Details

analyze440.0ms (7%)

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
25%	74.9%	0.1%	6
37.4%	62.4%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
65.5%	34.3%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
81.9%	17.9%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.4s (38.4%)

Results

1.0s	1330×	body	1024	valid
906.0ms	5878×	body	128	valid
313.0ms	718×	body	512	valid
88.0ms	327×	body	256	valid
7.0ms	3×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify21.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

230×	`fma-def_binary64`
171×	`fma-neg_binary64`
66×	`cancel-sign-sub-inv_binary64`
44×	`associate--r+_binary64`
44×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14

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

0.1b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series12.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

8.0ms	(*.f64 z (sin.f64 y))
4.0ms	(+.f64 x (cos.f64 y))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 37

Calls

2 calls:

3.0ms	(*.f64 z (sin.f64 y))
2.0ms	(+.f64 x (cos.f64 y))

simplify98.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

572×	`distribute-rgt-neg-in_binary64`
491×	`fma-neg_binary64`
348×	`sub-neg_binary64`
339×	`*-commutative_binary64`
292×	`unswap-sqr_binary64`

Counts

85 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	728
1	256	681
2	681	667
3	1823	667
4	3623	667
5	4821	667
6	4995	667
7	4866	667

prune51.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	6	73

Error

0.0b

Counts

73 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	29.8b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	32.8b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
▶	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	13.5b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))

Compiler

Compiled 1239 to 474 computations (61.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 z) (sin.f64 y))
✓	0.4b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
✓	0.6b	(cbrt.f64 z)
✓	0.6b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))

series274.0ms (4.4%)

Counts

4 → 72

Calls

4 calls:

178.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
46.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
29.0ms	(cbrt.f64 z)
21.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
5.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
3.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify120.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-def_binary64`
720×	`fma-neg_binary64`
501×	`cancel-sign-sub-inv_binary64`
496×	`*-commutative_binary64`
395×	`unswap-sqr_binary64`

Counts

175 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1734
1	311	1507
2	1181	1430
3	2385	1407
4	4566	1395
5	4973	1395
6	4943	1395

prune239.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	195	7	202

Error

0.0b

Counts

202 → 7

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	29.8b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
▶	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	32.8b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))) (sin.f64 y))))

Compiler

Compiled 4295 to 1156 computations (73.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
✓	0.3b	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
✓	0.6b	(cbrt.f64 (sin.f64 y))

series1.1s (17.6%)

Counts

4 → 72

Calls

4 calls:

606.0ms	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
253.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
239.0ms	(cbrt.f64 (sin.f64 y))
8.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 102

Calls

4 calls:

14.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))
5.0ms	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
5.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
1.0ms	(cbrt.f64 (sin.f64 y))

simplify138.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

601×	`unswap-sqr_binary64`
518×	`fma-neg_binary64`
478×	`*-commutative_binary64`
394×	`cancel-sign-sub-inv_binary64`
368×	`log-prod_binary64`

Counts

174 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	173	2226
1	429	1857
2	1367	1728
3	2548	1694
4	4453	1676
5	4953	1676
6	5033	1676

prune249.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	224	3	227
Fresh	3	1	4
Picked	1	0	1
Done	0	2	2
Total	228	6	234

Error

Counts

234 → 6

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))) (cbrt.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))))) (cbrt.f64 (sin.f64 y))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
▶	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y))))))
	1.7b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 5543 to 1686 computations (69.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
✓	0.3b	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y)))))
	0.5b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
	0.6b	(cbrt.f64 (sin.f64 y))

series8.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y)))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-cbrt-cube_binary64`
6×	`cbrt-unprod_binary64`
6×	`prod-exp_binary64`

Counts

1 → 23

Calls

1 calls:

7.0ms

(*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y)))))

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

835×	`fma-def_binary64`
367×	`fma-neg_binary64`
334×	`unswap-sqr_binary64`
301×	`*-commutative_binary64`
300×	`unsub-neg_binary64`

Counts

47 → 40

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	74	881
1	194	421
2	607	411
3	1056	407
4	1918	393
5	3246	393
6	4534	393
7	4961	393

prune265.0ms (4.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	222	6	228

Error

Counts

228 → 6

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))) (cbrt.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))))) (cbrt.f64 (sin.f64 y))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y))))))
	1.7b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (cbrt.f64 (sin.f64 y)))) (*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y))))))

Compiler

Compiled 5786 to 1659 computations (71.3% saved)

regimes568.0ms (9%)

Accuracy

Total 0.0b remaining (53.9%)

Threshold costs 0.0b (53.9%)

Counts

131 → 1

Compiler

Compiled 12908 to 7426 computations (42.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	16	14
2	26	14
3	32	14
4	36	14
5	37	14
6	37	14

end99.0ms (1.6%)

Compiler: Compiled 172 to 92 computations (46.5% saved)

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14

Details

analyze440.0ms (7%)

sample2.4s (38.4%)

simplify21.0ms (0.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series12.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify98.0ms (1.6%)

prune51.0ms (0.8%)

localize11.0ms (0.2%)

series274.0ms (4.4%)

rewrite21.0ms (0.3%)

simplify120.0ms (1.9%)

prune239.0ms (3.8%)

localize13.0ms (0.2%)

series1.1s (17.6%)

rewrite31.0ms (0.5%)

simplify138.0ms (2.2%)

prune249.0ms (3.9%)

localize16.0ms (0.3%)

series8.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify78.0ms (1.2%)

prune265.0ms (4.2%)

regimes568.0ms (9%)

simplify2.0ms (0%)

end99.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14