Details

analyze1.3s (19.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample2.7s (42.9%)

Results

1.0s	6320×	body	128	valid
674.0ms	1011×	body	1024	valid
324.0ms	1886×	body	128	invalid
278.0ms	613×	body	512	valid
138.0ms	206×	body	1024	invalid
101.0ms	230×	body	512	invalid
97.0ms	308×	body	256	valid
48.0ms	159×	body	256	invalid
5.0ms	4×	body	2048	valid
2.0ms	1×	body	2048	invalid

Compiler

Compiled 40 to 30 computations (25% saved)

preprocess95.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

820×	`unswap-sqr_binary64`
674×	`associate-/l/_binary64`
369×	`sqr-pow_binary64`
227×	`*-commutative_binary64`
161×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	96
1	76	96
2	194	96
3	790	96
4	1679	96
5	1730	96
6	1797	96
7	1874	96
8	1961	96
9	2067	96
10	4016	96
11	4164	96
12	4339	96
13	4521	96
14	4721	96
15	4947	96
0	3	3
1	3	3

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2
1

Call 2

Inputs
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 2 c)) (.f64 (pow.f64 x 2) (.f64 (.f64 c (pow.f64 s 2)) c)))
(/.f64 (cos.f64 (.f64 2 s)) (.f64 (pow.f64 c 2) (.f64 (.f64 s (pow.f64 x 2)) s)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (.f64 (.f64 x (pow.f64 c 2)) x)))

Outputs
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s)))))
(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 c c)) (.f64 x (.f64 x (*.f64 s s))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c (.f64 x s)) (.f64 c (.f64 x s))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 x (.f64 (.f64 c c) (.f64 x (.f64 s s)))))
(/.f64 (cos.f64 (.f64 2 c)) (.f64 (pow.f64 x 2) (.f64 (.f64 c (pow.f64 s 2)) c)))
(/.f64 (cos.f64 (.f64 2 c)) (.f64 (.f64 x x) (.f64 c (.f64 c (.f64 s s)))))
(/.f64 (cos.f64 (.f64 2 c)) (.f64 x (.f64 (.f64 c c) (.f64 x (.f64 s s)))))
(/.f64 (cos.f64 (.f64 2 c)) (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s)))))
(/.f64 (cos.f64 (.f64 2 c)) (.f64 (.f64 c (.f64 x s)) (.f64 c (.f64 x s))))
(/.f64 (cos.f64 (.f64 2 s)) (.f64 (pow.f64 c 2) (.f64 (.f64 s (pow.f64 x 2)) s)))
(/.f64 (cos.f64 (.f64 2 s)) (.f64 (.f64 c c) (.f64 s (.f64 s (.f64 x x)))))
(/.f64 (/.f64 (cos.f64 (.f64 2 s)) (.f64 x (.f64 x (.f64 s s)))) (*.f64 c c))
(/.f64 (cos.f64 (.f64 2 s)) (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s)))))
(/.f64 (cos.f64 (.f64 2 s)) (.f64 (.f64 c (.f64 x s)) (.f64 c (.f64 x s))))
(/.f64 (/.f64 (cos.f64 (.f64 2 s)) (.f64 c c)) (.f64 x (.f64 x (*.f64 s s))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (.f64 (.f64 x (pow.f64 c 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s)))))
(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 c c)) (.f64 x (.f64 x (*.f64 s s))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c (.f64 x s)) (.f64 c (.f64 x s))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 x (.f64 (.f64 c c) (.f64 x (.f64 s s)))))

Symmetry

(sort c s)

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Rules

750×	`unswap-sqr_binary64`
516×	`*-commutative_binary64`
376×	`associate-/l/_binary64`
309×	`sqr-pow_binary64`
243×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	30	24
2	72	24
3	254	24
4	1145	24
5	2128	24
6	3320	24
7	3397	24
8	3494	24
9	3628	24
10	3813	24
11	4060	24
12	4401	24
13	4796	24

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))

Outputs
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s)))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 x (.f64 (.f64 c c) (.f64 x (.f64 s s)))))
(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 c c)) (.f64 x (.f64 x (*.f64 s s))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (.f64 x (.f64 c (.f64 x (.f64 s s))))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

2.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	25.7b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
▶	2.9b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))

Compiler

Compiled 111 to 69 computations (37.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))
✓	0.2b	(cos.f64 (*.f64 2 x))
✓	0.3b	(.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s)))
✓	6.6b	(.f64 x (.f64 c s))

series29.0ms (0.5%)

Counts

4 → 112

Calls

30 calls:

Time	Variable		Expression
5.0ms	s	@	(.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s)))
2.0ms	x	@	(cos.f64 (*.f64 2 x))
2.0ms	c	@	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))
1.0ms	s	@	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))
1.0ms	x	@	(.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s)))

rewrite67.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

699×	`log-prod_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
205×	`prod-diff_binary64`
183×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	236	41
2	3216	41

Stop Event

1×	node limit

Counts

4 → 136

Calls

Call 1

Inputs
(.f64 x (.f64 c s))
(.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s)))
(cos.f64 (*.f64 2 x))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 c (.f64 s x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 c) s) x)) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 c) s) x)))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 c) s) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 c) s) x))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 c) s) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 c (.f64 s x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 c (.f64 s x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 c (.f64 s x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 c (.f64 s x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 c (.f64 s x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 c (.f64 s x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 c (.f64 s x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 c (.f64 s x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 c) s) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 c (.f64 s x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 c (.f64 s x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (.f64 c s) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 c s) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 c (.f64 s x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 c (.f64 s x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 c (.f64 s x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 c (.f64 s x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 c (.f64 s x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 c (.f64 s x)) 2))) (cbrt.f64 (exp.f64 (pow.f64 (.f64 c (.f64 s x)) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 c (.f64 s x)) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 c (.f64 s x)) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 c (.f64 s x)) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 c (.f64 s x)) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 c (.f64 s x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 c (.f64 s x)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (.f64 c (.f64 s x)) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (.f64 c (.f64 s x))) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 c (.f64 s x)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 c (.f64 s x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 c (.f64 s x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 c (.f64 s x)) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 c (.f64 s x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 c (.f64 s x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2 (log.f64 (.f64 c (.f64 s x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 c (.f64 s x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (.f64 c (*.f64 s x)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (cos.f64 (+.f64 x x)) (fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 x) (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (cos.f64 (+.f64 x x)) (fma.f64 (neg.f64 (sqrt.f64 (pow.f64 (sin.f64 x) 2))) (sqrt.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (cos.f64 x) 2) (neg.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (cos.f64 x) 2) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cos.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (pow.f64 (cos.f64 x) 2) (neg.f64 (.f64 (pow.f64 (sin.f64 x) 2) 1))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) 1 (.f64 (pow.f64 (sin.f64 x) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cos.f64 x) (cos.f64 x) (neg.f64 (.f64 (pow.f64 (sin.f64 x) 2) 1))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) 1 (.f64 (pow.f64 (sin.f64 x) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 2)) (cbrt.f64 (pow.f64 (cos.f64 x) 2))) (cbrt.f64 (pow.f64 (cos.f64 x) 2)) (neg.f64 (.f64 (pow.f64 (sin.f64 x) 2) 1))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) 1 (.f64 (pow.f64 (sin.f64 x) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (pow.f64 (cos.f64 x) 2)) (sqrt.f64 (pow.f64 (cos.f64 x) 2)) (neg.f64 (.f64 (pow.f64 (sin.f64 x) 2) 1))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) 1 (.f64 (pow.f64 (sin.f64 x) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (pow.f64 (cos.f64 x) 2) (neg.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2)))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2))) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2))) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cos.f64 x) (cos.f64 x) (neg.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2)))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2))) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2))) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 2)) (cbrt.f64 (pow.f64 (cos.f64 x) 2))) (cbrt.f64 (pow.f64 (cos.f64 x) 2)) (neg.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2)))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2))) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2))) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (pow.f64 (cos.f64 x) 2)) (sqrt.f64 (pow.f64 (cos.f64 x) 2)) (neg.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2)))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2))) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2))) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 2)) (cbrt.f64 (pow.f64 (sin.f64 x) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (cos.f64 (exp.f64 (log1p.f64 (+.f64 x x)))) (cos.f64 1)) (.f64 (sin.f64 (exp.f64 (log1p.f64 (+.f64 x x)))) (sin.f64 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (+.f64 x x)))) (cbrt.f64 (exp.f64 (cos.f64 (+.f64 x x)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x 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(cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (.f64 s x)) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))) 1))))))

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

527×	`cancel-sign-sub-inv_binary64`
480×	`fma-def_binary64`
443×	`associate-/l/_binary64`
344×	`unswap-sqr_binary64`
253×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	1828
1	145	1826
2	431	1822
3	2021	1815

Stop Event

1×	node limit

Counts

248 → 159

Calls

Call 1

Inputs
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 s (.f64 c x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 c (.f64 s x))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 s 2) (.f64 (pow.f64 c 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
(.f64 (pow.f64 c 2) (.f64 (pow.f64 s 2) (pow.f64 x 2)))
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1
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(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (*.f64 (pow.f64 c 2) (pow.f64 x 2))))

Outputs
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1
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(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (*.f64 (pow.f64 c 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 c c) (.f64 (.f64 s s) (.f64 x x))))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 x x) (.f64 (.f64 (.f64 s s) c) c)))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 x (.f64 c (.f64 (.f64 c (.f64 s s)) x))))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 c (.f64 (.f64 s x) (.f64 c (.f64 s x)))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (*.f64 (pow.f64 c 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 c c) (.f64 (.f64 s s) (.f64 x x))))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 x x) (.f64 (.f64 (.f64 s s) c) c)))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 x (.f64 c (.f64 (.f64 c (.f64 s s)) x))))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 c (.f64 (.f64 s x) (.f64 c (.f64 s x)))))
(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (*.f64 (pow.f64 c 2) (pow.f64 x 2))))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 c c) (.f64 (.f64 s s) (.f64 x x))))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 x x) (.f64 (.f64 (.f64 s s) c) c)))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 x (.f64 c (.f64 (.f64 c (.f64 s s)) x))))
(/.f64 (cos.f64 (.f64 x 2)) (.f64 c (.f64 (.f64 s x) (.f64 c (.f64 s x)))))

prune236.0ms (3.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	167	14	181
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	169	14	183

Error

0.0b

Counts

183 → 14

Alt Table

Status	Error	Program
	3.0b	(/.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (+.f64 x x))))) (.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s))))
▶	2.7b	(/.f64 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (sin.f64 x) 2)) (.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s))))
	22.8b	(/.f64 (cos.f64 (.f64 2 x)) (cbrt.f64 (pow.f64 (pow.f64 (.f64 c (*.f64 s x)) 2) 3)))
	31.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (*.f64 (pow.f64 c 2) (pow.f64 x 2))))
	3.6b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (*.f64 s x)) 2))
	5.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 s (.f64 c x))))
	14.4b	(.f64 (/.f64 1 x) (/.f64 (cos.f64 (+.f64 x x)) (.f64 (pow.f64 (*.f64 c s) 2) x)))
	5.7b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 c (.f64 s x))))
	9.7b	(.f64 (/.f64 1 (.f64 x (.f64 c (.f64 s x)))) (/.f64 (cos.f64 (+.f64 x x)) (*.f64 c s)))
	22.5b	(.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 (+.f64 x x)) (pow.f64 (*.f64 c s) 2)))
	3.8b	(.f64 (cbrt.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (.f64 s x)) -2))) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))) 2))
	3.5b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))
	19.0b	(/.f64 (pow.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) 2) (.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s))))
	5.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (.f64 (.f64 s x) (.f64 c (.f64 s x)))))

Compiler

Compiled 4728 to 1951 computations (58.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (cos.f64 x) 2)
✓	0.3b	(pow.f64 (sin.f64 x) 2)
✓	0.4b	(-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (sin.f64 x) 2))
	6.6b	(.f64 x (.f64 c s))

series5.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

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

rewrite45.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

781×	`pow1_binary64`
725×	`log1p-expm1-u_binary64`
725×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	175	18
2	2162	18

Stop Event

1×	node limit

Counts

3 → 88

Calls

Call 1

Inputs
(-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (sin.f64 x) 2))
(pow.f64 (sin.f64 x) 2)
(pow.f64 (cos.f64 x) 2)

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

Outputs

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

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

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

simplify32.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

649×	`associate-l_binary64`
626×	`fma-def_binary64`
489×	`cancel-sign-sub-inv_binary64`
296×	`sub-neg_binary64`
270×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	159
1	105	155
2	312	149
3	1080	147
4	4771	147

Stop Event

1×	node limit

Counts

100 → 109

Calls

Call 1

Inputs
1
(-.f64 1 (*.f64 2 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 4)) 1) (.f64 2 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 4)) 1) (+.f64 (.f64 4/45 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 2))))
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) (*.f64 1/3 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (.f64 1/3 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (+.f64 (.f64 1/3 (pow.f64 x 4)) (*.f64 1/315 (pow.f64 x 8))))
1
(-.f64 1 (pow.f64 x 2))
(-.f64 (+.f64 (*.f64 1/3 (pow.f64 x 4)) 1) (pow.f64 x 2))
(-.f64 (+.f64 (.f64 1/3 (pow.f64 x 4)) 1) (+.f64 (.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)))

Outputs
1
(-.f64 1 (*.f64 2 (pow.f64 x 2)))
(+.f64 1 (.f64 -2 (.f64 x x)))
(+.f64 1 (.f64 (.f64 x x) -2))
(fma.f64 (*.f64 x x) -2 1)
(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 4)) 1) (.f64 2 (pow.f64 x 2)))
(+.f64 (fma.f64 2/3 (pow.f64 x 4) 1) (.f64 -2 (.f64 x x)))
(+.f64 (fma.f64 2/3 (pow.f64 x 4) 1) (.f64 (.f64 x x) -2))
(fma.f64 2/3 (pow.f64 x 4) (fma.f64 (*.f64 x x) -2 1))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 2/3 -2) 1)
(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 4)) 1) (+.f64 (.f64 4/45 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 2))))
(-.f64 (fma.f64 2/3 (pow.f64 x 4) 1) (fma.f64 4/45 (pow.f64 x 6) (.f64 2 (.f64 x x))))
(-.f64 (fma.f64 2/3 (pow.f64 x 4) 1) (fma.f64 2 (.f64 x x) (.f64 4/45 (pow.f64 x 6))))
(-.f64 (fma.f64 2/3 (pow.f64 x 4) (fma.f64 (.f64 x x) -2 1)) (.f64 4/45 (pow.f64 x 6)))
(fma.f64 x (*.f64 x -2) (fma.f64 (pow.f64 x 6) -4/45 (fma.f64 2/3 (pow.f64 x 4) 1)))
(pow.f64 x 2)
(*.f64 x x)
(-.f64 (pow.f64 x 2) (*.f64 1/3 (pow.f64 x 4)))
(+.f64 (.f64 x x) (.f64 -1/3 (pow.f64 x 4)))
(fma.f64 x x (*.f64 (pow.f64 x 4) -1/3))
(-.f64 (+.f64 (.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (.f64 1/3 (pow.f64 x 4)))
(+.f64 (fma.f64 2/45 (pow.f64 x 6) (.f64 x x)) (.f64 -1/3 (pow.f64 x 4)))
(fma.f64 (pow.f64 x 6) 2/45 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (*.f64 (pow.f64 x 6) 2/45)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) -1/3 (*.f64 (pow.f64 x 6) 2/45)))
(-.f64 (+.f64 (.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)) (+.f64 (.f64 1/3 (pow.f64 x 4)) (*.f64 1/315 (pow.f64 x 8))))
(-.f64 (fma.f64 2/45 (pow.f64 x 6) (.f64 x x)) (fma.f64 1/3 (pow.f64 x 4) (.f64 1/315 (pow.f64 x 8))))
(-.f64 (fma.f64 (pow.f64 x 6) 2/45 (.f64 x x)) (fma.f64 (pow.f64 x 4) 1/3 (.f64 1/315 (pow.f64 x 8))))
(fma.f64 x x (fma.f64 (pow.f64 x 6) 2/45 (fma.f64 (pow.f64 x 4) -1/3 (*.f64 (pow.f64 x 8) -1/315))))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (fma.f64 (pow.f64 x 6) 2/45 (*.f64 (pow.f64 x 8) -1/315))))
1
(-.f64 1 (pow.f64 x 2))
(-.f64 1 (*.f64 x x))
(fma.f64 x (neg.f64 x) 1)
(-.f64 (+.f64 (*.f64 1/3 (pow.f64 x 4)) 1) (pow.f64 x 2))
(-.f64 (fma.f64 1/3 (pow.f64 x 4) 1) (*.f64 x x))
(-.f64 (fma.f64 (pow.f64 x 4) 1/3 1) (*.f64 x x))
(fma.f64 (pow.f64 x 4) 1/3 (fma.f64 x (neg.f64 x) 1))
(fma.f64 (pow.f64 x 4) 1/3 (-.f64 1 (*.f64 x x)))
(-.f64 (+.f64 (.f64 1/3 (pow.f64 x 4)) 1) (+.f64 (.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)))
(-.f64 (fma.f64 1/3 (pow.f64 x 4) 1) (fma.f64 2/45 (pow.f64 x 6) (*.f64 x x)))
(-.f64 (fma.f64 (pow.f64 x 4) 1/3 1) (fma.f64 (pow.f64 x 6) 2/45 (*.f64 x x)))
(-.f64 1 (fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (*.f64 (pow.f64 x 6) 2/45))))
(-.f64 (fma.f64 (pow.f64 x 4) 1/3 1) (fma.f64 x x (*.f64 (pow.f64 x 6) 2/45)))

prune282.0ms (4.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	153	14	167

Error

0.0b

Counts

167 → 14

Alt Table

Status	Error	Program
	22.8b	(/.f64 (cos.f64 (.f64 2 x)) (cbrt.f64 (pow.f64 (pow.f64 (.f64 c (*.f64 s x)) 2) 3)))
	31.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (*.f64 (pow.f64 c 2) (pow.f64 x 2))))
▶	2.9b	(/.f64 (log1p.f64 (expm1.f64 (cos.f64 (.f64 2 x)))) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))
	3.6b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (*.f64 s x)) 2))
	5.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 s (.f64 c x))))
	14.4b	(.f64 (/.f64 1 x) (/.f64 (cos.f64 (+.f64 x x)) (.f64 (pow.f64 (*.f64 c s) 2) x)))
	5.7b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 c (.f64 s x))))
	9.7b	(.f64 (/.f64 1 (.f64 x (.f64 c (.f64 s x)))) (/.f64 (cos.f64 (+.f64 x x)) (*.f64 c s)))
✓	2.7b	(/.f64 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (sin.f64 x) 2)) (.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s))))
	22.5b	(.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 (+.f64 x x)) (pow.f64 (*.f64 c s) 2)))
	3.8b	(.f64 (cbrt.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (.f64 s x)) -2))) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))) 2))
	3.5b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))
	19.0b	(/.f64 (pow.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) 2) (.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s))))
	5.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (.f64 (.f64 s x) (.f64 c (.f64 s x)))))

Compiler

Compiled 4490 to 1838 computations (59.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(cos.f64 (*.f64 2 x))
	0.3b	(.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s)))
✓	0.6b	(expm1.f64 (cos.f64 (*.f64 2 x)))
	6.6b	(.f64 x (.f64 c s))

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(expm1.f64 (cos.f64 (*.f64 2 x)))
0.0ms	x	@	inf	(expm1.f64 (cos.f64 (*.f64 2 x)))
0.0ms	x	@	-inf	(expm1.f64 (cos.f64 (*.f64 2 x)))

rewrite32.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

572×	`pow1_binary64`
527×	`add-log-exp_binary64`
527×	`log1p-expm1-u_binary64`
527×	`expm1-log1p-u_binary64`
517×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	122	8
2	1396	8

Stop Event

1×	node limit

Counts

1 → 18

Calls

Call 1

Inputs
(expm1.f64 (cos.f64 (*.f64 2 x)))

Outputs

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

simplify32.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

788×	`distribute-rgt-neg-in_binary64`
440×	`associate-l_binary64`
430×	`fma-def_binary64`
394×	`cancel-sign-sub-inv_binary64`
324×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	156
1	80	148
2	218	146
3	820	137
4	3891	137

Stop Event

1×	node limit

Counts

30 → 27

Calls

Call 1

Inputs
(-.f64 (E.f64) 1)
(-.f64 (E.f64) (+.f64 1 (.f64 2 (.f64 (E.f64) (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8/3 (.f64 (E.f64) (pow.f64 x 4))) (E.f64)) (+.f64 1 (.f64 2 (.f64 (E.f64) (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8/3 (.f64 (E.f64) (pow.f64 x 4))) (E.f64)) (+.f64 1 (+.f64 (.f64 2 (.f64 (E.f64) (pow.f64 x 2))) (.f64 124/45 (.f64 (E.f64) (pow.f64 x 6))))))
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)

Outputs
(-.f64 (E.f64) 1)
(+.f64 (E.f64) -1)
(expm1.f64 1)
(-.f64 (E.f64) (+.f64 1 (.f64 2 (.f64 (E.f64) (pow.f64 x 2)))))
(-.f64 (E.f64) (+.f64 1 (.f64 2 (.f64 (E.f64) (*.f64 x x)))))
(+.f64 (expm1.f64 1) (.f64 -2 (.f64 (E.f64) (*.f64 x x))))
(+.f64 (expm1.f64 1) (.f64 (.f64 x (*.f64 (E.f64) x)) -2))
(fma.f64 (E.f64) (.f64 (.f64 x x) -2) (expm1.f64 1))
(fma.f64 (E.f64) (.f64 x (.f64 x -2)) (expm1.f64 1))
(-.f64 (+.f64 (.f64 8/3 (.f64 (E.f64) (pow.f64 x 4))) (E.f64)) (+.f64 1 (.f64 2 (.f64 (E.f64) (pow.f64 x 2)))))
(-.f64 (fma.f64 8/3 (.f64 (E.f64) (pow.f64 x 4)) (E.f64)) (+.f64 1 (.f64 2 (.f64 (E.f64) (.f64 x x)))))
(-.f64 (fma.f64 8/3 (.f64 (E.f64) (pow.f64 x 4)) (E.f64)) (fma.f64 2 (.f64 (E.f64) (*.f64 x x)) 1))
(+.f64 (fma.f64 (E.f64) (.f64 8/3 (pow.f64 x 4)) (expm1.f64 1)) (.f64 (.f64 x (.f64 (E.f64) x)) -2))
(+.f64 -1 (.f64 (E.f64) (-.f64 (fma.f64 8/3 (pow.f64 x 4) 1) (.f64 2 (*.f64 x x)))))
(+.f64 -1 (.f64 (E.f64) (+.f64 (fma.f64 8/3 (pow.f64 x 4) 1) (.f64 x (*.f64 x -2)))))
(-.f64 (+.f64 (.f64 8/3 (.f64 (E.f64) (pow.f64 x 4))) (E.f64)) (+.f64 1 (+.f64 (.f64 2 (.f64 (E.f64) (pow.f64 x 2))) (.f64 124/45 (.f64 (E.f64) (pow.f64 x 6))))))
(-.f64 (-.f64 (fma.f64 8/3 (.f64 (E.f64) (pow.f64 x 4)) (E.f64)) 1) (fma.f64 2 (.f64 (E.f64) (.f64 x x)) (.f64 124/45 (*.f64 (E.f64) (pow.f64 x 6)))))
(fma.f64 8/3 (.f64 (E.f64) (pow.f64 x 4)) (-.f64 (expm1.f64 1) (fma.f64 2 (.f64 (E.f64) (.f64 x x)) (.f64 124/45 (*.f64 (E.f64) (pow.f64 x 6))))))
(-.f64 (fma.f64 (E.f64) (.f64 8/3 (pow.f64 x 4)) (expm1.f64 1)) (.f64 (E.f64) (+.f64 (.f64 2 (.f64 x x)) (*.f64 124/45 (pow.f64 x 6)))))
(-.f64 (expm1.f64 1) (.f64 (E.f64) (-.f64 (fma.f64 2 (.f64 x x) (.f64 124/45 (pow.f64 x 6))) (.f64 8/3 (pow.f64 x 4)))))
(+.f64 (expm1.f64 1) (.f64 (E.f64) (-.f64 (.f64 8/3 (pow.f64 x 4)) (fma.f64 2 (.f64 x x) (.f64 124/45 (pow.f64 x 6))))))
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(expm1.f64 (cos.f64 (*.f64 2 x)))
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(expm1.f64 (cos.f64 (*.f64 2 x)))
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(expm1.f64 (cos.f64 (*.f64 2 x)))
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(expm1.f64 (cos.f64 (*.f64 2 x)))
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(expm1.f64 (cos.f64 (*.f64 2 x)))
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(expm1.f64 (cos.f64 (*.f64 2 x)))
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(expm1.f64 (cos.f64 (*.f64 2 x)))
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(expm1.f64 (cos.f64 (*.f64 2 x)))

prune229.0ms (3.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	4	8	12
Picked	1	0	1
Done	0	1	1
Total	153	11	164

Error

0.0b

Counts

164 → 11

Alt Table

Status	Error	Program
	22.8b	(/.f64 (cos.f64 (.f64 2 x)) (cbrt.f64 (pow.f64 (pow.f64 (.f64 c (*.f64 s x)) 2) 3)))
	31.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (*.f64 (pow.f64 c 2) (pow.f64 x 2))))
	14.4b	(.f64 (/.f64 1 x) (/.f64 (cos.f64 (+.f64 x x)) (.f64 (pow.f64 (*.f64 c s) 2) x)))
	5.7b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 c (.f64 s x))))
	9.7b	(.f64 (/.f64 1 (.f64 x (.f64 c (.f64 s x)))) (/.f64 (cos.f64 (+.f64 x x)) (*.f64 c s)))
✓	2.7b	(/.f64 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (sin.f64 x) 2)) (.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s))))
	3.8b	(.f64 (cbrt.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (.f64 s x)) -2))) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))) 2))
	3.5b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))
	19.0b	(/.f64 (pow.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) 2) (.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s))))
▶	3.2b	(/.f64 (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 (cos.f64 (.f64 2 x)))) 3)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))
	3.6b	(/.f64 (log1p.f64 (expm1.f64 (cos.f64 (.f64 2 x)))) (pow.f64 (.f64 c (*.f64 s x)) 2))

Compiler

Compiled 4287 to 1953 computations (54.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(expm1.f64 (cos.f64 (*.f64 2 x)))
✓	0.7b	(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))
✓	0.8b	(pow.f64 (cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x)))) 3)
	6.6b	(.f64 x (.f64 c s))

series21.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	x	@	0	(pow.f64 (cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x)))) 3)
4.0ms	x	@	inf	(pow.f64 (cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x)))) 3)
2.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x)))) 3)
2.0ms	x	@	0	(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))
0.0ms	x	@	inf	(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))

rewrite43.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

724×	`pow1_binary64`
678×	`add-log-exp_binary64`
677×	`log1p-expm1-u_binary64`
677×	`expm1-log1p-u_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	189	18
2	1882	18

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x)))) 3)
(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))

Outputs

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

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

simplify38.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

310×	`cancel-sign-sub-inv_binary64`
283×	`times-frac_binary64`
254×	`associate-/l*_binary64`
240×	`associate-r_binary64`
214×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	1187
1	631	1018
2	2471	871

Stop Event

1×	node limit

Counts

67 → 61

Calls

Call 1

Inputs
(pow.f64 (*.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 2)) 1/3)
(-.f64 (pow.f64 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 2)) 1/3) (+.f64 (.f64 2/3 (.f64 (E.f64) (pow.f64 x 2))) (.f64 4/3 (.f64 (.f64 (exp.f64 1) (pow.f64 x 2)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (-.f64 (E.f64) 1)) 1/3)))))
(-.f64 (+.f64 (pow.f64 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 2)) 1/3) (+.f64 (.f64 4/9 (/.f64 (.f64 (pow.f64 (exp.f64 1) 2) (pow.f64 x 4)) (-.f64 (E.f64) 1))) (+.f64 (.f64 16/9 (.f64 (.f64 (exp.f64 1) (pow.f64 x 4)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (-.f64 (E.f64) 1)) 1/3))) (+.f64 (.f64 8/9 (.f64 (E.f64) (pow.f64 x 4))) (.f64 8/9 (.f64 (.f64 (exp.f64 1) (.f64 (E.f64) (pow.f64 x 4))) (pow.f64 (/.f64 1 (.f64 (pow.f64 (-.f64 (E.f64) 1) 2) (-.f64 (exp.f64 1) 1))) 1/3))))))) (+.f64 (.f64 2/3 (.f64 (E.f64) (pow.f64 x 2))) (+.f64 (.f64 4/3 (.f64 (.f64 (exp.f64 1) (pow.f64 x 2)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (-.f64 (E.f64) 1)) 1/3))) (+.f64 (.f64 8/9 (/.f64 (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 4)) (-.f64 (exp.f64 1) 1))) (.f64 4/9 (.f64 (*.f64 (pow.f64 (exp.f64 1) 2) (pow.f64 x 4)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (pow.f64 (-.f64 (E.f64) 1) 4)) 1/3)))))))
(-.f64 (+.f64 (.f64 16/9 (.f64 (.f64 (exp.f64 1) (pow.f64 x 4)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (-.f64 (E.f64) 1)) 1/3))) (+.f64 (.f64 64/27 (/.f64 (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 6)) (-.f64 (exp.f64 1) 1))) (+.f64 (.f64 8/9 (.f64 (.f64 (exp.f64 1) (.f64 (E.f64) (pow.f64 x 4))) (pow.f64 (/.f64 1 (.f64 (pow.f64 (-.f64 (E.f64) 1) 2) (-.f64 (exp.f64 1) 1))) 1/3))) (+.f64 (pow.f64 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 2)) 1/3) (+.f64 (.f64 32/27 (.f64 (.f64 (pow.f64 (exp.f64 1) 2) (pow.f64 x 6)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (pow.f64 (-.f64 (E.f64) 1) 4)) 1/3))) (+.f64 (.f64 4/9 (/.f64 (.f64 (pow.f64 (exp.f64 1) 2) (pow.f64 x 4)) (-.f64 (E.f64) 1))) (+.f64 (.f64 16/27 (.f64 (.f64 (exp.f64 1) (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 6))) (pow.f64 (/.f64 1 (.f64 (pow.f64 (-.f64 (E.f64) 1) 2) (pow.f64 (-.f64 (exp.f64 1) 1) 4))) 1/3))) (+.f64 (.f64 56/81 (/.f64 (.f64 (pow.f64 (exp.f64 1) 3) (pow.f64 x 6)) (pow.f64 (-.f64 (E.f64) 1) 2))) (+.f64 (.f64 8/9 (.f64 (E.f64) (pow.f64 x 4))) (.f64 64/81 (.f64 (pow.f64 (/.f64 1 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 5))) 1/3) (.f64 (pow.f64 (E.f64) 3) (pow.f64 x 6))))))))))))) (+.f64 (.f64 2/3 (.f64 (E.f64) (pow.f64 x 2))) (+.f64 (.f64 4/3 (.f64 (.f64 (exp.f64 1) (pow.f64 x 2)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (-.f64 (E.f64) 1)) 1/3))) (+.f64 (.f64 32/27 (/.f64 (.f64 (pow.f64 (exp.f64 1) 2) (pow.f64 x 6)) (-.f64 (E.f64) 1))) (+.f64 (.f64 8/9 (/.f64 (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 4)) (-.f64 (exp.f64 1) 1))) (+.f64 (.f64 64/27 (.f64 (.f64 (exp.f64 1) (.f64 (E.f64) (pow.f64 x 6))) (pow.f64 (/.f64 1 (.f64 (pow.f64 (-.f64 (E.f64) 1) 2) (-.f64 (exp.f64 1) 1))) 1/3))) (+.f64 (.f64 4/9 (.f64 (.f64 (pow.f64 (exp.f64 1) 2) (pow.f64 x 4)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (pow.f64 (-.f64 (E.f64) 1) 4)) 1/3))) (+.f64 (.f64 40/27 (.f64 (.f64 (pow.f64 (exp.f64 1) 2) (.f64 (E.f64) (pow.f64 x 6))) (pow.f64 (/.f64 1 (.f64 (pow.f64 (-.f64 (E.f64) 1) 4) (pow.f64 (-.f64 (exp.f64 1) 1) 2))) 1/3))) (+.f64 (.f64 248/135 (.f64 (.f64 (exp.f64 1) (pow.f64 x 6)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (-.f64 (E.f64) 1)) 1/3))) (+.f64 (.f64 16/27 (/.f64 (.f64 (exp.f64 1) (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 6))) (.f64 (-.f64 (E.f64) 1) (-.f64 (exp.f64 1) 1)))) (.f64 124/135 (.f64 (E.f64) (pow.f64 x 6)))))))))))))
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1)
(pow.f64 (-.f64 (exp.f64 1) 1) 1/3)
(-.f64 (pow.f64 (-.f64 (exp.f64 1) 1) 1/3) (.f64 2/3 (.f64 (*.f64 (exp.f64 1) (pow.f64 x 2)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3))))
(-.f64 (+.f64 (.f64 8/9 (.f64 (.f64 (exp.f64 1) (pow.f64 x 4)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3))) (pow.f64 (-.f64 (exp.f64 1) 1) 1/3)) (+.f64 (.f64 2/3 (.f64 (.f64 (exp.f64 1) (pow.f64 x 2)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3))) (.f64 4/9 (.f64 (pow.f64 (/.f64 1 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 4))) 1/3) (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 4))))))
(-.f64 (+.f64 (.f64 8/9 (.f64 (.f64 (exp.f64 1) (pow.f64 x 4)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3))) (+.f64 (.f64 32/27 (.f64 (pow.f64 (/.f64 1 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 4))) 1/3) (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 6)))) (+.f64 (pow.f64 (-.f64 (exp.f64 1) 1) 1/3) (.f64 8/81 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3) (/.f64 (.f64 (pow.f64 (E.f64) 3) (pow.f64 x 6)) (pow.f64 (-.f64 (exp.f64 1) 1) 2))))))) (+.f64 (.f64 2/3 (.f64 (.f64 (exp.f64 1) (pow.f64 x 2)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3))) (+.f64 (.f64 4/9 (.f64 (pow.f64 (/.f64 1 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 4))) 1/3) (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 4)))) (+.f64 (.f64 16/27 (.f64 (/.f64 (.f64 (pow.f64 (exp.f64 1) 2) (.f64 (E.f64) (pow.f64 x 6))) (-.f64 (exp.f64 1) 1)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 5)) 1/3))) (.f64 124/135 (.f64 (.f64 (exp.f64 1) (pow.f64 x 6)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3)))))))
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)

Outputs
(pow.f64 (*.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 2)) 1/3)
(cbrt.f64 (*.f64 (expm1.f64 1) (pow.f64 (expm1.f64 1) 2)))
(cbrt.f64 (pow.f64 (expm1.f64 1) 3))
(expm1.f64 1)
(-.f64 (pow.f64 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 2)) 1/3) (+.f64 (.f64 2/3 (.f64 (E.f64) (pow.f64 x 2))) (.f64 4/3 (.f64 (.f64 (exp.f64 1) (pow.f64 x 2)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (-.f64 (E.f64) 1)) 1/3)))))
(-.f64 (cbrt.f64 (.f64 (expm1.f64 1) (pow.f64 (expm1.f64 1) 2))) (fma.f64 2/3 (.f64 (E.f64) (.f64 x x)) (.f64 4/3 (.f64 (.f64 (E.f64) (*.f64 x x)) (cbrt.f64 (/.f64 (expm1.f64 1) (expm1.f64 1)))))))
(-.f64 (cbrt.f64 (pow.f64 (expm1.f64 1) 3)) (fma.f64 2/3 (.f64 (E.f64) (.f64 x x)) (.f64 4/3 (.f64 (E.f64) (*.f64 x x)))))
(-.f64 (expm1.f64 1) (.f64 (.f64 (E.f64) (*.f64 x x)) 2))
(-.f64 (+.f64 (pow.f64 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 2)) 1/3) (+.f64 (.f64 4/9 (/.f64 (.f64 (pow.f64 (exp.f64 1) 2) (pow.f64 x 4)) (-.f64 (E.f64) 1))) (+.f64 (.f64 16/9 (.f64 (.f64 (exp.f64 1) (pow.f64 x 4)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (-.f64 (E.f64) 1)) 1/3))) (+.f64 (.f64 8/9 (.f64 (E.f64) (pow.f64 x 4))) (.f64 8/9 (.f64 (.f64 (exp.f64 1) (.f64 (E.f64) (pow.f64 x 4))) (pow.f64 (/.f64 1 (.f64 (pow.f64 (-.f64 (E.f64) 1) 2) (-.f64 (exp.f64 1) 1))) 1/3))))))) (+.f64 (.f64 2/3 (.f64 (E.f64) (pow.f64 x 2))) (+.f64 (.f64 4/3 (.f64 (.f64 (exp.f64 1) (pow.f64 x 2)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (-.f64 (E.f64) 1)) 1/3))) (+.f64 (.f64 8/9 (/.f64 (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 4)) (-.f64 (exp.f64 1) 1))) (.f64 4/9 (.f64 (*.f64 (pow.f64 (exp.f64 1) 2) (pow.f64 x 4)) (pow.f64 (/.f64 (-.f64 (exp.f64 1) 1) (pow.f64 (-.f64 (E.f64) 1) 4)) 1/3)))))))
(+.f64 (cbrt.f64 (.f64 (expm1.f64 1) (pow.f64 (expm1.f64 1) 2))) (-.f64 (fma.f64 4/9 (/.f64 (pow.f64 (E.f64) 2) (/.f64 (expm1.f64 1) (pow.f64 x 4))) (fma.f64 16/9 (.f64 (cbrt.f64 (/.f64 (expm1.f64 1) (expm1.f64 1))) (.f64 (E.f64) (pow.f64 x 4))) (.f64 8/9 (+.f64 (.f64 (E.f64) (pow.f64 x 4)) (.f64 (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 4)) (cbrt.f64 (/.f64 1 (.f64 (expm1.f64 1) (pow.f64 (expm1.f64 1) 2))))))))) (fma.f64 2/3 (.f64 (E.f64) (.f64 x x)) (fma.f64 4/3 (.f64 (.f64 (E.f64) (.f64 x x)) (cbrt.f64 (/.f64 (expm1.f64 1) (expm1.f64 1)))) (fma.f64 8/9 (/.f64 (pow.f64 (E.f64) 2) (/.f64 (expm1.f64 1) (pow.f64 x 4))) (.f64 4/9 (.f64 (pow.f64 (E.f64) 2) (.f64 (pow.f64 x 4) (cbrt.f64 (/.f64 (expm1.f64 1) (pow.f64 (expm1.f64 1) 4)))))))))))
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(-.f64 (+.f64 (cbrt.f64 (expm1.f64 1)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2))) (-.f64 (.f64 (E.f64) (.f64 (pow.f64 x 4) 8/9)) (.f64 (E.f64) (.f64 (.f64 x x) 2/3))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 5))) (.f64 (*.f64 4/9 (exp.f64 2)) (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 8/9 (.f64 (.f64 (exp.f64 1) (pow.f64 x 4)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3))) (+.f64 (.f64 32/27 (.f64 (pow.f64 (/.f64 1 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 4))) 1/3) (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 6)))) (+.f64 (pow.f64 (-.f64 (exp.f64 1) 1) 1/3) (.f64 8/81 (.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3) (/.f64 (.f64 (pow.f64 (E.f64) 3) (pow.f64 x 6)) (pow.f64 (-.f64 (exp.f64 1) 1) 2))))))) (+.f64 (.f64 2/3 (.f64 (.f64 (exp.f64 1) (pow.f64 x 2)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3))) (+.f64 (.f64 4/9 (.f64 (pow.f64 (/.f64 1 (.f64 (-.f64 (E.f64) 1) (pow.f64 (-.f64 (exp.f64 1) 1) 4))) 1/3) (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 4)))) (+.f64 (.f64 16/27 (.f64 (/.f64 (.f64 (pow.f64 (exp.f64 1) 2) (.f64 (E.f64) (pow.f64 x 6))) (-.f64 (exp.f64 1) 1)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 5)) 1/3))) (.f64 124/135 (.f64 (.f64 (exp.f64 1) (pow.f64 x 6)) (pow.f64 (/.f64 1 (pow.f64 (-.f64 (E.f64) 1) 2)) 1/3)))))))
(-.f64 (fma.f64 8/9 (.f64 (.f64 (E.f64) (pow.f64 x 4)) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2)))) (fma.f64 32/27 (.f64 (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 6)) (cbrt.f64 (/.f64 1 (.f64 (expm1.f64 1) (pow.f64 (expm1.f64 1) 4))))) (+.f64 (cbrt.f64 (expm1.f64 1)) (.f64 8/81 (.f64 (/.f64 (pow.f64 (E.f64) 3) (/.f64 (pow.f64 (expm1.f64 1) 2) (pow.f64 x 6))) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2)))))))) (fma.f64 2/3 (.f64 (.f64 (E.f64) (.f64 x x)) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2)))) (fma.f64 4/9 (.f64 (.f64 (pow.f64 (E.f64) 2) (pow.f64 x 4)) (cbrt.f64 (/.f64 1 (.f64 (expm1.f64 1) (pow.f64 (expm1.f64 1) 4))))) (fma.f64 16/27 (.f64 (/.f64 (.f64 (pow.f64 x 6) (pow.f64 (E.f64) 3)) (expm1.f64 1)) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 5)))) (.f64 124/135 (.f64 (E.f64) (.f64 (pow.f64 x 6) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2))))))))))
(-.f64 (fma.f64 8/9 (.f64 (E.f64) (.f64 (pow.f64 x 4) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2))))) (fma.f64 32/27 (.f64 (exp.f64 2) (.f64 (pow.f64 x 6) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 5))))) (fma.f64 8/81 (.f64 (.f64 (/.f64 (pow.f64 (E.f64) 3) (pow.f64 (expm1.f64 1) 2)) (pow.f64 x 6)) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2)))) (cbrt.f64 (expm1.f64 1))))) (fma.f64 2/3 (.f64 (.f64 (E.f64) (.f64 x x)) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2)))) (fma.f64 4/9 (.f64 (exp.f64 2) (.f64 (pow.f64 x 4) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 5))))) (fma.f64 16/27 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 5))) (/.f64 (pow.f64 x 6) (/.f64 (expm1.f64 1) (pow.f64 (E.f64) 3)))) (.f64 (.f64 (E.f64) (pow.f64 x 6)) (*.f64 124/135 (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2)))))))))
(-.f64 (+.f64 (fma.f64 32/27 (.f64 (exp.f64 2) (.f64 (pow.f64 x 6) (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 5))))) (cbrt.f64 (expm1.f64 1))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2))) (+.f64 (.f64 8/81 (.f64 (/.f64 (exp.f64 3) (pow.f64 (expm1.f64 1) 2)) (pow.f64 x 6))) (.f64 (E.f64) (.f64 (pow.f64 x 4) 8/9))))) (+.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 5))) (+.f64 (.f64 (.f64 4/9 (exp.f64 2)) (pow.f64 x 4)) (.f64 16/27 (/.f64 (pow.f64 x 6) (/.f64 (expm1.f64 1) (exp.f64 3)))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 1) 2))) (+.f64 (.f64 (E.f64) (.f64 (pow.f64 x 6) 124/135)) (.f64 (E.f64) (.f64 (*.f64 x x) 2/3))))))
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))
(pow.f64 (-.f64 (exp.f64 (cos.f64 (*.f64 2 x))) 1) 1/3)
(cbrt.f64 (expm1.f64 (cos.f64 (*.f64 2 x))))

prune217.0ms (3.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	132	11	143

Error

0.0b

Counts

143 → 11

Alt Table

Status	Error	Program
	22.8b	(/.f64 (cos.f64 (.f64 2 x)) (cbrt.f64 (pow.f64 (pow.f64 (.f64 c (*.f64 s x)) 2) 3)))
	31.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (*.f64 (pow.f64 c 2) (pow.f64 x 2))))
	14.4b	(.f64 (/.f64 1 x) (/.f64 (cos.f64 (+.f64 x x)) (.f64 (pow.f64 (*.f64 c s) 2) x)))
	5.7b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 c (.f64 s x))))
	9.7b	(.f64 (/.f64 1 (.f64 x (.f64 c (.f64 s x)))) (/.f64 (cos.f64 (+.f64 x x)) (*.f64 c s)))
✓	2.7b	(/.f64 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (sin.f64 x) 2)) (.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s))))
	3.8b	(.f64 (cbrt.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (.f64 s x)) -2))) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))) 2))
	3.5b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))
	19.0b	(/.f64 (pow.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) 2) (.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s))))
✓	3.2b	(/.f64 (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 (cos.f64 (.f64 2 x)))) 3)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))
	3.6b	(/.f64 (log1p.f64 (expm1.f64 (cos.f64 (.f64 2 x)))) (pow.f64 (.f64 c (*.f64 s x)) 2))

Compiler

Compiled 4792 to 2917 computations (39.1% saved)

regimes447.0ms (7.1%)

Accuracy

Total 0.8b remaining (91.2%)

Threshold costs 0.8b (91.2%)

Counts

95 → 2

Compiler

Compiled 1787 to 626 computations (65% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(/.f64 (cos.f64 (*.f64 2 x)) (*.f64 (pow.f64 c 2) (*.f64 (*.f64 x (pow.f64 s 2)) x)))

Steps

Iters	Point		Range
#hash((type . real) (value . +inf))	∈ [	#hash((type . real) (value . +inf))	,	#hash((type . real) (value . NaN))	]

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	79
1	44	79
2	49	79
3	51	79
4	52	79

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 (pow.f64 c 2) (*.f64 (*.f64 x (pow.f64 s 2)) x))) +inf.0) (*.f64 (cos.f64 (+.f64 x x)) (pow.f64 (*.f64 c (*.f64 s x)) -2)) (/.f64 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (*.f64 x (*.f64 c s)) (*.f64 x (*.f64 c s)))))

Outputs

(if (<=.f64 (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 (pow.f64 c 2) (*.f64 (*.f64 x (pow.f64 s 2)) x))) +inf.0) (*.f64 (cos.f64 (+.f64 x x)) (pow.f64 (*.f64 c (*.f64 s x)) -2)) (/.f64 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (*.f64 x (*.f64 c s)) (*.f64 x (*.f64 c s)))))

(if (<=.f64 (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 (pow.f64 c 2) (*.f64 x (*.f64 x (pow.f64 s 2))))) +inf.0) (*.f64 (cos.f64 (+.f64 x x)) (pow.f64 (*.f64 c (*.f64 x s)) -2)) (/.f64 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (*.f64 x (*.f64 c s)) (*.f64 x (*.f64 c s)))))

end337.0ms (5.3%)

Stop Event

1×

fuel

Compiler

Compiled 450 to 289 computations (35.8% saved)

Details

analyze1.3s (19.9%)

sample2.7s (42.9%)

preprocess95.0ms (1.5%)

simplify66.0ms (1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series29.0ms (0.5%)

rewrite67.0ms (1.1%)

simplify51.0ms (0.8%)

prune236.0ms (3.7%)

localize13.0ms (0.2%)

series5.0ms (0.1%)

rewrite45.0ms (0.7%)

simplify32.0ms (0.5%)

prune282.0ms (4.4%)

localize12.0ms (0.2%)

series2.0ms (0%)

rewrite32.0ms (0.5%)

simplify32.0ms (0.5%)

prune229.0ms (3.6%)

localize13.0ms (0.2%)

series21.0ms (0.3%)

rewrite43.0ms (0.7%)

simplify38.0ms (0.6%)

prune217.0ms (3.4%)

regimes447.0ms (7.1%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end337.0ms (5.3%)

Profiling