Details

analyze349.0ms (7.5%)

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)

sample2.9s (62.6%)

Results

1.5s	2079×	body	2048	valid
465.0ms	1140×	body	1024	valid
437.0ms	1521×	body	512	valid
281.0ms	2650×	body	128	valid
150.0ms	748×	body	256	valid
79.0ms	118×	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

31.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.5b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 x)
✓	2.6b	(-.f64 1 (cos.f64 x))
✓	16.5b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series7.0ms (0.1%)

Counts

3 → 20

Calls

3 calls:

3.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms	(-.f64 1 (cos.f64 x))
1.0ms	(cos.f64 x)

rewrite62.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

818×	`log1p-expm1-u_binary64`
818×	`expm1-log1p-u_binary64`
259×	`prod-diff_binary64`
120×	`egg-rr`
76×	`add-sqr-sqrt_binary64`

Counts

3 → 120

Calls

3 calls:

59.0ms	(cos.f64 x)
59.0ms	(-.f64 1 (cos.f64 x))
59.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	152	21
2	2013	21
3	5515	21

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-def_binary64`
662×	`associate-l_binary64`
656×	`distribute-rgt-neg-in_binary64`
491×	`cancel-sign-sub-inv_binary64`
360×	`neg-mul-1_binary64`

Counts

140 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	276
1	118	272
2	317	262
3	916	258
4	3075	258
5	4510	258
6	4994	258

prune142.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	137	7	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	7	145

Error

Counts

145 → 7

Alt Table

Status	Error	Program
	31.3b	(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
	17.1b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
▶	17.1b	(/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
	31.6b	(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
	31.5b	(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
	31.7b	(+.f64 (fma.f64 1 (pow.f64 x -2) (neg.f64 (.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (.f64 x x)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (.f64 x x))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1) (.f64 (/.f64 (cbrt.f64 (cos.f64 x)) (*.f64 x x)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1))))
	31.3b	(*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))

Compiler

Compiled 3503 to 1741 computations (50.3% saved)

localize15.0ms (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 (+.f64 1 (cos.f64 x))))
✓	0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	0.4b	(+.f64 1 (cos.f64 x))
✓	16.4b	(/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.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 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
13.0ms	(.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
3.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))

rewrite80.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

482×	`prod-diff_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`
154×	`egg-rr`
126×	`add-sqr-sqrt_binary64`

Counts

4 → 154

Calls

4 calls:

77.0ms	(.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
77.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
77.0ms	(+.f64 1 (cos.f64 x))
77.0ms	(/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	46
1	254	30
2	3433	30
3	5022	30

simplify96.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

920×	`times-frac_binary64`
500×	`sub-neg_binary64`
452×	`fma-neg_binary64`
259×	`*-commutative_binary64`
195×	`unswap-sqr_binary64`

Counts

194 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	564
1	155	556
2	429	496
3	1294	496
4	3137	496
5	4855	496
6	4873	496
7	4946	496

prune117.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	188	6	194

Error

Counts

194 → 6

Alt Table

Status	Error	Program
	17.1b	(/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x))) (*.f64 x x))
	31.3b	(*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))
	31.3b	(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
▶	17.1b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
✓	17.1b	(/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
	31.6b	(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))

Compiler

Compiled 3411 to 1903 computations (44.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
✓	15.8b	(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))

series21.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

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

rewrite52.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`log-prod_binary64`
255×	`pow2_binary64`
180×	`pow1/3_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`

Counts

2 → 71

Calls

2 calls:

51.0ms	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
51.0ms	(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	198	29
2	2507	29
3	5050	29

simplify71.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

636×	`distribute-rgt-neg-in_binary64`
494×	`associate-l_binary64`
493×	`unswap-sqr_binary64`
419×	`associate-r_binary64`
418×	`fma-def_binary64`

Counts

95 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	467
1	114	465
2	280	457
3	775	455
4	2711	455
5	4674	455
6	4977	455

prune72.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	89	6	95

Error

Counts

95 → 6

Alt Table

Status	Error	Program
	31.3b	(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
✓	17.1b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
▶	17.0b	(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
✓	17.1b	(/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
	31.6b	(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
	31.3b	(*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))

Compiler

Compiled 1468 to 918 computations (37.5% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
✓	15.6b	(/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2)))

series35.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

18.0ms	(/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2)))
17.0ms	(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))

rewrite57.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

540×	`log-prod_binary64`
184×	`log-div_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`
160×	`log-pow_binary64`

Counts

2 → 86

Calls

2 calls:

55.0ms	(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
55.0ms	(/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	204	29
2	2726	29
3	4983	29

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-l_binary64`
518×	`associate-r_binary64`
513×	`fma-def_binary64`
506×	`unswap-sqr_binary64`
460×	`cancel-sign-sub-inv_binary64`

Counts

110 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	476
1	132	474
2	342	468
3	1019	464
4	3604	464
5	4962	464

prune70.0ms (1.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	104	6	110

Error

Counts

110 → 6

Alt Table

Status	Error	Program
	31.3b	(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
✓	17.1b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
✓	17.0b	(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x 2))))
✓	17.1b	(/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
	31.6b	(fma.f64 x (*.f64 x -1/24) (fma.f64 1/720 (pow.f64 x 4) 1/2))
	31.3b	(*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))

Compiler

Compiled 1776 to 1057 computations (40.5% saved)

regimes164.0ms (3.5%)

Accuracy

Total 0.1b remaining (82.8%)

Threshold costs 0.1b (82.8%)

Counts

89 → 1

Compiler

Compiled 3454 to 2145 computations (37.9% 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

end138.0ms (2.9%)

Compiler: Compiled 97 to 66 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

analyze349.0ms (7.5%)

sample2.9s (62.6%)

simplify23.0ms (0.5%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series7.0ms (0.1%)

rewrite62.0ms (1.3%)

simplify70.0ms (1.5%)

prune142.0ms (3%)

localize15.0ms (0.3%)

series31.0ms (0.7%)

rewrite80.0ms (1.7%)

simplify96.0ms (2.1%)

prune117.0ms (2.5%)

localize8.0ms (0.2%)

series21.0ms (0.4%)

rewrite52.0ms (1.1%)

simplify71.0ms (1.5%)

prune72.0ms (1.5%)

localize8.0ms (0.2%)

series35.0ms (0.8%)

rewrite57.0ms (1.2%)

simplify56.0ms (1.2%)

prune70.0ms (1.5%)

regimes164.0ms (3.5%)

simplify2.0ms (0%)

end138.0ms (2.9%)

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