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)

sample988.0ms (33.1%)

Results

977.0ms

8256×

body

256

valid

Bogosity

preprocess94.0ms (3.1%)

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)

simplify96.0ms (3.2%)

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

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 24 to 8 computations (66.7% saved)

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))))
1.0ms	x	@	inf	(/.f64 2 (+.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	@	0	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0ms	x	@	inf	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite120.0ms (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	34
1	216	34
2	3273	34
0	10	17
1	216	17
2	3273	17
0	10	17
0	8	11
1	169	11
2	2616	11
0	8	11

Stop Event

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

Counts

2 → 22

Calls

Call 1

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

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

Outputs

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

((#(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))))))))

simplify57.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1420×	`associate-r`
1162×	`associate-+r+`
996×	`associate-l`
988×	`associate-+l+`
846×	`associate-/l*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	96	998
1	227	966
2	902	692
3	5000	692

Stop Event

1×	node limit

Counts

46 → 53

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
2
(+.f64 2 (pow.f64 x 2))
(+.f64 2 (+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 2 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4)))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(.f64 2 (/.f64 1 (.f64 2 (cosh.f64 x))))
(.f64 1 (/.f64 2 (.f64 2 (cosh.f64 x))))
(.f64 (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)))))
(.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))))

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

eval14.0ms (0.5%)

Compiler: Compiled 654 to 443 computations (32.3% saved)

prune8.0ms (0.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	4	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Error

Counts

54 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	14.1b	(/.f64 2 (+.f64 2 (*.f64 x x)))
▶	0.0b	(/.f64 1 (cosh.f64 x))
▶	31.0b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	30.6b	1

Compiler

Compiled 23 to 18 computations (21.7% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 10 computations (47.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite65.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1076×	`add-sqr-sqrt`
1058×	`*-un-lft-identity`
1006×	`pow1`
986×	`add-cube-cbrt`
978×	`add-cbrt-cube`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1409	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

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

Outputs

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

simplify43.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1470×	`distribute-rgt-in`
1446×	`distribute-lft-in`
1164×	`log-prod`
760×	`associate-r`
704×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	299
1	93	299
2	347	299
3	1912	299

Stop Event

1×	node limit

Counts

23 → 14

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

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

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 9 to 5 computations (44.4% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite52.0ms (1.7%)

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))))))))

simplify57.0ms (1.9%)

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 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 2 (*.f64 x x))
✓	0.4b	(/.f64 2 (+.f64 2 (*.f64 x x)))

Compiler

Compiled 18 to 9 computations (50% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite62.0ms (2.1%)

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	32
1	157	24
2	2039	24

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

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

Outputs

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

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

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

806×	`associate-/r*`
672×	`unswap-sqr`
632×	`associate-+l-`
616×	`associate-+r-`
542×	`+-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	1594
1	372	1536
2	1585	1504
3	6394	1504

Stop Event

1×	node limit

Counts

80 → 95

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

eval37.0ms (1.2%)

Compiler: Compiled 1669 to 1172 computations (29.8% saved)

prune24.0ms (0.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	146	6	152

Error

Counts

152 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	46.2b	(/.f64 (/.f64 2 x) x)
✓	14.1b	(/.f64 2 (+.f64 2 (*.f64 x x)))
▶	45.9b	(/.f64 2 (*.f64 x x))
✓	0.0b	(/.f64 1 (cosh.f64 x))
✓	31.0b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	30.6b	1

Compiler

Compiled 35 to 26 computations (25.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.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))

rewrite57.0ms (1.9%)

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))))))))

simplify53.0ms (1.8%)

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 (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

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)

rewrite53.0ms (1.8%)

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

simplify84.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1522×	`associate-+r+`
1368×	`associate-+l+`
844×	`distribute-lft-in`
740×	`associate-*r/`
512×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	97	744
1	253	726
2	883	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 (/.f64 2 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 (/.f64 2 x) x) 1)
(*.f64 1 (/.f64 (/.f64 2 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 (/.f64 2 x) x)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 2 x) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 2 x) x)) 2) (cbrt.f64 (/.f64 (/.f64 2 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 (/.f64 2 x) x)))
(pow.f64 (/.f64 (/.f64 2 x) x) 1)
(pow.f64 (/.f64 (sqrt.f64 2) x) 2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 2 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 2 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 (/.f64 2 x) x) 2))
(log.f64 (exp.f64 (/.f64 (/.f64 2 x) x)))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 2 x) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (/.f64 2 x) x)))
(exp.f64 (log.f64 (/.f64 (/.f64 2 x) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 2 x) x)) 1))
(log1p.f64 (expm1.f64 (/.f64 (/.f64 2 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 (/.f64 2 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 (/.f64 2 x) x) 1)
(/.f64 2 (*.f64 x x))
(*.f64 1 (/.f64 (/.f64 2 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 (/.f64 2 x) x)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 2 x) x)) 2))
(/.f64 2 (*.f64 x x))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 2 x) x)) 2) (cbrt.f64 (/.f64 (/.f64 2 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 (/.f64 2 x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (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 (/.f64 2 x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (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 (/.f64 2 x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (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 (/.f64 2 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 (/.f64 2 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 (/.f64 2 x) x)) 3)
(/.f64 2 (*.f64 x x))
(pow.f64 (pow.f64 (/.f64 (/.f64 2 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 (/.f64 2 x) x) 2))
(/.f64 2 (*.f64 x x))
(log.f64 (exp.f64 (/.f64 (/.f64 2 x) x)))
(/.f64 2 (*.f64 x x))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 2 x) x) 3))
(/.f64 2 (*.f64 x x))
(expm1.f64 (log1p.f64 (/.f64 (/.f64 2 x) x)))
(/.f64 2 (*.f64 x x))
(exp.f64 (log.f64 (/.f64 (/.f64 2 x) x)))
(/.f64 2 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 2 x) x)) 1))
(/.f64 2 (*.f64 x x))
(log1p.f64 (expm1.f64 (/.f64 (/.f64 2 x) x)))
(/.f64 2 (*.f64 x x))

eval12.0ms (0.4%)

Compiler: Compiled 627 to 436 computations (30.5% saved)

prune36.0ms (1.2%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	1	1
Picked	0	1	1
Done	0	4	4
Total	65	8	73

Error

Counts

73 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	46.2b	(/.f64 (/.f64 2 x) x)
✓	14.1b	(/.f64 2 (+.f64 2 (*.f64 x x)))
✓	45.9b	(/.f64 2 (*.f64 x x))
✓	0.0b	(/.f64 1 (cosh.f64 x))
▶	33.5b	(-.f64 (+.f64 1 (/.f64 (/.f64 2 x) x)) 1)
✓	31.0b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
▶	46.2b	(*.f64 (/.f64 2 x) (/.f64 1 x))
	30.6b	1

Compiler

Compiled 53 to 40 computations (24.5% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 12 computations (29.4% saved)

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))

rewrite59.0ms (2%)

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

simplify58.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1214×	`associate-r`
1074×	`associate-l`
876×	`associate-+r+`
832×	`associate-+l+`
728×	`associate-*r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	628
1	209	628
2	738	628
3	5243	628

Stop Event

1×	node limit

Counts

48 → 37

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

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (/.f64 2 x) x)
✓	1.8b	(-.f64 (+.f64 1 (/.f64 (/.f64 2 x) x)) 1)

Compiler

Compiled 28 to 20 computations (28.6% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite80.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1296×	`associate-/r*`
934×	`associate-/l*`
826×	`*-commutative`
604×	`distribute-lft-in`
562×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	208	13
2	2927	13

Stop Event

1×	node limit

Counts

1 → 174

Calls

Call 1

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

Outputs

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

simplify113.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

498×	`distribute-lft-neg-out`
486×	`associate-/l/`
468×	`distribute-lft-neg-in`
464×	`*-commutative`
464×	`distribute-rgt-neg-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	445	6706
1	1247	6418
2	4703	6406

Stop Event

1×	node limit

Counts

186 → 273

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

eval118.0ms (4%)

Compiler: Compiled 6658 to 4807 computations (27.8% saved)

prune50.0ms (1.7%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	351	2	353
Fresh	0	1	1
Picked	0	1	1
Done	0	6	6
Total	351	10	361

Error

Counts

361 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	46.2b	(/.f64 (/.f64 2 x) x)
	45.9b	(/.f64 2 (/.f64 x (/.f64 1 x)))
✓	14.1b	(/.f64 2 (+.f64 2 (*.f64 x x)))
✓	45.9b	(/.f64 2 (*.f64 x x))
✓	0.0b	(/.f64 1 (cosh.f64 x))
✓	33.5b	(-.f64 (+.f64 1 (/.f64 (/.f64 2 x) x)) 1)
	33.5b	(+.f64 (+.f64 (/.f64 (/.f64 2 x) x) -1) 1)
✓	31.0b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	46.2b	(*.f64 (/.f64 2 x) (/.f64 1 x))
	30.6b	1

Compiler

Compiled 71 to 54 computations (23.9% saved)

regimes14.0ms (0.5%)

Counts

11 → 1

Calls

Call 1

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

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

Compiler

Compiled 88 to 62 computations (29.5% saved)

regimes18.0ms (0.6%)

Counts

9 → 3

Calls

Call 1

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

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

Calls

1 calls:

16.0ms

Results

Error	Segments	Branch
1.8b	3	`x`

Compiler

Compiled 60 to 41 computations (31.7% saved)

bsearch38.0ms (1.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
20.0ms	1.7501427039274028e-6	3087.9381171339805
18.0ms	-982.7266498769322	-0.005665755189545006

Results

34.0ms

288×

body

256

valid

Compiler

Compiled 373 to 298 computations (20.1% saved)

regimes18.0ms (0.6%)

Counts

8 → 3

Calls

Call 1

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

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

Calls

1 calls:

16.0ms

Results

Error	Segments	Branch
1.8b	3	`x`

Compiler

Compiled 51 to 34 computations (33.3% saved)

bsearch35.0ms (1.2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	1.7501427039274028e-6	3087.9381171339805
17.0ms	-982.7266498769322	-0.005665755189545006

Results

31.0ms

288×

body

256

valid

Compiler

Compiled 373 to 298 computations (20.1% saved)

regimes8.0ms (0.3%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
14.1b	1	`x`

Compiler

Compiled 42 to 27 computations (35.7% saved)

regimes14.0ms (0.5%)

Counts

5 → 3

Calls

Call 1

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

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

Calls

1 calls:

12.0ms

Results

Error	Segments	Branch
14.1b	3	`x`

Compiler

Compiled 28 to 18 computations (35.7% saved)

bsearch33.0ms (1.1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
16.0ms	1.7501427039274028e-6	3087.9381171339805
17.0ms	-982.7266498769322	-0.005665755189545006

Results

29.0ms

288×

body

256

valid

Compiler

Compiled 301 to 226 computations (24.9% saved)

regimes12.0ms (0.4%)

Accuracy

Total -47.8b remaining (-333.4%)

Threshold costs -47.8b (-333.4%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

1 calls:

11.0ms

Results

Error	Segments	Branch
14.3b	3	`x`

Compiler

Compiled 21 to 14 computations (33.3% saved)

bsearch32.0ms (1.1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
16.0ms	1.7501427039274028e-6	3087.9381171339805
16.0ms	-982.7266498769322	-0.005665755189545006

Results

29.0ms

288×

body

256

valid

Compiler

Compiled 193 to 154 computations (20.2% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	283
1	59	283
2	60	283

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 1 (cosh.f64 x))
(if (<=.f64 x -5/4) (-.f64 (+.f64 1 (/.f64 (/.f64 2 x) x)) 1) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) -1) 1)))
(if (<=.f64 x -5/4) (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) -1) 1) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) -1) 1)))
(/.f64 2 (+.f64 2 (*.f64 x x)))
(if (<=.f64 x -5/4) (/.f64 2 (.f64 x x)) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (/.f64 2 (.f64 x x))))
(if (<=.f64 x -799388933858263/562949953421312) (/.f64 2 (.f64 x x)) (if (<=.f64 x 3152519739159347/2251799813685248) 1 (/.f64 2 (.f64 x x))))
1

Outputs
(/.f64 1 (cosh.f64 x))
(if (<=.f64 x -5/4) (-.f64 (+.f64 1 (/.f64 (/.f64 2 x) x)) 1) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) -1) 1)))
(if (<=.f64 x -5/4) (+.f64 (+.f64 1 (/.f64 (/.f64 2 x) x)) -1) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (+.f64 1 (+.f64 (/.f64 (/.f64 2 x) x) -1))))
(if (<=.f64 x -5/4) (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) -1) 1) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (+.f64 (+.f64 (/.f64 (/.f64 2 x) x) -1) 1)))
(if (or (<=.f64 x -5/4) (not (<=.f64 x 5404319552844595/4503599627370496))) (+.f64 1 (+.f64 (/.f64 (/.f64 2 x) x) -1)) (+.f64 1 (.f64 -1/2 (.f64 x x))))
(/.f64 2 (+.f64 2 (*.f64 x x)))
(if (<=.f64 x -5/4) (/.f64 2 (.f64 x x)) (if (<=.f64 x 5404319552844595/4503599627370496) (+.f64 1 (.f64 -1/2 (.f64 x x))) (/.f64 2 (.f64 x x))))
(if (or (<=.f64 x -5/4) (not (<=.f64 x 5404319552844595/4503599627370496))) (/.f64 2 (.f64 x x)) (+.f64 1 (.f64 -1/2 (*.f64 x x))))
(if (<=.f64 x -799388933858263/562949953421312) (/.f64 2 (.f64 x x)) (if (<=.f64 x 3152519739159347/2251799813685248) 1 (/.f64 2 (.f64 x x))))
(if (or (<=.f64 x -799388933858263/562949953421312) (not (<=.f64 x 3152519739159347/2251799813685248))) (/.f64 2 (*.f64 x x)) 1)
1

Compiler

Compiled 113 to 85 computations (24.8% saved)

soundness79.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1420×	`associate-r`
1162×	`associate-+r+`
996×	`associate-l`
988×	`associate-+l+`
846×	`associate-/l*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	96	998
1	227	966
2	902	692
3	5000	692

Stop Event

1×	node limit

Compiler

Compiled 53 to 27 computations (49.1% saved)

end57.0ms (1.9%)

Compiler: Compiled 107 to 75 computations (29.9% saved)

Details

analyze0.0ms (0%)

sample988.0ms (33.1%)

preprocess94.0ms (3.1%)

simplify96.0ms (3.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.3%)

series2.0ms (0.1%)

rewrite120.0ms (4%)

simplify57.0ms (1.9%)

eval14.0ms (0.5%)

prune8.0ms (0.3%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite65.0ms (2.2%)

simplify43.0ms (1.4%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite52.0ms (1.7%)

simplify57.0ms (1.9%)

localize6.0ms (0.2%)

series2.0ms (0.1%)

rewrite62.0ms (2.1%)

simplify67.0ms (2.2%)

eval37.0ms (1.2%)

prune24.0ms (0.8%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite57.0ms (1.9%)

simplify53.0ms (1.8%)

localize5.0ms (0.2%)

series0.0ms (0%)

rewrite53.0ms (1.8%)

simplify84.0ms (2.8%)

eval12.0ms (0.4%)

prune36.0ms (1.2%)

localize7.0ms (0.2%)

series0.0ms (0%)

rewrite59.0ms (2%)

simplify58.0ms (2%)

localize10.0ms (0.3%)

series1.0ms (0%)

rewrite80.0ms (2.7%)

simplify113.0ms (3.8%)

eval118.0ms (4%)

prune50.0ms (1.7%)

regimes14.0ms (0.5%)

regimes18.0ms (0.6%)

bsearch38.0ms (1.3%)

regimes18.0ms (0.6%)

bsearch35.0ms (1.2%)

regimes8.0ms (0.3%)

regimes14.0ms (0.5%)

bsearch33.0ms (1.1%)

regimes12.0ms (0.4%)

bsearch32.0ms (1.1%)

simplify9.0ms (0.3%)

soundness79.0ms (2.7%)

end57.0ms (1.9%)

Profiling