Details

analyze795.0ms (12.5%)

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
31.2%	68.6%	0.1%	6
43.7%	56.2%	0.1%	7
59.3%	40.6%	0.1%	8
59.3%	40.6%	0.1%	9
68.6%	31.2%	0.1%	10
78%	21.8%	0.1%	11
78%	21.8%	0.1%	12
83.5%	16.4%	0.1%	13
88.5%	11.3%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample110.0ms (1.7%)

Algorithm

1×

intervals

Results

38.0ms	35×	body	1024	valid
38.0ms	181×	body	128	valid
12.0ms	25×	body	512	valid
5.0ms	15×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify47.0ms (0.7%)

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

prune3.0ms (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)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series53.0ms (0.8%)

Counts

3 → 64

Calls

3 calls:

33.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
14.0ms	(*.f64 z (sin.f64 y))
6.0ms	(sin.f64 y)

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

10.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
6.0ms	(*.f64 z (sin.f64 y))
2.0ms	(sin.f64 y)

simplify184.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

975×	`fma-neg_binary64`
452×	`fma-def_binary64`
402×	`associate-l_binary64`
328×	`associate-r_binary64`
277×	`distribute-rgt-neg-in_binary64`

Counts

117 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1442
1	303	1364
2	953	1316
3	3322	1306
4	4656	1306
5	5000	1306
6	4867	1306

prune125.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	99	7	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	8	107

Error

0.0b

Counts

107 → 8

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 z (.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y)))))
	2.9b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
▶	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y)))))
	25.6b	(.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)))))
	0.4b	(-.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))))
	30.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1840 to 604 computations (67.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y)))))
✓	0.1b	(expm1.f64 (sin.f64 y))
✓	0.1b	(*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y))))
✓	0.2b	(log1p.f64 (expm1.f64 (sin.f64 y)))

series31.0ms (0.5%)

Counts

4 → 84

Calls

4 calls:

17.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y)))))
8.0ms	(*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y))))
3.0ms	(expm1.f64 (sin.f64 y))
2.0ms	(log1p.f64 (expm1.f64 (sin.f64 y)))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 66

Calls

4 calls:

17.0ms	(*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y))))
11.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log1p.f64 (expm1.f64 (sin.f64 y)))))
1.0ms	(expm1.f64 (sin.f64 y))
0.0ms	(log1p.f64 (expm1.f64 (sin.f64 y)))

simplify146.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1006×	`fma-neg_binary64`
507×	`fma-def_binary64`
419×	`associate-l_binary64`
349×	`associate-r_binary64`
291×	`cancel-sign-sub-inv_binary64`

Counts

150 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	1661
1	349	1566
2	1084	1507
3	3676	1497
4	4648	1497
5	4878	1497

prune246.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	138	6	144

Error

0.0b

Counts

144 → 6

Alt Table

Status	Error	Program
	2.9b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (sin.f64 y)) 3)))))
▶	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	2.9b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
	0.4b	(-.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))))
	30.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 2389 to 738 computations (69.1% saved)

localize22.0ms (0.3%)

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)))
✓	0.4b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series483.0ms (7.6%)

Counts

4 → 72

Calls

4 calls:

294.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
78.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
72.0ms	(cbrt.f64 z)
39.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite53.0ms (0.8%)

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:

15.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
13.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
8.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify186.0ms (2.9%)

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

prune329.0ms (5.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	194	8	202

Error

Counts

202 → 8

Alt Table

Status	Error	Program
▶	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (sin.f64 y)))))
	2.9b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	0.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))))
	0.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 5) (cbrt.f64 (cbrt.f64 z))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.4b	(-.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))))
	30.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	2.9b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (sin.f64 y)) 3)))))

Compiler

Compiled 4324 to 1195 computations (72.4% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series518.0ms (8.1%)

Counts

2 → 48

Calls

2 calls:

476.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (sin.f64 y)))
42.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (sin.f64 y))))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
16×	`pow1_binary64`
12×	`associate-l_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 49

Calls

2 calls:

14.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (sin.f64 y))))
11.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (sin.f64 y)))

simplify218.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

835×	`fma-neg_binary64`
591×	`fma-def_binary64`
428×	`unswap-sqr_binary64`
386×	`distribute-rgt-neg-in_binary64`
376×	`*-commutative_binary64`

Counts

97 → 92

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	100	1586
1	257	1321
2	799	1081
3	1578	1073
4	3222	1045
5	4691	1045
6	4892	1045
7	4916	1045

prune275.0ms (4.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	190	8	198

Error

Counts

198 → 8

Alt Table

Status	Error	Program
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (sin.f64 y)))))
	2.9b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	0.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))))
	0.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 5) (cbrt.f64 (cbrt.f64 z))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.4b	(-.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))))
	30.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	2.9b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (sin.f64 y)) 3)))))

Compiler

Compiled 4127 to 1164 computations (71.8% saved)

regimes204.0ms (3.2%)

Accuracy

Total 0.0b remaining (61.5%)

Threshold costs 0.0b (61.5%)

Counts

43 → 1

Compiler

Compiled 2764 to 1786 computations (35.4% 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

end0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample2.2s (34.5%)

Algorithm

1×

intervals

Results

777.0ms	1301×	body	1024	valid
563.0ms	5733×	body	128	valid
191.0ms	659×	body	512	valid
81.0ms	306×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 179 to 112 computations (37.4% 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

analyze795.0ms (12.5%)

sample110.0ms (1.7%)

simplify47.0ms (0.7%)

prune3.0ms (0%)

localize15.0ms (0.2%)

series53.0ms (0.8%)

rewrite22.0ms (0.3%)

simplify184.0ms (2.9%)

prune125.0ms (2%)

localize12.0ms (0.2%)

series31.0ms (0.5%)

rewrite34.0ms (0.5%)

simplify146.0ms (2.3%)

prune246.0ms (3.9%)

localize22.0ms (0.3%)

series483.0ms (7.6%)

rewrite53.0ms (0.8%)

simplify186.0ms (2.9%)

prune329.0ms (5.2%)

localize23.0ms (0.4%)

series518.0ms (8.1%)

rewrite31.0ms (0.5%)

simplify218.0ms (3.4%)

prune275.0ms (4.3%)

regimes204.0ms (3.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (34.5%)

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