Details

analyze323.0ms (6.5%)

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)

sample3.0s (60.3%)

Results

1.6s	2120×	body	2048	valid
445.0ms	1130×	body	1024	valid
434.0ms	1526×	body	512	valid
278.0ms	2621×	body	128	valid
153.0ms	769×	body	256	valid
58.0ms	90×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify27.0ms (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

36.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.9b	(/.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
✓	2.2b	(-.f64 1 (cos.f64 x))
✓	18.7b	(/.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))
3.0ms	(-.f64 1 (cos.f64 x))

simplify96.0ms (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

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

prune78.0ms (1.6%)

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
	26.7b	(fma.f64 (*.f64 x x) -1/24 1/2)
	36.9b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
▶	19.1b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	37.0b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	36.9b	(/.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)))
	47.1b	(*.f64 (/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) x) (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))
	37.0b	(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x 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 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓	0.2b	(+.f64 1 (cos.f64 x))
✓	0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	18.4b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series37.0ms (0.7%)

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))

rewrite28.0ms (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)))
4.0ms	(+.f64 1 (cos.f64 x))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))

simplify101.0ms (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

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

prune138.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	209	4	213

Error

Counts

213 → 4

Alt Table

Status	Error	Program
	20.7b	(/.f64 (exp.f64 (log.f64 (.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))) (.f64 x x))
	36.9b	(/.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)))
▶	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
	19.1b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

Compiler

Compiled 4318 to 1919 computations (55.6% saved)

localize11.0ms (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)

series26.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

13.0ms	(*.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)

rewrite21.0ms (0.4%)

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

simplify115.0ms (2.3%)

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

prune117.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	176	4	180

Error

Counts

180 → 4

Alt Table

Status	Error	Program
	31.7b	(.f64 (/.f64 (sqrt.f64 (sin.f64 x)) 1) (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
	36.9b	(/.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)))
✓	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
▶	19.1b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

Compiler

Compiled 3452 to 1788 computations (48.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
	0.2b	(+.f64 1 (cos.f64 x))
✓	0.2b	(pow.f64 (sin.f64 x) 2)
✓	18.4b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

series22.0ms (0.5%)

Counts

3 → 12

Calls

3 calls:

15.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
4.0ms	(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
3.0ms	(pow.f64 (sin.f64 x) 2)

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-exp-log_binary64`
18×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`unpow-prod-down_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 97

Calls

3 calls:

7.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
7.0ms	(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
2.0ms	(pow.f64 (sin.f64 x) 2)

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

586×	`associate-/l*_binary64`
528×	`associate-/r*_binary64`
271×	`fma-def_binary64`
249×	`distribute-rgt-in_binary64`
227×	`distribute-lft-in_binary64`

Counts

109 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2111
1	375	1634
2	1292	1578
3	4680	1578
4	5000	1578

prune200.0ms (4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	184	4	188

Error

Counts

188 → 4

Alt Table

Status	Error	Program
	31.7b	(.f64 (/.f64 (sqrt.f64 (sin.f64 x)) 1) (.f64 (/.f64 (sqrt.f64 (sin.f64 x)) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
	36.9b	(/.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)))
✓	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
✓	19.1b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

Compiler

Compiled 3540 to 2189 computations (38.2% saved)

regimes419.0ms (8.4%)

Accuracy

Total 0.1b remaining (69.1%)

Threshold costs 0.1b (69.1%)

Counts

149 → 1

Compiler

Compiled 4823 to 3315 computations (31.3% 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

end73.0ms (1.5%)

Compiler: Compiled 91 to 59 computations (35.2% 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

analyze323.0ms (6.5%)

sample3.0s (60.3%)

simplify27.0ms (0.5%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite14.0ms (0.3%)

simplify96.0ms (1.9%)

prune78.0ms (1.6%)

localize9.0ms (0.2%)

series37.0ms (0.7%)

rewrite28.0ms (0.6%)

simplify101.0ms (2%)

prune138.0ms (2.8%)

localize11.0ms (0.2%)

series26.0ms (0.5%)

rewrite21.0ms (0.4%)

simplify115.0ms (2.3%)

prune117.0ms (2.3%)

localize8.0ms (0.2%)

series22.0ms (0.5%)

rewrite21.0ms (0.4%)

simplify75.0ms (1.5%)

prune200.0ms (4%)

regimes419.0ms (8.4%)

simplify2.0ms (0%)

end73.0ms (1.5%)

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