Details

analyze2.2s (11.8%)

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 (53.3%)

Symmetry

(sort c s)

Results

7.2s	3464×	body	8192	exit
1.2s	6317×	body	128	valid
684.0ms	971×	body	1024	valid
321.0ms	640×	body	512	valid
116.0ms	323×	body	256	valid
74.0ms	108×	body	1024	invalid
57.0ms	119×	body	512	invalid
27.0ms	74×	body	256	invalid
21.0ms	107×	body	128	invalid
5.0ms	5×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify112.0ms (0.6%)

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

27.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.9b	(/.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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
✓	3.5b	(.f64 (.f64 x (pow.f64 s 2)) x)
✓	9.1b	(*.f64 x (pow.f64 s 2))
✓	18.4b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

series231.0ms (1.2%)

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)))
48.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
11.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
10.0ms	(*.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:

8.0ms	(/.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))
6.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
4.0ms	(*.f64 x (pow.f64 s 2))

simplify156.0ms (0.8%)

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

prune254.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	174	13	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	13	188

Error

13.1b

Counts

188 → 13

Alt Table

Status	Error	Program
	41.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (.f64 s (sqrt.f64 x)) (.f64 s (sqrt.f64 x))) x)))
	29.4b	(.f64 (sqrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))) (sqrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x)))))
	57.4b	(/.f64 (cos.f64 (.f64 2 x)) (exp.f64 (fma.f64 2 (+.f64 (log.f64 c) (log.f64 s)) (.f64 2 (log.f64 x)))))
	31.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x)))))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))))
	27.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 (pow.f64 c 2) (.f64 x (pow.f64 s 2))) x))
▶	19.7b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (*.f64 s x)))))
	51.7b	(exp.f64 (-.f64 (log.f64 (cos.f64 (.f64 2 x))) (+.f64 (log.f64 (pow.f64 c 2)) (+.f64 (+.f64 (log.f64 x) (.f64 (log.f64 s) 2)) (log.f64 x)))))
	23.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (.f64 c (.f64 (*.f64 x (pow.f64 s 2)) x))))
	53.6b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 (sqrt.f64 c) 2) (.f64 c (.f64 (.f64 s s) (.f64 x x)))))
	31.7b	(.f64 (cos.f64 (.f64 2 x)) (/.f64 1 (.f64 (.f64 s s) (.f64 (.f64 c c) (*.f64 x x)))))
	20.6b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (*.f64 x s) s) x)))
	31.1b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (*.f64 s x) (pow.f64 (sqrt.f64 s) 2)) x)))
	23.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (.f64 x (pow.f64 (.f64 (cbrt.f64 s) (cbrt.f64 s)) 2)) (pow.f64 (cbrt.f64 s) 2)) x)))

Compiler

Compiled 4990 to 3000 computations (39.9% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (*.f64 s x)))
✓	0.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (*.f64 s x)))))
✓	18.4b	(.f64 (pow.f64 c 2) (.f64 (fabs.f64 (.f64 s x)) (fabs.f64 (.f64 s x))))

series219.0ms (1.2%)

Counts

3 → 96

Calls

3 calls:

178.0ms

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

30.0ms

(*.f64 (pow.f64 c 2) (*.f64 (fabs.f64 (*.f64 s x)) (fabs.f64 (*.f64 s x))))

11.0ms

(*.f64 (fabs.f64 (*.f64 s x)) (fabs.f64 (*.f64 s x)))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-exp-log_binary64`
19×	`add-cbrt-cube_binary64`
19×	`prod-exp_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`

Counts

3 → 94

Calls

3 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)))

simplify138.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

444×	`unswap-sqr_binary64`
365×	`associate-/l/_binary64`
258×	`associate-*r/_binary64`
247×	`fma-def_binary64`
237×	`associate-*l/_binary64`

Counts

190 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	3754
1	328	3350
2	1609	3296
3	4310	3242
4	4981	3242
5	5021	3242

prune234.0ms (1.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	136	10	146
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	143	16	159

Error

2.4b

Counts

159 → 16

Alt Table

Status	Error	Program
	41.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (.f64 s (sqrt.f64 x)) (.f64 s (sqrt.f64 x))) x)))
	16.7b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 (pow.f64 c 2) (fabs.f64 (.f64 s x))) (fabs.f64 (*.f64 s x))))
	57.4b	(/.f64 (cos.f64 (.f64 2 x)) (exp.f64 (fma.f64 2 (+.f64 (log.f64 c) (log.f64 s)) (.f64 2 (log.f64 x)))))
	20.6b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 (fabs.f64 (*.f64 s x)) (fabs.f64 s)) (fabs.f64 x))))
	20.3b	(.f64 (/.f64 1 (.f64 c c)) (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (fabs.f64 (.f64 s x)) 2)))
	31.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x)))))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))))
	29.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (cbrt.f64 (pow.f64 (fabs.f64 (*.f64 s x)) 6))))
	47.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 (pow.f64 (sqrt.f64 c) 2) (fabs.f64 (.f64 s x))) (.f64 (pow.f64 (sqrt.f64 c) 2) (fabs.f64 (.f64 s x)))))
	31.7b	(.f64 (cos.f64 (.f64 2 x)) (/.f64 1 (.f64 (.f64 s s) (.f64 (.f64 c c) (*.f64 x x)))))
	6.1b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c (.f64 c (fabs.f64 (.f64 s x)))) (fabs.f64 (.f64 s x))))
	51.7b	(exp.f64 (-.f64 (log.f64 (cos.f64 (.f64 2 x))) (+.f64 (log.f64 (pow.f64 c 2)) (+.f64 (+.f64 (log.f64 x) (.f64 (log.f64 s) 2)) (log.f64 x)))))
	22.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (fabs.f64 s) (.f64 (fabs.f64 x) (fabs.f64 (*.f64 s x))))))
	23.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (.f64 c (.f64 (*.f64 x (pow.f64 s 2)) x))))
	20.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (expm1.f64 (log1p.f64 (pow.f64 (fabs.f64 (*.f64 s x)) 2)))))
	19.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (pow.f64 (fabs.f64 (.f64 s x)) 2)))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (pow.f64 (fabs.f64 (.f64 s x)) 2))))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (pow.f64 (fabs.f64 (.f64 s x)) 2)))))
▶	2.9b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))

Compiler

Compiled 4429 to 2204 computations (50.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)
✓	0.3b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))
✓	5.3b	(.f64 c (fabs.f64 (.f64 s x)))

series211.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

183.0ms	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))
20.0ms	(pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)
8.0ms	(.f64 c (fabs.f64 (.f64 s x)))

rewrite19.0ms (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:

5.0ms	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))
3.0ms	(pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)
3.0ms	(.f64 c (fabs.f64 (.f64 s x)))

simplify102.0ms (0.5%)

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

prune176.0ms (0.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Error

0.1b

Counts

123 → 15

Alt Table

Status	Error	Program
	20.3b	(.f64 (/.f64 1 (.f64 c c)) (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (fabs.f64 (.f64 s x)) 2)))
	31.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x)))))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))))
	3.3b	(/.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))))
	22.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (fabs.f64 s) (.f64 (fabs.f64 x) (fabs.f64 (*.f64 s x))))))
	23.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (.f64 c (.f64 (*.f64 x (pow.f64 s 2)) x))))
	22.0b	(/.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))))
	20.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (expm1.f64 (log1p.f64 (pow.f64 (fabs.f64 (*.f64 s x)) 2)))))
	3.3b	(.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))))
	2.9b	(-.f64 (/.f64 (.f64 (cos.f64 x) (cos.f64 x)) (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)) (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (pow.f64 (.f64 c (fabs.f64 (.f64 s x))) 2)))
▶	2.8b	(.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)))))
	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))))
	3.3b	(.f64 (/.f64 1 (.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 (cos.f64 (.f64 2 x)) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))))
	6.1b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c (.f64 c (fabs.f64 (.f64 s x)))) (fabs.f64 (.f64 s x))))
	3.3b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 (*.f64 c (fabs.f64 s)) (fabs.f64 x)) 2))
	29.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (cbrt.f64 (pow.f64 (fabs.f64 (*.f64 s x)) 6))))

Compiler

Compiled 3327 to 1813 computations (45.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(cbrt.f64 (cos.f64 (*.f64 2 x)))
✓	0.6b	(/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (.f64 c (fabs.f64 (*.f64 s x))))
✓	0.6b	(/.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (cbrt.f64 (cos.f64 (.f64 2 x)))) (.f64 c (fabs.f64 (*.f64 s x))))
	5.3b	(.f64 c (fabs.f64 (.f64 s x)))

series2.0s (10.5%)

Counts

3 → 84

Calls

3 calls:

1.0s

(/.f64 (*.f64 (cbrt.f64 (cos.f64 (*.f64 2 x))) (cbrt.f64 (cos.f64 (*.f64 2 x)))) (*.f64 c (fabs.f64 (*.f64 s x))))

769.0ms

(/.f64 (cbrt.f64 (cos.f64 (*.f64 2 x))) (*.f64 c (fabs.f64 (*.f64 s x))))

172.0ms

(cbrt.f64 (cos.f64 (*.f64 2 x)))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
9×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

3 → 65

Calls

3 calls:

6.0ms

(/.f64 (*.f64 (cbrt.f64 (cos.f64 (*.f64 2 x))) (cbrt.f64 (cos.f64 (*.f64 2 x)))) (*.f64 c (fabs.f64 (*.f64 s x))))

4.0ms

(/.f64 (cbrt.f64 (cos.f64 (*.f64 2 x))) (*.f64 c (fabs.f64 (*.f64 s x))))

1.0ms

(cbrt.f64 (cos.f64 (*.f64 2 x)))

simplify128.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

621×	`associate-*l/_binary64`
575×	`associate-*r/_binary64`
435×	`fma-def_binary64`
316×	`associate-/l/_binary64`
180×	`times-frac_binary64`

Counts

149 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	3862
1	356	3070
2	1390	2995
3	4138	2995
4	4953	2995
5	4982	2995

prune500.0ms (2.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	230	6	236
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	237	14	251

Error

0.0b

Counts

251 → 14

Alt Table

Status	Error	Program
	3.1b	(.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 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (fabs.f64 (*.f64 s x)) (cbrt.f64 c)))))
	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))))
	3.2b	(.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 (.f64 c (.f64 (cbrt.f64 (fabs.f64 (.f64 s x))) (cbrt.f64 (fabs.f64 (.f64 s x))))) (cbrt.f64 (fabs.f64 (*.f64 s x))))))
	3.3b	(.f64 (/.f64 1 (.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 (cos.f64 (.f64 2 x)) (cbrt.f64 (pow.f64 (.f64 c (fabs.f64 (*.f64 s x))) 2))))
	5.6b	(.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 (*.f64 c (fabs.f64 s)) (fabs.f64 x))))
	2.7b	(.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 (.f64 2 x)) 2) 1/3) (/.f64 1 (.f64 c (fabs.f64 (.f64 s x))))) (/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (.f64 c (fabs.f64 (.f64 s x)))))
	6.1b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c (.f64 c (fabs.f64 (.f64 s x)))) (fabs.f64 (.f64 s x))))
	3.1b	(.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 (.f64 (cbrt.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (.f64 c (fabs.f64 (.f64 s x))))) (cbrt.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (.f64 c (fabs.f64 (.f64 s x)))))) (cbrt.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (.f64 c (fabs.f64 (*.f64 s x)))))))
	3.3b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 (*.f64 c (fabs.f64 s)) (fabs.f64 x)) 2))
	20.3b	(.f64 (/.f64 1 (.f64 c c)) (/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (fabs.f64 (.f64 s x)) 2)))
	31.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x)))))) (cbrt.f64 (/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 s s) (.f64 (.f64 c c) (.f64 x x))))))
	23.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 c (.f64 c (.f64 (*.f64 x (pow.f64 s 2)) x))))
	22.0b	(/.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))))
	2.8b	(.f64 (.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) c) (/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (fabs.f64 (.f64 s x)))) (/.f64 (cbrt.f64 (cos.f64 (.f64 2 x))) (.f64 c (fabs.f64 (.f64 s x)))))

Compiler

Compiled 9406 to 5038 computations (46.4% saved)

regimes1.6s (8.8%)

Accuracy

Total 0.7b remaining (81.2%)

Threshold costs 0.7b (81.2%)

Counts

173 → 2

Compiler

Compiled 30443 to 20319 computations (33.3% saved)

bsearch8.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`fabs-mul_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	79
1	42	79
2	43	79
3	41	79

end281.0ms (1.5%)

Compiler: Compiled 723 to 449 computations (37.9% saved)

Details

analyze2.2s (11.8%)

sample9.9s (53.3%)

simplify112.0ms (0.6%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series231.0ms (1.2%)

rewrite35.0ms (0.2%)

simplify156.0ms (0.8%)

prune254.0ms (1.4%)

localize10.0ms (0.1%)

series219.0ms (1.2%)

rewrite24.0ms (0.1%)

simplify138.0ms (0.7%)

prune234.0ms (1.3%)

localize10.0ms (0.1%)

series211.0ms (1.1%)

rewrite19.0ms (0.1%)

simplify102.0ms (0.5%)

prune176.0ms (0.9%)

localize12.0ms (0.1%)

series2.0s (10.5%)

rewrite16.0ms (0.1%)

simplify128.0ms (0.7%)

prune500.0ms (2.7%)

regimes1.6s (8.8%)

bsearch8.0ms (0%)

simplify3.0ms (0%)

end281.0ms (1.5%)

Profiling