Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample746.0ms (45.3%)

Results

734.0ms

8256×

body

256

valid

preprocess61.0ms (3.7%)

Algorithm

2×	egg-herbie

Rules

700×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`
311×	`fabs-div_binary64`
290×	`exp-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	21	13
3	28	13
4	47	13
5	87	13
6	184	13
7	419	13
8	1133	13
9	3111	13
10	4302	13
11	5484	13
12	7191	13
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 10 to 8 computations (20% saved)

simplify51.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`
311×	`fabs-div_binary64`
290×	`exp-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	21	13
3	28	13
4	47	13
5	87	13
6	184	13
7	419	13
8	1133	13
9	3111	13
10	4302	13
11	5484	13
12	7191	13

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize5.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series3.0ms (0.2%)

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

rewrite75.0ms (4.5%)

Algorithm

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	176	18
2	2824	18
0	8	9
1	176	9
2	2824	9
0	8	9
0	6	6
1	129	6
2	2129	6
0	6	6

Stop Event

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

Counts

2 → 22

Calls

Call 1

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

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

Outputs

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

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

simplify46.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

620×	`distribute-lft-out_binary64`
428×	`associate-/l/_binary64`
396×	`associate-+l+_binary64`
388×	`fma-def_binary64`
344×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	283
1	88	275
2	196	269
3	545	267
4	1913	267
5	3666	267
6	5200	267

Stop Event

1×	node limit

Counts

46 → 42

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)))

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

eval10.0ms (0.6%)

Compiler: Compiled 472 to 320 computations (32.2% saved)

prune8.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	4	43

Error

Counts

43 → 4

Alt Table

Click to see full alt table

Status	Error	Program
	34.1b	1
▶	0.0b	(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)))))
▶	34.6b	(fma.f64 x (*.f64 -1/2 x) 1)
▶	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 38 to 30 computations (21.1% saved)

localize3.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series4.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

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

rewrite39.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

603×	`pow1_binary64`
559×	`add-log-exp_binary64`
558×	`log1p-expm1-u_binary64`
558×	`expm1-log1p-u_binary64`
547×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	132	6
2	1583	6

Stop Event

1×	node limit

Counts

1 → 20

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

Outputs

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

simplify57.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
391×	`*-commutative_binary64`
372×	`associate-/l/_binary64`
345×	`fma-neg_binary64`
326×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	156
1	56	154
2	120	152
3	331	150
4	1128	150
5	2950	150
6	3717	150
7	4649	150
8	7728	150

Stop Event

1×	node limit

Counts

32 → 29

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)))

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

localize3.0ms (0.2%)

localize7.0ms (0.4%)

Local error

Found 6 expressions with local error:

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

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

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

rewrite58.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

815×	`pow1_binary64`
765×	`add-log-exp_binary64`
763×	`log1p-expm1-u_binary64`
763×	`expm1-log1p-u_binary64`
747×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	193	15
2	2303	15

Stop Event

1×	node limit

Counts

2 → 69

Calls

Call 1

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

Outputs

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

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

simplify44.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

701×	`distribute-rgt-neg-in_binary64`
634×	`distribute-lft-neg-in_binary64`
432×	`fma-def_binary64`
353×	`cancel-sign-sub-inv_binary64`
344×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	334
1	88	327
2	212	323
3	661	321
4	2462	321
5	6059	321

Stop Event

1×	node limit

Counts

93 → 86

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (.f64 -1 (pow.f64 x 2))))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 -1 (pow.f64 x 2)) (*.f64 -17/45 (pow.f64 x 6)))))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
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)))

Outputs
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (neg.f64 (*.f64 x x)))
(-.f64 1 (*.f64 x x))
(neg.f64 (fma.f64 x x -1))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (.f64 -1 (pow.f64 x 2))))
(fma.f64 2/3 (pow.f64 x 4) (+.f64 1 (neg.f64 (*.f64 x x))))
(-.f64 (fma.f64 2/3 (pow.f64 x 4) 1) (*.f64 x x))
(-.f64 (*.f64 2/3 (pow.f64 x 4)) (fma.f64 x x -1))
(-.f64 1 (fma.f64 x x (*.f64 (pow.f64 x 4) -2/3)))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 -1 (pow.f64 x 2)) (*.f64 -17/45 (pow.f64 x 6)))))
(fma.f64 2/3 (pow.f64 x 4) (+.f64 1 (fma.f64 -1 (.f64 x x) (.f64 -17/45 (pow.f64 x 6)))))
(+.f64 (-.f64 (.f64 -17/45 (pow.f64 x 6)) (.f64 x x)) (fma.f64 2/3 (pow.f64 x 4) 1))
(fma.f64 2/3 (pow.f64 x 4) (-.f64 (fma.f64 -17/45 (pow.f64 x 6) 1) (*.f64 x x)))
(-.f64 (fma.f64 2/3 (pow.f64 x 4) (fma.f64 -17/45 (pow.f64 x 6) 1)) (*.f64 x x))
(-.f64 (fma.f64 -17/45 (pow.f64 x 6) (fma.f64 2/3 (pow.f64 x 4) 1)) (*.f64 x x))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 1)
(fma.f64 x (*.f64 x -1/2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 (pow.f64 x 4) 5/24)))
(+.f64 1 (fma.f64 (.f64 x x) -1/2 (.f64 (pow.f64 x 4) 5/24)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 5/24 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 (pow.f64 x 4) 5/24))))
(+.f64 (fma.f64 (.f64 x x) -1/2 1) (fma.f64 (pow.f64 x 6) -61/720 (.f64 (pow.f64 x 4) 5/24)))
(+.f64 (fma.f64 x (.f64 x -1/2) 1) (fma.f64 (pow.f64 x 6) -61/720 (.f64 (pow.f64 x 4) 5/24)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 6) -61/720 (fma.f64 (pow.f64 x 4) 5/24 1)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

eval64.0ms (3.9%)

Compiler: Compiled 3378 to 2355 computations (30.3% saved)

prune24.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	1	0	1
Picked	1	0	1
Done	1	1	2
Total	202	4	206

Error

Counts

206 → 4

Alt Table

Click to see full alt table

Status	Error	Program
	34.1b	1
▶	0.0b	(/.f64 1 (cosh.f64 x))
▶	0.0b	(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
✓	34.6b	(fma.f64 x (*.f64 -1/2 x) 1)

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize4.0ms (0.3%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (/.f64 1 (cosh.f64 x)) 3)
	0.0b	(/.f64 1 (cosh.f64 x))
	0.0b	(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
✓	0.0b	(/.f64 1 (cosh.f64 x))
✓	0.0b	(pow.f64 (/.f64 1 (cosh.f64 x)) 3)

series6.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(pow.f64 (/.f64 1 (cosh.f64 x)) 3)
1.0ms	x	@	inf	(pow.f64 (/.f64 1 (cosh.f64 x)) 3)
1.0ms	x	@	0	(pow.f64 (/.f64 1 (cosh.f64 x)) 3)
0.0ms	x	@	0	(/.f64 1 (cosh.f64 x))
0.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))

rewrite54.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

634×	`pow1_binary64`
600×	`add-log-exp_binary64`
598×	`log1p-expm1-u_binary64`
598×	`expm1-log1p-u_binary64`
584×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	172	18
2	1744	18

Stop Event

1×	node limit

Counts

3 → 81

Calls

Call 1

Inputs
(pow.f64 (/.f64 1 (cosh.f64 x)) 3)
(/.f64 1 (cosh.f64 x))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))

Outputs

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

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

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

simplify44.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

706×	`times-frac_binary64`
448×	`associate-/r*_binary64`
432×	`fma-def_binary64`
420×	`distribute-rgt-out_binary64`
376×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	492
1	88	486
2	218	478
3	679	474
4	2268	474
5	4921	474

Stop Event

1×	node limit

Counts

117 → 74

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -3/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -3/2 (pow.f64 x 2)) (.f64 11/8 (pow.f64 x 4))))
(+.f64 (.f64 -241/240 (pow.f64 x 6)) (+.f64 1 (+.f64 (.f64 -3/2 (pow.f64 x 2)) (*.f64 11/8 (pow.f64 x 4)))))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))

Outputs
1
(+.f64 1 (*.f64 -3/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -3/2 (.f64 x x)))
(fma.f64 -3/2 (*.f64 x x) 1)
(+.f64 1 (+.f64 (.f64 -3/2 (pow.f64 x 2)) (.f64 11/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -3/2 (.f64 x x) (.f64 11/8 (pow.f64 x 4))))
(fma.f64 -3/2 (*.f64 x x) (fma.f64 11/8 (pow.f64 x 4) 1))
(+.f64 (.f64 -241/240 (pow.f64 x 6)) (+.f64 1 (+.f64 (.f64 -3/2 (pow.f64 x 2)) (*.f64 11/8 (pow.f64 x 4)))))
(fma.f64 -241/240 (pow.f64 x 6) (+.f64 1 (fma.f64 -3/2 (.f64 x x) (.f64 11/8 (pow.f64 x 4)))))
(+.f64 (fma.f64 -3/2 (.f64 x x) (.f64 11/8 (pow.f64 x 4))) (fma.f64 -241/240 (pow.f64 x 6) 1))
(fma.f64 -241/240 (pow.f64 x 6) (fma.f64 -3/2 (*.f64 x x) (fma.f64 11/8 (pow.f64 x 4) 1)))
(fma.f64 -3/2 (*.f64 x x) (fma.f64 11/8 (pow.f64 x 4) (fma.f64 -241/240 (pow.f64 x 6) 1)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 11/8 -3/2) (fma.f64 -241/240 (pow.f64 x 6) 1))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 3))
(/.f64 8 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 3))
(/.f64 8 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 3))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 1)
(fma.f64 x (*.f64 x -1/2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 (pow.f64 x 4) 5/24)))
(+.f64 1 (fma.f64 (.f64 x x) -1/2 (.f64 (pow.f64 x 4) 5/24)))
(fma.f64 (pow.f64 x 4) 5/24 (fma.f64 x (*.f64 x -1/2) 1))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 5/24 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 (pow.f64 x 4) 5/24))))
(+.f64 1 (fma.f64 (.f64 x x) -1/2 (fma.f64 (pow.f64 x 4) 5/24 (.f64 (pow.f64 x 6) -61/720))))
(+.f64 (.f64 (pow.f64 x 6) -61/720) (fma.f64 (pow.f64 x 4) 5/24 (fma.f64 x (.f64 x -1/2) 1)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 5/24) -1/2) (fma.f64 (pow.f64 x 6) -61/720 1))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 1)
(fma.f64 x (*.f64 x -1/2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 (pow.f64 x 4) 5/24)))
(+.f64 1 (fma.f64 (.f64 x x) -1/2 (.f64 (pow.f64 x 4) 5/24)))
(fma.f64 (pow.f64 x 4) 5/24 (fma.f64 x (*.f64 x -1/2) 1))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 5/24 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 (pow.f64 x 4) 5/24))))
(+.f64 1 (fma.f64 (.f64 x x) -1/2 (fma.f64 (pow.f64 x 4) 5/24 (.f64 (pow.f64 x 6) -61/720))))
(+.f64 (.f64 (pow.f64 x 6) -61/720) (fma.f64 (pow.f64 x 4) 5/24 (fma.f64 x (.f64 x -1/2) 1)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 5/24) -1/2) (fma.f64 (pow.f64 x 6) -61/720 1))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

localize2.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval28.0ms (1.7%)

Compiler: Compiled 1081 to 737 computations (31.8% saved)

prune12.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	107	4	111

Error

Counts

111 → 4

Alt Table

Click to see full alt table

Status	Error	Program
	34.1b	1
✓	0.0b	(/.f64 1 (cosh.f64 x))
▶	0.0b	(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
✓	34.6b	(fma.f64 x (*.f64 -1/2 x) 1)

Compiler

Compiled 20 to 16 computations (20% saved)

localize5.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series3.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

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

rewrite40.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

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

Outputs

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

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

simplify43.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

701×	`distribute-rgt-neg-in_binary64`
634×	`distribute-lft-neg-in_binary64`
432×	`fma-def_binary64`
353×	`cancel-sign-sub-inv_binary64`
344×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	334
1	88	327
2	212	323
3	661	321
4	2462	321
5	6059	321

Stop Event

1×	node limit

Counts

66 → 59

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (.f64 -1 (pow.f64 x 2))))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 -1 (pow.f64 x 2)) (*.f64 -17/45 (pow.f64 x 6)))))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
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)))

Outputs
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (neg.f64 (*.f64 x x)))
(-.f64 1 (*.f64 x x))
(neg.f64 (fma.f64 x x -1))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (.f64 -1 (pow.f64 x 2))))
(fma.f64 2/3 (pow.f64 x 4) (+.f64 1 (neg.f64 (*.f64 x x))))
(-.f64 (fma.f64 2/3 (pow.f64 x 4) 1) (*.f64 x x))
(-.f64 (*.f64 2/3 (pow.f64 x 4)) (fma.f64 x x -1))
(-.f64 1 (fma.f64 x x (*.f64 (pow.f64 x 4) -2/3)))
(+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 -1 (pow.f64 x 2)) (*.f64 -17/45 (pow.f64 x 6)))))
(fma.f64 2/3 (pow.f64 x 4) (+.f64 1 (fma.f64 -1 (.f64 x x) (.f64 -17/45 (pow.f64 x 6)))))
(+.f64 (-.f64 (.f64 -17/45 (pow.f64 x 6)) (.f64 x x)) (fma.f64 2/3 (pow.f64 x 4) 1))
(fma.f64 2/3 (pow.f64 x 4) (-.f64 (fma.f64 -17/45 (pow.f64 x 6) 1) (*.f64 x x)))
(-.f64 (fma.f64 2/3 (pow.f64 x 4) (fma.f64 -17/45 (pow.f64 x 6) 1)) (*.f64 x x))
(-.f64 (fma.f64 -17/45 (pow.f64 x 6) (fma.f64 2/3 (pow.f64 x 4) 1)) (*.f64 x x))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(/.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(/.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 1)
(fma.f64 x (*.f64 x -1/2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 (pow.f64 x 4) 5/24)))
(+.f64 1 (fma.f64 (.f64 x x) -1/2 (.f64 (pow.f64 x 4) 5/24)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 5/24 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 (pow.f64 x 4) 5/24))))
(+.f64 (fma.f64 (.f64 x x) -1/2 1) (fma.f64 (pow.f64 x 6) -61/720 (.f64 (pow.f64 x 4) 5/24)))
(+.f64 (fma.f64 x (.f64 x -1/2) 1) (fma.f64 (pow.f64 x 6) -61/720 (.f64 (pow.f64 x 4) 5/24)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 6) -61/720 (fma.f64 (pow.f64 x 4) 5/24 1)))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

eval17.0ms (1%)

Compiler: Compiled 563 to 387 computations (31.3% saved)

prune8.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	59	4	63

Error

Counts

63 → 4

Alt Table

Click to see full alt table

Status	Error	Program
	34.1b	1
✓	0.0b	(/.f64 1 (cosh.f64 x))
✓	0.0b	(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
✓	34.6b	(fma.f64 x (*.f64 -1/2 x) 1)

Compiler

Compiled 20 to 16 computations (20% saved)

regimes19.0ms (1.1%)

Counts

9 → 1

Calls

Call 1

Inputs
1
1
(/.f64 1 (cosh.f64 x))
(fma.f64 x (*.f64 -1/2 x) 1)
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(sqrt.f64 (pow.f64 (cosh.f64 x) -2))
(cbrt.f64 (pow.f64 (/.f64 1 (cosh.f64 x)) 3))
(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)))))

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

Calls

5 calls:

5.0ms	x
4.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

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

Compiler

Compiled 94 to 68 computations (27.7% saved)

regimes16.0ms (0.9%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

5 calls:

5.0ms	x
3.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

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

Compiler

Compiled 61 to 45 computations (26.2% saved)

regimes4.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
1
1

Outputs
1

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
34.1b	1	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	10	15

Stop Event

1×

saturated

Calls

Call 1

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

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

end22.0ms (1.3%)

Stop Event

1×

fuel

Compiler

Compiled 24 to 19 computations (20.8% saved)

Details

analyze0.0ms (0%)

sample746.0ms (45.3%)

preprocess61.0ms (3.7%)

simplify51.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite75.0ms (4.5%)

simplify46.0ms (2.8%)

eval10.0ms (0.6%)

prune8.0ms (0.5%)

localize3.0ms (0.2%)

series4.0ms (0.2%)

rewrite39.0ms (2.4%)

simplify57.0ms (3.4%)

localize3.0ms (0.2%)

localize7.0ms (0.4%)

series4.0ms (0.2%)

rewrite58.0ms (3.5%)

simplify44.0ms (2.7%)

eval64.0ms (3.9%)

prune24.0ms (1.4%)

localize4.0ms (0.3%)

series6.0ms (0.3%)

rewrite54.0ms (3.3%)

simplify44.0ms (2.6%)

localize2.0ms (0.2%)

rewrite0.0ms (0%)

simplify6.0ms (0.4%)

eval28.0ms (1.7%)

prune12.0ms (0.7%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite40.0ms (2.4%)

simplify43.0ms (2.6%)

eval17.0ms (1%)

prune8.0ms (0.5%)

regimes19.0ms (1.1%)

regimes16.0ms (0.9%)

regimes4.0ms (0.2%)

simplify3.0ms (0.2%)

end22.0ms (1.3%)

Profiling