Details

analyze341.0ms (7.3%)

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)

sample2.9s (63.1%)

Results

1.5s	2026×	body	2048	valid
494.0ms	1185×	body	1024	valid
421.0ms	1526×	body	512	valid
275.0ms	2607×	body	128	valid
176.0ms	824×	body	256	valid
62.0ms	88×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify23.0ms (0.5%)

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

32.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.0b	(/.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 2 expressions with local error:

New	Error	Program
✓	0.7b	(-.f64 1 (cos.f64 x))
✓	16.3b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series5.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

3.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms	(-.f64 1 (cos.f64 x))

rewrite17.0ms (0.4%)

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:

11.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms	(-.f64 1 (cos.f64 x))

simplify102.0ms (2.2%)

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

prune84.0ms (1.8%)

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
▶	17.0b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	32.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (.f64 x x))) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (.f64 x x)))) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
	31.6b	(-.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))))
	31.1b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
	32.0b	(/.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)))
	32.0b	(.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (.f64 x x)))
	31.8b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))

Compiler

Compiled 1730 to 867 computations (49.9% saved)

localize8.0ms (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))
✓	0.3b	(+.f64 1 (cos.f64 x))
✓	16.4b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series31.0ms (0.7%)

Counts

4 → 40

Calls

4 calls:

13.0ms	(/.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)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))

rewrite29.0ms (0.6%)

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:

8.0ms	(/.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)))
3.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))

simplify100.0ms (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

prune135.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	207	6	213

Error

Counts

213 → 6

Alt Table

Status	Error	Program
	16.2b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
	31.1b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
▶	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	16.6b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
	32.0b	(.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (.f64 x x)))
	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)

Compiler

Compiled 4348 to 1945 computations (55.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series22.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

10.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
9.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
3.0ms	(/.f64 (sin.f64 x) x)

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 111

Calls

3 calls:

8.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
3.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
2.0ms	(/.f64 (sin.f64 x) x)

simplify119.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

594×	`associate-/l*_binary64`
557×	`associate-*l/_binary64`
473×	`associate-l_binary64`
464×	`associate-*r/_binary64`
426×	`times-frac_binary64`

Counts

139 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	186	2636
1	469	2390
2	1309	2366
3	4506	2354
4	4947	2354
5	5047	2354

prune137.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	176	6	182

Error

Counts

182 → 6

Alt Table

Status	Error	Program
	16.2b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
	31.1b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
✓	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	16.6b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
	32.0b	(.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (.f64 x x)))
▶	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)

Compiler

Compiled 3472 to 1810 computations (47.9% saved)

localize7.0ms (0.2%)

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)))

series23.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

13.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
10.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-l_binary64`
13×	`times-frac_binary64`

Counts

2 → 64

Calls

2 calls:

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

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Rules

540×	`associate-/l/_binary64`
519×	`associate-*l/_binary64`
411×	`associate-l_binary64`
392×	`associate-/r*_binary64`
349×	`associate-r_binary64`

Counts

88 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1847
1	367	1610
2	1161	1604
3	4060	1600
4	4842	1600
5	4940	1600

prune103.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	145	6	151

Error

Counts

151 → 6

Alt Table

Status	Error	Program
	16.2b	(.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) x) (/.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) x))
	31.1b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
✓	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	16.6b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
	32.0b	(.f64 (-.f64 1 (cos.f64 x)) (/.f64 1 (.f64 x x)))
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)

Compiler

Compiled 2638 to 1324 computations (49.8% saved)

regimes184.0ms (4%)

Accuracy

Total 0.1b remaining (87.2%)

Threshold costs 0.1b (87.2%)

Counts

100 → 1

Compiler

Compiled 3010 to 2023 computations (32.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	12	21
2	12	21

end88.0ms (1.9%)

Compiler: Compiled 105 to 74 computations (29.5% 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

analyze341.0ms (7.3%)

sample2.9s (63.1%)

simplify23.0ms (0.5%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite17.0ms (0.4%)

simplify102.0ms (2.2%)

prune84.0ms (1.8%)

localize8.0ms (0.2%)

series31.0ms (0.7%)

rewrite29.0ms (0.6%)

simplify100.0ms (2.2%)

prune135.0ms (2.9%)

localize9.0ms (0.2%)

series22.0ms (0.5%)

rewrite22.0ms (0.5%)

simplify119.0ms (2.6%)

prune137.0ms (3%)

localize7.0ms (0.2%)

series23.0ms (0.5%)

rewrite19.0ms (0.4%)

simplify94.0ms (2%)

prune103.0ms (2.2%)

regimes184.0ms (4%)

simplify2.0ms (0%)

end88.0ms (1.9%)

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