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)

sample731.0ms (21.7%)

Results

714.0ms	8255×	body	64	valid
0.0ms	1×	body	128	valid

preprocess59.0ms (1.7%)

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 9 to 7 computations (22.2% saved)

simplify64.0ms (1.9%)

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))))

prune2.0ms (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

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

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series3.0ms (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))))
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))))

rewrite30.0ms (0.9%)

Algorithm

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

Rules

91×	`add-sqr-sqrt_binary64`
87×	`add-log-exp_binary64`
85×	`*-un-lft-identity_binary64`
85×	`add-exp-log_binary64`
85×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	176	9
2	2824	9
0	8	9

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

simplify54.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
400×	`associate-/l/_binary64`
362×	`*-commutative_binary64`
326×	`distribute-lft-out_binary64`
301×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	156
1	66	154
2	132	152
3	355	150
4	1205	150
5	3121	150
6	4299	150
7	7047	150

Stop Event

1×	node limit

Counts

22 → 20

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))))

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

prune27.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	2	21

Error

Counts

21 → 2

Alt Table

Status	Error	Program
	30.7b	(+.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)))))
▶	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)))))

Status

Error

Program

30.7b

(+.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)))))

▶

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)))))

Compiler

Compiled 298 to 226 computations (24.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.4%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(.f64 (.f64 (/.f64 2 (.f64 2 (cosh.f64 x))) (/.f64 2 (.f64 2 (cosh.f64 x)))) (/.f64 2 (*.f64 2 (cosh.f64 x))))
2.0ms	x	@	-inf	(/.f64 2 (*.f64 2 (cosh.f64 x)))
1.0ms	x	@	inf	(.f64 (.f64 (/.f64 2 (.f64 2 (cosh.f64 x))) (/.f64 2 (.f64 2 (cosh.f64 x)))) (/.f64 2 (*.f64 2 (cosh.f64 x))))
1.0ms	x	@	inf	(/.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))))

rewrite140.0ms (4.2%)

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	30
1	193	30
2	2303	30

Stop Event

1×	node limit

Counts

4 → 132

Calls

Call 1

Inputs
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(.f64 (/.f64 2 (.f64 2 (cosh.f64 x))) (/.f64 2 (*.f64 2 (cosh.f64 x))))
(.f64 (.f64 (/.f64 2 (.f64 2 (cosh.f64 x))) (/.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 (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 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 cbrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 3)))))) (#(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))))))) (#(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 (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 exp.f64 (*.f64 2 (neg.f64 (log.f64 (cosh.f64 x)))))))) (#(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 expm1.f64 (log1p.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2))))))))
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simplify45.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-def_binary64`
494×	`distribute-rgt-out_binary64`
490×	`distribute-lft-out_binary64`
477×	`associate-l_binary64`
382×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	670
1	120	659
2	303	649
3	991	645
4	3612	645

Stop Event

1×	node limit

Counts

180 → 133

Calls

Call 1

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

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 (fma.f64 -1/2 (.f64 x x) 1) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (fma.f64 -61/720 (pow.f64 x 6) 1)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 5/24) -1/2) (fma.f64 -61/720 (pow.f64 x 6) 1))
(/.f64 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 (pow.f64 x 2)))
(+.f64 1 (neg.f64 (*.f64 x x)))
(-.f64 1 (*.f64 x x))
(+.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 (pow.f64 x 4) 2/3 1) (*.f64 x x))
(-.f64 (*.f64 (pow.f64 x 4) 2/3) (fma.f64 x x -1))
(fma.f64 (pow.f64 x 4) 2/3 (-.f64 1 (*.f64 x x)))
(+.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 (pow.f64 x 6) -17/45))))
(+.f64 (-.f64 (.f64 (pow.f64 x 6) -17/45) (.f64 x x)) (fma.f64 (pow.f64 x 4) 2/3 1))
(fma.f64 (pow.f64 x 4) 2/3 (fma.f64 (pow.f64 x 6) -17/45 (-.f64 1 (*.f64 x x))))
(-.f64 (fma.f64 (pow.f64 x 4) 2/3 (fma.f64 (pow.f64 x 6) -17/45 1)) (*.f64 x x))
(fma.f64 (pow.f64 x 6) -17/45 (fma.f64 (pow.f64 x 4) 2/3 (-.f64 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 -3/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -3/2))
(fma.f64 (*.f64 x x) -3/2 1)
(fma.f64 x (*.f64 x -3/2) 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 (pow.f64 x 4) 11/8)))
(+.f64 (fma.f64 (.f64 x x) -3/2 1) (.f64 (pow.f64 x 4) 11/8))
(fma.f64 x (*.f64 x -3/2) (fma.f64 (pow.f64 x 4) 11/8 1))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 11/8 -3/2) 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 (pow.f64 x 4) 11/8))))
(+.f64 (fma.f64 (.f64 x x) -3/2 (.f64 (pow.f64 x 4) 11/8)) (fma.f64 (pow.f64 x 6) -241/240 1))
(fma.f64 (pow.f64 x 6) -241/240 (fma.f64 x (*.f64 x -3/2) (fma.f64 (pow.f64 x 4) 11/8 1)))
(fma.f64 (pow.f64 x 4) 11/8 (fma.f64 (pow.f64 x 6) -241/240 (fma.f64 x (*.f64 x -3/2) 1)))
(fma.f64 (pow.f64 x 4) 11/8 (fma.f64 (pow.f64 x 6) -241/240 (fma.f64 (*.f64 x x) -3/2 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 -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 (fma.f64 -1/2 (.f64 x x) 1) (fma.f64 5/24 (pow.f64 x 4) (.f64 -61/720 (pow.f64 x 6))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (fma.f64 -61/720 (pow.f64 x 6) 1)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 5/24) -1/2) (fma.f64 -61/720 (pow.f64 x 6) 1))
(/.f64 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))))

prune1.5s (44.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	201	2	203

Error

Counts

203 → 2

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x))) (sqrt.f64 (*.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)))))

Compiler

Compiled 3868 to 2729 computations (29.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite63.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

490×	`log-prod_binary64`
363×	`exp-prod_binary64`
349×	`prod-exp_binary64`
277×	`pow-prod-down_binary64`
234×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	199	12
2	2643	12

Stop Event

1×	node limit

Counts

2 → 122

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 2 (cosh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 2 (cosh.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 2 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (cosh.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 2 (cosh.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 1 (cosh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (cosh.f64 x)) 1)))) (#(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 (/.f64 2 (cosh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (cosh.f64 x))) (pow.f64 (cbrt.f64 (/.f64 2 (cosh.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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 (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4) (pow.f64 (/.f64 2 (cosh.f64 x)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (/.f64 1 (neg.f64 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cosh.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 3/4) (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 5/6) (pow.f64 (/.f64 2 (cosh.f64 x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (cosh.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 (cosh.f64 x) -2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 2 (cosh.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cosh.f64 x) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (cosh.f64 x) 1/2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 2 (cosh.f64 x)))) 2)) (cbrt.f64 (log.f64 (/.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 2 (cosh.f64 x))))) (sqrt.f64 (log.f64 (/.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 4 (pow.f64 (cosh.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (/.f64 2 (cosh.f64 x)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 2 (cosh.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 2 (cosh.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (cosh.f64 x) 1/2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1/2) (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) 1) (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1/2) (*.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (cosh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (cosh.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (cosh.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x))) (pow.f64 (*.f64 2 (cosh.f64 x)) -1/2))))) (#(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 2 (cosh.f64 x))) (*.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 1/6) (pow.f64 (*.f64 2 (cosh.f64 x)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) (cbrt.f64 (pow.f64 (cosh.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) -2)) (/.f64 1 (cbrt.f64 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cosh.f64 x) -1/2) (pow.f64 (cosh.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4) (*.f64 (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4) (pow.f64 (*.f64 2 (cosh.f64 x)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) (/.f64 1 (neg.f64 (sqrt.f64 (*.f64 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 (pow.f64 (*.f64 2 (cosh.f64 x)) -1/2) (sqrt.f64 (/.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 2 (cosh.f64 x))) (cbrt.f64 (*.f64 2 (cosh.f64 x)))) (/.f64 1 (cbrt.f64 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 2 (cosh.f64 x))) 1) (/.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 1/6) (sqrt.f64 (*.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4) 1) (/.f64 (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4) (sqrt.f64 (*.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 2 (cosh.f64 x)))) (/.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x))) (pow.f64 (*.f64 2 (cosh.f64 x)) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4) (cbrt.f64 (*.f64 2 (cosh.f64 x)))) (/.f64 (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4) (pow.f64 (*.f64 2 (cosh.f64 x)) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (cosh.f64 x)) -1/4) (/.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x))) (pow.f64 (*.f64 2 (cosh.f64 x)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 2 (cosh.f64 x))) (pow.f64 (*.f64 2 (cosh.f64 x)) 1/4)) (/.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 1/6) (pow.f64 (*.f64 2 (cosh.f64 x)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (/.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 2 (cosh.f64 x))) (sqrt.f64 2)) (/.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 1/6) (sqrt.f64 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4) (sqrt.f64 2)) (/.f64 (pow.f64 (*.f64 (cosh.f64 x) 1/2) -1/4) (sqrt.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 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 (pow.f64 (cosh.f64 x) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cosh.f64 x) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (cosh.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cosh.f64 x)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cosh.f64 x) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cosh.f64 x)) -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 (exp.f64 1) (neg.f64 (log.f64 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 3/2) (pow.f64 (*.f64 2 (cosh.f64 x)) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cosh.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log.f64 (cosh.f64 x)))) 2)) (cbrt.f64 (neg.f64 (log.f64 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log.f64 (cosh.f64 x))))) (sqrt.f64 (neg.f64 (log.f64 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x))) (neg.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cosh.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (cosh.f64 x) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 2 (cosh.f64 x)) 3/2) (pow.f64 (*.f64 2 (cosh.f64 x)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (cosh.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (*.f64 (log.f64 (cosh.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cosh.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (cosh.f64 x) -2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (cosh.f64 x) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (cbrt.f64 (cosh.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (cosh.f64 x) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cosh.f64 x)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log.f64 (cosh.f64 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1/2) (log.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) 1) (log.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) (*.f64 (log.f64 (*.f64 2 (cosh.f64 x))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1/2) (*.f64 (log.f64 (*.f64 2 (cosh.f64 x))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) 1) (*.f64 (log.f64 (*.f64 2 (cosh.f64 x))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1/2) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (cosh.f64 x)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1/2) (*.f64 -1/2 (log.f64 (*.f64 2 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) 1) (*.f64 -1/2 (log.f64 (*.f64 2 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 -1/2 (log.f64 (*.f64 2 (cosh.f64 x)))) (*.f64 (log.f64 (/.f64 2 (cosh.f64 x))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 -1/2 (log.f64 (*.f64 2 (cosh.f64 x)))) (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (cosh.f64 x)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (cosh.f64 x))))))))

simplify46.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

696×	`distribute-rgt-neg-in_binary64`
627×	`distribute-lft-neg-in_binary64`
410×	`fma-def_binary64`
371×	`distribute-rgt-out_binary64`
317×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	311
1	80	305
2	187	299
3	575	297
4	2229	297
5	5396	297

Stop Event

1×	node limit

Counts

146 → 140

Calls

Call 1

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

prune555.0ms (16.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	140	2	142

Error

Counts

142 → 2

Alt Table

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

Compiler

Compiled 1994 to 1410 computations (29.3% saved)

regimes10.0ms (0.3%)

Accuracy

Total -30.7b remaining (-785779.2%)

Threshold costs -30.7b (-785779.2%)

Counts

4 → 1

Calls

Call 1

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

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

Results

4.0ms	0.0b	`x`
2.0ms	0.0b	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
2.0ms	0.0b	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 78 to 59 computations (24.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	10	18

Stop Event

1×

saturated

Calls

Call 1

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

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

end16.0ms (0.5%)

Stop Event

1×

done

Compiler

Compiled 24 to 18 computations (25% saved)

Details

analyze0.0ms (0%)

sample731.0ms (21.7%)

preprocess59.0ms (1.7%)

simplify64.0ms (1.9%)

prune2.0ms (0%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite30.0ms (0.9%)

simplify54.0ms (1.6%)

prune27.0ms (0.8%)

localize7.0ms (0.2%)

series13.0ms (0.4%)

rewrite140.0ms (4.2%)

simplify45.0ms (1.4%)

prune1.5s (44.1%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite63.0ms (1.9%)

simplify46.0ms (1.4%)

prune555.0ms (16.5%)

regimes10.0ms (0.3%)

simplify2.0ms (0%)

end16.0ms (0.5%)

Profiling