Details

analyze1.9s (25.8%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
3.1%	96.7%	0.1%	9
3.1%	96.7%	0.1%	10
4.7%	95.2%	0.1%	11
8.2%	91.7%	0.1%	12
8.8%	91.1%	0.1%	13
10.2%	89.6%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.5s (32.9%)

Results

1.0s	1360×	body	1024	valid
990.0ms	5881×	body	128	valid
298.0ms	683×	body	512	valid
94.0ms	323×	body	256	valid
14.0ms	9×	body	2048	valid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify22.0ms (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)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series28.0ms (0.4%)

Counts

3 → 84

Calls

3 calls:

16.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))
5.0ms	(+.f64 x (cos.f64 y))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 61

Calls

3 calls:

5.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
3.0ms	(*.f64 z (sin.f64 y))
3.0ms	(+.f64 x (cos.f64 y))

simplify99.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-neg_binary64`
503×	`fma-def_binary64`
418×	`associate-l_binary64`
386×	`associate-r_binary64`
239×	`cancel-sign-sub-inv_binary64`

Counts

145 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1641
1	369	1578
2	1084	1530
3	3795	1520
4	4687	1520
5	4866	1520

prune88.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	8	121

Error

0.0b

Counts

121 → 8

Alt Table

Status	Error	Program
	25.5b	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	18.2b	(-.f64 x (fma.f64 y z -1))
	22.8b	(/.f64 (-.f64 (.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y))) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y)))) (+.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
	32.7b	(cbrt.f64 (.f64 (.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))) (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	36.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (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 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 2116 to 648 computations (69.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
✓	8.7b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series1.3s (16.6%)

Counts

3 → 72

Calls

3 calls:

751.0ms

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

481.0ms

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

23.0ms

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

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

9.0ms

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

4.0ms

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

2.0ms

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

simplify121.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
445×	`cancel-sign-sub-inv_binary64`
352×	`*-commutative_binary64`
346×	`fma-def_binary64`
253×	`distribute-rgt-neg-in_binary64`

Counts

151 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2495
1	410	2016
2	1169	1679
3	2733	1438
4	4659	1438
5	4981	1438
6	4891	1438

prune261.0ms (3.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	297	8	305

Error

0.0b

Counts

305 → 8

Alt Table

Status	Error	Program
	25.5b	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
▶	18.2b	(-.f64 x (fma.f64 y z -1))
	22.8b	(/.f64 (-.f64 (.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y))) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y)))) (+.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
	32.7b	(cbrt.f64 (.f64 (.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))) (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	36.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (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 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 8462 to 2077 computations (75.5% saved)

localize7.0ms (0.1%)

prune7.0ms (0.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	2	2
Total	8	8

Error

0.0b

Counts

8 → 8

Alt Table

Status	Error	Program
	25.5b	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
✓	18.2b	(-.f64 x (fma.f64 y z -1))
▶	22.8b	(/.f64 (-.f64 (.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y))) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y)))) (+.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
	32.7b	(cbrt.f64 (.f64 (.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))) (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	36.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (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 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 290 to 131 computations (54.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y)))
✓	0.2b	(.f64 (.f64 z (sin.f64 y)) (*.f64 z (sin.f64 y)))
✓	2.3b	(-.f64 (.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y))) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))))
✓	21.4b	(/.f64 (-.f64 (.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y))) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y)))) (+.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))

series222.0ms (2.9%)

Counts

4 → 120

Calls

4 calls:

139.0ms	(/.f64 (-.f64 (.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y))) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y)))) (+.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
51.0ms	(-.f64 (.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y))) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))))
22.0ms	(.f64 (.f64 z (sin.f64 y)) (*.f64 z (sin.f64 y)))
9.0ms	(*.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y)))

rewrite49.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`pow1_binary64`
31×	`*-un-lft-identity_binary64`
20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`

Counts

4 → 135

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y))) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y)))) (+.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
10.0ms	(-.f64 (.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y))) (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))))
7.0ms	(*.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y)))
6.0ms	(.f64 (.f64 z (sin.f64 y)) (*.f64 z (sin.f64 y)))

simplify161.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

419×	`associate-l_binary64`
390×	`times-frac_binary64`
367×	`associate-/l*_binary64`
326×	`fma-def_binary64`
193×	`associate-/r*_binary64`

Counts

255 → 267

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	487	8700
1	1493	8067
2	5085	8067

prune274.0ms (3.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	266	1	267
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	267	8	275

Error

Counts

275 → 8

Alt Table

Status	Error	Program
	25.5b	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
✓	18.2b	(-.f64 x (fma.f64 y z -1))
	32.7b	(cbrt.f64 (.f64 (.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))) (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
	36.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	22.8b	(/.f64 (-.f64 (.f64 (+.f64 x (cos.f64 y)) (+.f64 x (cos.f64 y))) (.f64 z (.f64 (sin.f64 y) (.f64 z (sin.f64 y))))) (+.f64 (+.f64 x (cos.f64 y)) (*.f64 z (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 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 12812 to 3492 computations (72.7% saved)

regimes346.0ms (4.6%)

Accuracy

Total 0.0b remaining (58.8%)

Threshold costs 0.0b (58.8%)

Counts

77 → 1

Compiler

Compiled 7184 to 3958 computations (44.9% saved)

simplify3.0ms (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

end104.0ms (1.4%)

Compiler: Compiled 192 to 95 computations (50.5% 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

analyze1.9s (25.8%)

sample2.5s (32.9%)

simplify22.0ms (0.3%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series28.0ms (0.4%)

rewrite13.0ms (0.2%)

simplify99.0ms (1.3%)

prune88.0ms (1.2%)

localize11.0ms (0.2%)

series1.3s (16.6%)

rewrite19.0ms (0.2%)

simplify121.0ms (1.6%)

prune261.0ms (3.5%)

localize7.0ms (0.1%)

prune7.0ms (0.1%)

localize15.0ms (0.2%)

series222.0ms (2.9%)

rewrite49.0ms (0.6%)

simplify161.0ms (2.1%)

prune274.0ms (3.6%)

regimes346.0ms (4.6%)

simplify3.0ms (0%)

end104.0ms (1.4%)

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