Details

analyze2.5s (18.5%)

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)

sample5.3s (39.7%)

Symmetry

(sort c s)

Results

1.9s	6292×	body	128	valid
1.1s	919×	body	1024	valid
597.0ms	1992×	body	128	invalid
557.0ms	665×	body	512	valid
283.0ms	273×	body	512	invalid
253.0ms	204×	body	1024	invalid
209.0ms	374×	body	256	valid
102.0ms	191×	body	256	invalid
12.0ms	6×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify137.0ms (1%)

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

prune5.0ms (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

28.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.9b	(/.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)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
✓	5.4b	(.f64 (.f64 x (pow.f64 s 2)) x)
✓	9.4b	(*.f64 x (pow.f64 s 2))
✓	18.8b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

series387.0ms (2.9%)

Counts

4 → 120

Calls

4 calls:

283.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
66.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
18.0ms	(*.f64 x (pow.f64 s 2))
18.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)

rewrite138.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

301×	`prod-diff_binary64`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
221×	`log-pow_binary64`
135×	`add-sqr-sqrt_binary64`

Counts

4 → 89

Calls

4 calls:

134.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
134.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
134.0ms	(*.f64 x (pow.f64 s 2))
134.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	57
1	275	57
2	3342	57
3	4862	57
4	5046	57
0	0	0
1	0	0

simplify189.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

877×	`associate-/l*_binary64`
439×	`associate-/l/_binary64`
361×	`cancel-sign-sub-inv_binary64`
359×	`unswap-sqr_binary64`
272×	`fma-neg_binary64`

Counts

209 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	1932
1	96	1930
2	310	1930
3	1464	1925
4	4903	1923
5	4968	1923

prune252.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	95	12	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	12	108

Error

13.0b

Counts

108 → 12

Alt Table

Status	Error	Program
	41.2b	(pow.f64 (/.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) (.f64 c (.f64 (sqrt.f64 x) (*.f64 s (sqrt.f64 x))))) 2)
	42.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (pow.f64 (.f64 (sqrt.f64 x) (.f64 s (sqrt.f64 x))) 2)))
	34.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 s 2) (*.f64 (pow.f64 c 2) (pow.f64 x 2))))
	43.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (pow.f64 (.f64 s (sqrt.f64 x)) 2) x)))
	32.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 (+.f64 x x))) 2) (.f64 c (.f64 (sqrt.f64 x) (.f64 s (sqrt.f64 x))))) (/.f64 (cbrt.f64 (cos.f64 (+.f64 x x))) (.f64 c (.f64 (sqrt.f64 x) (*.f64 s (sqrt.f64 x))))))
	29.1b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (pow.f64 (cbrt.f64 (.f64 x (*.f64 s s))) 3) x)))
	32.8b	(.f64 (/.f64 1 (.f64 c (.f64 (sqrt.f64 x) (.f64 s (sqrt.f64 x))))) (/.f64 (cos.f64 (+.f64 x x)) (.f64 c (.f64 (sqrt.f64 x) (*.f64 s (sqrt.f64 x))))))
	29.1b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (cbrt.f64 (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s))))) 3))
▶	27.3b	(.f64 (/.f64 1 (.f64 (.f64 c c) (.f64 x (*.f64 s s)))) (/.f64 (cos.f64 (+.f64 x x)) x))
	33.1b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (.f64 (sqrt.f64 x) (.f64 s (sqrt.f64 x)))) 2))
	29.0b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s))))) 2)) (/.f64 (cos.f64 (+.f64 x x)) (cbrt.f64 (.f64 (.f64 c c) (.f64 x (.f64 x (*.f64 s s)))))))
	29.3b	(.f64 (/.f64 (cos.f64 (+.f64 x x)) (.f64 c c)) (/.f64 1 (.f64 x (.f64 x (*.f64 s s)))))

Compiler

Compiled 2864 to 1186 computations (58.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (.f64 (.f64 c c) (.f64 x (.f64 s s))))
✓	4.6b	(.f64 (/.f64 1 (.f64 (.f64 c c) (.f64 x (*.f64 s s)))) (/.f64 (cos.f64 (+.f64 x x)) x))
✓	9.4b	(.f64 x (.f64 s s))
✓	17.5b	(.f64 (.f64 c c) (.f64 x (.f64 s s)))

series514.0ms (3.9%)

Counts

4 → 132

Calls

4 calls:

252.0ms	(.f64 (/.f64 1 (.f64 (.f64 c c) (.f64 x (*.f64 s s)))) (/.f64 (cos.f64 (+.f64 x x)) x))
200.0ms	(/.f64 1 (.f64 (.f64 c c) (.f64 x (.f64 s s))))
49.0ms	(.f64 (.f64 c c) (.f64 x (.f64 s s)))
13.0ms	(.f64 x (.f64 s s))

rewrite152.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

532×	`prod-diff_binary64`
153×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
142×	`add-cbrt-cube_binary64`

Counts

4 → 131

Calls

4 calls:

147.0ms	(/.f64 1 (.f64 (.f64 c c) (.f64 x (.f64 s s))))
147.0ms	(.f64 (/.f64 1 (.f64 (.f64 c c) (.f64 x (*.f64 s s)))) (/.f64 (cos.f64 (+.f64 x x)) x))
147.0ms	(.f64 x (.f64 s s))
147.0ms	(.f64 (.f64 c c) (.f64 x (.f64 s s)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	306	55
2	3944	55
3	4898	55
0	0	0
1	0	0

simplify132.0ms (1%)

Algorithm

1×	egg-herbie

Rules

877×	`associate-/l*_binary64`
468×	`associate-/l/_binary64`
406×	`unswap-sqr_binary64`
361×	`cancel-sign-sub-inv_binary64`
271×	`fma-def_binary64`

Counts

263 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	2160
1	106	2158
2	337	2158
3	1524	2153
4	5017	2153

prune422.0ms (3.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	134	16	150
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	142	20	162

Error

8.8b

Counts

162 → 20

Alt Table

Status	Error	Program
▶	20.4b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 c (.f64 x (*.f64 s s))))
	41.9b	(/.f64 (sqrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x)) (/.f64 (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2) (sqrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x))))
	34.1b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2)) 3)) (/.f64 (cos.f64 (+.f64 x x)) x))
	31.7b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) (.f64 c (.f64 s (sqrt.f64 x)))) (.f64 c (.f64 s (sqrt.f64 x))))
	44.4b	(.f64 (/.f64 1 (pow.f64 (pow.f64 (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2) 3) 1/3)) (/.f64 (cos.f64 (+.f64 x x)) x))
	27.8b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) (.f64 c c)) (.f64 x (*.f64 s s)))
	34.1b	(/.f64 (pow.f64 (cbrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x)) 2) (/.f64 (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2) (cbrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x))))
	42.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (pow.f64 (.f64 (sqrt.f64 x) (.f64 s (sqrt.f64 x))) 2)))
	28.9b	(/.f64 (.f64 (pow.f64 c -2) (cos.f64 (+.f64 x x))) (.f64 (.f64 x (.f64 s s)) x))
	32.8b	(.f64 (/.f64 1 (.f64 c (.f64 (sqrt.f64 x) (.f64 s (sqrt.f64 x))))) (/.f64 (cos.f64 (+.f64 x x)) (.f64 c (.f64 (sqrt.f64 x) (*.f64 s (sqrt.f64 x))))))
	29.1b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (cbrt.f64 (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s))))) 3))
	27.3b	(/.f64 (/.f64 (pow.f64 c -2) (.f64 x (.f64 s s))) (/.f64 x (cos.f64 (+.f64 x x))))
	29.0b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s))))) 2)) (/.f64 (cos.f64 (+.f64 x x)) (cbrt.f64 (.f64 (.f64 c c) (.f64 x (.f64 x (*.f64 s s)))))))
	33.9b	(.f64 (pow.f64 (/.f64 1 (.f64 c (*.f64 s (sqrt.f64 x)))) 2) (/.f64 (cos.f64 (+.f64 x x)) x))
	34.0b	(-.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (.f64 x (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2))) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2))))
	34.0b	(/.f64 (pow.f64 (cbrt.f64 (cos.f64 (+.f64 x x))) 2) (/.f64 (.f64 x (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2)) (cbrt.f64 (cos.f64 (+.f64 x x)))))
	23.2b	(.f64 (/.f64 1 (/.f64 c (/.f64 1 (.f64 c (.f64 x (.f64 s s)))))) (/.f64 (cos.f64 (+.f64 x x)) x))
	33.9b	(.f64 (/.f64 1 (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2)) (/.f64 (cos.f64 (+.f64 x x)) x))
	26.9b	(.f64 (/.f64 1 (.f64 (pow.f64 s 2) (*.f64 (pow.f64 c 2) x))) (/.f64 (cos.f64 (+.f64 x x)) x))
	34.1b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))

Compiler

Compiled 3952 to 1667 computations (57.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c)
✓	7.0b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 c (.f64 x (*.f64 s s))))
✓	8.5b	(.f64 c (.f64 x (*.f64 s s)))
	9.4b	(.f64 x (.f64 s s))

series354.0ms (2.7%)

Counts

3 → 96

Calls

3 calls:

285.0ms	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 c (.f64 x (*.f64 s s))))
36.0ms	(.f64 c (.f64 x (*.f64 s s)))
32.0ms	(/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c)

rewrite125.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

568×	`prod-diff_binary64`
144×	`add-sqr-sqrt_binary64`
135×	`log1p-expm1-u_binary64`
135×	`expm1-log1p-u_binary64`
134×	`add-log-exp_binary64`

Counts

3 → 109

Calls

3 calls:

119.0ms	(/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c)
119.0ms	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 c (.f64 x (*.f64 s s))))
119.0ms	(.f64 c (.f64 x (*.f64 s s)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	276	46
2	4033	46
3	5107	46
0	0	0
1	0	0

simplify133.0ms (1%)

Algorithm

1×	egg-herbie

Rules

477×	`associate-/l/_binary64`
474×	`cancel-sign-sub-inv_binary64`
402×	`fma-neg_binary64`
393×	`fma-def_binary64`
384×	`unswap-sqr_binary64`

Counts

205 → 131

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	1633
1	162	1631
2	459	1627
3	1862	1620
4	4674	1618
5	5056	1618

prune284.0ms (2.1%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	139	9	148
Fresh	7	12	19
Picked	0	1	1
Done	0	0	0
Total	146	22	168

Error

2.8b

Counts

168 → 22

Alt Table

Status	Error	Program
✓	20.4b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 c (.f64 x (*.f64 s s))))
	41.9b	(/.f64 (sqrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x)) (/.f64 (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2) (sqrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x))))
	34.1b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2)) 3)) (/.f64 (cos.f64 (+.f64 x x)) x))
	31.7b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) (.f64 c (.f64 s (sqrt.f64 x)))) (.f64 c (.f64 s (sqrt.f64 x))))
	44.4b	(.f64 (/.f64 1 (pow.f64 (pow.f64 (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2) 3) 1/3)) (/.f64 (cos.f64 (+.f64 x x)) x))
	34.1b	(/.f64 (pow.f64 (cbrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x)) 2) (/.f64 (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2) (cbrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x))))
	42.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (pow.f64 (.f64 (sqrt.f64 x) (.f64 s (sqrt.f64 x))) 2)))
	20.6b	(pow.f64 (.f64 (.f64 c (.f64 x (.f64 s s))) (*.f64 c (/.f64 x (cos.f64 (+.f64 x x))))) -1)
	34.0b	(/.f64 (pow.f64 (cbrt.f64 (cos.f64 (+.f64 x x))) 2) (/.f64 (.f64 x (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2)) (cbrt.f64 (cos.f64 (+.f64 x x)))))
	36.4b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (pow.f64 (.f64 (sqrt.f64 (.f64 c x)) s) 2))
	33.9b	(.f64 (/.f64 1 (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2)) (/.f64 (cos.f64 (+.f64 x x)) x))
	20.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c)) 2) (.f64 c x)) (/.f64 (cbrt.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c)) (*.f64 s s)))
	29.1b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (cbrt.f64 (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s))))) 3))
	24.8b	(.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) (.f64 c x)) (/.f64 (/.f64 1 c) (*.f64 s s)))
▶	17.1b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 (pow.f64 s 2) (.f64 c x)))
	35.7b	(.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) (.f64 (sqrt.f64 (.f64 c x)) s)) (/.f64 (/.f64 1 c) (.f64 (sqrt.f64 (*.f64 c x)) s)))
	34.1b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
	33.9b	(.f64 (pow.f64 (/.f64 1 (.f64 c (*.f64 s (sqrt.f64 x)))) 2) (/.f64 (cos.f64 (+.f64 x x)) x))
	34.0b	(-.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (.f64 x (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2))) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2))))
	20.4b	(.f64 (/.f64 (cos.f64 (+.f64 x x)) (.f64 c (.f64 x (.f64 s s)))) (/.f64 (/.f64 1 x) c))
	42.1b	(pow.f64 (/.f64 (sqrt.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c)) (.f64 (sqrt.f64 (.f64 c x)) s)) 2)
	34.7b	(.f64 (/.f64 1 (.f64 (sqrt.f64 (.f64 c x)) s)) (/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 (sqrt.f64 (*.f64 c x)) s)))

Compiler

Compiled 4315 to 1448 computations (66.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cos.f64 (+.f64 x x)) x)
	0.2b	(/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c)
✓	7.0b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 (pow.f64 s 2) (.f64 c x)))
✓	13.1b	(.f64 (pow.f64 s 2) (.f64 c x))

series169.0ms (1.3%)

Counts

3 → 64

Calls

3 calls:

145.0ms	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 (pow.f64 s 2) (.f64 c x)))
21.0ms	(.f64 (pow.f64 s 2) (.f64 c x))
3.0ms	(/.f64 (cos.f64 (+.f64 x x)) x)

rewrite90.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

583×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
141×	`add-log-exp_binary64`

Counts

3 → 103

Calls

3 calls:

87.0ms	(/.f64 (cos.f64 (+.f64 x x)) x)
87.0ms	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 (pow.f64 s 2) (.f64 c x)))
87.0ms	(.f64 (pow.f64 s 2) (.f64 c x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	297	43
2	4169	43
3	5265	43
0	0	0
1	0	0

simplify49.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

475×	`associate-*l/_binary64`
441×	`associate-/l/_binary64`
441×	`cancel-sign-sub-inv_binary64`
436×	`fma-def_binary64`
385×	`unswap-sqr_binary64`

Counts

167 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	1239
1	142	1233
2	425	1229
3	1789	1222
4	5021	1222

prune213.0ms (1.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	3	17	20
Picked	1	0	1
Done	0	1	1
Total	175	20	195

Error

2.8b

Counts

195 → 20

Alt Table

Status	Error	Program
	42.1b	(pow.f64 (/.f64 (sqrt.f64 (/.f64 (cos.f64 (+.f64 x x)) (.f64 c x))) (.f64 s (sqrt.f64 (*.f64 c x)))) 2)
✓	20.4b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 c (.f64 x (*.f64 s s))))
	41.9b	(/.f64 (sqrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x)) (/.f64 (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2) (sqrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x))))
	34.1b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2)) 3)) (/.f64 (cos.f64 (+.f64 x x)) x))
	31.7b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) (.f64 c (.f64 s (sqrt.f64 x)))) (.f64 c (.f64 s (sqrt.f64 x))))
	44.4b	(.f64 (/.f64 1 (pow.f64 (pow.f64 (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2) 3) 1/3)) (/.f64 (cos.f64 (+.f64 x x)) x))
	34.1b	(/.f64 (pow.f64 (cbrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x)) 2) (/.f64 (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2) (cbrt.f64 (/.f64 (cos.f64 (+.f64 x x)) x))))
	42.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (pow.f64 (.f64 (sqrt.f64 x) (.f64 s (sqrt.f64 x))) 2)))
	36.4b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (pow.f64 (.f64 (sqrt.f64 (.f64 c x)) s) 2))
	17.1b	(.f64 (/.f64 (cos.f64 (+.f64 x x)) (.f64 c x)) (/.f64 1 (.f64 (.f64 s s) (*.f64 c x))))
	33.9b	(.f64 (/.f64 1 (pow.f64 (.f64 c (*.f64 s (sqrt.f64 x))) 2)) (/.f64 (cos.f64 (+.f64 x x)) x))
	35.7b	(.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) (.f64 (sqrt.f64 (.f64 c x)) s)) (/.f64 (/.f64 1 c) (.f64 (sqrt.f64 (*.f64 c x)) s)))
	34.1b	(/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
	33.9b	(.f64 (pow.f64 (/.f64 1 (.f64 c (*.f64 s (sqrt.f64 x)))) 2) (/.f64 (cos.f64 (+.f64 x x)) x))
	34.0b	(-.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (.f64 x (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2))) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (pow.f64 (.f64 c (.f64 s (sqrt.f64 x))) 2))))
	20.4b	(.f64 (/.f64 (cos.f64 (+.f64 x x)) (.f64 c (.f64 x (.f64 s s)))) (/.f64 (/.f64 1 x) c))
	20.6b	(pow.f64 (.f64 (.f64 c (.f64 x (.f64 s s))) (*.f64 c (/.f64 x (cos.f64 (+.f64 x x))))) -1)
	29.1b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (cbrt.f64 (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s))))) 3))
	34.7b	(.f64 (/.f64 1 (.f64 (sqrt.f64 (.f64 c x)) s)) (/.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) c) (.f64 (sqrt.f64 (*.f64 c x)) s)))
	24.8b	(.f64 (/.f64 (/.f64 (cos.f64 (+.f64 x x)) x) (.f64 c x)) (/.f64 (/.f64 1 c) (*.f64 s s)))

Compiler

Compiled 4336 to 1563 computations (64% saved)

regimes1.4s (10.7%)

Accuracy

Total 3.5b remaining (43.2%)

Threshold costs 0b (0%)

Counts

134 → 2

Compiler

Compiled 18695 to 11660 computations (37.6% saved)

bsearch56.0ms (0.4%)

Steps

Iters	Range		Point
5	-3.56414877511012e-307	9.81047130578343e-294	2.549378178247403e-309

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	64
1	32	64
2	31	64

end262.0ms (2%)

Remove: (sort c s)
Compiler: Compiled 645 to 379 computations (41.2% saved)

Details

analyze2.5s (18.5%)

sample5.3s (39.7%)

simplify137.0ms (1%)

prune5.0ms (0%)

localize24.0ms (0.2%)

series387.0ms (2.9%)

rewrite138.0ms (1%)

simplify189.0ms (1.4%)

prune252.0ms (1.9%)

localize23.0ms (0.2%)

series514.0ms (3.9%)

rewrite152.0ms (1.1%)

simplify132.0ms (1%)

prune422.0ms (3.2%)

localize21.0ms (0.2%)

series354.0ms (2.7%)

rewrite125.0ms (0.9%)

simplify133.0ms (1%)

prune284.0ms (2.1%)

localize10.0ms (0.1%)

series169.0ms (1.3%)

rewrite90.0ms (0.7%)

simplify49.0ms (0.4%)

prune213.0ms (1.6%)

regimes1.4s (10.7%)

bsearch56.0ms (0.4%)

simplify5.0ms (0%)

end262.0ms (2%)

Profiling