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)

sample719.0ms (44.2%)

Results

707.0ms

8256×

body

256

valid

Bogosity

preprocess95.0ms (5.8%)

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)

simplify98.0ms (6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.01%

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.01%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize8.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.01%	(/.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

1 → 12

Calls

3 calls:

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

rewrite37.0ms (2.3%)

Algorithm

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	216	17
2	3273	17
0	10	17

Stop Event

1×	iter limit
1×	unsound

Counts

1 → 10

Calls

Call 1

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

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)))))))))

simplify57.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1426×	`associate-/r*`
1258×	`associate--r+`
726×	`associate-/r/`
658×	`distribute-lft-out`
624×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	550
1	115	546
2	395	290
3	1879	286
4	6144	286

Stop Event

1×	node limit

Counts

22 → 27

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

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

eval6.0ms (0.4%)

Compiler: Compiled 300 to 216 computations (28% saved)

prune4.0ms (0.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	23	4	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	4	28

Error

Counts

28 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.01%	(/.f64 1 (cosh.f64 x))
▶	54.13%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
▶	0%	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
	53.34%	1

Compiler

Compiled 31 to 25 computations (19.4% saved)

localize14.0ms (0.8%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 37 to 25 computations (32.4% saved)

series3.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

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

rewrite53.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1576×	`add-sqr-sqrt`
1554×	`*-un-lft-identity`
1444×	`add-cube-cbrt`
1430×	`add-cbrt-cube`
1416×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	170	11
2	2065	11

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

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

Outputs

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

simplify62.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1244×	`associate-/r/`
776×	`associate-r`
636×	`fma-def`
628×	`associate-l`
518×	`distribute-rgt-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	825
1	168	821
2	516	411
3	2690	407
4	6760	407

Stop Event

1×	node limit

Counts

33 → 38

Calls

Call 1

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

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

localize6.0ms (0.4%)

Compiler: Compiled 19 to 10 computations (47.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 9 to 5 computations (44.4% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite50.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify47.0ms (2.9%)

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))

eval40.0ms (2.5%)

Compiler: Compiled 1707 to 1195 computations (30% saved)

prune14.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	115	4	119

Error

Counts

119 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0%	(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
✓	0.01%	(/.f64 1 (cosh.f64 x))
✓	54.13%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	53.34%	1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize6.0ms (0.4%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0%	(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
✓	0.01%	(/.f64 1 (cosh.f64 x))
✓	54.13%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	53.34%	1

Compiler

Compiled 22 to 18 computations (18.2% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0%	(pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)
✓	0.01%	(/.f64 1 (cosh.f64 x))
✓	54.13%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	53.34%	1

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes10.0ms (0.6%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	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%	1	`x`
0%	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 60 to 44 computations (26.7% saved)

regimes10.0ms (0.6%)

Counts

4 → 1

Calls

Call 1

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

5.0ms	x
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
0.01%	1	`x`
0.01%	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0.01%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 39 to 29 computations (25.6% saved)

regimes4.0ms (0.2%)

Accuracy

Total -0.7b remaining (-2%)

Threshold costs -0.7b (-2%)

Counts

2 → 1

Calls

Call 1

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

Outputs
1

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
53.34%	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	13	29

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 14 to 12 computations (14.3% saved)

soundness253.0ms (15.5%)

Algorithm

1×	egg-herbie

Rules

1426×	`associate-/r*`
1258×	`associate--r+`
726×	`associate-/r/`
658×	`distribute-lft-out`
624×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	550
1	115	546
2	395	290
3	1879	286
4	6144	286

Stop Event

1×	node limit

Compiler

Compiled 53 to 27 computations (49.1% saved)

end18.0ms (1.1%)

Compiler: Compiled 12 to 9 computations (25% saved)

Details

analyze0.0ms (0%)

sample719.0ms (44.2%)

preprocess95.0ms (5.8%)

simplify98.0ms (6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.5%)

series2.0ms (0.1%)

rewrite37.0ms (2.3%)

simplify57.0ms (3.5%)

eval6.0ms (0.4%)

prune4.0ms (0.3%)

localize14.0ms (0.8%)

series3.0ms (0.2%)

rewrite53.0ms (3.2%)

simplify62.0ms (3.8%)

localize6.0ms (0.4%)

localize4.0ms (0.2%)

series0.0ms (0%)

rewrite50.0ms (3.1%)

simplify47.0ms (2.9%)

eval40.0ms (2.5%)

prune14.0ms (0.8%)

localize6.0ms (0.4%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes10.0ms (0.6%)

regimes10.0ms (0.6%)

regimes4.0ms (0.2%)

simplify4.0ms (0.2%)

soundness253.0ms (15.5%)

end18.0ms (1.1%)

Profiling