Details

analyze1.0ms (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)

sample778.0ms (27.9%)

Results

766.0ms

8256×

body

256

valid

Bogosity

preprocess84.0ms (3%)

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)

simplify72.0ms (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)

series3.0ms (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)))

rewrite94.0ms (3.4%)

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))))))))

simplify61.0ms (2.2%)

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))

eval11.0ms (0.4%)

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

prune7.0ms (0.2%)

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
▶	32.8b	(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
	32.0b	1
▶	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))
▶	0.5b	(/.f64 2 (expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x)))))

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize20.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 -1/2 (pow.f64 x 2))
✓	0.1b	(*.f64 5/24 (pow.f64 x 4))
✓	14.4b	(+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4)))

Compiler

Compiled 47 to 38 computations (19.1% saved)

series4.0ms (0.2%)

Counts

3 → 3

Calls

9 calls:

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

rewrite68.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

446×	`log-prod_binary64`
335×	`exp-prod_binary64`
304×	`fma-def_binary64`
298×	`prod-exp_binary64`
270×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	239	28
2	2732	28

Stop Event

1×	node limit

Counts

3 → 117

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (pow.f64 x 4) 1/4) (fma.f64 -1/2 (.f64 x x) (.f64 -5/24 (pow.f64 x 4)))) (/.f64 (.f64 (pow.f64 x 8) 25/576) (fma.f64 -1/2 (.f64 x x) (.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))) (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))) 2) (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 5/24 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exp.f64 (.f64 (.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (.f64 x x) (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (.f64 x -1/2) (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) -1/2 (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) (.f64 (.f64 x x) 5/24) (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/2 (.f64 x x)) 1 (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 5/24 (pow.f64 x 4) (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 4) 5/24 (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 5/24 (pow.f64 x 4)) 1 (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 -1/2 (.f64 x x)) (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 5/24 (pow.f64 x 4)) (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 x) x) (.f64 (pow.f64 (cbrt.f64 x) 2) -1/2) (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 8) (.f64 (.f64 (cbrt.f64 x) x) 5/24) (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 -1/2 (.f64 x x))) (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)) (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)) (cbrt.f64 (.f64 -1/2 (.f64 x x))) (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 5/24 (pow.f64 x 4))) (cbrt.f64 (.f64 (pow.f64 x 8) 25/576)) (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (pow.f64 x 8) 25/576)) (cbrt.f64 (.f64 5/24 (pow.f64 x 4))) (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (sqrt.f64 -1/2)) (.f64 x (sqrt.f64 -1/2)) (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (.f64 x x) (sqrt.f64 5/24)) (.f64 (.f64 x x) (sqrt.f64 5/24)) (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/2 x) x (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/2 (.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2) (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 5/24 (.f64 x x)) (.f64 x x) (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 5/24 (pow.f64 (cbrt.f64 x) 8)) (.f64 (cbrt.f64 x) x) (.f64 -1/2 (.f64 x x)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 5/24 (pow.f64 x 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 5/24 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 8) 25/576) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 5/24 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 x x) (sqrt.f64 5/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 12) 125/13824) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 5/24 (pow.f64 x 4)))) 2)) (cbrt.f64 (log.f64 (.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 5/24 (pow.f64 x 4))))) (sqrt.f64 (log.f64 (.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 x 8) 25/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 12) 125/13824))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 5/24 (pow.f64 x 4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 5/24 (pow.f64 x 4)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (.f64 x x) (sqrt.f64 5/24))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 12) 125/13824)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 5/24 (pow.f64 x 4))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 5/24 (pow.f64 x 4))) 3) 1/3))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 -1/2 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (.f64 x -1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (.f64 x -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 -1/2 (.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/2 (.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 4) 1/4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 -1/2 (.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (sqrt.f64 -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 6) -1/8) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (.f64 -1/2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 -1/2 (.f64 x x)))) 2)) (cbrt.f64 (log.f64 (.f64 -1/2 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 -1/2 (.f64 x x))))) (sqrt.f64 (log.f64 (.f64 -1/2 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 x 4) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 -1/2 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 6) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 -1/2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 -1/2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 -1/2 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 -1/2 (.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 -1/2 (.f64 x x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) -1/8)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 -1/2 (.f64 x x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 -1/2 (.f64 x x))) 3) 1/3))))))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 5/24 (pow.f64 x 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 5/24 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 8) 25/576) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 5/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 12) 125/13824) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4)))) 2)) (cbrt.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))))) (sqrt.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 8) 25/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 12) 125/13824))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 5/24 (pow.f64 x 4)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) (sqrt.f64 5/24))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 12) 125/13824)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 5/24 (pow.f64 x 4))) 3) 1/3))))))

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simplify176.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

1319×	`sqr-pow_binary64`
659×	`pow-sqr_binary64`
493×	`cube-prod_binary64`
406×	`fabs-mul_binary64`
386×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	19	21
2	39	21
3	90	21
4	294	21
5	1173	21
6	1917	21
7	2041	21
8	2210	21
9	2409	21
10	2680	21
11	3037	21
12	3491	21
13	4022	21
14	4652	21
15	5403	21
16	5713	21
17	5939	21
18	6137	21
19	6195	21
20	6217	21
21	7051	21
22	7964	21

Stop Event

1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 5/24 (pow.f64 x 4))
(*.f64 5/24 (pow.f64 x 4))

Outputs
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(*.f64 5/24 (pow.f64 x 4))
(*.f64 5/24 (pow.f64 x 4))

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x))))
✓	0.0b	(cosh.f64 x)
✓	0.0b	(/.f64 2 (expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x)))))
✓	1.2b	(log1p.f64 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 28 to 18 computations (35.7% saved)

series59.0ms (2.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
28.0ms	x	@	inf	(log1p.f64 (*.f64 2 (cosh.f64 x)))
26.0ms	x	@	-inf	(log1p.f64 (*.f64 2 (cosh.f64 x)))
2.0ms	x	@	0	(log1p.f64 (*.f64 2 (cosh.f64 x)))
1.0ms	x	@	inf	(/.f64 2 (expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x)))))
1.0ms	x	@	-inf	(/.f64 2 (expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x)))))

rewrite61.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

684×	`pow1_binary64`
633×	`add-log-exp_binary64`
632×	`expm1-log1p-u_binary64`
631×	`log1p-expm1-u_binary64`
619×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	150	23
2	1813	23

Stop Event

1×	node limit

Counts

4 → 90

Calls

Call 1

Inputs
(log1p.f64 (*.f64 2 (cosh.f64 x)))
(/.f64 2 (expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x)))))
(cosh.f64 x)
(expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x))))

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

simplify84.0ms (3%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
619×	`distribute-rgt-out_binary64`
524×	`associate-l_binary64`
518×	`distribute-lft-out_binary64`
431×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	589
1	145	579
2	351	563
3	1005	559
4	3677	559
5	5927	559
6	7540	559

Stop Event

1×	node limit

Counts

138 → 124

Calls

Call 1

Inputs
(log.f64 3)
(+.f64 (*.f64 1/3 (pow.f64 x 2)) (log.f64 3))
(+.f64 (.f64 1/3 (pow.f64 x 2)) (+.f64 (.f64 -1/36 (pow.f64 x 4)) (log.f64 3)))
(+.f64 (.f64 13/3240 (pow.f64 x 6)) (+.f64 (.f64 1/3 (pow.f64 x 2)) (+.f64 (*.f64 -1/36 (pow.f64 x 4)) (log.f64 3))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log.f64 (+.f64 1 (+.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)))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6)))))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 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 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))

Outputs
(log.f64 3)
(+.f64 (*.f64 1/3 (pow.f64 x 2)) (log.f64 3))
(fma.f64 1/3 (*.f64 x x) (log.f64 3))
(+.f64 (.f64 1/3 (pow.f64 x 2)) (+.f64 (.f64 -1/36 (pow.f64 x 4)) (log.f64 3)))
(fma.f64 1/3 (*.f64 x x) (fma.f64 -1/36 (pow.f64 x 4) (log.f64 3)))
(+.f64 (.f64 13/3240 (pow.f64 x 6)) (+.f64 (.f64 1/3 (pow.f64 x 2)) (+.f64 (*.f64 -1/36 (pow.f64 x 4)) (log.f64 3))))
(fma.f64 13/3240 (pow.f64 x 6) (fma.f64 1/3 (*.f64 x x) (fma.f64 -1/36 (pow.f64 x 4) (log.f64 3))))
(fma.f64 1/3 (*.f64 x x) (fma.f64 13/3240 (pow.f64 x 6) (fma.f64 -1/36 (pow.f64 x 4) (log.f64 3))))
(fma.f64 1/3 (*.f64 x x) (fma.f64 -1/36 (pow.f64 x 4) (fma.f64 13/3240 (pow.f64 x 6) (log.f64 3))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log1p.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log1p.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log1p.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log1p.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log1p.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log1p.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log1p.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(log.f64 (+.f64 1 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(log1p.f64 (+.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 (fma.f64 (.f64 x x) -1/2 1) (.f64 (pow.f64 x 4) 5/24))
(fma.f64 (pow.f64 x 4) 5/24 (fma.f64 (*.f64 x x) -1/2 1))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 5/24 1))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/24 -1/2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -61/720 (pow.f64 x 6)) (*.f64 5/24 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -61/720 (pow.f64 x 6) (.f64 (pow.f64 x 4) 5/24))))
(+.f64 (fma.f64 (.f64 x x) -1/2 1) (fma.f64 (pow.f64 x 4) 5/24 (.f64 (pow.f64 x 6) -61/720)))
(+.f64 1 (fma.f64 (pow.f64 x 4) 5/24 (fma.f64 (pow.f64 x 6) -61/720 (.f64 (.f64 x x) -1/2))))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 5/24 (fma.f64 (pow.f64 x 6) -61/720 1)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 5/24 -1/2) (fma.f64 (pow.f64 x 6) -61/720 1))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) 1/2))
(fma.f64 (*.f64 x x) 1/2 1)
(fma.f64 x (*.f64 x 1/2) 1)
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 1/2 (.f64 x x) (.f64 (pow.f64 x 4) 1/24)))
(+.f64 1 (fma.f64 (pow.f64 x 4) 1/24 (.f64 x (.f64 x 1/2))))
(fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) 1/24 1))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 1/24 1/2) 1)
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 1/2 (.f64 x x) (fma.f64 1/24 (pow.f64 x 4) (.f64 (pow.f64 x 6) 1/720))))
(+.f64 (fma.f64 (.f64 x x) 1/2 1) (fma.f64 (pow.f64 x 4) 1/24 (.f64 (pow.f64 x 6) 1/720)))
(+.f64 1 (fma.f64 x (.f64 x 1/2) (fma.f64 (pow.f64 x 4) 1/24 (.f64 (pow.f64 x 6) 1/720))))
(fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) 1/24 (fma.f64 (pow.f64 x 6) 1/720 1)))
(fma.f64 (pow.f64 x 4) 1/24 (fma.f64 (pow.f64 x 6) 1/720 (fma.f64 (*.f64 x x) 1/2 1)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (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 (fma.f64 x x 2) (*.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 x x (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 2)))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 15 to 9 computations (40% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite46.0ms (1.6%)

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))))))))

simplify72.0ms (2.6%)

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))))

eval96.0ms (3.4%)

Compiler: Compiled 4280 to 3186 computations (25.6% saved)

prune39.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	302	4	306
Fresh	1	0	1
Picked	0	1	1
Done	2	0	2
Total	305	5	310

Error

Counts

310 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	32.7b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	32.0b	1
▶	32.8b	(+.f64 1 (+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4))))
✓	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))
▶	0.0b	(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))

Compiler

Compiled 43 to 34 computations (20.9% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 10 computations (47.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite39.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`pow1_binary64`
420×	`add-sqr-sqrt_binary64`
411×	`*-un-lft-identity_binary64`
401×	`add-log-exp_binary64`
401×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1148	7

Stop Event

1×	node limit

Counts

1 → 14

Calls

Call 1

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

Outputs

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

simplify172.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
554×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
441×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	23	84
3	44	84
4	105	84
5	331	84
6	1250	84
7	2123	84
8	2287	84
9	2471	84
10	2679	84
11	2976	84
12	3371	84
13	3852	84
14	4418	84
15	5102	84
16	5935	84
17	6327	84
18	6619	84
19	6895	84
20	6969	84
21	7003	84
22	7944	84

Stop Event

1×	node limit

Counts

26 → 16

Calls

Call 1

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

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

localize21.0ms (0.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(.f64 -1/2 (.f64 x x))
	0.1b	(*.f64 5/24 (pow.f64 x 4))
✓	14.4b	(+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

Compiler

Compiled 58 to 39 computations (32.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

(+.f64 (+.f64 0 (*.f64 -1/2 (*.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

0.0ms

inf

(+.f64 (+.f64 0 (*.f64 -1/2 (*.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

0.0ms

-inf

(+.f64 (+.f64 0 (*.f64 -1/2 (*.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

rewrite64.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

477×	`fma-def_binary64`
456×	`log-prod_binary64`
344×	`exp-prod_binary64`
297×	`pow-prod-down_binary64`
262×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	271	14
2	3130	14

Stop Event

1×	node limit

Counts

1 → 81

Calls

Call 1

Inputs
(+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 4) 1/4) (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))) (/.f64 (*.f64 25/576 (pow.f64 x 8)) (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2) (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8)) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8))) (/.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4))) (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8)) (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8)) (fma.f64 25/576 (pow.f64 x 8) (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8))) (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8))) (neg.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8)))) (neg.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 0 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 3)) (+.f64 0 (-.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 2) (*.f64 0 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 2)) (-.f64 0 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 25/576 (pow.f64 x 8)) (*.f64 (pow.f64 x 4) 1/4)) (fma.f64 5/24 (pow.f64 x 4) (neg.f64 (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4))) (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))) 2)) (cbrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))) (sqrt.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x)))) (pow.f64 (exp.f64 5/24) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 -1/2) x) x) (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x)))) (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4)))) (pow.f64 (pow.f64 (exp.f64 -1/2) x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 5/24) (pow.f64 x 4)) (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 5/24 (pow.f64 x 4)))) (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (*.f64 x x) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 -1/2 x) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) -1/2 (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) 5/24) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/2 (*.f64 x x)) 1 (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 4) 5/24 (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (pow.f64 x 4)) 1 (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 -1/2 (*.f64 x x)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 5/24 (pow.f64 x 4)) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) (cbrt.f64 (*.f64 25/576 (pow.f64 x 8))) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 25/576 (pow.f64 x 8))) (cbrt.f64 (*.f64 5/24 (pow.f64 x 4))) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 2) (cbrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (*.f64 (pow.f64 (cbrt.f64 x) 2) -1/2) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 8) (*.f64 (*.f64 (cbrt.f64 x) x) 5/24) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/4)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/4)) (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 5/24)) (*.f64 (*.f64 x x) (sqrt.f64 5/24)) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) (sqrt.f64 (fma.f64 5/24 (pow.f64 x 4) (*.f64 -1/2 (*.f64 x x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 -1/2)) (*.f64 x (sqrt.f64 -1/2)) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 x 6) -1/8) (pow.f64 (*.f64 -1/2 (*.f64 x x)) -2) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 125/13824 (pow.f64 x 12) (*.f64 (pow.f64 x 6) -1/8)) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 4) 1/4 (*.f64 25/576 (pow.f64 x 8))) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 x x)) 5/24) (pow.f64 x 4)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (*.f64 (pow.f64 x 4) 1/4)) (/.f64 1 (neg.f64 (*.f64 -1/2 (*.f64 x x)))) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/4) (*.f64 25/576 (pow.f64 x 8))) (/.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 -5/24 (pow.f64 x 4)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/2 x) x (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (*.f64 x x)) (*.f64 x x) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 5/24 (pow.f64 (cbrt.f64 x) 8)) (*.f64 (cbrt.f64 x) x) (*.f64 -1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/2 (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/2 x) 1) x (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/2 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 5/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/2 x) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 5/24 (pow.f64 x 4)))))))

simplify197.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

1057×	`sqr-pow_binary64`
538×	`fma-def_binary64`
506×	`pow-sqr_binary64`
443×	`cube-prod_binary64`
425×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	147
1	22	147
2	45	147
3	114	147
4	355	147
5	1427	147
6	2658	147
7	3120	147
8	3289	147
9	3488	147
10	3761	147
11	4118	147
12	4568	147
13	5099	147
14	5729	147
15	6484	147
16	6794	147
17	7018	147
18	7216	147
19	7270	147
20	7292	147

Stop Event

1×	node limit

Counts

93 → 86

Calls

Call 1

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

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

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 26 to 14 computations (46.2% saved)

series4.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

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

rewrite64.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

849×	`pow1_binary64`
794×	`add-log-exp_binary64`
793×	`log1p-expm1-u_binary64`
793×	`expm1-log1p-u_binary64`
776×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	175	20
2	2271	20

Stop Event

1×	node limit

Counts

3 → 76

Calls

Call 1

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

Outputs

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

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

simplify55.0ms (2%)

Algorithm

1×	egg-herbie

Rules

735×	`fma-def_binary64`
604×	`fma-neg_binary64`
585×	`cancel-sign-sub-inv_binary64`
512×	`associate-l_binary64`
467×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	139
1	102	129
2	264	119
3	829	113
4	3634	113
5	6770	113

Stop Event

1×	node limit

Counts

88 → 96

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 x)))
(+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 -1 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)))))
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)))))

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

eval142.0ms (5.1%)

Compiler: Compiled 3856 to 2754 computations (28.6% saved)

prune30.0ms (1.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	239	5	244

Error

Counts

244 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.7b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	32.0b	1
✓	32.8b	(+.f64 1 (+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4))))
✓	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))
✓	0.0b	(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))

Compiler

Compiled 43 to 34 computations (20.9% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.7b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
	32.0b	1
✓	32.8b	(+.f64 1 (+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4))))
✓	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))
✓	0.0b	(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))

Compiler

Compiled 43 to 34 computations (20.9% saved)

regimes60.0ms (2.2%)

Counts

9 → 1

Calls

Call 1

Inputs
1
1
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(+.f64 1 (+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 5/24 (pow.f64 x 4))))
(/.f64 2 (expm1.f64 (log1p.f64 (*.f64 2 (cosh.f64 x)))))

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

Calls

5 calls:

48.0ms	x
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

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

Compiler

Compiled 103 to 77 computations (25.2% saved)

regimes16.0ms (0.6%)

Counts

6 → 1

Calls

Call 1

Inputs
1
1
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(/.f64 2 (*.f64 2 (cosh.f64 x)))
(+.f64 1 (+.f64 (+.f64 0 (.f64 -1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

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

Calls

5 calls:

5.0ms	x
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
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 73 to 55 computations (24.7% saved)

regimes6.0ms (0.2%)

Accuracy

Total -0.7b remaining (-2.3%)

Threshold costs -0.7b (-2.3%)

Counts

3 → 1

Calls

Call 1

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

Outputs
1

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
32.0b	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	15	24

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

Outputs
(/.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 2 (+.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(/.f64 2 (*.f64 2 (cosh.f64 x)))
1

Compiler

Compiled 19 to 15 computations (21.1% saved)

soundness0.0ms (0%)

end24.0ms (0.9%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

Details

analyze1.0ms (0%)

sample778.0ms (27.9%)

preprocess84.0ms (3%)

simplify72.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.3%)

series3.0ms (0.1%)

rewrite94.0ms (3.4%)

simplify61.0ms (2.2%)

eval11.0ms (0.4%)

prune7.0ms (0.2%)

localize20.0ms (0.7%)

series4.0ms (0.2%)

rewrite68.0ms (2.4%)

simplify176.0ms (6.3%)

localize15.0ms (0.5%)

series59.0ms (2.1%)

rewrite61.0ms (2.2%)

simplify84.0ms (3%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite46.0ms (1.6%)

simplify72.0ms (2.6%)

eval96.0ms (3.4%)

prune39.0ms (1.4%)

localize7.0ms (0.3%)

series1.0ms (0%)

rewrite39.0ms (1.4%)

simplify172.0ms (6.2%)

localize21.0ms (0.8%)

series1.0ms (0%)

rewrite64.0ms (2.3%)

simplify197.0ms (7.1%)

localize10.0ms (0.4%)

series4.0ms (0.1%)

rewrite64.0ms (2.3%)

simplify55.0ms (2%)

eval142.0ms (5.1%)

prune30.0ms (1.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes60.0ms (2.2%)

regimes16.0ms (0.6%)

regimes6.0ms (0.2%)

simplify4.0ms (0.1%)

soundness0.0ms (0%)

end24.0ms (0.9%)

Profiling