Details

analyze463.0ms (7.9%)

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)

sample123.0ms (2.1%)

Algorithm

1×

intervals

Results

67.0ms	71×	body	2048	valid
19.0ms	43×	body	1024	valid
13.0ms	48×	body	512	valid
6.0ms	73×	body	128	valid
4.0ms	20×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify70.0ms (1.2%)

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

prune3.0ms (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

34.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	34.4b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.8b	(-.f64 1 (cos.f64 x))
✓	16.5b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series11.0ms (0.2%)

Counts

2 → 16

Calls

2 calls:

7.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
7×	`add-cbrt-cube_binary64`

Counts

2 → 63

Calls

2 calls:

14.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
7.0ms	(-.f64 1 (cos.f64 x))

simplify136.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-neg_binary64`
411×	`associate-l_binary64`
405×	`times-frac_binary64`
353×	`associate-r_binary64`
344×	`fma-def_binary64`

Counts

79 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1152
1	283	1017
2	853	961
3	3327	961
4	4699	961
5	4954	961
6	4828	961

prune128.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	7	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Error

0.0b

Counts

92 → 7

Alt Table

Status	Error	Program
	34.6b	(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
	34.4b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (*.f64 x (fma.f64 x (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)) x)))
	34.4b	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
	34.5b	(/.f64 (-.f64 (.f64 1 1) (.f64 (cos.f64 x) (cos.f64 x))) (.f64 (.f64 x x) (+.f64 1 (cos.f64 x))))
	28.6b	(fma.f64 (*.f64 x x) -1/24 1/2)
	33.8b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
▶	16.9b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

Compiler

Compiled 1692 to 847 computations (49.9% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓	0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	0.4b	(+.f64 1 (cos.f64 x))
✓	16.3b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series70.0ms (1.2%)

Counts

4 → 40

Calls

4 calls:

31.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
26.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
7.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
5.0ms	(+.f64 1 (cos.f64 x))

rewrite56.0ms (1%)

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:

18.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
11.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
8.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
5.0ms	(+.f64 1 (cos.f64 x))

simplify130.0ms (2.2%)

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

prune163.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	208	5	213

Error

Counts

213 → 5

Alt Table

Status	Error	Program
	17.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 x (fma.f64 x (cos.f64 x) x)))
	33.8b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
	34.4b	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
	28.6b	(fma.f64 (*.f64 x x) -1/24 1/2)
▶	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)

Compiler

Compiled 4314 to 1915 computations (55.6% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
✓	0.1b	(/.f64 (sin.f64 x) x)
✓	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

series47.0ms (0.8%)

Counts

3 → 28

Calls

3 calls:

23.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
19.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
6.0ms	(/.f64 (sin.f64 x) x)

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 93

Calls

3 calls:

10.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
8.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
4.0ms	(/.f64 (sin.f64 x) x)

simplify178.0ms (3%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary64`
593×	`associate-/l/_binary64`
549×	`associate-*l/_binary64`
440×	`associate-l_binary64`
391×	`associate-/r*_binary64`

Counts

121 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	2266
1	433	2003
2	1333	1993
3	4088	1989
4	4749	1989
5	5173	1989

prune246.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	147	5	152

Error

Counts

152 → 5

Alt Table

Status	Error	Program
▶	17.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 x (fma.f64 x (cos.f64 x) x)))
	33.8b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
	34.4b	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
	28.6b	(fma.f64 (*.f64 x x) -1/24 1/2)
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)

Compiler

Compiled 2720 to 1354 computations (50.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x (fma.f64 x (cos.f64 x) x))
	0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	0.4b	(fma.f64 x (cos.f64 x) x)
✓	16.7b	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 x (fma.f64 x (cos.f64 x) x)))

series54.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

34.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 x (fma.f64 x (cos.f64 x) x)))
13.0ms	(*.f64 x (fma.f64 x (cos.f64 x) x))
7.0ms	(fma.f64 x (cos.f64 x) x)

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`cbrt-unprod_binary64`

Counts

3 → 57

Calls

3 calls:

11.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 x (fma.f64 x (cos.f64 x) x)))
6.0ms	(*.f64 x (fma.f64 x (cos.f64 x) x))
1.0ms	(fma.f64 x (cos.f64 x) x)

simplify111.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

785×	`associate-/l*_binary64`
658×	`fma-def_binary64`
657×	`associate-/r*_binary64`
320×	`associate-*l/_binary64`
193×	`associate-/l/_binary64`

Counts

93 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1654
1	333	1352
2	1210	1311
3	4510	1311
4	4978	1311

prune130.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	154	5	159

Error

Counts

159 → 5

Alt Table

Status	Error	Program
✓	17.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 x (fma.f64 x (cos.f64 x) x)))
	33.8b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
	34.4b	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
	28.6b	(fma.f64 (*.f64 x x) -1/24 1/2)
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)

Compiler

Compiled 2900 to 854 computations (70.6% saved)

regimes298.0ms (5.1%)

Accuracy

Total 0.1b remaining (73.9%)

Threshold costs 0.1b (73.9%)

Counts

86 → 1

Compiler

Compiled 2699 to 1757 computations (34.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	9	17

end0.0ms (0%)

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

sample3.3s (56.2%)

Algorithm

1×

intervals

Results

1.6s	2028×	body	2048	valid
459.0ms	1134×	body	1024	valid
375.0ms	1461×	body	512	valid
201.0ms	2577×	body	128	valid
114.0ms	705×	body	256	valid
70.0ms	95×	body	4096	valid

Compiler

Compiled 83 to 55 computations (33.7% 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

analyze463.0ms (7.9%)

sample123.0ms (2.1%)

simplify70.0ms (1.2%)

prune3.0ms (0%)

localize11.0ms (0.2%)

series11.0ms (0.2%)

rewrite27.0ms (0.5%)

simplify136.0ms (2.3%)

prune128.0ms (2.2%)

localize19.0ms (0.3%)

series70.0ms (1.2%)

rewrite56.0ms (1%)

simplify130.0ms (2.2%)

prune163.0ms (2.8%)

localize17.0ms (0.3%)

series47.0ms (0.8%)

rewrite33.0ms (0.6%)

simplify178.0ms (3%)

prune246.0ms (4.2%)

localize10.0ms (0.2%)

series54.0ms (0.9%)

rewrite26.0ms (0.4%)

simplify111.0ms (1.9%)

prune130.0ms (2.2%)

regimes298.0ms (5.1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (56.2%)

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