Details

analyze915.0ms (10.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
34.3%	65.5%	0.1%	7
46.8%	53%	0.1%	8
48%	51.9%	0.1%	9
63%	36.9%	0.1%	10
71.7%	28.2%	0.1%	11
72%	27.8%	0.1%	12
80.5%	19.4%	0.1%	13
85.4%	14.5%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample87.0ms (1%)

Algorithm

1×

intervals

Results

30.0ms	34×	body	1024	valid
28.0ms	189×	body	128	valid
11.0ms	25×	body	512	valid
2.0ms	8×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	22	12
3	26	12
4	26	12

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
▶	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

Compiler

Compiled 66 to 39 computations (40.9% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sin.f64 y))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
✓	0.1b	(*.f64 z (cos.f64 y))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`fma-def_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 56

Calls

3 calls:

13.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
6.0ms	(*.f64 z (cos.f64 y))
5.0ms	(+.f64 x (sin.f64 y))

series137.0ms (1.6%)

Counts

3 → 84

Calls

3 calls:

71.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
47.0ms	(*.f64 z (cos.f64 y))
18.0ms	(+.f64 x (sin.f64 y))

simplify187.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-neg_binary64`
472×	`fma-def_binary64`
359×	`associate-l_binary64`
320×	`associate-r_binary64`
247×	`distribute-rgt-neg-in_binary64`

Counts

140 → 210

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	1385
1	336	1325
2	977	1308
3	3255	1308
4	4656	1308
5	4995	1308
6	4925	1308

prune147.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	204	6	210
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	205	7	212

Error

Counts

212 → 7

Alt Table

Status	Error	Program
	29.6b	(/.f64 (.f64 (+.f64 (sin.f64 y) (fma.f64 (cos.f64 y) z x)) (-.f64 (+.f64 (sin.f64 y) x) (.f64 (cos.f64 y) z))) (-.f64 (+.f64 (sin.f64 y) x) (*.f64 (cos.f64 y) z)))
	41.8b	(cbrt.f64 (.f64 (.f64 (+.f64 (+.f64 x (sin.f64 y)) (.f64 z (cos.f64 y))) (+.f64 (+.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))) (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))))
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	14.4b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
▶	0.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	30.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	34.5b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y)))))

Compiler

Compiled 1860 to 557 computations (70.1% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
	0.3b	(cbrt.f64 (cos.f64 y))
	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.3b	(cbrt.f64 (cos.f64 y))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

10.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
1.0ms	(cbrt.f64 (cos.f64 y))

series970.0ms (11.1%)

Counts

2 → 24

Calls

2 calls:

490.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
479.0ms	(cbrt.f64 (cos.f64 y))

simplify185.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

731×	`log-prod_binary64`
650×	`fma-def_binary64`
499×	`unswap-sqr_binary64`
392×	`cancel-sign-sub-inv_binary64`
342×	`*-commutative_binary64`

Counts

79 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	81	826
1	165	744
2	485	706
3	1335	682
4	3572	562
5	4133	562
6	4540	562
7	4976	562
8	4880	562

prune272.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	269	2	271
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	271	7	278

Error

Counts

278 → 7

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
✓	0.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	29.6b	(/.f64 (.f64 (+.f64 (sin.f64 y) (fma.f64 (cos.f64 y) z x)) (-.f64 (+.f64 (sin.f64 y) x) (.f64 (cos.f64 y) z))) (-.f64 (+.f64 (sin.f64 y) x) (*.f64 (cos.f64 y) z)))
	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))))
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	14.4b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	30.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))

Compiler

Compiled 3190 to 1002 computations (68.6% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
✓	0.1b	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
✓	0.2b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64`
14×	`unpow-prod-down_binary64`
11×	`prod-exp_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

3 → 74

Calls

3 calls:

12.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
5.0ms	(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
3.0ms	(pow.f64 (cos.f64 y) 2)

series570.0ms (6.5%)

Counts

3 → 32

Calls

3 calls:

514.0ms	(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
44.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
11.0ms	(pow.f64 (cos.f64 y) 2)

simplify150.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
702×	`fma-def_binary64`
340×	`*-commutative_binary64`
207×	`cancel-sign-sub-inv_binary64`
206×	`associate-+l+_binary64`

Counts

106 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	1427
1	340	1221
2	1046	1093
3	2083	1083
4	4495	1083
5	4934	1083

prune341.0ms (3.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	341	7	348

Error

Counts

348 → 7

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
✓	0.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	29.6b	(/.f64 (.f64 (+.f64 (sin.f64 y) (fma.f64 (cos.f64 y) z x)) (-.f64 (+.f64 (sin.f64 y) x) (.f64 (cos.f64 y) z))) (-.f64 (+.f64 (sin.f64 y) x) (*.f64 (cos.f64 y) z)))
▶	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))))
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	14.4b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	30.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))

Compiler

Compiled 3313 to 1610 computations (51.4% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
	0.2b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.4b	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

rewrite79.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`cbrt-prod_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 41

Calls

2 calls:

72.0ms	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

series608.0ms (6.9%)

Counts

2 → 36

Calls

2 calls:

561.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
47.0ms	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))

simplify153.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary64`
503×	`fma-def_binary64`
412×	`unswap-sqr_binary64`
370×	`cancel-sign-sub-inv_binary64`
326×	`*-commutative_binary64`

Counts

77 → 122

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	103	1073
1	236	917
2	778	880
3	1492	870
4	3176	715
5	3939	697
6	4411	697
7	4989	697

prune269.0ms (3.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	497	0	497
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	497	7	504

Error

Counts

504 → 7

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
✓	0.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	29.6b	(/.f64 (.f64 (+.f64 (sin.f64 y) (fma.f64 (cos.f64 y) z x)) (-.f64 (+.f64 (sin.f64 y) x) (.f64 (cos.f64 y) z))) (-.f64 (+.f64 (sin.f64 y) x) (*.f64 (cos.f64 y) z)))
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))))
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	14.4b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	30.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))

Compiler

Compiled 2644 to 1208 computations (54.3% saved)

regimes307.0ms (3.5%)

Accuracy

Total 0.0b remaining (61.9%)

Threshold costs 0.0b (61.9%)

Compiler

Compiled 2607 to 1539 computations (41% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

end1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample3.2s (36.5%)

Algorithm

1×

intervals

Results

1.2s	1254×	body	1024	valid
852.0ms	5768×	body	128	valid
299.0ms	643×	body	512	valid
109.0ms	334×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 163 to 97 computations (40.5% saved)

Details

analyze915.0ms (10.4%)

sample87.0ms (1%)

simplify21.0ms (0.2%)

prune6.0ms (0.1%)

localize15.0ms (0.2%)

rewrite29.0ms (0.3%)

series137.0ms (1.6%)

simplify187.0ms (2.1%)

prune147.0ms (1.7%)

localize23.0ms (0.3%)

rewrite16.0ms (0.2%)

series970.0ms (11.1%)

simplify185.0ms (2.1%)

prune272.0ms (3.1%)

localize28.0ms (0.3%)

rewrite27.0ms (0.3%)

series570.0ms (6.5%)

simplify150.0ms (1.7%)

prune341.0ms (3.9%)

localize24.0ms (0.3%)

rewrite79.0ms (0.9%)

series608.0ms (6.9%)

simplify153.0ms (1.7%)

prune269.0ms (3.1%)

regimes307.0ms (3.5%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample3.2s (36.5%)

Profiling