Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.8s (50.2%)

Results

1.1s	1306×	body	1024	valid
1.1s	5886×	body	128	valid
340.0ms	712×	body	512	valid
112.0ms	349×	body	256	valid
6.0ms	3×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify23.0ms (0.4%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series29.0ms (0.5%)

Counts

4 → 88

Calls

4 calls:

14.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
9.0ms	(*.f64 z (sin.f64 y))
4.0ms	(+.f64 x (cos.f64 y))
2.0ms	(cos.f64 y)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64`
9×	`add-cube-cbrt_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 70

Calls

4 calls:

5.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
5.0ms	(*.f64 z (sin.f64 y))
3.0ms	(+.f64 x (cos.f64 y))
1.0ms	(cos.f64 y)

simplify101.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-neg_binary64`
528×	`fma-def_binary64`
418×	`associate-l_binary64`
386×	`associate-r_binary64`
267×	`cancel-sign-sub-inv_binary64`

Counts

158 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	1750
1	389	1683
2	1120	1631
3	3858	1621
4	4733	1621
5	4889	1621

prune140.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Error

0.0b

Counts

138 → 6

Alt Table

Status	Error	Program
	31.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.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))))
	28.8b	(-.f64 x (fma.f64 y (+.f64 z (*.f64 y 1/2)) -1))
	27.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.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 2239 to 719 computations (67.9% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series414.0ms (7.5%)

Counts

4 → 72

Calls

4 calls:

225.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
76.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
72.0ms	(cbrt.f64 z)
41.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite48.0ms (0.9%)

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:

21.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
8.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
8.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify188.0ms (3.4%)

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

prune217.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	196	6	202

Error

0.0b

Counts

202 → 6

Alt Table

Status	Error	Program
	31.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	3.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 (*.f64 z (pow.f64 (sin.f64 y) 3)))))
▶	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (sin.f64 y) (cbrt.f64 z))))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	28.8b	(-.f64 x (fma.f64 y (+.f64 z (*.f64 y 1/2)) -1))

Compiler

Compiled 4240 to 1145 computations (73% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series287.0ms (5.2%)

Counts

2 → 48

Calls

2 calls:

263.0ms	(*.f64 (sin.f64 y) (cbrt.f64 z))
24.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (sin.f64 y) (cbrt.f64 z)))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`cbrt-unprod_binary64`
9×	`add-cbrt-cube_binary64`

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (sin.f64 y) (cbrt.f64 z)))
4.0ms	(*.f64 (sin.f64 y) (cbrt.f64 z))

simplify97.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-neg_binary64`
642×	`fma-def_binary64`
420×	`*-commutative_binary64`
399×	`unswap-sqr_binary64`
339×	`cancel-sign-sub-inv_binary64`

Counts

96 → 79

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	109	1394
1	271	919
2	872	895
3	1825	887
4	4132	881
5	4969	881
6	4904	881

prune174.0ms (3.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	195	6	201

Error

0.0b

Counts

201 → 6

Alt Table

Status	Error	Program
	31.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	3.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 (*.f64 z (pow.f64 (sin.f64 y) 3)))))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (sin.f64 y) (cbrt.f64 z))))
▶	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	28.8b	(-.f64 x (fma.f64 y (+.f64 z (*.f64 y 1/2)) -1))

Compiler

Compiled 4219 to 1144 computations (72.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))))
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 (cbrt.f64 z))
	0.6b	(cbrt.f64 z)

series323.0ms (5.8%)

Counts

2 → 24

Calls

2 calls:

278.0ms	(cbrt.f64 (cbrt.f64 z))
45.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`

Counts

2 → 41

Calls

2 calls:

7.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))))
2.0ms	(cbrt.f64 (cbrt.f64 z))

simplify107.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-l_binary64`
408×	`log-prod_binary64`
368×	`associate-r_binary64`
314×	`sqr-pow_binary64`
296×	`fma-def_binary64`

Counts

65 → 62

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	65	839
1	129	839
2	386	807
3	1284	500
4	1046	500
5	1413	500
6	2116	486
7	4255	486
8	4979	486
9	4830	486

prune179.0ms (3.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	216	6	222

Error

0.0b

Counts

222 → 6

Alt Table

Status	Error	Program
	31.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	3.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 (*.f64 z (pow.f64 (sin.f64 y) 3)))))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (sin.f64 y) (cbrt.f64 z))))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	28.8b	(-.f64 x (fma.f64 y (+.f64 z (*.f64 y 1/2)) -1))

Compiler

Compiled 6097 to 1454 computations (76.2% saved)

regimes211.0ms (3.8%)

Accuracy

Total 0.0b remaining (43.1%)

Threshold costs 0.0b (43.1%)

Counts

38 → 1

Compiler

Compiled 2408 to 1526 computations (36.6% saved)

simplify3.0ms (0.1%)

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

end100.0ms (1.8%)

Compiler: Compiled 133 to 83 computations (37.6% 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

analyze3.0ms (0.1%)

sample2.8s (50.2%)

simplify23.0ms (0.4%)

prune2.0ms (0%)

localize9.0ms (0.2%)

series29.0ms (0.5%)

rewrite16.0ms (0.3%)

simplify101.0ms (1.8%)

prune140.0ms (2.5%)

localize26.0ms (0.5%)

series414.0ms (7.5%)

rewrite48.0ms (0.9%)

simplify188.0ms (3.4%)

prune217.0ms (3.9%)

localize11.0ms (0.2%)

series287.0ms (5.2%)

rewrite17.0ms (0.3%)

simplify97.0ms (1.8%)

prune174.0ms (3.2%)

localize16.0ms (0.3%)

series323.0ms (5.8%)

rewrite11.0ms (0.2%)

simplify107.0ms (1.9%)

prune179.0ms (3.2%)

regimes211.0ms (3.8%)

simplify3.0ms (0.1%)

end100.0ms (1.8%)

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