Details

analyze344.0ms (8.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample63.0ms (1.6%)

Algorithm

1×

intervals

Results

30.0ms	62×	body	2048	valid
10.0ms	42×	body	1024	valid
8.0ms	46×	body	512	valid
4.0ms	82×	body	128	valid
2.0ms	21×	body	256	valid
1.0ms	3×	body	4096	valid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify24.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

426×	`fma-def_binary64`
293×	`fma-neg_binary64`
85×	`div-sub_binary64`
74×	`associate-/l*_binary64`
63×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.2b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 x)
✓	1.8b	(-.f64 1 (cos.f64 x))
✓	15.5b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series27.0ms (0.7%)

Counts

3 → 20

Calls

3 calls:

23.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms	(-.f64 1 (cos.f64 x))
2.0ms	(cos.f64 x)

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
8×	`add-cbrt-cube_binary64`

Counts

3 → 72

Calls

3 calls:

7.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms	(-.f64 1 (cos.f64 x))
1.0ms	(cos.f64 x)

simplify84.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-neg_binary64`
414×	`associate-l_binary64`
405×	`times-frac_binary64`
398×	`fma-def_binary64`
365×	`associate-r_binary64`

Counts

92 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1257
1	307	1122
2	931	1062
3	3591	1062
4	4890	1062
5	4908	1062

prune86.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	99	9	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	9	109

Error

0.0b

Counts

109 → 9

Alt Table

Status	Error	Program
	31.2b	(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (cos.f64 x)))) (*.f64 x x))
	31.1b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	45.1b	(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
	32.1b	(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 1/24 (.f64 x x) (.f64 1/40320 (pow.f64 x 6))))
	31.3b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 1 (cos.f64 x)) (-.f64 1 (cos.f64 x))) (-.f64 1 (cos.f64 x)))) (*.f64 x x))
	30.7b	(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
	45.0b	(*.f64 (/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) x) (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))
▶	15.9b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	31.2b	(.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (.f64 x x))) (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))

Compiler

Compiled 2002 to 1023 computations (48.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓	0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	0.4b	(+.f64 1 (cos.f64 x))
✓	15.2b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series37.0ms (0.9%)

Counts

4 → 40

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
13.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
25×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
17×	`add-sqr-sqrt_binary64`

Counts

4 → 122

Calls

4 calls:

12.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
6.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms	(+.f64 1 (cos.f64 x))

simplify104.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-*l/_binary64`
540×	`associate-/r/_binary64`
423×	`fma-def_binary64`
335×	`fma-neg_binary64`
214×	`cancel-sign-sub-inv_binary64`

Counts

162 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	2904
1	504	2230
2	1767	2192
3	4643	2192
4	4935	2192

prune136.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	209	6	215

Error

Counts

215 → 6

Alt Table

Status	Error	Program
	31.2b	(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (cos.f64 x)))) (*.f64 x x))
	31.1b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	15.7b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
	0.3b	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
▶	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	15.9b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

Compiler

Compiled 4356 to 1947 computations (55.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 x)
✓	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
✓	0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
✓	0.1b	(/.f64 (sin.f64 x) x)

series32.0ms (0.8%)

Counts

4 → 32

Calls

4 calls:

15.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
12.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
3.0ms	(/.f64 (sin.f64 x) x)
2.0ms	(sin.f64 x)

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 120

Calls

4 calls:

10.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
3.0ms	(/.f64 (sin.f64 x) x)
1.0ms	(sin.f64 x)

simplify113.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-/l*_binary64`
589×	`associate-l_binary64`
478×	`times-frac_binary64`
389×	`fma-def_binary64`
348×	`associate-/l/_binary64`

Counts

152 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	2748
1	516	2495
2	1462	2467
3	4574	2455
4	4992	2455
5	4957	2455

prune110.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	172	5	177

Error

Counts

177 → 5

Alt Table

Status	Error	Program
	16.1b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
	31.2b	(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (cos.f64 x)))) (*.f64 x x))
▶	15.7b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
✓	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	15.9b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

Compiler

Compiled 3249 to 1742 computations (46.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
	0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
	0.4b	(+.f64 1 (cos.f64 x))
✓	14.9b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) x)

series24.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

16.0ms	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
7.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) x)

rewrite48.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`times-frac_binary64`
73×	`add-sqr-sqrt_binary64`
69×	`*-un-lft-identity_binary64`
67×	`add-exp-log_binary64`
58×	`associate-r_binary64`

Counts

2 → 136

Calls

2 calls:

20.0ms	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
6.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) x)

simplify123.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

592×	`associate-/r*_binary64`
440×	`associate-/r/_binary64`
269×	`associate-*l/_binary64`
262×	`associate-*r/_binary64`
238×	`fma-neg_binary64`

Counts

160 → 217

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	3858
1	625	3290
2	2254	3022
3	4779	3022
4	5020	3022

prune176.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	292	5	297

Error

Counts

297 → 5

Alt Table

Status	Error	Program
	16.1b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
	31.2b	(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (cos.f64 x)))) (*.f64 x x))
✓	15.7b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
✓	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	15.9b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

Compiler

Compiled 7230 to 3577 computations (50.5% saved)

regimes158.0ms (4%)

Accuracy

Total 0.1b remaining (79.2%)

Threshold costs 0.1b (79.2%)

Counts

92 → 1

Compiler

Compiled 2676 to 1817 computations (32.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	10	17
2	10	17

end0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample2.1s (53.9%)

Algorithm

1×

intervals

Results

1.0s	2061×	body	2048	valid
269.0ms	1090×	body	1024	valid
231.0ms	1474×	body	512	valid
122.0ms	2510×	body	128	valid
87.0ms	764×	body	256	valid
45.0ms	101×	body	4096	valid

Compiler

Compiled 89 to 62 computations (30.3% saved)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

Details

analyze344.0ms (8.8%)

sample63.0ms (1.6%)

simplify24.0ms (0.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series27.0ms (0.7%)

rewrite14.0ms (0.4%)

simplify84.0ms (2.2%)

prune86.0ms (2.2%)

localize9.0ms (0.2%)

series37.0ms (0.9%)

rewrite32.0ms (0.8%)

simplify104.0ms (2.7%)

prune136.0ms (3.5%)

localize8.0ms (0.2%)

series32.0ms (0.8%)

rewrite23.0ms (0.6%)

simplify113.0ms (2.9%)

prune110.0ms (2.8%)

localize11.0ms (0.3%)

series24.0ms (0.6%)

rewrite48.0ms (1.2%)

simplify123.0ms (3.1%)

prune176.0ms (4.5%)

regimes158.0ms (4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.1s (53.9%)

Profiling

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12