Details

analyze1.3s (21.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
12.5%	87.5%	0%	5
18.7%	81.2%	0%	6
21.9%	78.1%	0%	7
23.4%	76.5%	0%	8
23.4%	76.5%	0%	9
23.4%	76.5%	0%	10
23.6%	76.3%	0%	11
23.7%	76.2%	0%	12
23.7%	76.2%	0%	13
23.7%	76.2%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample3.3s (54.7%)

Results

1.6s	2091×	body	2048	valid
649.0ms	1197×	body	1024	valid
472.0ms	1530×	body	512	valid
334.0ms	2584×	body	128	valid
162.0ms	755×	body	256	valid
70.0ms	99×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify27.0ms (0.4%)

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

33.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	33.2b	(/.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 2 expressions with local error:

New	Error	Program
✓	2.6b	(-.f64 1 (cos.f64 x))
✓	16.6b	(/.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 (0.2%)

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:

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

simplify121.0ms (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

prune77.0ms (1.3%)

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
	33.4b	(/.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))
	29.4b	1/2
▶	17.0b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	33.3b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	33.2b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
	32.4b	(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))
	33.2b	(/.f64 (-.f64 (.f64 1 1) (.f64 (cos.f64 x) (cos.f64 x))) (.f64 (.f64 x x) (+.f64 1 (cos.f64 x))))

Compiler

Compiled 1698 to 845 computations (50.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series36.0ms (0.6%)

Counts

4 → 40

Calls

4 calls:

17.0ms	(/.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)))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))

rewrite57.0ms (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:

32.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
8.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
6.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms	(+.f64 1 (cos.f64 x))

simplify107.0ms (1.8%)

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	2912
1	504	2230
2	1767	2192
3	4643	2192
4	4935	2192

prune163.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	208	5	213

Error

Counts

213 → 5

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	33.4b	(/.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))
	33.3b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	16.9b	(/.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (.f64 x x))

Compiler

Compiled 4330 to 1919 computations (55.7% saved)

localize9.0ms (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)
✓	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

series29.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

14.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
12.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
3.0ms	(/.f64 (sin.f64 x) x)

rewrite22.0ms (0.4%)

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:

8.0ms	(/.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)

simplify112.0ms (1.9%)

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

prune108.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	147	5	152

Error

Counts

152 → 5

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
▶	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	0.2b	(/.f64 (.f64 (sin.f64 x) (.f64 (/.f64 1 x) (tan.f64 (/.f64 x 2)))) x)
	33.3b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	16.9b	(/.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (.f64 x x))

Compiler

Compiled 2726 to 1358 computations (50.2% 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)

series23.0ms (0.4%)

Counts

2 → 24

Calls

2 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)

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
24×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 82

Calls

2 calls:

13.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

simplify135.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

551×	`associate-/l*_binary64`
517×	`associate-*l/_binary64`
470×	`associate-*r/_binary64`
456×	`associate-l_binary64`
400×	`times-frac_binary64`

Counts

106 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	2217
1	408	1997
2	1136	1977
3	4399	1965
4	4648	1965
5	4990	1965
6	4984	1965

prune125.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	178	5	183

Error

Counts

183 → 5

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
✓	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	0.2b	(/.f64 (.f64 (sin.f64 x) (.f64 (/.f64 1 x) (tan.f64 (/.f64 x 2)))) x)
	33.3b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	16.9b	(/.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (.f64 x x))

Compiler

Compiled 3444 to 1767 computations (48.7% saved)

regimes151.0ms (2.5%)

Accuracy

Total 0.1b remaining (81.8%)

Threshold costs 0.1b (81.8%)

Counts

73 → 1

Compiler

Compiled 2491 to 1555 computations (37.6% 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

end79.0ms (1.3%)

Compiler: Compiled 87 to 57 computations (34.5% 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

analyze1.3s (21.3%)

sample3.3s (54.7%)

simplify27.0ms (0.4%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite14.0ms (0.2%)

simplify121.0ms (2%)

prune77.0ms (1.3%)

localize9.0ms (0.2%)

series36.0ms (0.6%)

rewrite57.0ms (1%)

simplify107.0ms (1.8%)

prune163.0ms (2.7%)

localize9.0ms (0.2%)

series29.0ms (0.5%)

rewrite22.0ms (0.4%)

simplify112.0ms (1.9%)

prune108.0ms (1.8%)

localize9.0ms (0.2%)

series23.0ms (0.4%)

rewrite22.0ms (0.4%)

simplify135.0ms (2.2%)

prune125.0ms (2.1%)

regimes151.0ms (2.5%)

simplify2.0ms (0%)

end79.0ms (1.3%)

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