (pow.f64 x 4) (fma.f64 -1/8 (pow.f64 x 6) 1)))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 (/.f64 2 x) x)
(-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (/.f64 2 (*.f64 x x)) (/.f64 4 (pow.f64 x 4)))
(+.f64 (/.f64 2 (*.f64 x x)) (/.f64 -4 (pow.f64 x 4)))
(+.f64 (/.f64 (/.f64 2 x) x) (/.f64 -4 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 8 (pow.f64 x 6)) (-.f64 (/.f64 2 (*.f64 x x)) (/.f64 4 (pow.f64 x 4))))
(+.f64 (/.f64 2 (*.f64 x x)) (-.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 4 (pow.f64 x 4))))
(+.f64 (/.f64 (/.f64 2 x) x) (+.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 -4 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 4))) (.f64 16 (/.f64 1 (pow.f64 x 8)))))
(+.f64 (/.f64 8 (pow.f64 x 6)) (-.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 16 (pow.f64 x 8)))))
(+.f64 (/.f64 (/.f64 2 x) x) (+.f64 (+.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 -4 (pow.f64 x 4))) (/.f64 -16 (pow.f64 x 8))))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 (/.f64 2 x) x)
(-.f64 (.f64 2 (/.f64 1 (pow.f64 x 2))) (.f64 4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (/.f64 2 (*.f64 x x)) (/.f64 4 (pow.f64 x 4)))
(+.f64 (/.f64 2 (*.f64 x x)) (/.f64 -4 (pow.f64 x 4)))
(+.f64 (/.f64 (/.f64 2 x) x) (/.f64 -4 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (*.f64 4 (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 8 (pow.f64 x 6)) (-.f64 (/.f64 2 (*.f64 x x)) (/.f64 4 (pow.f64 x 4))))
(+.f64 (/.f64 2 (*.f64 x x)) (-.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 4 (pow.f64 x 4))))
(+.f64 (/.f64 (/.f64 2 x) x) (+.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 -4 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 6))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 4))) (.f64 16 (/.f64 1 (pow.f64 x 8)))))
(+.f64 (/.f64 8 (pow.f64 x 6)) (-.f64 (/.f64 2 (*.f64 x x)) (+.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 16 (pow.f64 x 8)))))
(+.f64 (/.f64 (/.f64 2 x) x) (+.f64 (+.f64 (/.f64 8 (pow.f64 x 6)) (/.f64 -4 (pow.f64 x 4))) (/.f64 -16 (pow.f64 x 8))))
(-.f64 (+.f64 1 (/.f64 2 (fma.f64 x x 2))) 1)
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(*.f64 2 (/.f64 1 (fma.f64 x x 2)))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(*.f64 1 (/.f64 2 (fma.f64 x x 2)))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(*.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 2) (cbrt.f64 (/.f64 2 (fma.f64 x x 2))))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(*.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) (sqrt.f64 (/.f64 2 (fma.f64 x x 2))))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(*.f64 -2 (/.f64 1 (neg.f64 (fma.f64 x x 2))))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(*.f64 (/.f64 1 (fma.f64 x x 2)) 2)
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(.f64 (/.f64 2 (+.f64 8 (pow.f64 x 6))) (+.f64 4 (+.f64 (pow.f64 x 4) (.f64 -2 (*.f64 x x)))))
(.f64 (/.f64 2 (+.f64 (pow.f64 x 6) 8)) (+.f64 4 (+.f64 (pow.f64 x 4) (.f64 (*.f64 x x) -2))))
(.f64 (/.f64 2 (+.f64 (pow.f64 x 6) 8)) (+.f64 4 (fma.f64 (.f64 x x) -2 (pow.f64 x 4))))
(.f64 (/.f64 2 (+.f64 (pow.f64 x 6) 8)) (fma.f64 (.f64 x x) (fma.f64 x x -2) 4))
(.f64 (/.f64 2 (-.f64 4 (pow.f64 x 4))) (-.f64 2 (.f64 x x)))
(/.f64 (fma.f64 x (*.f64 x -2) 4) (-.f64 4 (pow.f64 x 4)))
(pow.f64 (/.f64 2 (fma.f64 x x 2)) 1)
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3) 1/3)
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x 2))) 3)
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x 2))) 2)
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(pow.f64 (*.f64 (fma.f64 x x 2) 1/2) -1)
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(sqrt.f64 (/.f64 4 (pow.f64 (fma.f64 x x 2) 2)))
(fabs.f64 (/.f64 2 (fma.f64 x x 2)))
(log.f64 (exp.f64 (/.f64 2 (fma.f64 x x 2))))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(cbrt.f64 (pow.f64 (/.f64 2 (fma.f64 x x 2)) 3))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(expm1.f64 (log1p.f64 (/.f64 2 (fma.f64 x x 2))))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(log1p.f64 (expm1.f64 (/.f64 2 (fma.f64 x x 2))))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))
(exp.f64 (log.f64 (/.f64 2 (fma.f64 x x 2))))
(+.f64 1 (-.f64 (/.f64 2 (fma.f64 x x 2)) 1))
(+.f64 (/.f64 2 (fma.f64 x x 2)) 0)
(/.f64 2 (fma.f64 x x 2))

localize14.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
✓	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 30 to 20 computations (33.3% saved)

series52.0ms (1.7%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
27.0ms	x	@	inf	(log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))
22.0ms	x	@	-inf	(log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))
1.0ms	x	@	0	(log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))
0.0ms	x	@	0	(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
0.0ms	x	@	0	(/.f64 2 (*.f64 2 (cosh.f64 x)))

rewrite51.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

684×	`pow1_binary64`
633×	`add-log-exp_binary64`
633×	`expm1-log1p-u_binary64`
632×	`log1p-expm1-u_binary64`
619×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	153	20
2	1820	20

Stop Event

1×	node limit

Counts

3 → 68

Calls

Call 1

Inputs
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))

Outputs

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

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

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

simplify54.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

444×	`fma-def_binary64`
336×	`times-frac_binary64`
326×	`unswap-sqr_binary64`
276×	`fma-neg_binary64`
252×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1450
1	327	814
2	1029	802
3	5782	802

Stop Event

1×	node limit

Counts

104 → 82

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(log.f64 2)
(+.f64 (log.f64 2) (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 7/96 (pow.f64 x 4))))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 7/96 (pow.f64 x 4)) (*.f64 -31/1440 (pow.f64 x 6)))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(+.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) -1)
(-.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) 1)
(*.f64 2 (/.f64 1/2 (cosh.f64 x)))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2))
(*.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(.f64 -2 (/.f64 1 (.f64 (cosh.f64 x) -2)))
(*.f64 (/.f64 1/2 (cosh.f64 x)) 2)
(pow.f64 (cosh.f64 x) -1)
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 2)
(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(+.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) -1)
(-.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) 1)
(*.f64 2 (/.f64 1/2 (cosh.f64 x)))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2))
(*.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(.f64 -2 (/.f64 1 (.f64 (cosh.f64 x) -2)))
(*.f64 (/.f64 1/2 (cosh.f64 x)) 2)
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(/.f64 2 (neg.f64 (*.f64 (cosh.f64 x) -2)))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x)))
(/.f64 -2 (*.f64 (cosh.f64 x) -2))
(/.f64 -1 (neg.f64 (cosh.f64 x)))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) 3) 1) (+.f64 (.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) (+.f64 (/.f64 1 (cosh.f64 x)) 1)) (+.f64 1 (.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) (+.f64 (/.f64 1 (cosh.f64 x)) 1)) 1) (+.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) 1))
(/.f64 (/.f64 2 (cosh.f64 x)) 2)
(/.f64 (/.f64 2 (sqrt.f64 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (/.f64 2 (cbrt.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)))) (cbrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1)
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 2)
(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(-.f64 (+.f64 1 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)
(*.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 1)
(*.f64 1 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(*.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) (pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2))
(*.f64 (pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2) (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 1)
(pow.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 3) 1/3)
(pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 3)
(pow.f64 (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2)
(sqrt.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 2))
(log.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1))
(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 3))
(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(exp.f64 (log.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 5/24 (pow.f64 x 4) (fma.f64 -61/720 (pow.f64 x 6) (.f64 -1/2 (.f64 x x)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 5/24 (pow.f64 x 4) (fma.f64 -61/720 (pow.f64 x 6) (.f64 -1/2 (.f64 x x)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 2)
(+.f64 (log.f64 2) (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 (log.f64 2) (.f64 (.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 (log.f64 2))
(fma.f64 x (*.f64 x -1/4) (log.f64 2))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 7/96 (pow.f64 x 4))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (.f64 x x) (.f64 (pow.f64 x 4) 7/96)))
(+.f64 (log.f64 2) (fma.f64 (.f64 x x) -1/4 (.f64 (pow.f64 x 4) 7/96)))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) 7/96 (log.f64 2)))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 7/96 (pow.f64 x 4)) (*.f64 -31/1440 (pow.f64 x 6)))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (.f64 x x) (fma.f64 7/96 (pow.f64 x 4) (.f64 (pow.f64 x 6) -31/1440))))
(+.f64 (log.f64 2) (fma.f64 (.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) 7/96 (.f64 (pow.f64 x 6) -31/1440))))
(+.f64 (fma.f64 (pow.f64 x 4) 7/96 (log.f64 2)) (fma.f64 (pow.f64 x 6) -31/1440 (.f64 x (.f64 x -1/4))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(+.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 2 (/.f64 1/2 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(.f64 -2 (/.f64 1 (.f64 (cosh.f64 x) -2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1/2 (cosh.f64 x)) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (cosh.f64 x) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(+.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 2 (/.f64 1/2 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(.f64 -2 (/.f64 1 (.f64 (cosh.f64 x) -2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1/2 (cosh.f64 x)) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (neg.f64 (*.f64 (cosh.f64 x) -2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 -2 (*.f64 (cosh.f64 x) -2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 -1 (neg.f64 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) 3) 1) (+.f64 (.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) (+.f64 (/.f64 1 (cosh.f64 x)) 1)) (+.f64 1 (.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) 1))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1) (fma.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 (/.f64 1 (cosh.f64 x)) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (fma.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 1 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) (+.f64 (/.f64 1 (cosh.f64 x)) 1)) 1) (+.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1) 1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 2 (cosh.f64 x)) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 2 (sqrt.f64 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 2 (cbrt.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)))) (cbrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 2 (.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) (cbrt.f64 (*.f64 4 (pow.f64 (cosh.f64 x) 2)))))
(/.f64 2 (.f64 (cbrt.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2))) (cbrt.f64 (*.f64 2 (cosh.f64 x)))))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (cosh.f64 x) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (+.f64 1 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(*.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 1)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(*.f64 1 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(*.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) (pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2) (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 1)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(pow.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 3) 1/3)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 3)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(pow.f64 (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(sqrt.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 2))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 1))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 3))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(exp.f64 (log.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))

localize15.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 37 to 25 computations (32.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

-inf

(*.f64 (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))

0.0ms

(*.f64 (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))

0.0ms

inf

(*.f64 (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))

rewrite41.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

688×	`pow1_binary64`
640×	`add-log-exp_binary64`
639×	`log1p-expm1-u_binary64`
639×	`expm1-log1p-u_binary64`
624×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	6
1	173	6
2	1892	6

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))

Outputs

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

simplify44.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

557×	`associate-/r/_binary64`
529×	`fma-neg_binary64`
341×	`fma-def_binary64`
319×	`*-commutative_binary64`
195×	`exp-prod_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	514
1	199	506
2	503	280
3	2735	278
4	6975	278

Stop Event

1×	node limit

Counts

38 → 45

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(/.f64 2 (neg.f64 (*.f64 (cosh.f64 x) -2)))
(/.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 -2 (*.f64 (cosh.f64 x) -2))
(/.f64 -1 (neg.f64 (cosh.f64 x)))
(/.f64 (/.f64 2 (cosh.f64 x)) 2)
(/.f64 (/.f64 2 (sqrt.f64 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (/.f64 2 (pow.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) 2)) (cbrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(/.f64 (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 2)) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(pow.f64 (cosh.f64 x) -1)
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 2)
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(pow.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)) 1/2)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
(fabs.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 5/24) -1/2) (fma.f64 -61/720 (pow.f64 x 6) 1))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (neg.f64 (*.f64 (cosh.f64 x) -2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 -2 (*.f64 (cosh.f64 x) -2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 -1 (neg.f64 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 2 (cosh.f64 x)) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 2 (sqrt.f64 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 2 (pow.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) 2)) (cbrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x))) (sqrt.f64 2)))
(/.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (*.f64 2 (cosh.f64 x))))
(/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (cosh.f64 x)) (sqrt.f64 (.f64 2 (cosh.f64 x)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 2)) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x))) (sqrt.f64 2)))
(/.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (*.f64 2 (cosh.f64 x))))
(/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (cosh.f64 x)) (sqrt.f64 (.f64 2 (cosh.f64 x)))))
(pow.f64 (cosh.f64 x) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)) 1/2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(fabs.f64 (/.f64 1 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))

eval78.0ms (2.6%)

Compiler: Compiled 3854 to 2735 computations (29% saved)

prune41.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	305	5	310
Fresh	0	1	1
Picked	1	0	1
Done	1	3	4
Total	307	9	316

Error

Counts

316 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	48.0b	(/.f64 (/.f64 2 x) x)
✓	16.3b	(/.f64 2 (+.f64 2 (*.f64 x x)))
▶	48.0b	(/.f64 2 (*.f64 x x))
✓	0.0b	(/.f64 1 (cosh.f64 x))
▶	0.3b	(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
✓	31.0b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
▶	0.3b	(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
▶	0.0b	(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
	30.5b	1

Compiler

Compiled 91 to 72 computations (20.9% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 1 (cosh.f64 x)))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
	0.0b	(/.f64 1 (cosh.f64 x))

Compiler

Compiled 20 to 12 computations (40% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
0.0ms	x	@	inf	(log1p.f64 (/.f64 1 (cosh.f64 x)))
0.0ms	x	@	-inf	(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
0.0ms	x	@	-inf	(log1p.f64 (/.f64 1 (cosh.f64 x)))
0.0ms	x	@	inf	(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))

rewrite44.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

542×	`pow1_binary64`
524×	`add-sqr-sqrt_binary64`
502×	`add-log-exp_binary64`
500×	`expm1-log1p-u_binary64`
499×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	121	14
2	1403	14

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

Inputs
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))

Outputs

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

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

simplify46.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

500×	`fma-neg_binary64`
456×	`fma-def_binary64`
369×	`unswap-sqr_binary64`
287×	`times-frac_binary64`
174×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	971
1	315	573
2	987	563
3	4830	563

Stop Event

1×	node limit

Counts

67 → 78

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(log.f64 2)
(+.f64 (log.f64 2) (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 7/96 (pow.f64 x 4))))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 7/96 (pow.f64 x 4)) (*.f64 -31/1440 (pow.f64 x 6)))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(+.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1)
(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))
(*.f64 -1 (/.f64 1 (neg.f64 (cosh.f64 x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1))
(.f64 (/.f64 1 (.f64 2 (cosh.f64 x))) 2)
(/.f64 1 (cosh.f64 x))
(/.f64 1 (neg.f64 (neg.f64 (cosh.f64 x))))
(/.f64 (pow.f64 (cosh.f64 x) -1/2) (sqrt.f64 (cosh.f64 x)))
(/.f64 -1 (neg.f64 (cosh.f64 x)))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) 1) (+.f64 (.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 1 (/.f64 1 (cosh.f64 x)))) (+.f64 1 (.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 1 (/.f64 1 (cosh.f64 x)))) 1) (+.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1)
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(-.f64 (+.f64 1 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)
(*.f64 1 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(*.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 1)
(*.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) (pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2))
(*.f64 (pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2) (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 1)
(pow.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 3) 1/3)
(pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 3)
(pow.f64 (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2)
(sqrt.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 2))
(log.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))))
(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 3))
(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(exp.f64 (log.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 5/24 (pow.f64 x 4) (fma.f64 -1/2 (.f64 x x) (.f64 -61/720 (pow.f64 x 6)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 2)
(+.f64 (log.f64 2) (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 (log.f64 2) (.f64 (.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 (log.f64 2))
(fma.f64 x (*.f64 x -1/4) (log.f64 2))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 7/96 (pow.f64 x 4))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (.f64 x x) (.f64 (pow.f64 x 4) 7/96)))
(+.f64 (log.f64 2) (fma.f64 (.f64 x x) -1/4 (.f64 (pow.f64 x 4) 7/96)))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) 7/96 (log.f64 2)))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 7/96 (pow.f64 x 4)) (*.f64 -31/1440 (pow.f64 x 6)))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (.f64 x x) (fma.f64 7/96 (pow.f64 x 4) (.f64 (pow.f64 x 6) -31/1440))))
(+.f64 (log.f64 2) (fma.f64 (.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) 7/96 (.f64 (pow.f64 x 6) -31/1440))))
(+.f64 (log.f64 2) (fma.f64 x (.f64 x -1/4) (fma.f64 (pow.f64 x 4) 7/96 (.f64 (pow.f64 x 6) -31/1440))))
(+.f64 (fma.f64 (pow.f64 x 4) 7/96 (log.f64 2)) (fma.f64 (pow.f64 x 6) -31/1440 (.f64 x (.f64 x -1/4))))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(+.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(/.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (cosh.f64 x)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(/.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (cosh.f64 x)))
(*.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 -1 (/.f64 1 (neg.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(.f64 (/.f64 1 (.f64 2 (cosh.f64 x))) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (neg.f64 (neg.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (pow.f64 (cosh.f64 x) -1/2) (sqrt.f64 (cosh.f64 x)))
(/.f64 -1 (neg.f64 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) 1) (+.f64 (.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 1 (/.f64 1 (cosh.f64 x)))) (+.f64 1 (.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1) (fma.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 1 (+.f64 1 (/.f64 1 (cosh.f64 x))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (fma.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 1 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 1 (/.f64 1 (cosh.f64 x)))) 1) (+.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (cosh.f64 x) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (+.f64 1 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(*.f64 1 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(*.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 1)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(*.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) (pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2) (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 1)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(pow.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 3) 1/3)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 3)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(pow.f64 (sqrt.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 2)
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(sqrt.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 2))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))) 3))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))
(exp.f64 (log.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))))
(log1p.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(log1p.f64 (/.f64 1 (cosh.f64 x)))

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 2 (*.f64 x x))

Compiler

Compiled 11 to 5 computations (54.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite36.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

491×	`pow1_binary64`
479×	`add-sqr-sqrt_binary64`
458×	`add-log-exp_binary64`
458×	`log1p-expm1-u_binary64`
458×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	108	7
2	1297	7

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(/.f64 2 (*.f64 x x))

Outputs

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

simplify32.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

614×	`log-prod_binary64`
557×	`associate-/r*_binary64`
323×	`associate-l_binary64`
305×	`associate-r_binary64`
299×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	233
1	125	233
2	406	233
3	2601	233

Stop Event

1×	node limit

Counts

33 → 24

Calls

Call 1

Inputs
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
(*.f64 2 (pow.f64 x -2))
(.f64 (/.f64 2 (.f64 x x)) 1)
(.f64 1 (/.f64 2 (.f64 x x)))
(.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) (cbrt.f64 (/.f64 4 (pow.f64 x 4))))
(.f64 (cbrt.f64 (/.f64 4 (pow.f64 x 4))) (cbrt.f64 (/.f64 2 (.f64 x x))))
(*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))
(.f64 -2 (/.f64 1 (.f64 x (neg.f64 x))))
(*.f64 (pow.f64 x -2) 2)
(*.f64 (/.f64 2 x) (/.f64 1 x))
(pow.f64 (/.f64 2 (*.f64 x x)) 1)
(pow.f64 (pow.f64 (/.f64 2 (*.f64 x x)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) 3)
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(pow.f64 (.f64 (.f64 x x) 1/2) -1)
(sqrt.f64 (/.f64 4 (pow.f64 x 4)))
(log.f64 (exp.f64 (/.f64 2 (*.f64 x x))))
(cbrt.f64 (pow.f64 (/.f64 2 (*.f64 x x)) 3))
(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 x x))))
(log1p.f64 (expm1.f64 (/.f64 2 (*.f64 x x))))
(exp.f64 (log.f64 (/.f64 2 (*.f64 x x))))

Outputs
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (*.f64 x x))
(.f64 (/.f64 2 (.f64 x x)) 1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(.f64 1 (/.f64 2 (.f64 x x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) (cbrt.f64 (/.f64 4 (pow.f64 x 4))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(.f64 (cbrt.f64 (/.f64 4 (pow.f64 x 4))) (cbrt.f64 (/.f64 2 (.f64 x x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(.f64 -2 (/.f64 1 (.f64 x (neg.f64 x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(*.f64 (pow.f64 x -2) 2)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(*.f64 (/.f64 2 x) (/.f64 1 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (/.f64 2 (*.f64 x x)) 1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (pow.f64 (/.f64 2 (*.f64 x x)) 3) 1/3)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) 3)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (.f64 (.f64 x x) 1/2) -1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(sqrt.f64 (/.f64 4 (pow.f64 x 4)))
(sqrt.f64 (*.f64 4 (pow.f64 x -4)))
(log.f64 (exp.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(cbrt.f64 (pow.f64 (/.f64 2 (*.f64 x x)) 3))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(log1p.f64 (expm1.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(exp.f64 (log.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 2 x) x)

Compiler

Compiled 11 to 7 computations (36.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/.f64 (/.f64 2 x) x)
0.0ms	x	@	-inf	(/.f64 (/.f64 2 x) x)
0.0ms	x	@	inf	(/.f64 (/.f64 2 x) x)

rewrite38.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

581×	`pow1_binary64`
544×	`add-log-exp_binary64`
544×	`log1p-expm1-u_binary64`
544×	`expm1-log1p-u_binary64`
534×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	112	7
2	1475	7

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(/.f64 (/.f64 2 x) x)

Outputs

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

simplify36.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

426×	`log-prod_binary64`
355×	`log-div_binary64`
345×	`fma-def_binary64`
309×	`distribute-rgt-in_binary64`
279×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	350
1	244	350
2	796	350
3	3529	350

Stop Event

1×	node limit

Counts

47 → 39

Calls

Call 1

Inputs
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
(.f64 2 (.f64 (/.f64 1 x) (/.f64 1 x)))
(*.f64 2 (/.f64 (/.f64 1 x) x))
(.f64 2 (/.f64 1 (.f64 x x)))
(*.f64 (/.f64 2 x) (/.f64 1 x))
(.f64 (/.f64 2 (.f64 x x)) 1)
(.f64 1 (/.f64 2 (.f64 x x)))
(.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) (pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) 2))
(.f64 (pow.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) 2) (cbrt.f64 (/.f64 2 (*.f64 x x))))
(.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (.f64 (cbrt.f64 (/.f64 2 x)) (/.f64 1 x)))
(*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 (/.f64 2 x)) (.f64 (sqrt.f64 (/.f64 2 x)) (/.f64 1 x)))
(*.f64 (/.f64 -2 x) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (/.f64 2 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) 1) (/.f64 (cbrt.f64 (/.f64 2 x)) x))
(*.f64 (/.f64 (sqrt.f64 (/.f64 2 x)) 1) (/.f64 (sqrt.f64 (/.f64 2 x)) x))
(*.f64 (/.f64 2 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 1 x) (cbrt.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 2 x) (cbrt.f64 x)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 2 (.f64 x x))))
(*.f64 (/.f64 (sqrt.f64 (/.f64 2 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (/.f64 2 x)) (cbrt.f64 x)))
(*.f64 (/.f64 2 (sqrt.f64 x)) (/.f64 (/.f64 1 x) (sqrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 2 x) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 2 x)) (sqrt.f64 x)))
(pow.f64 (/.f64 2 (*.f64 x x)) 1)
(pow.f64 (pow.f64 (/.f64 2 (*.f64 x x)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) 3)
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(pow.f64 (.f64 x (.f64 x 1/2)) -1)
(neg.f64 (/.f64 (/.f64 2 x) (neg.f64 x)))
(sqrt.f64 (pow.f64 (/.f64 2 (*.f64 x x)) 2))
(log.f64 (exp.f64 (/.f64 2 (*.f64 x x))))
(cbrt.f64 (pow.f64 (/.f64 2 (*.f64 x x)) 3))
(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 x x))))
(log1p.f64 (expm1.f64 (/.f64 2 (*.f64 x x))))
(exp.f64 (log.f64 (/.f64 2 (*.f64 x x))))

Outputs
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
(/.f64 2 (*.f64 x x))
(.f64 2 (.f64 (/.f64 1 x) (/.f64 1 x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (/.f64 (/.f64 1 x) x))
(/.f64 2 (*.f64 x x))
(.f64 2 (/.f64 1 (.f64 x x)))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 2 x) (/.f64 1 x))
(/.f64 2 (*.f64 x x))
(.f64 (/.f64 2 (.f64 x x)) 1)
(/.f64 2 (*.f64 x x))
(.f64 1 (/.f64 2 (.f64 x x)))
(/.f64 2 (*.f64 x x))
(.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) (pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) 2))
(/.f64 2 (*.f64 x x))
(.f64 (pow.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) 2) (cbrt.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (.f64 (cbrt.f64 (/.f64 2 x)) (/.f64 1 x)))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))
(/.f64 2 (*.f64 x x))
(.f64 (sqrt.f64 (/.f64 2 x)) (.f64 (sqrt.f64 (/.f64 2 x)) (/.f64 1 x)))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 -2 x) (/.f64 1 (neg.f64 x)))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 1 x) (/.f64 2 x))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) 1) (/.f64 (cbrt.f64 (/.f64 2 x)) x))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 (sqrt.f64 (/.f64 2 x)) 1) (/.f64 (sqrt.f64 (/.f64 2 x)) x))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 2 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 1 x) (cbrt.f64 x)))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 2 x) (cbrt.f64 x)))
(/.f64 2 (*.f64 x x))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 2 (.f64 x x))))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (cbrt.f64 (/.f64 2 (.f64 x x)))) (pow.f64 (cbrt.f64 x) 2))
(.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) (/.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (/.f64 (sqrt.f64 (/.f64 2 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (/.f64 2 x)) (cbrt.f64 x)))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 2 (sqrt.f64 x)) (/.f64 (/.f64 1 x) (sqrt.f64 x)))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 2 x) (sqrt.f64 x)))
(/.f64 2 (*.f64 x x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 2 x)) (sqrt.f64 x)))
(/.f64 2 (*.f64 x x))
(pow.f64 (/.f64 2 (*.f64 x x)) 1)
(/.f64 2 (*.f64 x x))
(pow.f64 (pow.f64 (/.f64 2 (*.f64 x x)) 3) 1/3)
(/.f64 2 (*.f64 x x))
(pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) 3)
(/.f64 2 (*.f64 x x))
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(/.f64 2 (*.f64 x x))
(pow.f64 (.f64 x (.f64 x 1/2)) -1)
(/.f64 2 (*.f64 x x))
(neg.f64 (/.f64 (/.f64 2 x) (neg.f64 x)))
(/.f64 2 (*.f64 x x))
(sqrt.f64 (pow.f64 (/.f64 2 (*.f64 x x)) 2))
(/.f64 2 (*.f64 x x))
(log.f64 (exp.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(cbrt.f64 (pow.f64 (/.f64 2 (*.f64 x x)) 3))
(/.f64 2 (*.f64 x x))
(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(log1p.f64 (expm1.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(exp.f64 (log.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 1 (cosh.f64 x)))
	0.0b	(/.f64 1 (cosh.f64 x))
✓	0.1b	(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)

Compiler

Compiled 23 to 15 computations (34.8% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
0.0ms	x	@	-inf	(+.f64 1 (/.f64 1 (cosh.f64 x)))
0.0ms	x	@	0	(+.f64 1 (/.f64 1 (cosh.f64 x)))
0.0ms	x	@	inf	(+.f64 1 (/.f64 1 (cosh.f64 x)))
0.0ms	x	@	inf	(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)

rewrite48.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

802×	`pow1_binary64`
754×	`add-log-exp_binary64`
752×	`log1p-expm1-u_binary64`
752×	`expm1-log1p-u_binary64`
740×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	163	15
2	2339	15

Stop Event

1×	node limit

Counts

2 → 81

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(+.f64 1 (/.f64 1 (cosh.f64 x)))

Outputs

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

simplify49.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

472×	`distribute-rgt-in_binary64`
427×	`cancel-sign-sub-inv_binary64`
419×	`distribute-lft-in_binary64`
372×	`fma-neg_binary64`
350×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	1872
1	466	1379
2	1686	1370

Stop Event

1×	node limit

Counts

105 → 124

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(+.f64 1 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) 1))
(+.f64 (/.f64 1 (cosh.f64 x)) 0)
(+.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1)
(+.f64 -1 (+.f64 1 (/.f64 1 (cosh.f64 x))))
(+.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) 1)
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))
(*.f64 -1 (/.f64 1 (neg.f64 (cosh.f64 x))))
(*.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 (/.f64 1 (cosh.f64 x)) 2))))
(*.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1) (/.f64 1 (+.f64 (/.f64 1 (cosh.f64 x)) 2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1))
(*.f64 (+.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) 1) (-.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) 1))
(.f64 (/.f64 1 (.f64 2 (cosh.f64 x))) 2)
(/.f64 1 (cosh.f64 x))
(/.f64 1 (neg.f64 (neg.f64 (cosh.f64 x))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 (/.f64 1 (cosh.f64 x)) 2)) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1)))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 2) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1)))
(/.f64 (pow.f64 (cosh.f64 x) -1/2) (sqrt.f64 (cosh.f64 x)))
(/.f64 -1 (neg.f64 (cosh.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 (/.f64 1 (cosh.f64 x)) 2)))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1) (+.f64 (/.f64 1 (cosh.f64 x)) 2))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1) (-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 (/.f64 1 (cosh.f64 x)) 2))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1)) (neg.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 2)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) (+.f64 (/.f64 1 (cosh.f64 x)) -1)) (+.f64 (/.f64 1 (cosh.f64 x)) -1))))
(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) (+.f64 (/.f64 1 (cosh.f64 x)) -1))) (-.f64 1 (+.f64 (/.f64 1 (cosh.f64 x)) -1)))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1)
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
(pow.f64 (pow.f64 (cosh.f64 x) -3) 1/3)
(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(cbrt.f64 (pow.f64 (cosh.f64 x) -3))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(fma.f64 1 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 2) (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) -1)
(fma.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) -1)
(-.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 2) 1)
(-.f64 (/.f64 1 (-.f64 1 (/.f64 1 (cosh.f64 x)))) (/.f64 (pow.f64 (cosh.f64 x) -2) (-.f64 1 (/.f64 1 (cosh.f64 x)))))
(*.f64 1 (+.f64 1 (/.f64 1 (cosh.f64 x))))
(*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(*.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 2) (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))))
(.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 2) (.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 1))
(*.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)))
(.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) (.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) 1))
(*.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (/.f64 1 (-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cosh.f64 x)))))
(*.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (-.f64 1 (/.f64 1 (cosh.f64 x)))))
(/.f64 1 (/.f64 (-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cosh.f64 x))) (+.f64 1 (pow.f64 (cosh.f64 x) -3))))
(/.f64 1 (/.f64 (-.f64 1 (/.f64 1 (cosh.f64 x))) (-.f64 1 (pow.f64 (cosh.f64 x) -2))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cosh.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 (pow.f64 (cosh.f64 x) -2) (-.f64 1 (/.f64 1 (cosh.f64 x)))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (-.f64 1 (/.f64 1 (cosh.f64 x))))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3))) (neg.f64 (-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cosh.f64 x)))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2))) (neg.f64 (-.f64 1 (/.f64 1 (cosh.f64 x)))))
(/.f64 (-.f64 (pow.f64 (cosh.f64 x) -2) 1) (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) 1) (-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cosh.f64 x))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) 1) (-.f64 1 (/.f64 1 (cosh.f64 x))))
(pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 3)
(pow.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) 2)
(pow.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) 1/3)
(sqrt.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2))
(log.f64 (exp.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))))
(cbrt.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3))
(expm1.f64 (log.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 2)))
(log1p.f64 (expm1.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))))
(exp.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(fma.f64 1 (/.f64 1 (cosh.f64 x)) 1)
(fma.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))) 1)
(fma.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2) 1)

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (.f64 5/24 (pow.f64 x 4)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 2)
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 2 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(+.f64 1 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(+.f64 1 (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(+.f64 1 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) 1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(+.f64 (/.f64 1 (cosh.f64 x)) 0)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(+.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(+.f64 -1 (+.f64 1 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(+.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(/.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (cosh.f64 x)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(/.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (cosh.f64 x)))
(*.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 -1 (/.f64 1 (neg.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 (/.f64 1 (cosh.f64 x)) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 1 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(*.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1) (/.f64 1 (+.f64 (/.f64 1 (cosh.f64 x)) 2)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2)) (/.f64 1 (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2)) (+.f64 2 (/.f64 1 (cosh.f64 x))))
(/.f64 (/.f64 (+.f64 2 (/.f64 1 (cosh.f64 x))) (cosh.f64 x)) (+.f64 2 (/.f64 1 (cosh.f64 x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1))
(pow.f64 (sqrt.f64 (cosh.f64 x)) -2)
(*.f64 (+.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) 1) (-.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) 1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(.f64 (/.f64 1 (.f64 2 (cosh.f64 x))) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (neg.f64 (neg.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 (/.f64 1 (cosh.f64 x)) 2)) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 1 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 2) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2)) (/.f64 1 (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2)) (+.f64 2 (/.f64 1 (cosh.f64 x))))
(/.f64 (/.f64 (+.f64 2 (/.f64 1 (cosh.f64 x))) (cosh.f64 x)) (+.f64 2 (/.f64 1 (cosh.f64 x))))
(/.f64 (pow.f64 (cosh.f64 x) -1/2) (sqrt.f64 (cosh.f64 x)))
(/.f64 -1 (neg.f64 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 (/.f64 1 (cosh.f64 x)) 2)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 1 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 1 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1) (+.f64 (/.f64 1 (cosh.f64 x)) 2))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2)) (/.f64 1 (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2)) (+.f64 2 (/.f64 1 (cosh.f64 x))))
(/.f64 (/.f64 (+.f64 2 (/.f64 1 (cosh.f64 x))) (cosh.f64 x)) (+.f64 2 (/.f64 1 (cosh.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1) (-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2)) (/.f64 1 (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2)) (+.f64 2 (/.f64 1 (cosh.f64 x))))
(/.f64 (/.f64 (+.f64 2 (/.f64 1 (cosh.f64 x))) (cosh.f64 x)) (+.f64 2 (/.f64 1 (cosh.f64 x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 (/.f64 1 (cosh.f64 x)) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3)) (+.f64 1 (*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) (+.f64 2 (/.f64 1 (cosh.f64 x))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1)) (neg.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 2)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2)) (/.f64 1 (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2)) (+.f64 2 (/.f64 1 (cosh.f64 x))))
(/.f64 (/.f64 (+.f64 2 (/.f64 1 (cosh.f64 x))) (cosh.f64 x)) (+.f64 2 (/.f64 1 (cosh.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) (+.f64 (/.f64 1 (cosh.f64 x)) -1)) (+.f64 (/.f64 1 (cosh.f64 x)) -1))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) 3)) (+.f64 1 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) (-.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) 1))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) 3)) (+.f64 1 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) (+.f64 (/.f64 1 (cosh.f64 x)) -2))))
(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) (+.f64 (/.f64 1 (cosh.f64 x)) -1))) (-.f64 1 (+.f64 (/.f64 1 (cosh.f64 x)) -1)))
(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 1 (cosh.f64 x)) -1) (+.f64 (/.f64 1 (cosh.f64 x)) -1))) (-.f64 2 (/.f64 1 (cosh.f64 x))))
(/.f64 (-.f64 (/.f64 1 (cosh.f64 x)) (+.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 -1 (cosh.f64 x)))) (+.f64 2 (/.f64 -1 (cosh.f64 x))))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (cosh.f64 x) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (cosh.f64 x) -3) 1/3)
(cbrt.f64 (pow.f64 (cosh.f64 x) -3))
(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (pow.f64 (cosh.f64 x) -3))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(fma.f64 1 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 2) (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(fma.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 2) 1)
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(-.f64 (/.f64 1 (-.f64 1 (/.f64 1 (cosh.f64 x)))) (/.f64 (pow.f64 (cosh.f64 x) -2) (-.f64 1 (/.f64 1 (cosh.f64 x)))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (-.f64 1 (/.f64 1 (cosh.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (+.f64 1 (/.f64 -1 (cosh.f64 x))))
(/.f64 (+.f64 -1 (pow.f64 (cosh.f64 x) -2)) (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(*.f64 1 (+.f64 1 (/.f64 1 (cosh.f64 x))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 2))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 2) (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 2) (.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 1))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) (.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) 1))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (/.f64 1 (-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (-.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (+.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 -1 (cosh.f64 x)))))
(*.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (-.f64 1 (/.f64 1 (cosh.f64 x)))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (-.f64 1 (/.f64 1 (cosh.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (+.f64 1 (/.f64 -1 (cosh.f64 x))))
(/.f64 (+.f64 -1 (pow.f64 (cosh.f64 x) -2)) (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(/.f64 1 (/.f64 (-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cosh.f64 x))) (+.f64 1 (pow.f64 (cosh.f64 x) -3))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (-.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (+.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 -1 (cosh.f64 x)))))
(/.f64 1 (/.f64 (-.f64 1 (/.f64 1 (cosh.f64 x))) (-.f64 1 (pow.f64 (cosh.f64 x) -2))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (-.f64 1 (/.f64 1 (cosh.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (+.f64 1 (/.f64 -1 (cosh.f64 x))))
(/.f64 (+.f64 -1 (pow.f64 (cosh.f64 x) -2)) (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cosh.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (-.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (+.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 -1 (cosh.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 (pow.f64 (cosh.f64 x) -2) (-.f64 1 (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (-.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (+.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 -1 (cosh.f64 x)))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (-.f64 1 (/.f64 1 (cosh.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (+.f64 1 (/.f64 -1 (cosh.f64 x))))
(/.f64 (+.f64 -1 (pow.f64 (cosh.f64 x) -2)) (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3))) (neg.f64 (-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (-.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (+.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 -1 (cosh.f64 x)))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2))) (neg.f64 (-.f64 1 (/.f64 1 (cosh.f64 x)))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (-.f64 1 (/.f64 1 (cosh.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (+.f64 1 (/.f64 -1 (cosh.f64 x))))
(/.f64 (+.f64 -1 (pow.f64 (cosh.f64 x) -2)) (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(/.f64 (-.f64 (pow.f64 (cosh.f64 x) -2) 1) (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (-.f64 1 (/.f64 1 (cosh.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (+.f64 1 (/.f64 -1 (cosh.f64 x))))
(/.f64 (+.f64 -1 (pow.f64 (cosh.f64 x) -2)) (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) 1) (-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cosh.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (-.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 1 (cosh.f64 x)))))
(/.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -3)) (+.f64 1 (+.f64 (pow.f64 (cosh.f64 x) -2) (/.f64 -1 (cosh.f64 x)))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) 1) (-.f64 1 (/.f64 1 (cosh.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (-.f64 1 (/.f64 1 (cosh.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cosh.f64 x) -2)) (+.f64 1 (/.f64 -1 (cosh.f64 x))))
(/.f64 (+.f64 -1 (pow.f64 (cosh.f64 x) -2)) (+.f64 (/.f64 1 (cosh.f64 x)) -1))
(pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))) 3)
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(pow.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) 2)
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3) 1/3)
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(sqrt.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(log.f64 (exp.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(cbrt.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 3))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(expm1.f64 (log.f64 (+.f64 (/.f64 1 (cosh.f64 x)) 2)))
(expm1.f64 (log.f64 (+.f64 2 (/.f64 1 (cosh.f64 x)))))
(expm1.f64 (log1p.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))))
(log1p.f64 (expm1.f64 (+.f64 1 (/.f64 1 (cosh.f64 x)))))
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(exp.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(fma.f64 1 (/.f64 1 (cosh.f64 x)) 1)
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))
(fma.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))) 1)
(+.f64 1 (/.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (cosh.f64 x))))
(fma.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2) 1)
(+.f64 1 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 1 (/.f64 1 (cosh.f64 x)))

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (cosh.f64 x) -2)
✓	0.2b	(sqrt.f64 (pow.f64 (cosh.f64 x) -2))

Compiler

Compiled 14 to 8 computations (42.9% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(pow.f64 (cosh.f64 x) -2)
1.0ms	x	@	inf	(pow.f64 (cosh.f64 x) -2)
1.0ms	x	@	-inf	(pow.f64 (cosh.f64 x) -2)
0.0ms	x	@	0	(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
0.0ms	x	@	inf	(sqrt.f64 (pow.f64 (cosh.f64 x) -2))

rewrite39.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`pow1_binary64`
521×	`add-log-exp_binary64`
519×	`log1p-expm1-u_binary64`
519×	`expm1-log1p-u_binary64`
507×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	128	12
2	1443	12

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

Inputs
(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
(pow.f64 (cosh.f64 x) -2)

Outputs

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

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

simplify49.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

519×	`associate-*l/_binary64`
478×	`times-frac_binary64`
412×	`unswap-sqr_binary64`
400×	`fma-def_binary64`
284×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	946
1	278	939
2	847	747
3	3360	511

Stop Event

1×	node limit

Counts

66 → 76

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (.f64 -1 (pow.f64 x 2))))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 -1 (pow.f64 x 2)) (*.f64 -17/45 (pow.f64 x 6)))))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(*.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (/.f64 1 (cosh.f64 x))))
(*.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -4))) (sqrt.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1))
(*.f64 (pow.f64 1 1/2) (/.f64 1 (cosh.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -4)) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) 1/2))
(/.f64 1 (cosh.f64 x))
(pow.f64 (cosh.f64 x) -1)
(pow.f64 (pow.f64 (cosh.f64 x) -2) 1/2)
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(pow.f64 (pow.f64 (cosh.f64 x) -3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) 3)
(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
(fabs.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(cbrt.f64 (pow.f64 (cosh.f64 x) -3))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(exp.f64 (*.f64 (log.f64 (cosh.f64 x)) -1))
(-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) 1)
(*.f64 (pow.f64 (cosh.f64 x) -2) 1)
(*.f64 (/.f64 1 (cosh.f64 x)) (/.f64 1 (cosh.f64 x)))
(*.f64 1 (pow.f64 (cosh.f64 x) -2))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (pow.f64 (cosh.f64 x) -4)))
(.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (/.f64 1 (cosh.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -4)) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(.f64 (pow.f64 (cosh.f64 x) -1/2) (.f64 (pow.f64 (cosh.f64 x) -1/2) (/.f64 1 (cosh.f64 x))))
(.f64 (.f64 (/.f64 1 (cosh.f64 x)) (pow.f64 (cosh.f64 x) -1/2)) (pow.f64 (cosh.f64 x) -1/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -2) (pow.f64 (cbrt.f64 (cosh.f64 x)) -2))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -2) (pow.f64 (sqrt.f64 (cosh.f64 x)) -2))
(.f64 (.f64 (/.f64 1 (cosh.f64 x)) (cbrt.f64 (pow.f64 (cosh.f64 x) -2))) (cbrt.f64 (/.f64 1 (cosh.f64 x))))
(sqrt.f64 (pow.f64 (cosh.f64 x) -4))
(log.f64 (exp.f64 (pow.f64 (cosh.f64 x) -2)))
(cbrt.f64 (pow.f64 (pow.f64 (cosh.f64 x) -2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (cosh.f64 x) -2)))
(log1p.f64 (expm1.f64 (pow.f64 (cosh.f64 x) -2)))
(exp.f64 (*.f64 -2 (log.f64 (cosh.f64 x))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (fma.f64 5/24 (pow.f64 x 4) 1)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (neg.f64 (*.f64 x x)))
(-.f64 1 (*.f64 x x))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (.f64 -1 (pow.f64 x 2))))
(fma.f64 2/3 (pow.f64 x 4) (+.f64 1 (neg.f64 (*.f64 x x))))
(-.f64 (fma.f64 (pow.f64 x 4) 2/3 1) (*.f64 x x))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 -1 (pow.f64 x 2)) (*.f64 -17/45 (pow.f64 x 6)))))
(fma.f64 2/3 (pow.f64 x 4) (+.f64 1 (fma.f64 -1 (.f64 x x) (.f64 (pow.f64 x 6) -17/45))))
(+.f64 (-.f64 (fma.f64 (pow.f64 x 4) 2/3 1) (.f64 x x)) (.f64 (pow.f64 x 6) -17/45))
(fma.f64 (pow.f64 x 4) 2/3 (-.f64 (fma.f64 (pow.f64 x 6) -17/45 1) (*.f64 x x)))
(-.f64 (fma.f64 (pow.f64 x 4) 2/3 (fma.f64 (pow.f64 x 6) -17/45 1)) (*.f64 x x))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -4))) (sqrt.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(/.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) -2) (cbrt.f64 (cosh.f64 x)))
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1))
(pow.f64 (sqrt.f64 (cosh.f64 x)) -2)
(*.f64 (pow.f64 1 1/2) (/.f64 1 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -4)) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) 1/2))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -4))) (sqrt.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(pow.f64 (cosh.f64 x) -1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (cosh.f64 x) -2) 1/2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (cosh.f64 x) -3) 1/3)
(cbrt.f64 (pow.f64 (cosh.f64 x) -3))
(pow.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) 3)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(fabs.f64 (/.f64 1 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (pow.f64 (cosh.f64 x) -3))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (*.f64 (log.f64 (cosh.f64 x)) -1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (+.f64 1 (pow.f64 (cosh.f64 x) -2)) 1)
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(*.f64 (pow.f64 (cosh.f64 x) -2) 1)
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(*.f64 (/.f64 1 (cosh.f64 x)) (/.f64 1 (cosh.f64 x)))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(*.f64 1 (pow.f64 (cosh.f64 x) -2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (pow.f64 (cosh.f64 x) -4)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -4)) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (/.f64 1 (cosh.f64 x))))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -4)) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (pow.f64 (cosh.f64 x) -4)))
(.f64 (pow.f64 (cosh.f64 x) -1/2) (.f64 (pow.f64 (cosh.f64 x) -1/2) (/.f64 1 (cosh.f64 x))))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(.f64 (.f64 (/.f64 1 (cosh.f64 x)) (pow.f64 (cosh.f64 x) -1/2)) (pow.f64 (cosh.f64 x) -1/2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -2) (pow.f64 (cbrt.f64 (cosh.f64 x)) -2))
(/.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -2) (pow.f64 (cbrt.f64 (cosh.f64 x)) 2))
(pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) -2) 3)
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -2) (pow.f64 (sqrt.f64 (cosh.f64 x)) -2))
(pow.f64 (sqrt.f64 (cosh.f64 x)) -4)
(.f64 (.f64 (/.f64 1 (cosh.f64 x)) (cbrt.f64 (pow.f64 (cosh.f64 x) -2))) (cbrt.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(sqrt.f64 (pow.f64 (cosh.f64 x) -4))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(log.f64 (exp.f64 (pow.f64 (cosh.f64 x) -2)))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(cbrt.f64 (pow.f64 (pow.f64 (cosh.f64 x) -2) 3))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(expm1.f64 (log1p.f64 (pow.f64 (cosh.f64 x) -2)))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(log1p.f64 (expm1.f64 (pow.f64 (cosh.f64 x) -2)))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)
(exp.f64 (*.f64 -2 (log.f64 (cosh.f64 x))))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 (cosh.f64 x) -2)

eval195.0ms (6.6%)

Compiler: Compiled 4841 to 3409 computations (29.6% saved)

prune144.0ms (4.8%)

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	417	2	419
Fresh	0	1	1
Picked	0	1	1
Done	0	7	7
Total	417	11	428

Error

Counts

428 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	48.0b	(/.f64 (/.f64 2 x) x)
✓	16.3b	(/.f64 2 (+.f64 2 (*.f64 x x)))
✓	48.0b	(/.f64 2 (*.f64 x x))
✓	0.0b	(/.f64 1 (cosh.f64 x))
▶	32.9b	(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
✓	0.3b	(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
✓	31.0b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
▶	48.0b	(*.f64 (/.f64 2 x) (/.f64 1 x))
✓	0.3b	(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
	30.5b	1

Compiler

Compiled 75 to 59 computations (21.3% saved)

localize17.0ms (0.6%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 2 x) (/.f64 1 x))

Compiler

Compiled 17 to 12 computations (29.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite38.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`pow1_binary64`
597×	`add-log-exp_binary64`
597×	`log1p-expm1-u_binary64`
597×	`expm1-log1p-u_binary64`
586×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	149	7
2	1771	7

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

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

Outputs

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

simplify40.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

763×	`log-prod_binary64`
422×	`associate-l_binary64`
412×	`associate-r_binary64`
303×	`fma-def_binary64`
289×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	99	350
1	232	350
2	715	350
3	4533	350

Stop Event

1×	node limit

Counts

50 → 40

Calls

Call 1

Inputs
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x -2))) 1)
(/.f64 2 (*.f64 x x))
(/.f64 2 (*.f64 (neg.f64 x) (neg.f64 x)))
(/.f64 2 (/.f64 x (/.f64 1 x)))
(/.f64 (/.f64 2 x) x)
(/.f64 1 (.f64 (.f64 x 1/2) x))
(/.f64 1 (.f64 x (.f64 x 1/2)))
(/.f64 1 (/.f64 (*.f64 x x) 2))
(/.f64 1 (/.f64 x (/.f64 2 x)))
(/.f64 (/.f64 1 x) (*.f64 x 1/2))
(/.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (/.f64 x (cbrt.f64 (/.f64 2 x))))
(/.f64 (sqrt.f64 (/.f64 2 x)) (/.f64 x (sqrt.f64 (/.f64 2 x))))
(/.f64 -1 (.f64 (neg.f64 x) (.f64 x 1/2)))
(/.f64 -1 (.f64 (.f64 x 1/2) (neg.f64 x)))
(/.f64 -2 (neg.f64 (*.f64 x x)))
(/.f64 -2 (*.f64 (neg.f64 x) x))
(/.f64 -2 (*.f64 x (neg.f64 x)))
(/.f64 (neg.f64 (/.f64 2 x)) (neg.f64 x))
(/.f64 (/.f64 (/.f64 2 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (/.f64 (/.f64 2 x) 1) x)
(/.f64 (/.f64 (/.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(/.f64 (*.f64 -2 (/.f64 1 x)) (neg.f64 x))
(/.f64 (*.f64 -1 (/.f64 2 x)) (neg.f64 x))
(/.f64 (*.f64 (/.f64 2 x) -1) (neg.f64 x))
(/.f64 (*.f64 (/.f64 1 x) -2) (neg.f64 x))
(pow.f64 (*.f64 2 (pow.f64 x -2)) 1)
(pow.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 3)
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(sqrt.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 2))
(log.f64 (exp.f64 (*.f64 2 (pow.f64 x -2))))
(cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 3))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 2 x) 3) (pow.f64 x 3)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 2 x) 3) (/.f64 (pow.f64 x -2) x)))
(cbrt.f64 (*.f64 (/.f64 (pow.f64 x -2) x) (pow.f64 (/.f64 2 x) 3)))
(expm1.f64 (log1p.f64 (*.f64 2 (pow.f64 x -2))))
(log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x -2))))
(exp.f64 (log.f64 (*.f64 2 (pow.f64 x -2))))

Outputs
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x -2))) 1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (*.f64 (neg.f64 x) (neg.f64 x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (/.f64 x (/.f64 1 x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (/.f64 2 x) x)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 1 (.f64 (.f64 x 1/2) x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 1 (.f64 x (.f64 x 1/2)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 1 (/.f64 (*.f64 x x) 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 1 (/.f64 x (/.f64 2 x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (/.f64 1 x) (*.f64 x 1/2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (/.f64 x (cbrt.f64 (/.f64 2 x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (sqrt.f64 (/.f64 2 x)) (/.f64 x (sqrt.f64 (/.f64 2 x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 -1 (.f64 (neg.f64 x) (.f64 x 1/2)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 -1 (.f64 (.f64 x 1/2) (neg.f64 x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 -2 (neg.f64 (*.f64 x x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 -2 (*.f64 (neg.f64 x) x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 -2 (*.f64 x (neg.f64 x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (neg.f64 (/.f64 2 x)) (neg.f64 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (/.f64 (/.f64 2 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (/.f64 (/.f64 2 x) 1) x)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (/.f64 (/.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (*.f64 -2 (/.f64 1 x)) (neg.f64 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (*.f64 -1 (/.f64 2 x)) (neg.f64 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (*.f64 (/.f64 2 x) -1) (neg.f64 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (*.f64 (/.f64 1 x) -2) (neg.f64 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (*.f64 2 (pow.f64 x -2)) 1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 3) 1/3)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 3)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(sqrt.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(log.f64 (exp.f64 (*.f64 2 (pow.f64 x -2))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x -2)) 3))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 2 x) 3) (pow.f64 x 3)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 2 x) 3) (/.f64 (pow.f64 x -2) x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(cbrt.f64 (*.f64 (/.f64 (pow.f64 x -2) x) (pow.f64 (/.f64 2 x) 3)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(expm1.f64 (log1p.f64 (*.f64 2 (pow.f64 x -2))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x -2))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(exp.f64 (log.f64 (*.f64 2 (pow.f64 x -2))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 2 (*.f64 x x))
✓	0.9b	(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)

Compiler

Compiled 28 to 16 computations (42.9% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite44.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

863×	`pow1_binary64`
812×	`add-log-exp_binary64`
811×	`log1p-expm1-u_binary64`
811×	`expm1-log1p-u_binary64`
798×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	184	7
2	2532	7

Stop Event

1×	node limit

Counts

1 → 54

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 2 (pow.f64 x -2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 2 (*.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2 (pow.f64 x -2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 2 (pow.f64 x -2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2 (pow.f64 x -2) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) (cbrt.f64 (/.f64 4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 4 (pow.f64 x 4))) (cbrt.f64 (/.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (*.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1) (/.f64 1 (+.f64 (/.f64 2 (*.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) 1) (-.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (*.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (*.f64 x x)) 2)) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 2 (*.f64 x x)) 2) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 (*.f64 x x) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (neg.f64 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -2 (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (*.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (-.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (*.f64 (*.f64 x x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1) (+.f64 (/.f64 2 (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1) (-.f64 (fma.f64 2 (pow.f64 x -2) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 2 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (*.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1)) (neg.f64 (+.f64 (/.f64 2 (*.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 2 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 2 (pow.f64 x -2) -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 2 (pow.f64 x -2) -1) (fma.f64 2 (pow.f64 x -2) -1)) (fma.f64 2 (pow.f64 x -2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) -1) (fma.f64 2 (pow.f64 x -2) -1))) (-.f64 1 (fma.f64 2 (pow.f64 x -2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 2 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 2 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 8 (pow.f64 (pow.f64 x -2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 4 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 8 (pow.f64 (pow.f64 x -2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 2 (pow.f64 x -2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1)) 2) (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) -1)))))

simplify52.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

536×	`div-sub_binary64`
388×	`unswap-sqr_binary64`
371×	`log-prod_binary64`
266×	`fma-def_binary64`
264×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	752
1	323	730
2	904	716
3	4514	716

Stop Event

1×	node limit

Counts

66 → 68

Calls

Call 1

Inputs
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(+.f64 1 (fma.f64 2 (pow.f64 x -2) -1))
(+.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) -1) 1))
(+.f64 (/.f64 2 (*.f64 x x)) 0)
(+.f64 (fma.f64 2 (pow.f64 x -2) 1) -1)
(+.f64 -1 (fma.f64 2 (pow.f64 x -2) 1))
(+.f64 (fma.f64 2 (pow.f64 x -2) -1) 1)
(.f64 1 (/.f64 2 (.f64 x x)))
(*.f64 2 (pow.f64 x -2))
(.f64 (/.f64 2 (.f64 x x)) 1)
(.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) (cbrt.f64 (/.f64 4 (pow.f64 x 4))))
(.f64 (cbrt.f64 (/.f64 4 (pow.f64 x 4))) (cbrt.f64 (/.f64 2 (.f64 x x))))
(*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))
(.f64 -2 (/.f64 1 (.f64 x (neg.f64 x))))
(.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (.f64 x x)) 2))))
(*.f64 (pow.f64 x -2) 2)
(.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1) (/.f64 1 (+.f64 (/.f64 2 (.f64 x x)) 2)))
(*.f64 (/.f64 2 x) (/.f64 1 x))
(*.f64 (+.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) 1) (-.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) 1))
(/.f64 1 (.f64 (.f64 x x) 1/2))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (*.f64 x x)) 2)) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1)))
(/.f64 1 (/.f64 (+.f64 (/.f64 2 (*.f64 x x)) 2) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1)))
(/.f64 1 (/.f64 (.f64 (.f64 x x) 1/2) 1))
(/.f64 2 (*.f64 x x))
(/.f64 2 (neg.f64 (*.f64 x (neg.f64 x))))
(/.f64 -2 (*.f64 x (neg.f64 x)))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (*.f64 x x)) 2)))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (-.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) 1) -1))))
(/.f64 -1 (neg.f64 (.f64 (.f64 x x) 1/2)))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1) (+.f64 (/.f64 2 (*.f64 x x)) 2))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1) (-.f64 (fma.f64 2 (pow.f64 x -2) 1) -1))
(/.f64 (/.f64 2 x) x)
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (*.f64 x x)) 2))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1)) (neg.f64 (+.f64 (/.f64 2 (*.f64 x x)) 2)))
(/.f64 (neg.f64 (/.f64 2 x)) (neg.f64 x))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 2 (pow.f64 x -2) -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 2 (pow.f64 x -2) -1) (fma.f64 2 (pow.f64 x -2) -1)) (fma.f64 2 (pow.f64 x -2) -1))))
(/.f64 (-.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) -1) (fma.f64 2 (pow.f64 x -2) -1))) (-.f64 1 (fma.f64 2 (pow.f64 x -2) -1)))
(/.f64 (/.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(/.f64 (/.f64 (/.f64 2 x) 1) x)
(/.f64 (/.f64 (/.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(/.f64 (/.f64 (/.f64 2 x) (sqrt.f64 x)) (sqrt.f64 x))
(pow.f64 (/.f64 2 (*.f64 x x)) 1)
(pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) 3)
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(pow.f64 (*.f64 8 (pow.f64 (pow.f64 x -2) 3)) 1/3)
(pow.f64 (.f64 (.f64 x x) 1/2) -1)
(sqrt.f64 (/.f64 4 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))
(cbrt.f64 (*.f64 8 (pow.f64 (pow.f64 x -2) 3)))
(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 x x))))
(log1p.f64 (expm1.f64 (/.f64 2 (*.f64 x x))))
(exp.f64 (log.f64 (/.f64 2 (*.f64 x x))))
(fma.f64 1 (fma.f64 2 (pow.f64 x -2) 1) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1)) 2) (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1)) -1)
(fma.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) -1)

Outputs
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(+.f64 1 (fma.f64 2 (pow.f64 x -2) -1))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(+.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) -1) 1))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(+.f64 (/.f64 2 (*.f64 x x)) 0)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(+.f64 (fma.f64 2 (pow.f64 x -2) 1) -1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(+.f64 -1 (fma.f64 2 (pow.f64 x -2) 1))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(+.f64 (fma.f64 2 (pow.f64 x -2) -1) 1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(.f64 1 (/.f64 2 (.f64 x x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (*.f64 x x))
(.f64 (/.f64 2 (.f64 x x)) 1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) (cbrt.f64 (/.f64 4 (pow.f64 x 4))))
(.f64 (cbrt.f64 (.f64 2 (pow.f64 x -2))) (cbrt.f64 (/.f64 4 (pow.f64 x 4))))
(.f64 (cbrt.f64 (/.f64 4 (pow.f64 x 4))) (cbrt.f64 (/.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) (cbrt.f64 (/.f64 4 (pow.f64 x 4))))
(.f64 (cbrt.f64 (.f64 2 (pow.f64 x -2))) (cbrt.f64 (/.f64 4 (pow.f64 x 4))))
(*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(.f64 -2 (/.f64 1 (.f64 x (neg.f64 x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (.f64 x x)) 2))))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 2 (/.f64 2 (.f64 x x))))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (+.f64 (*.f64 2 (pow.f64 x -2)) (+.f64 2 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (+.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) 1) (fma.f64 2 (pow.f64 x -2) 2))))
(*.f64 (pow.f64 x -2) 2)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1) (/.f64 1 (+.f64 (/.f64 2 (.f64 x x)) 2)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(*.f64 (/.f64 2 x) (/.f64 1 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(*.f64 (+.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) 1) (-.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) 1))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 1 (.f64 (.f64 x x) 1/2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (*.f64 x x)) 2)) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1)))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 2 (/.f64 2 (.f64 x x))))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (+.f64 (*.f64 2 (pow.f64 x -2)) (+.f64 2 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (+.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) 1) (fma.f64 2 (pow.f64 x -2) 2))))
(/.f64 1 (/.f64 (+.f64 (/.f64 2 (*.f64 x x)) 2) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 1 (/.f64 (.f64 (.f64 x x) 1/2) 1))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 2 (neg.f64 (*.f64 x (neg.f64 x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 -2 (*.f64 x (neg.f64 x)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (*.f64 x x)) 2)))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 2 (/.f64 2 (.f64 x x))))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (+.f64 (*.f64 2 (pow.f64 x -2)) (+.f64 2 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (+.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) 1) (fma.f64 2 (pow.f64 x -2) 2))))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (-.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) 1) -1))))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 2 (/.f64 2 (.f64 x x))))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (+.f64 (*.f64 2 (pow.f64 x -2)) (+.f64 2 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (+.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) 1) (fma.f64 2 (pow.f64 x -2) 2))))
(/.f64 -1 (neg.f64 (.f64 (.f64 x x) 1/2)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1) (+.f64 (/.f64 2 (*.f64 x x)) 2))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1) (-.f64 (fma.f64 2 (pow.f64 x -2) 1) -1))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (/.f64 2 x) x)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 (/.f64 2 (*.f64 x x)) 2))))
(.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) (+.f64 2 (/.f64 2 (.f64 x x))))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (+.f64 (*.f64 2 (pow.f64 x -2)) (+.f64 2 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 3)) (+.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) 1) (fma.f64 2 (pow.f64 x -2) 2))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1) 2) -1)) (neg.f64 (+.f64 (/.f64 2 (*.f64 x x)) 2)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (neg.f64 (/.f64 2 x)) (neg.f64 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 2 (pow.f64 x -2) -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 2 (pow.f64 x -2) -1) (fma.f64 2 (pow.f64 x -2) -1)) (fma.f64 2 (pow.f64 x -2) -1))))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 2 (pow.f64 x -2) -1) 3)) (+.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) -1) (-.f64 (fma.f64 2 (pow.f64 x -2) -1) 1))))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 2 (pow.f64 x -2) -1) 3)) (fma.f64 (fma.f64 2 (pow.f64 x -2) -1) (+.f64 (*.f64 2 (pow.f64 x -2)) -2) 1))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 2 (pow.f64 x -2) -1) 3)) (fma.f64 (fma.f64 2 (pow.f64 x -2) -1) (+.f64 (/.f64 2 (*.f64 x x)) -2) 1))
(/.f64 (-.f64 1 (*.f64 (fma.f64 2 (pow.f64 x -2) -1) (fma.f64 2 (pow.f64 x -2) -1))) (-.f64 1 (fma.f64 2 (pow.f64 x -2) -1)))
(/.f64 (-.f64 1 (.f64 (fma.f64 2 (pow.f64 x -2) -1) (fma.f64 2 (pow.f64 x -2) -1))) (-.f64 2 (.f64 2 (pow.f64 x -2))))
(/.f64 (neg.f64 (.f64 (/.f64 2 (.f64 x x)) (+.f64 (/.f64 2 (.f64 x x)) -2))) (+.f64 2 (/.f64 -2 (.f64 x x))))
(/.f64 (/.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(/.f64 2 (*.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4))))
(/.f64 (/.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (pow.f64 x 4)))
(/.f64 2 (*.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2)))
(/.f64 (/.f64 (/.f64 2 x) 1) x)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (/.f64 (/.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(/.f64 (/.f64 (/.f64 2 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (/.f64 2 (*.f64 x x)) 1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) 3)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(pow.f64 (*.f64 8 (pow.f64 (pow.f64 x -2) 3)) 1/3)
(cbrt.f64 (*.f64 8 (pow.f64 (pow.f64 x -2) 3)))
(cbrt.f64 (*.f64 8 (pow.f64 (/.f64 1 x) 6)))
(pow.f64 (.f64 (.f64 x x) 1/2) -1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(sqrt.f64 (/.f64 4 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x -2)))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(cbrt.f64 (*.f64 8 (pow.f64 (pow.f64 x -2) 3)))
(cbrt.f64 (*.f64 8 (pow.f64 (/.f64 1 x) 6)))
(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(log1p.f64 (expm1.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(exp.f64 (log.f64 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(fma.f64 1 (fma.f64 2 (pow.f64 x -2) 1) -1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1)) 2) (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1)) -1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))
(fma.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) (hypot.f64 1 (/.f64 (sqrt.f64 2) x)) -1)
(/.f64 2 (*.f64 x x))
(*.f64 2 (pow.f64 x -2))

eval35.0ms (1.2%)

Compiler: Compiled 1501 to 1156 computations (23% saved)

prune19.0ms (0.6%)

Pruning

11 alts after pruning (1 fresh and 10 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	9	9
Total	132	11	143

Error

Counts

143 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	48.0b	(/.f64 (/.f64 2 x) x)
✓	16.3b	(/.f64 2 (+.f64 2 (*.f64 x x)))
✓	48.0b	(/.f64 2 (*.f64 x x))
✓	0.0b	(/.f64 1 (cosh.f64 x))
✓	32.9b	(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
✓	0.3b	(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
✓	31.0b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	48.0b	(*.f64 (/.f64 2 x) (/.f64 1 x))
✓	0.3b	(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
	30.5b	1

Compiler

Compiled 75 to 59 computations (21.3% saved)

regimes36.0ms (1.2%)

Counts

14 → 1

Calls

Call 1

Inputs
1
(/.f64 2 (*.f64 x x))
(/.f64 (/.f64 2 x) x)
(*.f64 (/.f64 2 x) (/.f64 1 x))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(/.f64 2 (+.f64 2 (*.f64 x x)))
(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
(/.f64 1 (cosh.f64 x))
(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(expm1.f64 (log1p.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))

Outputs
(/.f64 1 (cosh.f64 x))

Calls

3 calls:

24.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
7.0ms	x
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0.0b	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 114 to 79 computations (30.7% saved)

regimes30.0ms (1%)

Counts

7 → 3

Calls

Call 1

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

Outputs
(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
(/.f64 2 (+.f64 2 (*.f64 x x)))
(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)

Calls

1 calls:

28.0ms

Results

Error	Segments	Branch
1.2b	3	`x`

Compiler

Compiled 44 to 28 computations (36.4% saved)

bsearch37.0ms (1.2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	2781.7607340953587	167520204576.8098
19.0ms	-463121901538293.94	-0.25416657783811014

Results

33.0ms

304×

body

256

valid

Compiler

Compiled 393 to 314 computations (20.1% saved)

regimes7.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

Outputs
(/.f64 2 (+.f64 2 (*.f64 x x)))

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
16.3b	1	`x`

Compiler

Compiled 35 to 22 computations (37.1% saved)

regimes14.0ms (0.5%)

Counts

5 → 3

Calls

Call 1

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

Outputs
(/.f64 2 (*.f64 x x))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(/.f64 2 (*.f64 x x))

Calls

1 calls:

13.0ms

Results

Error	Segments	Branch
16.4b	3	`x`

Compiler

Compiled 28 to 18 computations (35.7% saved)

bsearch33.0ms (1.1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
14.0ms	0.1616564278786402	11.04586415502466
19.0ms	-463121901538293.94	-0.25416657783811014

Results

29.0ms

272×

body

256

valid

Compiler

Compiled 285 to 214 computations (24.9% saved)

regimes14.0ms (0.5%)

Accuracy

Total -45.4b remaining (-274.1%)

Threshold costs -45.4b (-274.1%)

Counts

4 → 3

Calls

Call 1

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

Outputs
(/.f64 2 (*.f64 x x))
1
(/.f64 2 (*.f64 x x))

Calls

1 calls:

11.0ms

Results

Error	Segments	Branch
16.6b	3	`x`

Compiler

Compiled 21 to 14 computations (33.3% saved)

bsearch34.0ms (1.1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
14.0ms	0.1616564278786402	11.04586415502466
20.0ms	-463121901538293.94	-0.25416657783811014

Results

31.0ms

272×

body

256

valid

Compiler

Compiled 183 to 146 computations (20.2% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	128
1	43	128
2	44	128

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 1 (cosh.f64 x))
(if (<=.f64 x -400000) (-.f64 (+.f64 1 (/.f64 2 (.f64 x x))) 1) (if (<=.f64 x 3200000) (/.f64 2 (+.f64 2 (.f64 x x))) (-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)))
(/.f64 2 (+.f64 2 (*.f64 x x)))
(if (<=.f64 x -5404319552844595/4503599627370496) (/.f64 2 (.f64 x x)) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (/.f64 2 (.f64 x x))))
(if (<=.f64 x -3152519739159347/2251799813685248) (/.f64 2 (.f64 x x)) (if (<=.f64 x 3152519739159347/2251799813685248) 1 (/.f64 2 (.f64 x x))))
1

Outputs
(/.f64 1 (cosh.f64 x))
(if (<=.f64 x -400000) (-.f64 (+.f64 1 (/.f64 2 (.f64 x x))) 1) (if (<=.f64 x 3200000) (/.f64 2 (+.f64 2 (.f64 x x))) (-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)))
(if (<=.f64 x -400000) (+.f64 (+.f64 1 (/.f64 2 (.f64 x x))) -1) (if (<=.f64 x 3200000) (/.f64 2 (+.f64 2 (.f64 x x))) (+.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) -1)))
(/.f64 2 (+.f64 2 (*.f64 x x)))
(if (<=.f64 x -5404319552844595/4503599627370496) (/.f64 2 (.f64 x x)) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (/.f64 2 (.f64 x x))))
(if (<=.f64 x -5404319552844595/4503599627370496) (/.f64 2 (.f64 x x)) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 (.f64 x x) -1/2)) (/.f64 2 (.f64 x x))))
(if (<=.f64 x -3152519739159347/2251799813685248) (/.f64 2 (.f64 x x)) (if (<=.f64 x 3152519739159347/2251799813685248) 1 (/.f64 2 (.f64 x x))))
1

Compiler

Compiled 95 to 65 computations (31.6% saved)

soundness67.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-def_binary64`
488×	`associate-l_binary64`
407×	`associate-/l*_binary64`
394×	`distribute-rgt-in_binary64`
393×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	566
1	223	550
2	836	413
3	4593	335

Stop Event

1×	node limit

Compiler

Compiled 56 to 45 computations (19.6% saved)

end49.0ms (1.6%)

Compiler: Compiled 90 to 57 computations (36.7% saved)

Details

analyze0.0ms (0%)

sample696.0ms (23.4%)

preprocess69.0ms (2.3%)

simplify61.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.3%)

series3.0ms (0.1%)

rewrite46.0ms (1.6%)

simplify44.0ms (1.5%)

eval14.0ms (0.5%)

prune10.0ms (0.4%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite36.0ms (1.2%)

simplify34.0ms (1.1%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite36.0ms (1.2%)

simplify39.0ms (1.3%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite41.0ms (1.4%)

simplify37.0ms (1.3%)

localize14.0ms (0.5%)

series52.0ms (1.7%)

rewrite51.0ms (1.7%)

simplify54.0ms (1.8%)

localize15.0ms (0.5%)

series1.0ms (0%)

rewrite41.0ms (1.4%)

simplify44.0ms (1.5%)

eval78.0ms (2.6%)

prune41.0ms (1.4%)

localize11.0ms (0.4%)

series2.0ms (0.1%)

rewrite44.0ms (1.5%)

simplify46.0ms (1.6%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite36.0ms (1.2%)

simplify32.0ms (1.1%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite38.0ms (1.3%)

simplify36.0ms (1.2%)

localize9.0ms (0.3%)

series2.0ms (0.1%)

rewrite48.0ms (1.6%)

simplify49.0ms (1.7%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite39.0ms (1.3%)

simplify49.0ms (1.7%)

eval195.0ms (6.6%)

prune144.0ms (4.8%)

localize17.0ms (0.6%)

series1.0ms (0%)

rewrite38.0ms (1.3%)

simplify40.0ms (1.3%)

localize9.0ms (0.3%)

series2.0ms (0.1%)

rewrite44.0ms (1.5%)

simplify52.0ms (1.8%)

eval35.0ms (1.2%)

prune19.0ms (0.6%)

regimes36.0ms (1.2%)

regimes30.0ms (1%)

bsearch37.0ms (1.2%)

regimes7.0ms (0.2%)

regimes14.0ms (0.5%)

bsearch33.0ms (1.1%)

regimes14.0ms (0.5%)

bsearch34.0ms (1.1%)

simplify7.0ms (0.2%)

soundness67.0ms (2.2%)

end49.0ms (1.6%)

Profiling