Details

analyze354.0ms (7.7%)

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)

sample97.0ms (2.1%)

Algorithm

1×

intervals

Results

28.0ms	55×	body	2048	valid
11.0ms	36×	body	1024	valid
11.0ms	63×	body	512	valid
4.0ms	79×	body	128	valid
2.0ms	22×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify25.0ms (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

27.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.9b	(/.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
✓	2.0b	(-.f64 1 (cos.f64 x))
✓	12.4b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series6.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

4.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms	(-.f64 1 (cos.f64 x))

rewrite14.0ms (0.3%)

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:

8.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

simplify99.0ms (2.1%)

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

prune86.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	81	10	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Error

0.0b

Counts

92 → 10

Alt Table

Status	Error	Program
	27.9b	(/.f64 (+.f64 1 (.f64 (neg.f64 1) (cos.f64 x))) (.f64 x x))
	28.1b	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
	27.1b	(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
	35.2b	(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
	28.1b	(.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))))
	28.2b	(/.f64 (+.f64 1 (.f64 (neg.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x)))) (cbrt.f64 (cos.f64 x)))) (*.f64 x x))
	28.1b	(/.f64 (-.f64 (.f64 1 1) (.f64 (cos.f64 x) (cos.f64 x))) (.f64 (.f64 x x) (+.f64 1 (cos.f64 x))))
▶	12.9b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	47.7b	(/.f64 (fma.f64 1/2 (.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 (pow.f64 x 8) -1/40320 (.f64 (pow.f64 x 4) -1/24)))) (*.f64 x x))
	27.9b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))

Compiler

Compiled 1844 to 943 computations (48.9% saved)

localize12.0ms (0.3%)

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))
✓	12.3b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series37.0ms (0.8%)

Counts

4 → 40

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
15.0ms	(/.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))

rewrite30.0ms (0.7%)

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)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms	(+.f64 1 (cos.f64 x))

simplify96.0ms (2.1%)

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

prune158.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	210	6	216

Error

Counts

216 → 6

Alt Table

Status	Error	Program
	27.9b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
	0.2b	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
	13.2b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 (*.f64 x x) (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x)))))
▶	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	35.2b	(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
	12.5b	(.f64 (/.f64 (sqrt.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x) (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x))

Compiler

Compiled 4388 to 1969 computations (55.1% saved)

localize10.0ms (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))
✓	0.2b	(/.f64 (sin.f64 x) x)
✓	0.2b	(/.f64 (tan.f64 (/.f64 x 2)) x)

series26.0ms (0.6%)

Counts

3 → 28

Calls

3 calls:

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

9.0ms	(*.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)

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

prune153.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	176	6	182

Error

Counts

182 → 6

Alt Table

Status	Error	Program
	27.9b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
	0.2b	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
	13.2b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 (*.f64 x x) (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x)))))
▶	0.2b	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
✓	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	12.5b	(.f64 (/.f64 (sqrt.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x) (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x))

Compiler

Compiled 3516 to 1836 computations (47.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
✓	0.1b	(/.f64 x (sin.f64 x))
✓	0.1b	(/.f64 1 (/.f64 x (sin.f64 x)))
	0.2b	(/.f64 (tan.f64 (/.f64 x 2)) x)

series24.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

13.0ms	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
7.0ms	(/.f64 x (sin.f64 x))
3.0ms	(/.f64 1 (/.f64 x (sin.f64 x)))

rewrite47.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

176×	`times-frac_binary64`
128×	`add-sqr-sqrt_binary64`
99×	`*-un-lft-identity_binary64`
95×	`add-cube-cbrt_binary64`
61×	`add-exp-log_binary64`

Counts

3 → 208

Calls

3 calls:

18.0ms	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
5.0ms	(/.f64 1 (/.f64 x (sin.f64 x)))
2.0ms	(/.f64 x (sin.f64 x))

simplify158.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

507×	`fma-neg_binary64`
451×	`associate-/l/_binary64`
451×	`fma-def_binary64`
442×	`associate-/r/_binary64`
429×	`*-commutative_binary64`

Counts

236 → 330

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	4573
1	543	4008
2	1738	3943
3	3577	3915
4	4704	3915
5	5014	3915

prune306.0ms (6.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	372	0	372
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	372	6	378

Error

Counts

378 → 6

Alt Table

Status	Error	Program
	27.9b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
	0.2b	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
	13.2b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 (*.f64 x x) (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x)))))
✓	0.2b	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
✓	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	12.5b	(.f64 (/.f64 (sqrt.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x) (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x))

Compiler

Compiled 8170 to 4361 computations (46.6% saved)

regimes429.0ms (9.3%)

Accuracy

Total 0.1b remaining (84.1%)

Threshold costs 0.1b (84.1%)

Counts

220 → 1

Compiler

Compiled 7375 to 4917 computations (33.3% saved)

simplify2.0ms (0%)

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)

sample2.3s (49.3%)

Algorithm

1×

intervals

Results

1.1s	2081×	body	2048	valid
302.0ms	1076×	body	1024	valid
268.0ms	1518×	body	512	valid
127.0ms	2478×	body	128	valid
81.0ms	730×	body	256	valid
71.0ms	117×	body	4096	valid

Compiler

Compiled 122 to 83 computations (32% 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

analyze354.0ms (7.7%)

sample97.0ms (2.1%)

simplify25.0ms (0.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite14.0ms (0.3%)

simplify99.0ms (2.1%)

prune86.0ms (1.9%)

localize12.0ms (0.3%)

series37.0ms (0.8%)

rewrite30.0ms (0.7%)

simplify96.0ms (2.1%)

prune158.0ms (3.4%)

localize10.0ms (0.2%)

series26.0ms (0.6%)

rewrite22.0ms (0.5%)

simplify119.0ms (2.6%)

prune153.0ms (3.3%)

localize10.0ms (0.2%)

series24.0ms (0.5%)

rewrite47.0ms (1%)

simplify158.0ms (3.4%)

prune306.0ms (6.7%)

regimes429.0ms (9.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (49.3%)

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