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)

sample695.0ms (28.6%)

Results

683.0ms

8256×

body

256

valid

Bogosity

preprocess83.0ms (3.4%)

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)

simplify63.0ms (2.6%)

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)))

rewrite57.0ms (2.3%)

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))))))))

simplify43.0ms (1.8%)

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))

eval13.0ms (0.5%)

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

prune35.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	5	56

Error

Counts

56 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	15.4b	(/.f64 2 (+.f64 2 (*.f64 x x)))
▶	0.0b	(/.f64 1 (cosh.f64 x))
▶	31.3b	(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
▶	31.1b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	30.7b	1

Compiler

Compiled 36 to 28 computations (22.2% saved)

localize6.0ms (0.3%)

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 (0.1%)

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))

rewrite53.0ms (2.2%)

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))))))))

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))))))))

simplify40.0ms (1.7%)

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))

localize16.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 5/24 (pow.f64 x 4))
✓	12.2b	(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))

Compiler

Compiled 39 to 26 computations (33.3% saved)

series2.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
0.0ms	x	@	0	(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
0.0ms	x	@	0	(*.f64 5/24 (pow.f64 x 4))
0.0ms	x	@	-inf	(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
0.0ms	x	@	inf	(*.f64 5/24 (pow.f64 x 4))

rewrite48.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

730×	`pow1_binary64`
681×	`add-log-exp_binary64`
681×	`log1p-expm1-u_binary64`
681×	`expm1-log1p-u_binary64`
667×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	186	21
2	1934	21

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

Inputs
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(*.f64 5/24 (pow.f64 x 4))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 5/24 (pow.f64 x 4)) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/2 (*.f64 x x)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 1) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))) 2) (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))) (sqrt.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3) (pow.f64 (*.f64 5/24 (pow.f64 x 4)) 3)) (+.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) (*.f64 -1/2 (*.f64 x x))) (-.f64 (*.f64 25/576 (pow.f64 x 8)) (*.f64 (*.f64 -1/2 (*.f64 x x)) (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) (*.f64 -1/2 (*.f64 x x))) (*.f64 25/576 (pow.f64 x 8))) (-.f64 (*.f64 -1/2 (*.f64 x x)) (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 5/24 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 5/24 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 5/24 (pow.f64 x 4)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 5/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 25/576 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 5/24 (pow.f64 x 4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))))))))

simplify46.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

505×	`associate-/l*_binary64`
488×	`fma-neg_binary64`
368×	`log-prod_binary64`
367×	`unswap-sqr_binary64`
365×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	582
1	218	569
2	962	562
3	4186	559

Stop Event

1×	node limit

Counts

44 → 44

Calls

Call 1

Inputs
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(*.f64 5/24 (pow.f64 x 4))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(*.f64 5/24 (pow.f64 x 4))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 5/24 (pow.f64 x 4)) (.f64 -1/2 (*.f64 x x)))
(+.f64 (.f64 -1/2 (.f64 x x)) (*.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 (.f64 -1/2 (.f64 x x)) 1) (.f64 5/24 (pow.f64 x 4)))
(-.f64 (+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) 1)
(.f64 (fma.f64 -1/2 (.f64 x x) (*.f64 5/24 (pow.f64 x 4))) 1)
(.f64 1 (fma.f64 -1/2 (.f64 x x) (*.f64 5/24 (pow.f64 x 4))))
(.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) (*.f64 5/24 (pow.f64 x 4)))) 2))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) 2) (cbrt.f64 (fma.f64 -1/2 (.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))
(.f64 (sqrt.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) (sqrt.f64 (fma.f64 -1/2 (.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 (+.f64 (pow.f64 (.f64 -1/2 (.f64 x x)) 3) (pow.f64 (.f64 5/24 (pow.f64 x 4)) 3)) (+.f64 (.f64 (.f64 -1/2 (.f64 x x)) (.f64 -1/2 (.f64 x x))) (-.f64 (.f64 25/576 (pow.f64 x 8)) (.f64 (.f64 -1/2 (.f64 x x)) (*.f64 5/24 (pow.f64 x 4))))))
(/.f64 (-.f64 (.f64 (.f64 -1/2 (.f64 x x)) (.f64 -1/2 (.f64 x x))) (.f64 25/576 (pow.f64 x 8))) (-.f64 (.f64 -1/2 (.f64 x x)) (*.f64 5/24 (pow.f64 x 4))))
(pow.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))) 1)
(pow.f64 (pow.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))) 3) 1/3)
(pow.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) 3)
(pow.f64 (sqrt.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) 2)
(sqrt.f64 (pow.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))) 2))
(log.f64 (exp.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))))
(cbrt.f64 (pow.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))) 3))
(expm1.f64 (log1p.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))))
(log1p.f64 (expm1.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))))
(exp.f64 (log.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))))
(-.f64 (+.f64 1 (*.f64 5/24 (pow.f64 x 4))) 1)
(pow.f64 (*.f64 5/24 (pow.f64 x 4)) 1)
(pow.f64 (pow.f64 (*.f64 5/24 (pow.f64 x 4)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) 3)
(pow.f64 (.f64 (.f64 x x) (sqrt.f64 5/24)) 2)
(sqrt.f64 (*.f64 25/576 (pow.f64 x 8)))
(log.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))
(cbrt.f64 (pow.f64 (*.f64 5/24 (pow.f64 x 4)) 3))
(expm1.f64 (log1p.f64 (*.f64 5/24 (pow.f64 x 4))))
(log1p.f64 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))
(exp.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))))

Outputs
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(*.f64 5/24 (pow.f64 x 4))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(*.f64 5/24 (pow.f64 x 4))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 5/24 (pow.f64 x 4)) (.f64 -1/2 (*.f64 x x)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 -1/2 (.f64 x x)) (*.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(+.f64 (.f64 (.f64 -1/2 (.f64 x x)) 1) (.f64 5/24 (pow.f64 x 4)))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(-.f64 (+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) 1)
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(.f64 (fma.f64 -1/2 (.f64 x x) (*.f64 5/24 (pow.f64 x 4))) 1)
(fma.f64 -1/2 (.f64 x x) (.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) (.f64 5/24 (pow.f64 x 4)))
(.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) (*.f64 5/24 (pow.f64 x 4)))) 2))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) 2) (cbrt.f64 (fma.f64 -1/2 (.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(.f64 (sqrt.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) (sqrt.f64 (fma.f64 -1/2 (.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(/.f64 (+.f64 (pow.f64 (.f64 -1/2 (.f64 x x)) 3) (pow.f64 (.f64 5/24 (pow.f64 x 4)) 3)) (+.f64 (.f64 (.f64 -1/2 (.f64 x x)) (.f64 -1/2 (.f64 x x))) (-.f64 (.f64 25/576 (pow.f64 x 8)) (.f64 (.f64 -1/2 (.f64 x x)) (*.f64 5/24 (pow.f64 x 4))))))
(/.f64 (+.f64 (.f64 -1/8 (pow.f64 (.f64 x x) 3)) (.f64 125/13824 (pow.f64 (pow.f64 x 4) 3))) (-.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 25/576 (pow.f64 x 8))) (.f64 -1/2 (.f64 (.f64 x x) (*.f64 5/24 (pow.f64 x 4))))))
(/.f64 (fma.f64 125/13824 (pow.f64 (pow.f64 x 4) 3) (.f64 -1/8 (pow.f64 (.f64 x x) 3))) (fma.f64 1/4 (pow.f64 x 4) (fma.f64 25/576 (pow.f64 x 8) (.f64 1/2 (.f64 (pow.f64 (*.f64 x x) 3) 5/24)))))
(/.f64 (fma.f64 125/13824 (pow.f64 (pow.f64 x 4) 3) (.f64 -1/8 (pow.f64 x 6))) (fma.f64 25/576 (pow.f64 x 8) (.f64 (pow.f64 x 4) (+.f64 (.f64 (.f64 x x) 5/48) 1/4))))
(/.f64 (fma.f64 125/13824 (pow.f64 x 12) (.f64 -1/8 (pow.f64 x 6))) (-.f64 (.f64 25/576 (pow.f64 x 8)) (.f64 (pow.f64 x 4) (fma.f64 (.f64 x x) -5/48 -1/4))))
(/.f64 (-.f64 (.f64 (.f64 -1/2 (.f64 x x)) (.f64 -1/2 (.f64 x x))) (.f64 25/576 (pow.f64 x 8))) (-.f64 (.f64 -1/2 (.f64 x x)) (*.f64 5/24 (pow.f64 x 4))))
(/.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 -25/576 (pow.f64 x 8))) (+.f64 (.f64 -1/2 (.f64 x x)) (*.f64 -5/24 (pow.f64 x 4))))
(/.f64 (fma.f64 1/4 (pow.f64 x 4) (.f64 (pow.f64 x 8) -25/576)) (fma.f64 -1/2 (.f64 x x) (*.f64 (pow.f64 x 4) -5/24)))
(/.f64 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (pow.f64 x 8) -25/576)) (fma.f64 -1/2 (.f64 x x) (*.f64 (pow.f64 x 4) -5/24)))
(pow.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))) 1)
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(pow.f64 (pow.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))) 3) 1/3)
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(pow.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) 3)
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(pow.f64 (sqrt.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))) 2)
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(sqrt.f64 (pow.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))) 2))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(log.f64 (exp.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(cbrt.f64 (pow.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))) 3))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(expm1.f64 (log1p.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(log1p.f64 (expm1.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(exp.f64 (log.f64 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))))
(fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))
(-.f64 (+.f64 1 (*.f64 5/24 (pow.f64 x 4))) 1)
(*.f64 5/24 (pow.f64 x 4))
(pow.f64 (*.f64 5/24 (pow.f64 x 4)) 1)
(*.f64 5/24 (pow.f64 x 4))
(pow.f64 (pow.f64 (*.f64 5/24 (pow.f64 x 4)) 3) 1/3)
(*.f64 5/24 (pow.f64 x 4))
(pow.f64 (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) 3)
(*.f64 5/24 (pow.f64 x 4))
(pow.f64 (.f64 (.f64 x x) (sqrt.f64 5/24)) 2)
(*.f64 5/24 (pow.f64 x 4))
(sqrt.f64 (*.f64 25/576 (pow.f64 x 8)))
(*.f64 5/24 (pow.f64 x 4))
(log.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))
(*.f64 5/24 (pow.f64 x 4))
(cbrt.f64 (pow.f64 (*.f64 5/24 (pow.f64 x 4)) 3))
(*.f64 5/24 (pow.f64 x 4))
(expm1.f64 (log1p.f64 (*.f64 5/24 (pow.f64 x 4))))
(*.f64 5/24 (pow.f64 x 4))
(log1p.f64 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))
(*.f64 5/24 (pow.f64 x 4))
(exp.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))))
(*.f64 5/24 (pow.f64 x 4))

localize4.0ms (0.2%)

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
1.0ms	x	@	-inf	(/.f64 1 (cosh.f64 x))
1.0ms	x	@	inf	(/.f64 1 (cosh.f64 x))
1.0ms	x	@	0	(/.f64 1 (cosh.f64 x))

rewrite39.0ms (1.6%)

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))))))))

simplify35.0ms (1.5%)

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 (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0.1%)

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)))

rewrite61.0ms (2.5%)

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))))))))

simplify40.0ms (1.6%)

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))

eval44.0ms (1.8%)

Compiler: Compiled 2029 to 1457 computations (28.2% saved)

prune27.0ms (1.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	155	7	162

Error

Counts

162 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	47.2b	(/.f64 (/.f64 2 x) x)
✓	15.4b	(/.f64 2 (+.f64 2 (*.f64 x x)))
▶	46.9b	(/.f64 2 (*.f64 x x))
✓	0.0b	(/.f64 1 (cosh.f64 x))
▶	0.1b	(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
✓	31.1b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	30.7b	1

Compiler

Compiled 44 to 34 computations (22.7% saved)

localize9.0ms (0.4%)

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	@	inf	(+.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)
0.0ms	x	@	0	(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
0.0ms	x	@	0	(+.f64 1 (/.f64 1 (cosh.f64 x)))

rewrite69.0ms (2.8%)

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 1 (/.f64 1 (cosh.f64 x))) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 2) -1) (+.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 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((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))))))) (#(struct:change #<rule egg-rr> (2) ((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)))))) (#(struct:change #<rule egg-rr> (2) ((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))))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))) (#(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 (/.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 pow.f64 (pow.f64 (cosh.f64 x) -3) 1/3)))) (#(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 (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 fma.f64 1 (+.f64 1 (/.f64 1 (cosh.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((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)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) (hypot.f64 1 (pow.f64 (cosh.f64 x) -1/2)) -1)))))

((#(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 (2%)

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

localize26.0ms (1.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(/.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))

rewrite35.0ms (1.4%)

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))))))))

simplify31.0ms (1.3%)

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))

localize5.0ms (0.2%)

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 (1.6%)

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))))))))

simplify37.0ms (1.5%)

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))

eval81.0ms (3.3%)

Compiler: Compiled 2791 to 2013 computations (27.9% saved)

prune30.0ms (1.2%)

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	0	1	1
Picked	0	1	1
Done	0	5	5
Total	224	9	233

Error

Counts

233 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	47.2b	(/.f64 (/.f64 2 x) x)
✓	15.4b	(/.f64 2 (+.f64 2 (*.f64 x x)))
✓	46.9b	(/.f64 2 (*.f64 x x))
✓	0.0b	(/.f64 1 (cosh.f64 x))
▶	32.3b	(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
✓	0.1b	(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
✓	31.1b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
▶	47.2b	(*.f64 (/.f64 2 x) (/.f64 1 x))
	30.7b	1

Compiler

Compiled 62 to 48 computations (22.6% saved)

localize8.0ms (0.3%)

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))

rewrite41.0ms (1.7%)

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))))))))

simplify39.0ms (1.6%)

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 (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.4b	(/.f64 2 (*.f64 x x))
✓	2.5b	(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)

Compiler

Compiled 28 to 16 computations (42.9% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite47.0ms (1.9%)

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)))))

simplify49.0ms (2%)

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 (1.5%)

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

prune17.0ms (0.7%)

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	1	1
Picked	0	1	1
Done	0	7	7
Total	131	10	141

Error

Counts

141 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	47.2b	(/.f64 (/.f64 2 x) x)
	46.9b	(/.f64 2 (/.f64 x (/.f64 1 x)))
✓	15.4b	(/.f64 2 (+.f64 2 (*.f64 x x)))
✓	46.9b	(/.f64 2 (*.f64 x x))
✓	0.0b	(/.f64 1 (cosh.f64 x))
✓	32.3b	(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
✓	0.1b	(-.f64 (+.f64 1 (/.f64 1 (cosh.f64 x))) 1)
✓	31.1b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	47.2b	(*.f64 (/.f64 2 x) (/.f64 1 x))
	30.7b	1

Compiler

Compiled 70 to 54 computations (22.9% saved)

regimes19.0ms (0.8%)

Counts

12 → 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 2 (/.f64 x (/.f64 1 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))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))

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

Calls

5 calls:

7.0ms	x
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 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 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0.0b	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0.0b	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 115 to 80 computations (30.4% saved)

regimes16.0ms (0.7%)

Counts

8 → 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 2 (/.f64 x (/.f64 1 x)))
(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)

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

Calls

1 calls:

14.0ms

Results

Error	Segments	Branch
0.7b	3	`x`

Compiler

Compiled 51 to 33 computations (35.3% saved)

bsearch39.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
14.0ms	0.00018484038833668372	11.392289093474282
24.0ms	-79029.74128439106	-1.973632536082958e-6

Results

35.0ms

288×

body

256

valid

Compiler

Compiled 373 to 298 computations (20.1% saved)

regimes8.0ms (0.3%)

Counts

7 → 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 2 (/.f64 x (/.f64 1 x)))

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

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
15.4b	1	`x`

Compiler

Compiled 42 to 27 computations (35.7% saved)

regimes13.0ms (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:

12.0ms

Results

Error	Segments	Branch
15.4b	3	`x`

Compiler

Compiled 28 to 18 computations (35.7% saved)

bsearch33.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
15.0ms	0.00018484038833668372	11.392289093474282
18.0ms	-79029.74128439106	-1.973632536082958e-6

Results

30.0ms

288×

body

256

valid

Compiler

Compiled 301 to 226 computations (24.9% saved)

regimes13.0ms (0.5%)

Accuracy

Total -46.5b remaining (-299.4%)

Threshold costs -46.5b (-299.4%)

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:

12.0ms

Results

Error	Segments	Branch
15.5b	3	`x`

Compiler

Compiled 21 to 14 computations (33.3% saved)

bsearch32.0ms (1.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
15.0ms	0.00018484038833668372	11.392289093474282
17.0ms	-79029.74128439106	-1.973632536082958e-6

Results

29.0ms

288×

body

256

valid

Compiler

Compiled 193 to 154 computations (20.2% saved)

simplify6.0ms (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	30	128
1	39	128
2	40	128

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 1 (cosh.f64 x))
(if (<=.f64 x -5/4) (-.f64 (+.f64 1 (/.f64 2 (.f64 x x))) 1) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (-.f64 (+.f64 1 (/.f64 2 (.f64 x x))) 1)))
(/.f64 2 (+.f64 2 (*.f64 x x)))
(if (<=.f64 x -5/4) (/.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 -799388933858263/562949953421312) (/.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 -5/4) (-.f64 (+.f64 1 (/.f64 2 (.f64 x x))) 1) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (-.f64 (+.f64 1 (/.f64 2 (.f64 x x))) 1)))
(if (<=.f64 x -5/4) (+.f64 (+.f64 1 (/.f64 2 (.f64 x x))) -1) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 (.f64 x x) -1/2)) (+.f64 (+.f64 1 (/.f64 2 (.f64 x x))) -1)))
(/.f64 2 (+.f64 2 (*.f64 x x)))
(if (<=.f64 x -5/4) (/.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 -5/4) (/.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 -799388933858263/562949953421312) (/.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)

soundness72.0ms (2.9%)

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)

end47.0ms (1.9%)

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

Details

analyze0.0ms (0%)

sample695.0ms (28.6%)

preprocess83.0ms (3.4%)

simplify63.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.3%)

series3.0ms (0.1%)

rewrite57.0ms (2.3%)

simplify43.0ms (1.8%)

eval13.0ms (0.5%)

prune35.0ms (1.4%)

localize6.0ms (0.3%)

series1.0ms (0.1%)

rewrite53.0ms (2.2%)

simplify40.0ms (1.7%)

localize16.0ms (0.7%)

series2.0ms (0.1%)

rewrite48.0ms (2%)

simplify46.0ms (1.9%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite39.0ms (1.6%)

simplify35.0ms (1.5%)

localize6.0ms (0.3%)

series1.0ms (0.1%)

rewrite61.0ms (2.5%)

simplify40.0ms (1.6%)

eval44.0ms (1.8%)

prune27.0ms (1.1%)

localize9.0ms (0.4%)

series2.0ms (0.1%)

rewrite69.0ms (2.8%)

simplify49.0ms (2%)

localize26.0ms (1.1%)

series1.0ms (0%)

rewrite35.0ms (1.4%)

simplify31.0ms (1.3%)

localize5.0ms (0.2%)

series1.0ms (0%)

rewrite38.0ms (1.6%)

simplify37.0ms (1.5%)

eval81.0ms (3.3%)

prune30.0ms (1.2%)

localize8.0ms (0.3%)

series1.0ms (0%)

rewrite41.0ms (1.7%)

simplify39.0ms (1.6%)

localize9.0ms (0.4%)

series1.0ms (0%)

rewrite47.0ms (1.9%)

simplify49.0ms (2%)

eval35.0ms (1.5%)

prune17.0ms (0.7%)

regimes19.0ms (0.8%)

regimes16.0ms (0.7%)

bsearch39.0ms (1.6%)

regimes8.0ms (0.3%)

regimes13.0ms (0.5%)

bsearch33.0ms (1.4%)

regimes13.0ms (0.5%)

bsearch32.0ms (1.3%)

simplify6.0ms (0.2%)

soundness72.0ms (2.9%)

end47.0ms (1.9%)

Profiling