Details

analyze2.3s (13.9%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
3.1%	96.7%	0.1%	9
6.2%	93.6%	0.1%	10
10.9%	88.9%	0.1%	11
13.3%	86.6%	0.1%	12
16.4%	83.5%	0.1%	13
19.8%	80.1%	0.1%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample9.9s (60.2%)

Symmetry

(sort c s)

Results

7.0s	3439×	body	8192	exit
1.2s	6293×	body	128	valid
838.0ms	1000×	body	1024	valid
311.0ms	640×	body	512	valid
108.0ms	319×	body	256	valid
72.0ms	103×	body	1024	invalid
57.0ms	106×	body	512	invalid
23.0ms	92×	body	128	invalid
21.0ms	66×	body	256	invalid
4.0ms	4×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify112.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

750×	`unswap-sqr_binary64`
704×	`sqr-pow_binary64`
582×	`*-commutative_binary64`
574×	`fabs-mul_binary64`
502×	`cube-prod_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	29	24
2	68	24
3	214	24
4	833	24
5	1367	24
6	2084	24
7	2149	24
8	2230	24
9	2331	24
10	2464	24
11	2501	24
12	2580	24
13	2853	24
14	3277	24
15	3804	24
16	4518	24
17	4911	24

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.1b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))

Compiler

Compiled 73 to 51 computations (30.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
✓	4.3b	(.f64 (.f64 x (pow.f64 s 2)) x)
✓	9.8b	(*.f64 x (pow.f64 s 2))
✓	16.7b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

series244.0ms (1.5%)

Counts

4 → 120

Calls

4 calls:

163.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
60.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
11.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
11.0ms	(*.f64 x (pow.f64 s 2))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-exp-log_binary64`
82×	`prod-exp_binary64`
34×	`add-cbrt-cube_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`pow-exp_binary64`

Counts

4 → 127

Calls

4 calls:

9.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
7.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
5.0ms	(*.f64 x (pow.f64 s 2))
4.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)

simplify148.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

709×	`associate-/l*_binary64`
426×	`*-commutative_binary64`
391×	`fma-def_binary64`
263×	`associate-/l/_binary64`
226×	`associate-l_binary64`

Counts

247 → 187

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	4648
1	423	4174
2	1479	4157
3	4565	4141
4	4972	4141
5	5020	4141

prune235.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	175	12	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	176	12	188

Error

10.8b

Counts

188 → 12

Alt Table

Status	Error	Program
	32.9b	(.f64 (sqrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))) (sqrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (*.f64 x x))))))
	20.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (*.f64 x s) s) x)))
	58.5b	(exp.f64 (-.f64 (log.f64 (cos.f64 (.f64 2 x))) (+.f64 (.f64 (log.f64 c) 2) (+.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 s) 2)) (log.f64 x)))))
	48.3b	(/.f64 (cos.f64 (.f64 2 x)) (exp.f64 (+.f64 (log.f64 (pow.f64 c 2)) (+.f64 (+.f64 (log.f64 x) (.f64 (log.f64 s) 2)) (log.f64 x)))))
	27.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 (pow.f64 c 2) (.f64 x (pow.f64 s 2))) x))
	57.1b	(/.f64 (cos.f64 (.f64 2 x)) (exp.f64 (fma.f64 2 (+.f64 (log.f64 c) (log.f64 s)) (.f64 2 (log.f64 x)))))
	24.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (.f64 c (.f64 (*.f64 x (pow.f64 s 2)) x))))
	32.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (sqrt.f64 (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x)))) (sqrt.f64 (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))))
	42.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (.f64 s (sqrt.f64 x)) (.f64 s (sqrt.f64 x))) x)))
	44.3b	(/.f64 (sqrt.f64 (cos.f64 (.f64 2 x))) (/.f64 (.f64 c c) (/.f64 (sqrt.f64 (cos.f64 (.f64 2 x))) (.f64 (.f64 s s) (.f64 x x)))))
	28.1b	(/.f64 1 (/.f64 (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)) (cos.f64 (.f64 2 x))))
▶	17.7b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (*.f64 s x)))))

Compiler

Compiled 4900 to 2936 computations (40.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 (*.f64 2 x))
✓	0.2b	(.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (*.f64 s x)))
✓	0.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (*.f64 s x)))))
✓	16.7b	(.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (.f64 s x))))

series228.0ms (1.4%)

Counts

4 → 100

Calls

4 calls:

187.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (*.f64 s x)))))
31.0ms	(.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (.f64 s x))))
8.0ms	(.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (*.f64 s x)))
2.0ms	(cos.f64 (*.f64 2 x))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
19×	`prod-exp_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`

Counts

4 → 104

Calls

4 calls:

7.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (*.f64 s x)))))
6.0ms	(.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (.f64 s x))))
4.0ms	(.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (*.f64 s x)))
1.0ms	(cos.f64 (*.f64 2 x))

simplify118.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

444×	`unswap-sqr_binary64`
365×	`associate-/l/_binary64`
256×	`associate-*r/_binary64`
250×	`associate-*l/_binary64`
239×	`fma-def_binary64`

Counts

204 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	3918
1	356	3501
2	1704	3443
3	4496	3389
4	5074	3389

prune255.0ms (1.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	153	11	164
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	159	17	176

Error

2.4b

Counts

176 → 17

Alt Table

Status	Error	Program
	24.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (.f64 c (.f64 (*.f64 x (pow.f64 s 2)) x))))
	6.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c (.f64 c (fabs.f64 (.f64 s x)))) (fabs.f64 (.f64 s x))))
	32.9b	(.f64 (sqrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))) (sqrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (*.f64 x x))))))
	17.8b	(/.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (cbrt.f64 (cos.f64 (.f64 2 x)))) (/.f64 (.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (.f64 s x)))) (cbrt.f64 (cos.f64 (.f64 2 x)))))
	17.7b	(.f64 (cos.f64 (.f64 2 x)) (/.f64 1 (.f64 (.f64 c c) (pow.f64 (fabs.f64 (*.f64 s x)) 2))))
	12.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (.f64 c (pow.f64 (fabs.f64 (.f64 s x)) 2))))
	42.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (.f64 s (sqrt.f64 x)) (.f64 s (sqrt.f64 x))) x)))
	19.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (fabs.f64 s) (.f64 (fabs.f64 x) (fabs.f64 (*.f64 s x))))))
	17.9b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (cbrt.f64 (fabs.f64 (.f64 s x))) (cbrt.f64 (fabs.f64 (.f64 s x)))) (.f64 (cbrt.f64 (fabs.f64 (.f64 s x))) (fabs.f64 (*.f64 s x))))))
	17.9b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c c) (pow.f64 (fabs.f64 (.f64 s x)) 2))) (cbrt.f64 (.f64 (.f64 c c) (pow.f64 (fabs.f64 (.f64 s x)) 2)))) (cbrt.f64 (.f64 (.f64 c c) (pow.f64 (fabs.f64 (.f64 s x)) 2)))))
	58.5b	(exp.f64 (-.f64 (log.f64 (cos.f64 (.f64 2 x))) (+.f64 (.f64 (log.f64 c) 2) (+.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 s) 2)) (log.f64 x)))))
	48.3b	(/.f64 (cos.f64 (.f64 2 x)) (exp.f64 (+.f64 (log.f64 (pow.f64 c 2)) (+.f64 (+.f64 (log.f64 x) (.f64 (log.f64 s) 2)) (log.f64 x)))))
	17.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (sqrt.f64 (fabs.f64 (.f64 s x))) (sqrt.f64 (fabs.f64 (.f64 s x)))) (.f64 (sqrt.f64 (fabs.f64 (.f64 s x))) (sqrt.f64 (fabs.f64 (*.f64 s x)))))))
▶	2.8b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))
	17.9b	(.f64 (/.f64 1 (.f64 c c)) (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (fabs.f64 (.f64 s x)) 2)))
	13.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) 2) (.f64 (pow.f64 (fabs.f64 (*.f64 s x)) 2) (pow.f64 (cbrt.f64 c) 2))))
	57.1b	(/.f64 (cos.f64 (.f64 2 x)) (exp.f64 (fma.f64 2 (+.f64 (log.f64 c) (log.f64 s)) (.f64 2 (log.f64 x)))))

Compiler

Compiled 4920 to 2436 computations (50.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 (*.f64 2 x))
✓	0.3b	(pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)
✓	0.4b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))
✓	4.6b	(.f64 c (fabs.f64 (.f64 s x)))

series210.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

183.0ms	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))
19.0ms	(pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)
8.0ms	(.f64 c (fabs.f64 (.f64 s x)))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 86

Calls

3 calls:

4.0ms	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))
3.0ms	(.f64 c (fabs.f64 (.f64 s x)))
3.0ms	(pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

702×	`associate-/l*_binary64`
356×	`fma-def_binary64`
308×	`associate-/l/_binary64`
208×	`*-commutative_binary64`
202×	`associate-*r/_binary64`

Counts

158 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	3209
1	295	3090
2	1163	3083
3	4210	3081
4	4954	3081

prune233.0ms (1.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	114	11	125
Fresh	9	7	16
Picked	1	0	1
Done	0	0	0
Total	124	18	142

Error

0.0b

Counts

142 → 18

Alt Table

Status	Error	Program
	32.9b	(.f64 (sqrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))) (sqrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (*.f64 x x))))))
	23.4b	(.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 2 x))) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)))) (/.f64 (sqrt.f64 (cos.f64 (.f64 2 x))) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2))))
	3.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2))) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))))
	17.7b	(.f64 (cos.f64 (.f64 2 x)) (/.f64 1 (.f64 (.f64 c c) (pow.f64 (fabs.f64 (*.f64 s x)) 2))))
	3.2b	(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)))) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)))
	17.9b	(.f64 (/.f64 1 (.f64 c c)) (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (fabs.f64 (.f64 s x)) 2)))
▶	2.6b	(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 c (fabs.f64 (.f64 s x)))) (.f64 c (fabs.f64 (*.f64 s x))))
	3.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (cbrt.f64 (cos.f64 (.f64 2 x)))) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)))) (/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2))))
	42.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (.f64 s (sqrt.f64 x)) (.f64 s (sqrt.f64 x))) x)))
	2.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (cbrt.f64 (cos.f64 (.f64 2 x)))) (.f64 c (fabs.f64 (.f64 s x)))) (/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (.f64 c (fabs.f64 (*.f64 s x)))))
	58.5b	(exp.f64 (-.f64 (log.f64 (cos.f64 (.f64 2 x))) (+.f64 (.f64 (log.f64 c) 2) (+.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 s) 2)) (log.f64 x)))))
	2.8b	(.f64 (cos.f64 (.f64 2 x)) (/.f64 1 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)))
	3.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))))
	17.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (sqrt.f64 (fabs.f64 (.f64 s x))) (sqrt.f64 (fabs.f64 (.f64 s x)))) (.f64 (sqrt.f64 (fabs.f64 (.f64 s x))) (sqrt.f64 (fabs.f64 (*.f64 s x)))))))
	21.3b	(/.f64 (cos.f64 (.f64 2 x)) (cbrt.f64 (.f64 (.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2) (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))))
	17.9b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (cbrt.f64 (fabs.f64 (.f64 s x))) (cbrt.f64 (fabs.f64 (.f64 s x)))) (.f64 (cbrt.f64 (fabs.f64 (.f64 s x))) (fabs.f64 (*.f64 s x))))))
	2.8b	(/.f64 1 (/.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2) (cos.f64 (*.f64 2 x))))
	2.7b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 (*.f64 c (fabs.f64 s)) (fabs.f64 x)) 2))

Compiler

Compiled 3830 to 2091 computations (45.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 (*.f64 2 x))
✓	0.2b	(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 c (fabs.f64 (.f64 s x)))) (.f64 c (fabs.f64 (*.f64 s x))))
✓	0.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (fabs.f64 (*.f64 s x))))
	4.6b	(.f64 c (fabs.f64 (.f64 s x)))

series239.0ms (1.5%)

Counts

2 → 40

Calls

2 calls:

192.0ms	(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 c (fabs.f64 (.f64 s x)))) (.f64 c (fabs.f64 (*.f64 s x))))
47.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (fabs.f64 (*.f64 s x))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cbrt-cube_binary64`
28×	`add-exp-log_binary64`
16×	`times-frac_binary64`
12×	`cbrt-undiv_binary64`
12×	`div-exp_binary64`

Counts

2 → 65

Calls

2 calls:

7.0ms	(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 c (fabs.f64 (.f64 s x)))) (.f64 c (fabs.f64 (*.f64 s x))))
4.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (fabs.f64 (*.f64 s x))))

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

759×	`associate-l_binary64`
681×	`associate-*l/_binary64`
579×	`associate-*r/_binary64`
483×	`associate-/r/_binary64`
215×	`associate-/r*_binary64`

Counts

105 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	3223
1	369	2754
2	1492	2725
3	5131	2725

prune311.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	176	7	183
Fresh	11	6	17
Picked	1	0	1
Done	0	0	0
Total	188	13	201

Error

0.0b

Counts

201 → 13

Alt Table

Status	Error	Program
	13.0b	(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 c (fabs.f64 (.f64 s x)))) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 3)))
	3.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2))) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))))
	12.4b	(.f64 (/.f64 (cos.f64 (.f64 x 2)) c) (/.f64 (/.f64 1 c) (pow.f64 (fabs.f64 (*.f64 s x)) 2)))
	42.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (.f64 s (sqrt.f64 x)) (.f64 s (sqrt.f64 x))) x)))
	3.0b	(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 c (fabs.f64 (.f64 s x)))) (.f64 (.f64 c (.f64 (cbrt.f64 (fabs.f64 (.f64 s x))) (cbrt.f64 (fabs.f64 (.f64 s x))))) (cbrt.f64 (fabs.f64 (*.f64 s x)))))
	58.5b	(exp.f64 (-.f64 (log.f64 (cos.f64 (.f64 2 x))) (+.f64 (.f64 (log.f64 c) 2) (+.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 s) 2)) (log.f64 x)))))
	3.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))))
	23.4b	(.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 2 x))) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)))) (/.f64 (sqrt.f64 (cos.f64 (.f64 2 x))) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2))))
	2.7b	(/.f64 (/.f64 1 (/.f64 c (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s x))))) (.f64 c (fabs.f64 (.f64 s x))))
	2.9b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (cbrt.f64 (cos.f64 (.f64 2 x)))) c) (/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (fabs.f64 (.f64 s x)))) (.f64 c (fabs.f64 (.f64 s x))))
	4.7b	(/.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 c (fabs.f64 (.f64 s x)))) (.f64 (*.f64 c (fabs.f64 s)) (fabs.f64 x)))
	2.7b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 (*.f64 c (fabs.f64 s)) (fabs.f64 x)) 2))
	21.3b	(.f64 (sqrt.f64 (/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 c c) (pow.f64 (fabs.f64 (.f64 s x)) 2)))) (sqrt.f64 (/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 c c) (pow.f64 (fabs.f64 (*.f64 s x)) 2)))))

Compiler

Compiled 5304 to 2058 computations (61.2% saved)

regimes1.3s (8.2%)

Accuracy

Total 0.6b remaining (80.5%)

Threshold costs 0.6b (80.5%)

Counts

200 → 2

Compiler

Compiled 34013 to 22450 computations (34% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	79
1	38	79
2	39	79
3	39	79

end231.0ms (1.4%)

Remove: (sort c s)
Compiler: Compiled 602 to 386 computations (35.9% saved)

Details

analyze2.3s (13.9%)

sample9.9s (60.2%)

simplify112.0ms (0.7%)

prune3.0ms (0%)

localize17.0ms (0.1%)

series244.0ms (1.5%)

rewrite35.0ms (0.2%)

simplify148.0ms (0.9%)

prune235.0ms (1.4%)

localize10.0ms (0.1%)

series228.0ms (1.4%)

rewrite26.0ms (0.2%)

simplify118.0ms (0.7%)

prune255.0ms (1.6%)

localize9.0ms (0.1%)

series210.0ms (1.3%)

rewrite16.0ms (0.1%)

simplify98.0ms (0.6%)

prune233.0ms (1.4%)

localize9.0ms (0.1%)

series239.0ms (1.5%)

rewrite16.0ms (0.1%)

simplify73.0ms (0.4%)

prune311.0ms (1.9%)

regimes1.3s (8.2%)

bsearch9.0ms (0.1%)

simplify3.0ms (0%)

end231.0ms (1.4%)

Profiling