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)

sample799.0ms (21.8%)

Results

789.0ms

8256×

body

256

valid

Bogosity

preprocess91.0ms (2.5%)

Algorithm

2×	egg-herbie

Rules

1198×	`fma-def`
778×	`sqr-pow`
712×	`fabs-mul`
684×	`*-commutative`
530×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	17	25
2	22	25
3	29	25
4	49	25
5	91	25
6	196	25
7	417	25
8	989	25
9	2380	25
10	3382	25
11	4575	25
12	6270	25
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)

simplify94.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1198×	`fma-def`
778×	`sqr-pow`
712×	`fabs-mul`
684×	`*-commutative`
530×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	17	25
2	22	25
3	29	25
4	49	25
5	91	25
6	196	25
7	417	25
8	989	25
9	2380	25
10	3382	25
11	4575	25
12	6270	25

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

0.02%

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.02%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.02%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	0.02%	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 24 to 8 computations (66.7% saved)

series2.0ms (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))))
0.0ms	x	@	inf	(/.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	@	0	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	-inf	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite90.0ms (2.4%)

Algorithm

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

Rules

222×	`add-sqr-sqrt`
222×	`add-sqr-sqrt`
210×	`add-exp-log`
210×	`pow1`
210×	`*-un-lft-identity`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	216	22
2	3273	22
0	8	11
1	169	11
2	2616	11
0	8	11
0	10	17
1	216	17
2	3273	17
0	10	17

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

2 → 22

Calls

Call 1

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

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

Outputs

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

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

simplify57.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1396×	`associate-r`
1156×	`associate-+r+`
992×	`associate-+l+`
972×	`associate-l`
830×	`associate-/l*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	96	998
1	227	966
2	904	692
3	4945	692

Stop Event

1×	node limit

Counts

46 → 56

Calls

Call 1

Inputs
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)))
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))))
(.f64 1 (.f64 2 (cosh.f64 x)))
(.f64 (sqrt.f64 (.f64 2 (cosh.f64 x))) (sqrt.f64 (*.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 2 (cosh.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))))
(/.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))))))
(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))))
(exp.f64 (log.f64 (*.f64 2 (cosh.f64 x))))
(log1p.f64 (expm1.f64 (*.f64 2 (cosh.f64 x))))
(.f64 2 (/.f64 1 (.f64 2 (cosh.f64 x))))
(.f64 1 (/.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)))))
(.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)))))
(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)))))
(exp.f64 (log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
(log1p.f64 (expm1.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))

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

eval17.0ms (0.5%)

Compiler: Compiled 689 to 472 computations (31.5% saved)

prune8.0ms (0.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	5	57

Error

0.01%

Counts

57 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	26.23%	(/.f64 2 (+.f64 2 (*.f64 x x)))
▶	0.02%	(/.f64 1 (cosh.f64 x))
▶	54.56%	(+.f64 1 (.f64 (.f64 x x) -1/2))
▶	0.02%	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
	53.65%	1

Compiler

Compiled 39 to 31 computations (20.5% saved)

localize52.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.01%	(cosh.f64 x)
✓	0.01%	(sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))
✓	0.02%	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
✓	0.02%	(/.f64 2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 37 to 25 computations (32.4% saved)

series4.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

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

rewrite70.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1744×	`add-sqr-sqrt`
1724×	`*-un-lft-identity`
1604×	`add-cube-cbrt`
1590×	`add-cbrt-cube`
182×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	193	42
2	2330	42

Stop Event

1×	node limit

Counts

4 → 115

Calls

Call 1

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

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

simplify83.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1674×	`associate-/l*`
1134×	`associate-/r/`
744×	`*-commutative`
556×	`distribute-lft-in`
524×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	2923
1	493	2807
2	2242	2711

Stop Event

1×	node limit

Counts

163 → 151

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
1
(+.f64 1 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 7/96 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -139/5760 (pow.f64 x 6)) (*.f64 7/96 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6)))))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)
(*.f64 2 (/.f64 1/2 (cosh.f64 x)))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4) (.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4) (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2))
(.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))) (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(*.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (/.f64 1/2 (cosh.f64 x)) 2)
(.f64 -2 (/.f64 1 (.f64 (cosh.f64 x) -2)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4)) (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 1 (cbrt.f64 (cosh.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(pow.f64 (cosh.f64 x) -1)
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 2)
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(pow.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)) 1/2)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
(fabs.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(log.f64 (+.f64 1 (expm1.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))))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(exp.f64 (*.f64 (neg.f64 (log.f64 (cosh.f64 x))) 1))
(exp.f64 (.f64 (.f64 1/2 (neg.f64 (log.f64 (cosh.f64 x)))) 2))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(/.f64 2 (neg.f64 (*.f64 (cosh.f64 x) -2)))
(/.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 -2 (*.f64 (cosh.f64 x) -2))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 2)) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (/.f64 2 (cosh.f64 x)) 2)
(/.f64 (/.f64 2 (sqrt.f64 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (/.f64 2 (pow.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) 2)) (cbrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(/.f64 -1 (neg.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1)
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 2)
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(pow.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)) 1/2)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
(fabs.f64 (/.f64 1 (cosh.f64 x)))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(log.f64 (+.f64 1 (expm1.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))))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(exp.f64 (*.f64 (neg.f64 (log.f64 (cosh.f64 x))) 1))
(exp.f64 (.f64 (.f64 1/2 (neg.f64 (log.f64 (cosh.f64 x)))) 2))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))))) 1)
(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 1)
(*.f64 1 (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(*.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4) (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (cosh.f64 x))))
(.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (.f64 2 (cosh.f64 x)))))
(*.f64 (sqrt.f64 2) (pow.f64 (/.f64 1/2 (cosh.f64 x)) 1/2))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2)) (sqrt.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x)))))
(*.f64 (pow.f64 1 1/2) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(*.f64 (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2) 1/2) (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 1/2))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 2 (cosh.f64 x))))
(/.f64 (sqrt.f64 -2) (sqrt.f64 (*.f64 (cosh.f64 x) -2)))
(/.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x)))))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1/2)
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 1)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4) 2)
(pow.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))) 3)
(pow.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)) 1/4)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3/2) 1/3)
(fabs.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(log.f64 (exp.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))))))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(exp.f64 (*.f64 1/2 (neg.f64 (log.f64 (cosh.f64 x)))))
(exp.f64 (*.f64 (neg.f64 (log.f64 (cosh.f64 x))) 1/2))
(exp.f64 (.f64 (.f64 1/2 (neg.f64 (log.f64 (cosh.f64 x)))) 1))
(log1p.f64 (expm1.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(-.f64 (exp.f64 (log1p.f64 (cosh.f64 x))) 1)
(*.f64 (cosh.f64 x) 1)
(.f64 (.f64 2 (cosh.f64 x)) 1/2)
(*.f64 1 (cosh.f64 x))
(*.f64 (sqrt.f64 (cosh.f64 x)) (sqrt.f64 (cosh.f64 x)))
(*.f64 (cbrt.f64 (cosh.f64 x)) (pow.f64 (cbrt.f64 (cosh.f64 x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) (cbrt.f64 (cosh.f64 x)))
(/.f64 2 (/.f64 2 (cosh.f64 x)))
(/.f64 (cosh.f64 x) 1)
(/.f64 (*.f64 2 (cosh.f64 x)) 2)
(/.f64 1 (/.f64 1 (cosh.f64 x)))
(/.f64 (sqrt.f64 (.f64 2 (cosh.f64 x))) (/.f64 2 (sqrt.f64 (.f64 2 (cosh.f64 x)))))
(/.f64 (pow.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) 2) (/.f64 2 (cbrt.f64 (.f64 2 (cosh.f64 x)))))
(/.f64 (*.f64 (cosh.f64 x) -2) -2)
(pow.f64 (cosh.f64 x) 1)
(pow.f64 (sqrt.f64 (cosh.f64 x)) 2)
(pow.f64 (cbrt.f64 (cosh.f64 x)) 3)
(pow.f64 (pow.f64 (cosh.f64 x) 3) 1/3)
(sqrt.f64 (pow.f64 (cosh.f64 x) 2))
(log.f64 (exp.f64 (cosh.f64 x)))
(log.f64 (+.f64 1 (expm1.f64 (cosh.f64 x))))
(cbrt.f64 (pow.f64 (cosh.f64 x) 3))
(expm1.f64 (log1p.f64 (cosh.f64 x)))
(exp.f64 (log.f64 (cosh.f64 x)))
(exp.f64 (*.f64 (log.f64 (cosh.f64 x)) 1))
(log1p.f64 (expm1.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 1 (fma.f64 5/24 (pow.f64 x 4) (.f64 (.f64 -1/2 x) x)))
(+.f64 1 (fma.f64 5/24 (pow.f64 x 4) (.f64 x (.f64 -1/2 x))))
(+.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 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.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 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.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 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.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 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 5/24 (pow.f64 x 4) (.f64 (.f64 -1/2 x) x)))
(+.f64 1 (fma.f64 5/24 (pow.f64 x 4) (.f64 x (.f64 -1/2 x))))
(+.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 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.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 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.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 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.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 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1
(+.f64 1 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 1)
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 7/96 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/4 (.f64 x x) (.f64 (pow.f64 x 4) 7/96)))
(+.f64 1 (fma.f64 (pow.f64 x 4) 7/96 (.f64 (.f64 x x) -1/4)))
(+.f64 (fma.f64 (.f64 x x) -1/4 1) (.f64 (pow.f64 x 4) 7/96))
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -139/5760 (pow.f64 x 6)) (*.f64 7/96 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/4 (.f64 x x) (fma.f64 -139/5760 (pow.f64 x 6) (.f64 (pow.f64 x 4) 7/96))))
(+.f64 (fma.f64 (.f64 x x) -1/4 1) (fma.f64 (pow.f64 x 4) 7/96 (.f64 (pow.f64 x 6) -139/5760)))
(+.f64 (fma.f64 (.f64 x x) -1/4 1) (fma.f64 (pow.f64 x 6) -139/5760 (.f64 (pow.f64 x 4) 7/96)))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) 1/2))
(fma.f64 (*.f64 x x) 1/2 1)
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 1/2 (.f64 x x) (.f64 (pow.f64 x 4) 1/24)))
(+.f64 (fma.f64 (.f64 x x) 1/2 1) (.f64 (pow.f64 x 4) 1/24))
(+.f64 1 (fma.f64 (pow.f64 x 4) 1/24 (.f64 x (.f64 x 1/2))))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 1/2 (.f64 x x) (fma.f64 1/24 (pow.f64 x 4) (.f64 (pow.f64 x 6) 1/720))))
(+.f64 (fma.f64 (.f64 x x) 1/2 1) (fma.f64 (pow.f64 x 6) 1/720 (.f64 (pow.f64 x 4) 1/24)))
(+.f64 (fma.f64 (.f64 x x) 1/2 1) (fma.f64 (pow.f64 x 4) 1/24 (.f64 (pow.f64 x 6) 1/720)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)
(/.f64 1 (cosh.f64 x))
(*.f64 2 (/.f64 1/2 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4) (.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4) (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2))
(/.f64 1 (cosh.f64 x))
(.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))) (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))))))
(/.f64 (pow.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))) 4) (cbrt.f64 (cosh.f64 x)))
(/.f64 (pow.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)) 4) (cbrt.f64 (cosh.f64 x)))
(*.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.f64 1/2 (cosh.f64 x)) 2)
(/.f64 1 (cosh.f64 x))
(.f64 -2 (/.f64 1 (.f64 (cosh.f64 x) -2)))
(/.f64 1 (cosh.f64 x))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4)) (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4))
(/.f64 1 (cosh.f64 x))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 1 (cbrt.f64 (cosh.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))))))
(/.f64 (pow.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))) 4) (cbrt.f64 (cosh.f64 x)))
(/.f64 (pow.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)) 4) (cbrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1)
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 2)
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)) 1/2)
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(/.f64 1 (cosh.f64 x))
(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
(/.f64 1 (cosh.f64 x))
(fabs.f64 (/.f64 1 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (cosh.f64 x)))))
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(/.f64 1 (cosh.f64 x))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (*.f64 (neg.f64 (log.f64 (cosh.f64 x))) 1))
(/.f64 1 (cosh.f64 x))
(exp.f64 (.f64 (.f64 1/2 (neg.f64 (log.f64 (cosh.f64 x)))) 2))
(/.f64 1 (cosh.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)
(/.f64 1 (cosh.f64 x))
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (neg.f64 (*.f64 (cosh.f64 x) -2)))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 1 (cosh.f64 x))
(/.f64 -2 (*.f64 (cosh.f64 x) -2))
(/.f64 1 (cosh.f64 x))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 2)) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x))) (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 2 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x))))
(/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (cosh.f64 x)) (sqrt.f64 (.f64 2 (cosh.f64 x)))))
(/.f64 (.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x))) (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 2 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x))))
(/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (cosh.f64 x)) (sqrt.f64 (.f64 2 (cosh.f64 x)))))
(/.f64 (/.f64 2 (cosh.f64 x)) 2)
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 2 (sqrt.f64 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 2 (pow.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) 2)) (cbrt.f64 (.f64 2 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 -1 (neg.f64 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(pow.f64 (cosh.f64 x) -1)
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1)
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 2)
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)
(/.f64 1 (cosh.f64 x))
(pow.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)) 1/2)
(/.f64 1 (cosh.f64 x))
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3) 1/3)
(/.f64 1 (cosh.f64 x))
(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
(/.f64 1 (cosh.f64 x))
(fabs.f64 (/.f64 1 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (cosh.f64 x)))))
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(/.f64 1 (cosh.f64 x))
(expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (*.f64 (neg.f64 (log.f64 (cosh.f64 x))) 1))
(/.f64 1 (cosh.f64 x))
(exp.f64 (.f64 (.f64 1/2 (neg.f64 (log.f64 (cosh.f64 x)))) 2))
(/.f64 1 (cosh.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(/.f64 1 (cosh.f64 x))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))))) 1)
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 1)
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(*.f64 1 (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(*.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4) (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (cosh.f64 x))))
(.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (.f64 2 (cosh.f64 x)))))
(/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 2 (cosh.f64 x))))
(*.f64 (sqrt.f64 2) (pow.f64 (/.f64 1/2 (cosh.f64 x)) 1/2))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 (cosh.f64 x))))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(/.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))) (cbrt.f64 (cosh.f64 x)))
(/.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)) (cbrt.f64 (cosh.f64 x)))
(*.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(/.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))) (cbrt.f64 (cosh.f64 x)))
(/.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)) (cbrt.f64 (cosh.f64 x)))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2)) (sqrt.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x)))))
(*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x)))) (sqrt.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x)))))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (sqrt.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x)))))
(*.f64 (pow.f64 1 1/2) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(*.f64 (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2) 1/2) (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 2)) (sqrt.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x)))))
(*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x)))) (sqrt.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x)))))
(*.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (sqrt.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x)))))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 2 (cosh.f64 x))))
(.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (.f64 2 (cosh.f64 x)))))
(/.f64 (sqrt.f64 -2) (sqrt.f64 (*.f64 (cosh.f64 x) -2)))
(/.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x)))))
(.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (.f64 2 (cosh.f64 x)))))
(/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 2 (cosh.f64 x))))
(pow.f64 (/.f64 1 (cosh.f64 x)) 1/2)
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(pow.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) 1)
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 1/4) 2)
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(pow.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))) 3)
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(pow.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)) 1/4)
(pow.f64 (pow.f64 (cosh.f64 x) -2) 1/4)
(pow.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3/2))
(cbrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 3/2)))
(fabs.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(log.f64 (exp.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))))))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3/2))
(cbrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 3/2)))
(expm1.f64 (log1p.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(exp.f64 (*.f64 1/2 (neg.f64 (log.f64 (cosh.f64 x)))))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(exp.f64 (*.f64 (neg.f64 (log.f64 (cosh.f64 x))) 1/2))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(exp.f64 (.f64 (.f64 1/2 (neg.f64 (log.f64 (cosh.f64 x)))) 1))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(log1p.f64 (expm1.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x)))))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(-.f64 (exp.f64 (log1p.f64 (cosh.f64 x))) 1)
(cosh.f64 x)
(*.f64 (cosh.f64 x) 1)
(cosh.f64 x)
(.f64 (.f64 2 (cosh.f64 x)) 1/2)
(cosh.f64 x)
(*.f64 1 (cosh.f64 x))
(cosh.f64 x)
(*.f64 (sqrt.f64 (cosh.f64 x)) (sqrt.f64 (cosh.f64 x)))
(cosh.f64 x)
(*.f64 (cbrt.f64 (cosh.f64 x)) (pow.f64 (cbrt.f64 (cosh.f64 x)) 2))
(cosh.f64 x)
(*.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) (cbrt.f64 (cosh.f64 x)))
(cosh.f64 x)
(/.f64 2 (/.f64 2 (cosh.f64 x)))
(cosh.f64 x)
(/.f64 (cosh.f64 x) 1)
(cosh.f64 x)
(/.f64 (*.f64 2 (cosh.f64 x)) 2)
(cosh.f64 x)
(/.f64 1 (/.f64 1 (cosh.f64 x)))
(cosh.f64 x)
(/.f64 (sqrt.f64 (.f64 2 (cosh.f64 x))) (/.f64 2 (sqrt.f64 (.f64 2 (cosh.f64 x)))))
(cosh.f64 x)
(/.f64 (pow.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) 2) (/.f64 2 (cbrt.f64 (.f64 2 (cosh.f64 x)))))
(cosh.f64 x)
(/.f64 (*.f64 (cosh.f64 x) -2) -2)
(cosh.f64 x)
(pow.f64 (cosh.f64 x) 1)
(cosh.f64 x)
(pow.f64 (sqrt.f64 (cosh.f64 x)) 2)
(cosh.f64 x)
(pow.f64 (cbrt.f64 (cosh.f64 x)) 3)
(cosh.f64 x)
(pow.f64 (pow.f64 (cosh.f64 x) 3) 1/3)
(cosh.f64 x)
(sqrt.f64 (pow.f64 (cosh.f64 x) 2))
(cosh.f64 x)
(log.f64 (exp.f64 (cosh.f64 x)))
(cosh.f64 x)
(log.f64 (+.f64 1 (expm1.f64 (cosh.f64 x))))
(cosh.f64 x)
(cbrt.f64 (pow.f64 (cosh.f64 x) 3))
(cosh.f64 x)
(expm1.f64 (log1p.f64 (cosh.f64 x)))
(cosh.f64 x)
(exp.f64 (log.f64 (cosh.f64 x)))
(cosh.f64 x)
(exp.f64 (*.f64 (log.f64 (cosh.f64 x)) 1))
(cosh.f64 x)
(log1p.f64 (expm1.f64 (cosh.f64 x)))
(cosh.f64 x)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.31%	(.f64 (.f64 x x) -1/2)

Compiler

Compiled 19 to 10 computations (47.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite86.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1074×	`add-sqr-sqrt`
1056×	`*-un-lft-identity`
1004×	`pow1`
984×	`add-cube-cbrt`
976×	`add-cbrt-cube`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1407	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

Outputs

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

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1650×	`distribute-rgt-in`
1626×	`distribute-lft-in`
1316×	`log-prod`
928×	`associate-r`
822×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	299
1	92	299
2	360	299
3	2121	299

Stop Event

1×	node limit

Counts

23 → 13

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

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

localize35.0ms (0.9%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.01%	(cosh.f64 x)
✓	0.02%	(/.f64 1 (cosh.f64 x))

Compiler

Compiled 9 to 5 computations (44.4% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite49.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1290×	`add-sqr-sqrt`
1272×	`*-un-lft-identity`
1180×	`add-cube-cbrt`
1166×	`add-cbrt-cube`
1156×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	140	11
2	1630	11

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

simplify47.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1416×	`associate-/r*`
1090×	`associate-r`
870×	`associate-l`
710×	`distribute-lft-neg-out`
678×	`distribute-rgt-neg-out`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	851
1	178	847
2	592	487
3	3111	481

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

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

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.44%	(/.f64 2 (+.f64 2 (*.f64 x x)))

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	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)))

rewrite55.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1624×	`add-sqr-sqrt`
1596×	`*-un-lft-identity`
1500×	`add-cube-cbrt`
1490×	`add-cbrt-cube`
154×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	157	15
2	2039	15

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

Outputs

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

simplify51.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1628×	`associate-/l*`
1470×	`associate-/r*`
1322×	`associate-r`
1102×	`associate-l`
888×	`associate-+r+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	848
1	237	840
2	841	836
3	4306	836

Stop Event

1×	node limit

Counts

36 → 57

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

eval202.0ms (5.5%)

Compiler: Compiled 6899 to 4896 computations (29% saved)

prune69.0ms (1.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	433	4	437
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	434	8	442

Error

Counts

442 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.02%	(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
▶	0.02%	(pow.f64 (sqrt.f64 (cosh.f64 x)) -2)
▶	70.95%	(/.f64 (/.f64 2 x) x)
✓	26.23%	(/.f64 2 (+.f64 2 (*.f64 x x)))
▶	69.63%	(/.f64 2 (*.f64 x x))
✓	0.02%	(/.f64 1 (cosh.f64 x))
✓	54.56%	(+.f64 1 (.f64 (.f64 x x) -1/2))
	53.65%	1

Compiler

Compiled 48 to 37 computations (22.9% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.55%	(/.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
0.0ms	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))

rewrite55.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1198×	`add-sqr-sqrt`
1176×	`*-un-lft-identity`
1120×	`pow1`
1100×	`add-cube-cbrt`
1092×	`add-cbrt-cube`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	128	13
2	1563	13

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

simplify46.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1406×	`distribute-rgt-in`
1398×	`associate-/r*`
1372×	`distribute-lft-in`
992×	`associate-+r+`
956×	`associate-+l+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	485
1	134	485
2	448	485
3	2605	485

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

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2%	(/.f64 (/.f64 2 x) x)

Compiler

Compiled 11 to 7 computations (36.4% saved)

series0.0ms (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)

rewrite52.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1378×	`add-sqr-sqrt`
1356×	`*-un-lft-identity`
1274×	`add-cube-cbrt`
1260×	`add-cbrt-cube`
1248×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	132	13
2	1713	13

Stop Event

1×	node limit

Counts

1 → 36

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

simplify50.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1518×	`associate-+r+`
1368×	`associate-+l+`
882×	`distribute-rgt-in`
850×	`distribute-lft-in`
736×	`associate-*r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	97	744
1	255	726
2	879	726
3	3763	726

Stop Event

1×	node limit

Counts

48 → 43

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

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.01%	(cosh.f64 x)
✓	0.02%	(pow.f64 (sqrt.f64 (cosh.f64 x)) -2)

Compiler

Compiled 13 to 6 computations (53.8% saved)

series5.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite50.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1500×	`add-sqr-sqrt`
1472×	`*-un-lft-identity`
1374×	`add-cube-cbrt`
1360×	`add-cbrt-cube`
1348×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	167	11
2	1933	11

Stop Event

1×	node limit

Counts

1 → 18

Calls

Call 1

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

Outputs

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

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

886×	`unswap-sqr`
802×	`associate-/l*`
660×	`associate-+r+`
624×	`associate-+l+`
592×	`associate-*r/`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	1128
1	173	772
2	433	460
3	1241	456
4	5372	456

Stop Event

1×	node limit

Counts

30 → 38

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

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

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.01%	(pow.f64 (cosh.f64 x) -1/2)
	0.01%	(cosh.f64 x)
✓	0.02%	(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)

Compiler

Compiled 16 to 10 computations (37.5% saved)

series48.0ms (1.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	x	@	inf	(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
21.0ms	x	@	-inf	(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
1.0ms	x	@	0	(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
0.0ms	x	@	inf	(pow.f64 (cosh.f64 x) -1/2)
0.0ms	x	@	-inf	(pow.f64 (cosh.f64 x) -1/2)

rewrite74.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

1636×	`add-sqr-sqrt`
1606×	`*-un-lft-identity`
1500×	`add-cube-cbrt`
1486×	`add-cbrt-cube`
178×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	193	22
2	2144	22

Stop Event

1×	node limit

Counts

2 → 41

Calls

Call 1

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

Outputs

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

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

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1422×	`associate-/l*`
1342×	`fma-def`
814×	`associate-r`
714×	`associate-l`
628×	`associate-*r/`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1667
1	256	1659
2	669	1309
3	2858	1295

Stop Event

1×	node limit

Counts

65 → 81

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
1
(+.f64 1 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 7/96 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -139/5760 (pow.f64 x 6)) (*.f64 7/96 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)
(*.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))
(*.f64 (/.f64 1 (cosh.f64 x)) 1)
(*.f64 1 (/.f64 1 (cosh.f64 x)))
(.f64 (pow.f64 (cosh.f64 x) -1/4) (.f64 (pow.f64 (cosh.f64 x) -1/4) (pow.f64 (cosh.f64 x) -1/2)))
(*.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)) (pow.f64 (cosh.f64 x) -1/2)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (/.f64 1 (cosh.f64 x))))
(.f64 (.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/4)) (pow.f64 (cosh.f64 x) -1/4))
(.f64 (.f64 (pow.f64 (cosh.f64 x) -1/2) (cbrt.f64 (/.f64 1 (cosh.f64 x)))) (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1))
(/.f64 1 (cosh.f64 x))
(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
(log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))
(log.f64 (+.f64 1 (expm1.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))))
(exp.f64 (*.f64 -1 (log.f64 (cosh.f64 x))))
(exp.f64 (*.f64 (log.f64 (cosh.f64 x)) -1))
(exp.f64 (.f64 (.f64 -1 (log.f64 (cosh.f64 x))) 1))
(log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (cosh.f64 x) -1/2))) 1)
(*.f64 (pow.f64 (cosh.f64 x) -1/2) 1)
(*.f64 1 (pow.f64 (cosh.f64 x) -1/2))
(*.f64 (pow.f64 (cosh.f64 x) -1/4) (pow.f64 (cosh.f64 x) -1/4))
(*.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)) (cbrt.f64 (/.f64 1 (cosh.f64 x))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2))) (sqrt.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x)))))
(*.f64 (pow.f64 1 -1/2) (pow.f64 (cosh.f64 x) -1/2))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1/2) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1/2) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1/2))
(sqrt.f64 (/.f64 1 (cosh.f64 x)))
(fabs.f64 (pow.f64 (cosh.f64 x) -1/2))
(log.f64 (exp.f64 (pow.f64 (cosh.f64 x) -1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (cosh.f64 x) -1/2))))
(cbrt.f64 (pow.f64 (cosh.f64 x) -3/2))
(expm1.f64 (log1p.f64 (pow.f64 (cosh.f64 x) -1/2)))
(exp.f64 (*.f64 -1/2 (log.f64 (cosh.f64 x))))
(exp.f64 (.f64 (.f64 -1/2 (log.f64 (cosh.f64 x))) 1))
(log1p.f64 (expm1.f64 (pow.f64 (cosh.f64 x) -1/2)))

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 -1/2 (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))
(fma.f64 (.f64 x x) (fma.f64 (.f64 5/24 x) x -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 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6)))))
(+.f64 (fma.f64 -61/720 (pow.f64 x 6) (.f64 -1/2 (.f64 x x))) (fma.f64 5/24 (pow.f64 x 4) 1))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (fma.f64 5/24 (pow.f64 x 4) 1)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
1
(+.f64 1 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 1)
(fma.f64 x (*.f64 x -1/4) 1)
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 7/96 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/4 (.f64 x x) (.f64 (pow.f64 x 4) 7/96)))
(+.f64 1 (fma.f64 (pow.f64 x 4) 7/96 (.f64 (.f64 x x) -1/4)))
(fma.f64 (pow.f64 x 4) 7/96 (fma.f64 (*.f64 x x) -1/4 1))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 7/96) -1/4) 1)
(+.f64 1 (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -139/5760 (pow.f64 x 6)) (*.f64 7/96 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/4 (.f64 x x) (fma.f64 -139/5760 (pow.f64 x 6) (.f64 (pow.f64 x 4) 7/96))))
(+.f64 1 (fma.f64 (.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) 7/96 (.f64 (pow.f64 x 6) -139/5760))))
(+.f64 1 (fma.f64 (pow.f64 x 4) 7/96 (fma.f64 (pow.f64 x 6) -139/5760 (.f64 (.f64 x x) -1/4))))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) 7/96 (fma.f64 (pow.f64 x 6) -139/5760 1)))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (/.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 (pow.f64 (cosh.f64 x) -1/4) (.f64 (pow.f64 (cosh.f64 x) -1/4) (pow.f64 (cosh.f64 x) -1/2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(*.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)) (pow.f64 (cosh.f64 x) -1/2)))
(.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (.f64 (pow.f64 (cosh.f64 x) -1/2) (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2))))
(.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)) (.f64 (pow.f64 (cosh.f64 x) -1/2) (cbrt.f64 (/.f64 1 (cosh.f64 x)))))
(.f64 (pow.f64 (cosh.f64 x) -1/2) (.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2))))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (cbrt.f64 (/.f64 1 (cosh.f64 x))))
(*.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))
(.f64 (.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/4)) (pow.f64 (cosh.f64 x) -1/4))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(.f64 (.f64 (pow.f64 (cosh.f64 x) -1/2) (cbrt.f64 (/.f64 1 (cosh.f64 x)))) (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)))
(.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (.f64 (pow.f64 (cosh.f64 x) -1/2) (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2))))
(.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)) (.f64 (pow.f64 (cosh.f64 x) -1/2) (cbrt.f64 (/.f64 1 (cosh.f64 x)))))
(.f64 (pow.f64 (cosh.f64 x) -1/2) (.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2))))
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1))
(pow.f64 (sqrt.f64 (cosh.f64 x)) -2)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)))
(/.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) -2) (cbrt.f64 (cosh.f64 x)))
(/.f64 1 (cosh.f64 x))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.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))
(log.f64 (+.f64 1 (expm1.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))
(exp.f64 (*.f64 -1 (log.f64 (cosh.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (*.f64 (log.f64 (cosh.f64 x)) -1))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 1 (cosh.f64 x))
(exp.f64 (.f64 (.f64 -1 (log.f64 (cosh.f64 x))) 1))
(/.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))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (cosh.f64 x) -1/2))) 1)
(pow.f64 (cosh.f64 x) -1/2)
(*.f64 (pow.f64 (cosh.f64 x) -1/2) 1)
(pow.f64 (cosh.f64 x) -1/2)
(*.f64 1 (pow.f64 (cosh.f64 x) -1/2))
(pow.f64 (cosh.f64 x) -1/2)
(*.f64 (pow.f64 (cosh.f64 x) -1/4) (pow.f64 (cosh.f64 x) -1/4))
(pow.f64 (cosh.f64 x) -1/2)
(*.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)))
(*.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)) (cbrt.f64 (/.f64 1 (cosh.f64 x))))
(*.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -1/2)))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2))) (sqrt.f64 (cbrt.f64 (/.f64 1 (cosh.f64 x)))))
(*.f64 (pow.f64 1 -1/2) (pow.f64 (cosh.f64 x) -1/2))
(pow.f64 (cosh.f64 x) -1/2)
(*.f64 (pow.f64 (sqrt.f64 (cosh.f64 x)) -1/2) (pow.f64 (sqrt.f64 (cosh.f64 x)) -1/2))
(/.f64 1 (sqrt.f64 (cosh.f64 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) -1/2) (pow.f64 (cbrt.f64 (cosh.f64 x)) -1/2))
(sqrt.f64 (/.f64 1 (cosh.f64 x)))
(pow.f64 (cosh.f64 x) -1/2)
(fabs.f64 (pow.f64 (cosh.f64 x) -1/2))
(pow.f64 (cosh.f64 x) -1/2)
(log.f64 (exp.f64 (pow.f64 (cosh.f64 x) -1/2)))
(pow.f64 (cosh.f64 x) -1/2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (cosh.f64 x) -1/2))))
(pow.f64 (cosh.f64 x) -1/2)
(cbrt.f64 (pow.f64 (cosh.f64 x) -3/2))
(expm1.f64 (log1p.f64 (pow.f64 (cosh.f64 x) -1/2)))
(pow.f64 (cosh.f64 x) -1/2)
(exp.f64 (*.f64 -1/2 (log.f64 (cosh.f64 x))))
(pow.f64 (cosh.f64 x) -1/2)
(exp.f64 (.f64 (.f64 -1/2 (log.f64 (cosh.f64 x))) 1))
(pow.f64 (cosh.f64 x) -1/2)
(log1p.f64 (expm1.f64 (pow.f64 (cosh.f64 x) -1/2)))
(pow.f64 (cosh.f64 x) -1/2)

eval67.0ms (1.8%)

Compiler: Compiled 2803 to 1912 computations (31.8% saved)

prune31.0ms (0.9%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	264	2	266
Fresh	0	1	1
Picked	0	1	1
Done	0	6	6
Total	264	10	274

Error

Counts

274 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.02%	(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
✓	0.02%	(pow.f64 (sqrt.f64 (cosh.f64 x)) -2)
✓	70.95%	(/.f64 (/.f64 2 x) x)
✓	26.23%	(/.f64 2 (+.f64 2 (*.f64 x x)))
✓	69.63%	(/.f64 2 (*.f64 x x))
✓	0.02%	(/.f64 1 (cosh.f64 x))
▶	44.56%	(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
✓	54.56%	(+.f64 1 (.f64 (.f64 x x) -1/2))
▶	70.95%	(*.f64 (/.f64 2 x) (/.f64 1 x))
	53.65%	1

Compiler

Compiled 66 to 51 computations (22.7% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.43%	(*.f64 (/.f64 2 x) (/.f64 1 x))

Compiler

Compiled 17 to 12 computations (29.4% saved)

series0.0ms (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))

rewrite55.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1504×	`add-sqr-sqrt`
1480×	`*-un-lft-identity`
1386×	`add-cube-cbrt`
1368×	`add-cbrt-cube`
1352×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	170	13
2	1994	13

Stop Event

1×	node limit

Counts

1 → 36

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

simplify288.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

1148×	`associate-/r/`
954×	`distribute-lft-in`
948×	`distribute-rgt-in`
866×	`associate-r`
678×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	628
1	212	628
2	676	628
3	3309	628

Stop Event

1×	node limit

Counts

48 → 38

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

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.98%	(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
	1.55%	(/.f64 2 (*.f64 x x))

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)

rewrite71.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1950×	`add-sqr-sqrt`
1924×	`*-un-lft-identity`
1812×	`add-cube-cbrt`
1802×	`add-cbrt-cube`
196×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	204	13
2	2779	13

Stop Event

1×	node limit

Counts

1 → 56

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

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1054×	`associate-+r-`
902×	`associate--l+`
818×	`associate-+l-`
728×	`associate-r`
726×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1740
1	338	1634
2	1037	1622
3	4978	1622

Stop Event

1×	node limit

Counts

68 → 76

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

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

eval66.0ms (1.8%)

Compiler: Compiled 1618 to 1275 computations (21.2% saved)

prune20.0ms (0.5%)

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	1	1
Picked	0	1	1
Done	0	8	8
Total	137	11	148

Error

Counts

148 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.02%	(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
✓	0.02%	(pow.f64 (sqrt.f64 (cosh.f64 x)) -2)
✓	70.95%	(/.f64 (/.f64 2 x) x)
	69.63%	(/.f64 2 (/.f64 x (/.f64 1 x)))
✓	26.23%	(/.f64 2 (+.f64 2 (*.f64 x x)))
✓	69.63%	(/.f64 2 (*.f64 x x))
✓	0.02%	(/.f64 1 (cosh.f64 x))
✓	44.56%	(-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)
✓	54.56%	(+.f64 1 (.f64 (.f64 x x) -1/2))
✓	70.95%	(*.f64 (/.f64 2 x) (/.f64 1 x))
	53.65%	1

Compiler

Compiled 74 to 57 computations (23% saved)

regimes16.0ms (0.4%)

Counts

13 → 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 (.f64 x x) -1/2))
(/.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 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(pow.f64 (sqrt.f64 (cosh.f64 x)) -2)
(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))

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

Calls

3 calls:

9.0ms	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))))

Results

Error	Segments	Branch
0.02%	1	`x`
0.02%	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0.02%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 105 to 72 computations (31.4% saved)

regimes15.0ms (0.4%)

Counts

10 → 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 (.f64 x x) -1/2))
(/.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 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

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

Calls

3 calls:

6.0ms	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)))

Results

Error	Segments	Branch
0.02%	1	`x`
0.02%	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0.02%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 79 to 54 computations (31.6% saved)

regimes16.0ms (0.4%)

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

Calls

1 calls:

14.0ms

Results

Error	Segments	Branch
1.16%	3	`x`

Compiler

Compiled 51 to 33 computations (35.3% saved)

bsearch39.0ms (1.1%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
17.0ms	10.176983630866347	99837.72296770896
22.0ms	-9.56460543999104e+30	-0.12316677777372591

Results

35.0ms

304×

body

256

valid

Compiler

Compiled 393 to 314 computations (20.1% saved)

regimes6.0ms (0.2%)

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

5.0ms

Results

Error	Segments	Branch
26.23%	1	`x`

Compiler

Compiled 42 to 27 computations (35.7% saved)

regimes15.0ms (0.4%)

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

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

Calls

1 calls:

14.0ms

Results

Error	Segments	Branch
26.25%	3	`x`

Compiler

Compiled 28 to 18 computations (35.7% saved)

bsearch42.0ms (1.1%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.00010492763201347872	10.176983630866347
23.0ms	-9.56460543999104e+30	-0.12316677777372591

Results

38.0ms

320×

body

256

valid

Compiler

Compiled 333 to 250 computations (24.9% saved)

regimes13.0ms (0.4%)

Accuracy

Total -45.0b remaining (-265.2%)

Threshold costs -45b (-265.2%)

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
26.5%	3	`x`

Compiler

Compiled 21 to 14 computations (33.3% saved)

bsearch37.0ms (1%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
16.0ms	0.00010492763201347872	10.176983630866347
21.0ms	-9.56460543999104e+30	-0.12316677777372591

Results

34.0ms

320×

body

256

valid

Compiler

Compiled 213 to 170 computations (20.2% saved)

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative`
6×	`if-if-or-not`
2×	`sub-neg`
2×	`1-exp`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	211
1	61	211
2	62	211

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (cosh.f64 x)) -2)
(/.f64 1 (cosh.f64 x))
(if (<=.f64 x -135000000) (-.f64 (+.f64 1 (/.f64 2 (.f64 x x))) 1) (if (<=.f64 x 36000) (/.f64 2 (+.f64 2 (.f64 x x))) (-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)))
(/.f64 2 (+.f64 2 (*.f64 x x)))
(if (<=.f64 x -5/4) (/.f64 2 (.f64 x x)) (if (<=.f64 x 5/4) (+.f64 1 (.f64 (.f64 x x) -1/2)) (/.f64 2 (.f64 x x))))
(if (<=.f64 x -3152519739159347/2251799813685248) (/.f64 2 (.f64 x x)) (if (<=.f64 x 3152519739159347/2251799813685248) 1 (/.f64 2 (.f64 x x))))
1

Outputs
(pow.f64 (sqrt.f64 (cosh.f64 x)) -2)
(/.f64 1 (cosh.f64 x))
(if (<=.f64 x -135000000) (-.f64 (+.f64 1 (/.f64 2 (.f64 x x))) 1) (if (<=.f64 x 36000) (/.f64 2 (+.f64 2 (.f64 x x))) (-.f64 (+.f64 1 (/.f64 2 (*.f64 x x))) 1)))
(if (or (<=.f64 x -135000000) (not (<=.f64 x 36000))) (+.f64 (+.f64 1 (/.f64 2 (.f64 x x))) -1) (/.f64 2 (+.f64 2 (.f64 x x))))
(/.f64 2 (+.f64 2 (*.f64 x x)))
(if (<=.f64 x -5/4) (/.f64 2 (.f64 x x)) (if (<=.f64 x 5/4) (+.f64 1 (.f64 (.f64 x x) -1/2)) (/.f64 2 (.f64 x x))))
(if (or (<=.f64 x -5/4) (not (<=.f64 x 5/4))) (/.f64 2 (.f64 x x)) (+.f64 1 (.f64 (*.f64 x x) -1/2)))
(if (<=.f64 x -3152519739159347/2251799813685248) (/.f64 2 (.f64 x x)) (if (<=.f64 x 3152519739159347/2251799813685248) 1 (/.f64 2 (.f64 x x))))
(if (or (<=.f64 x -3152519739159347/2251799813685248) (not (<=.f64 x 3152519739159347/2251799813685248))) (/.f64 2 (*.f64 x x)) 1)
1

Compiler

Compiled 85 to 63 computations (25.9% saved)

soundness148.0ms (4%)

Algorithm

2×	egg-herbie

Rules

1416×	`associate-/r*`
1396×	`associate-r`
1156×	`associate-+r+`
1090×	`associate-r`
992×	`associate-+l+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	998
1	227	966
2	904	692
3	4945	692
0	75	851
1	178	847
2	592	487
3	3111	481

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 77 to 41 computations (46.8% saved)

end77.0ms (2.1%)

Compiler: Compiled 79 to 53 computations (32.9% saved)

Details

analyze0.0ms (0%)

sample799.0ms (21.8%)

preprocess91.0ms (2.5%)

simplify94.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.2%)

series2.0ms (0.1%)

rewrite90.0ms (2.4%)

simplify57.0ms (1.5%)

eval17.0ms (0.5%)

prune8.0ms (0.2%)

localize52.0ms (1.4%)

series4.0ms (0.1%)

rewrite70.0ms (1.9%)

simplify83.0ms (2.3%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite86.0ms (2.3%)

simplify40.0ms (1.1%)

localize35.0ms (0.9%)

series0.0ms (0%)

rewrite49.0ms (1.3%)

simplify47.0ms (1.3%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite55.0ms (1.5%)

simplify51.0ms (1.4%)

eval202.0ms (5.5%)

prune69.0ms (1.9%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite55.0ms (1.5%)

simplify46.0ms (1.2%)

localize5.0ms (0.1%)

series0.0ms (0%)

rewrite52.0ms (1.4%)

simplify50.0ms (1.4%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite50.0ms (1.4%)

simplify58.0ms (1.6%)

localize7.0ms (0.2%)

series48.0ms (1.3%)

rewrite74.0ms (2%)

simplify57.0ms (1.6%)

eval67.0ms (1.8%)

prune31.0ms (0.9%)

localize7.0ms (0.2%)

series0.0ms (0%)

rewrite55.0ms (1.5%)

simplify288.0ms (7.9%)

localize12.0ms (0.3%)

series1.0ms (0%)

rewrite71.0ms (1.9%)

simplify71.0ms (1.9%)

eval66.0ms (1.8%)

prune20.0ms (0.5%)

regimes16.0ms (0.4%)

regimes15.0ms (0.4%)

regimes16.0ms (0.4%)

bsearch39.0ms (1.1%)

regimes6.0ms (0.2%)

regimes15.0ms (0.4%)

bsearch42.0ms (1.1%)

regimes13.0ms (0.4%)

bsearch37.0ms (1%)

simplify13.0ms (0.4%)

soundness148.0ms (4%)

end77.0ms (2.1%)

Profiling