Details

analyze453.0ms (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)

sample70.0ms (1.1%)

Algorithm

1×

intervals

Results

34.0ms	58×	body	2048	valid
8.0ms	31×	body	1024	valid
8.0ms	47×	body	512	valid
5.0ms	84×	body	128	valid
4.0ms	32×	body	256	valid
2.0ms	4×	body	4096	valid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify32.0ms (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 → 0

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

28.4b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	28.4b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.8b	(-.f64 1 (cos.f64 x))
14.7b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite77.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

27.3b

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:

9.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
5.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 1055 to 469 computations (55.5% saved)

series20.0ms (0.3%)

Error

0.6b

Counts

2 → 12

Calls

2 calls:

8.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
5.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 321 to 243 computations (24.3% saved)

simplify116.0ms (1.9%)

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

75 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1092
1	283	957
2	853	901
3	3327	901
4	4699	901
5	4954	901
6	4828	901

prune29.0ms (0.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	35	9	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	9	45

Error

0.3b

Counts

45 → 9

Alt Table

Status	Error	Program
▶	15.3b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	34.5b	(-.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))))
	49.1b	(/.f64 (fma.f64 1/720 (pow.f64 x 6) (.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2))) (.f64 x x))
	46.1b	(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
	28.0b	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 x (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))
	28.6b	(/.f64 (-.f64 (.f64 1 1) (.f64 (cos.f64 x) (cos.f64 x))) (*.f64 x (fma.f64 x (cos.f64 x) x)))
	28.5b	(/.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)))
	28.0b	(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
	40.1b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 3))

Compiler

Compiled 661 to 376 computations (43.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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))
14.7b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite166.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

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:

10.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
9.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 2517 to 963 computations (61.7% saved)

series48.0ms (0.8%)

Error

0.3b

Counts

4 → 24

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)))
7.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
6.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 837 to 583 computations (30.3% saved)

simplify126.0ms (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

146 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	2676
1	504	2038
2	1767	2000
3	4643	2000
4	4935	2000

prune76.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Error

Counts

122 → 6

Alt Table

Status	Error	Program
	28.4b	(/.f64 (.f64 1 (-.f64 1 (cos.f64 x))) (.f64 x x))
	14.7b	(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 1 (fma.f64 x (cos.f64 x) x)))
	24.4b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) 3)) (.f64 x x))
	0.2b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
▶	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	0.2b	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))

Compiler

Compiled 1581 to 826 computations (47.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sin.f64 x)
0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.2b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

rewrite123.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

27×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 102

Calls

4 calls:

11.0ms	(/.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)))
3.0ms	(/.f64 (sin.f64 x) x)
2.0ms	(sin.f64 x)

Compiler

Compiled 1795 to 845 computations (52.9% saved)

series103.0ms (1.6%)

Error

Counts

4 → 24

Calls

4 calls:

27.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
27.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
13.0ms	(/.f64 (sin.f64 x) x)
9.0ms	(sin.f64 x)

Compiler

Compiled 772 to 577 computations (25.3% saved)

simplify128.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-/l/_binary64`
549×	`associate-*l/_binary64`
459×	`associate-l_binary64`
417×	`fma-def_binary64`
391×	`associate-/r*_binary64`

Counts

126 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	2114
1	464	1844
2	1427	1830
3	4317	1826
4	4747	1826
5	4947	1826

prune41.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	62	6	68

Error

Counts

68 → 6

Alt Table

Status	Error	Program
	28.4b	(/.f64 (.f64 1 (-.f64 1 (cos.f64 x))) (.f64 x x))
	14.7b	(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 1 (fma.f64 x (cos.f64 x) x)))
	24.4b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) 3)) (.f64 x x))
▶	0.2b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	0.2b	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))

Compiler

Compiled 996 to 550 computations (44.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.2b	(/.f64 (sin.f64 x) x)
0.2b	(/.f64 (tan.f64 (/.f64 x 2)) x)

rewrite120.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

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 → 122

Calls

4 calls:

9.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
3.0ms	(/.f64 (sin.f64 x) x)
0.0ms	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))

Compiler

Compiled 2515 to 1364 computations (45.8% saved)

series92.0ms (1.5%)

Error

Counts

4 → 24

Calls

4 calls:

39.0ms	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
16.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
11.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
8.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 902 to 725 computations (19.6% saved)

simplify133.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

594×	`associate-/l*_binary64`
557×	`associate-*l/_binary64`
464×	`associate-*r/_binary64`
426×	`times-frac_binary64`
426×	`fma-def_binary64`

Counts

146 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	2747
1	518	2466
2	1451	2438
3	4637	2426
4	4997	2426
5	4945	2426

prune46.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	75	6	81

Error

Counts

81 → 6

Alt Table

Status	Error	Program
	28.4b	(/.f64 (.f64 1 (-.f64 1 (cos.f64 x))) (.f64 x x))
	14.7b	(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) x) (/.f64 1 (fma.f64 x (cos.f64 x) x)))
	24.4b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) 3)) (.f64 x x))
	0.2b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	0.2b	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))

Compiler

Compiled 1198 to 702 computations (41.4% saved)

regimes519.0ms (8.3%)

Accuracy

Total 0.1b remaining (84.1%)

Threshold costs 0.1b (84.1%)

Compiler

Compiled 5527 to 3613 computations (34.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	9	17

end1.0ms (0%)

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

sample3.7s (59%)

Algorithm

1×

intervals

Results

1.9s	1981×	body	2048	valid
524.0ms	1118×	body	1024	valid
411.0ms	1484×	body	512	valid
226.0ms	2541×	body	128	valid
147.0ms	772×	body	256	valid
91.0ms	104×	body	4096	valid

Compiler

Compiled 104 to 73 computations (29.8% 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

analyze453.0ms (7.3%)

sample70.0ms (1.1%)

simplify32.0ms (0.5%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite77.0ms (1.2%)

series20.0ms (0.3%)

simplify116.0ms (1.9%)

prune29.0ms (0.5%)

localize9.0ms (0.1%)

rewrite166.0ms (2.7%)

series48.0ms (0.8%)

simplify126.0ms (2%)

prune76.0ms (1.2%)

localize8.0ms (0.1%)

rewrite123.0ms (2%)

series103.0ms (1.6%)

simplify128.0ms (2.1%)

prune41.0ms (0.7%)

localize11.0ms (0.2%)

rewrite120.0ms (1.9%)

series92.0ms (1.5%)

simplify133.0ms (2.1%)

prune46.0ms (0.7%)

regimes519.0ms (8.3%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample3.7s (59%)

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