Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample911.0ms (29.8%)

Results

887.0ms

8256×

body

256

valid

Bogosity

preprocess114.0ms (3.7%)

Algorithm

2×	egg-herbie

Rules

702×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`
290×	`exp-prod_binary64`
264×	`*-commutative_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	434	13
8	1195	13
9	3176	13
10	4367	13
11	5548	13
12	7298	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)

simplify79.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

702×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`
290×	`exp-prod_binary64`
264×	`*-commutative_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	434	13
8	1195	13
9	3176	13
10	4367	13
11	5548	13
12	7298	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)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 24 to 8 computations (66.7% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite150.0ms (4.9%)

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	2839	18
0	8	9
1	176	9
2	2839	9
0	8	9
0	6	6
1	129	6
2	2150	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 expm1.f64 (log1p.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 exp.f64 (log.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 expm1.f64 (log1p.f64 (.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.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 expm1.f64 (log1p.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 exp.f64 (log.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 expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (cosh.f64 x))))))))

simplify89.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

629×	`distribute-lft-out_binary64`
423×	`associate-/l/_binary64`
388×	`fma-def_binary64`
380×	`distribute-rgt-out_binary64`
342×	`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	2008	267
5	3750	267
6	5278	267

Stop Event

1×	node limit

Counts

46 → 40

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

eval10.0ms (0.3%)

Compiler: Compiled 456 to 313 computations (31.4% saved)

prune152.0ms (5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Error

Counts

41 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.9b	(+.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)))))
▶	30.7b	(fma.f64 -1/2 (*.f64 x x) 1)
	30.3b	1
▶	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 36 to 30 computations (16.7% saved)

localize31.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4))))
✓	0.1b	(*.f64 -61/720 (pow.f64 x 6))
✓	0.1b	(*.f64 5/24 (pow.f64 x 4))
✓	25.0b	(+.f64 (.f64 -61/720 (pow.f64 x 6)) (.f64 5/24 (pow.f64 x 4)))

Compiler

Compiled 80 to 65 computations (18.8% saved)

series7.0ms (0.2%)

Counts

4 → 9

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4))))
1.0ms	x	@	inf	(+.f64 (.f64 -61/720 (pow.f64 x 6)) (.f64 5/24 (pow.f64 x 4)))
1.0ms	x	@	0	(+.f64 (.f64 -61/720 (pow.f64 x 6)) (.f64 5/24 (pow.f64 x 4)))
0.0ms	x	@	inf	(*.f64 -61/720 (pow.f64 x 6))
0.0ms	x	@	0	(*.f64 5/24 (pow.f64 x 4))

rewrite102.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

662×	`log-prod_binary64`
627×	`fma-def_binary64`
330×	`fma-neg_binary64`
271×	`expm1-udef_binary64`
271×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	358	49
2	4323	49

Stop Event

1×	node limit

Counts

4 → 181

Calls

Call 1

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

Outputs
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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (.f64 x (.f64 x -1/2)))) (sqrt.f64 (fma.f64 -61/720 (pow.f64 x 6) (.f64 x (.f64 x -1/2)))) (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/2 x) x (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2) (fma.f64 -61/720 (pow.f64 x 6) (.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -61/720 (pow.f64 x 4)) (.f64 x x) (fma.f64 5/24 (pow.f64 x 4) (.f64 x (.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -61/720 (pow.f64 x 3)) (pow.f64 x 3) (fma.f64 5/24 (pow.f64 x 4) (.f64 x (.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 5/24 (.f64 x x)) (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 x (.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 5/24 (cbrt.f64 (pow.f64 x 8))) (cbrt.f64 (pow.f64 x 4)) (fma.f64 -61/720 (pow.f64 x 6) (.f64 x (.f64 x -1/2))))))))

simplify165.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

1124×	`sqr-pow_binary64`
653×	`pow-sqr_binary64`
597×	`cube-prod_binary64`
416×	`fma-def_binary64`
382×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	84
1	34	84
2	69	84
3	192	84
4	835	84
5	2061	84
6	2491	84
7	2687	84
8	2881	84
9	3132	84
10	3447	84
11	3855	84
12	4290	84
13	4787	84
14	5394	84
15	5650	84
16	5898	84
17	6162	84
18	6436	84
19	6700	84

Stop Event

1×	node limit

Counts

190 → 189

Calls

Call 1

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

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

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 15 to 9 computations (40% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite77.0ms (2.5%)

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	1613	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 expm1.f64 (log1p.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))))))))

simplify198.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
406×	`*-commutative_binary64`
369×	`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	332	150
4	1193	150
5	3031	150
6	3798	150
7	4734	150
8	7840	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))
(+.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) (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))))

localize5.0ms (0.2%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

eval405.0ms (13.2%)

Compiler: Compiled 5046 to 4073 computations (19.3% saved)

prune54.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	218	4	222

Error

Counts

222 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
▶	30.7b	(+.f64 1 (.f64 x (.f64 x -1/2)))
	30.3b	1
✓	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 25 to 21 computations (16% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
✓	0.0b	(pow.f64 (cosh.f64 x) 2)
✓	0.0b	(/.f64 1 (pow.f64 (cosh.f64 x) 2))

Compiler

Compiled 23 to 15 computations (34.8% saved)

series6.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/.f64 1 (pow.f64 (cosh.f64 x) 2))
1.0ms	x	@	-inf	(/.f64 1 (pow.f64 (cosh.f64 x) 2))
1.0ms	x	@	0	(/.f64 1 (pow.f64 (cosh.f64 x) 2))
0.0ms	x	@	0	(pow.f64 (cosh.f64 x) 2)
0.0ms	x	@	inf	(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))

rewrite104.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

667×	`pow1_binary64`
620×	`add-log-exp_binary64`
619×	`log1p-expm1-u_binary64`
619×	`expm1-log1p-u_binary64`
603×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	169	18
2	1851	18

Stop Event

1×	node limit

Counts

3 → 77

Calls

Call 1

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

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

simplify104.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-def_binary64`
446×	`associate-l_binary64`
421×	`distribute-rgt-out_binary64`
399×	`distribute-lft-out_binary64`
366×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	509
1	109	496
2	275	488
3	891	486
4	3566	486
5	7424	486

Stop Event

1×	node limit

Counts

113 → 102

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

localize8.0ms (0.3%)

Compiler: Compiled 19 to 13 computations (31.6% saved)

eval25.0ms (0.8%)

Compiler: Compiled 1021 to 698 computations (31.6% saved)

prune15.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	1	1
Picked	0	1	1
Done	2	0	2
Total	102	4	106

Error

Counts

106 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(/.f64 1 (cosh.f64 x))
✓	30.7b	(+.f64 1 (.f64 x (.f64 x -1/2)))
	30.3b	1
▶	0.0b	(pow.f64 (pow.f64 (cosh.f64 x) 2) -1/2)

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 9 to 5 computations (44.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite43.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

461×	`pow1_binary64`
448×	`add-sqr-sqrt_binary64`
438×	`*-un-lft-identity_binary64`
428×	`add-log-exp_binary64`
426×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	102	6
2	1198	6

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify71.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
406×	`*-commutative_binary64`
369×	`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	332	150
4	1193	150
5	3031	150
6	3798	150
7	4734	150
8	7840	150

Stop Event

1×	node limit

Counts

33 → 30

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))
(+.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) (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))))

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

eval15.0ms (0.5%)

Compiler: Compiled 585 to 391 computations (33.2% saved)

prune9.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	62	4	66

Error

Counts

66 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(/.f64 1 (cosh.f64 x))
✓	30.7b	(+.f64 1 (.f64 x (.f64 x -1/2)))
	30.3b	1
✓	0.0b	(pow.f64 (pow.f64 (cosh.f64 x) 2) -1/2)

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes18.0ms (0.6%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

5 calls:

5.0ms	x
3.0ms	(/.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)))
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 99 to 74 computations (25.3% saved)

regimes16.0ms (0.5%)

Counts

6 → 1

Calls

Call 1

Inputs
1
(+.f64 1 (.f64 x (.f64 x -1/2)))
(/.f64 1 (cosh.f64 x))
(fma.f64 -1/2 (*.f64 x 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 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)))
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 67 to 49 computations (26.9% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.7b remaining (-2.1%)

Threshold costs -0.7b (-2.1%)

Counts

2 → 1

Calls

Call 1

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

Outputs
1

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
30.3b	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	11	16

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 14 to 12 computations (14.3% saved)

soundness0.0ms (0%)

end22.0ms (0.7%)

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

Details

analyze0.0ms (0%)

sample911.0ms (29.8%)

preprocess114.0ms (3.7%)

simplify79.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.3%)

series4.0ms (0.1%)

rewrite150.0ms (4.9%)

simplify89.0ms (2.9%)

eval10.0ms (0.3%)

prune152.0ms (5%)

localize31.0ms (1%)

series7.0ms (0.2%)

rewrite102.0ms (3.3%)

simplify165.0ms (5.4%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite77.0ms (2.5%)

simplify198.0ms (6.5%)

localize5.0ms (0.2%)

eval405.0ms (13.2%)

prune54.0ms (1.8%)

localize9.0ms (0.3%)

series6.0ms (0.2%)

rewrite104.0ms (3.4%)

simplify104.0ms (3.4%)

localize8.0ms (0.3%)

eval25.0ms (0.8%)

prune15.0ms (0.5%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite43.0ms (1.4%)

simplify71.0ms (2.3%)

localize7.0ms (0.2%)

eval15.0ms (0.5%)

prune9.0ms (0.3%)

regimes18.0ms (0.6%)

regimes16.0ms (0.5%)

regimes4.0ms (0.1%)

simplify6.0ms (0.2%)

soundness0.0ms (0%)

end22.0ms (0.7%)

Profiling