Details

analyze423.0ms (5.5%)

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)

sample54.0ms (0.7%)

Algorithm

1×

intervals

Results

22.0ms	40×	body	1024	valid
15.0ms	184×	body	128	valid
5.0ms	20×	body	512	valid
2.0ms	12×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify20.0ms (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)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series13.0ms (0.2%)

Counts

3 → 52

Calls

3 calls:

7.0ms	(*.f64 z (sin.f64 y))
4.0ms	(+.f64 x (cos.f64 y))
2.0ms	(sin.f64 y)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 46

Calls

3 calls:

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

simplify132.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-neg_binary64`
427×	`sub-neg_binary64`
302×	`associate-l_binary64`
269×	`fma-def_binary64`
246×	`unswap-sqr_binary64`

Counts

98 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	844
1	283	782
2	755	764
3	2034	764
4	4139	764
5	4961	764
6	4989	764
7	4997	764
8	4911	764

prune67.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Error

0.0b

Counts

90 → 5

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	46.0b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y)))))
	12.3b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
	1.6b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))

Compiler

Compiled 1488 to 574 computations (61.4% saved)

localize11.0ms (0.1%)

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)))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.7b	(cbrt.f64 z)

series247.0ms (3.2%)

Counts

4 → 72

Calls

4 calls:

155.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
38.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
35.0ms	(cbrt.f64 z)
20.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite22.0ms (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)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
4.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify117.0ms (1.5%)

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

prune177.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	193	8	201

Error

Counts

201 → 8

Alt Table

Status	Error	Program
	1.6b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
	30.0b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.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))))
	46.0b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y)))))
	12.3b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	30.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
▶	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 2) (cbrt.f64 (cbrt.f64 z)))) (.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 4363 to 1204 computations (72.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 2)
✓	0.5b	(.f64 (cbrt.f64 z) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 2) (cbrt.f64 (cbrt.f64 z))))
✓	0.6b	(cbrt.f64 (cbrt.f64 z))
	0.7b	(cbrt.f64 z)

series551.0ms (7.2%)

Counts

3 → 36

Calls

3 calls:

262.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 2)
252.0ms	(cbrt.f64 (cbrt.f64 z))
37.0ms	(.f64 (cbrt.f64 z) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 2) (cbrt.f64 (cbrt.f64 z))))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`cbrt-prod_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`

Counts

3 → 67

Calls

3 calls:

7.0ms	(.f64 (cbrt.f64 z) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 2) (cbrt.f64 (cbrt.f64 z))))
2.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 2)
1.0ms	(cbrt.f64 (cbrt.f64 z))

simplify108.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

804×	`log-prod_binary64`
793×	`fma-def_binary64`
481×	`associate-l_binary64`
346×	`sqr-pow_binary64`
287×	`associate-r_binary64`

Counts

103 → 99

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	1028
1	185	943
2	429	882
3	1489	880
4	2764	875
5	3950	875
6	4974	875
7	4898	875

prune213.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	197	8	205

Error

Counts

205 → 8

Alt Table

Status	Error	Program
	1.6b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
	30.0b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.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))))
	46.0b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y)))))
	12.3b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	30.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
▶	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 2) (cbrt.f64 (cbrt.f64 z)))) (.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 5633 to 1820 computations (67.7% saved)

localize11.0ms (0.1%)

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 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y))))
✓	0.4b	(*.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y))))
✓	0.4b	(cbrt.f64 (+.f64 x (cos.f64 y)))

series525.0ms (6.8%)

Counts

3 → 72

Calls

3 calls:

286.0ms

(*.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y))))

232.0ms

(cbrt.f64 (+.f64 x (cos.f64 y)))

6.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y))))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
33×	`cbrt-prod_binary64`
32×	`frac-times_binary64`

Counts

3 → 136

Calls

3 calls:

12.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y))))

8.0ms

(*.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y))))

2.0ms

(cbrt.f64 (+.f64 x (cos.f64 y)))

simplify156.0ms (2%)

Algorithm

1×	egg-herbie

Rules

570×	`times-frac_binary64`
449×	`unswap-sqr_binary64`
448×	`cancel-sign-sub-inv_binary64`
304×	`associate-r_binary64`
282×	`associate-l_binary64`

Counts

208 → 255

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	336	5093
1	853	4734
2	2692	4584
3	4578	4492
4	5499	4492

prune368.0ms (4.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	412	0	412
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	412	8	420

Error

Counts

420 → 8

Alt Table

Status	Error	Program
	1.6b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))
	30.0b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.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))))
	46.0b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y)))))
	12.3b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	30.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 2) (cbrt.f64 (cbrt.f64 z)))) (.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 14593 to 4796 computations (67.1% saved)

regimes907.0ms (11.8%)

Accuracy

Total 0.0b remaining (46.1%)

Threshold costs 0.0b (46.1%)

Counts

121 → 1

Compiler

Compiled 9472 to 5950 computations (37.2% saved)

simplify5.0ms (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	11	14
1	20	14
2	29	14
3	35	14
4	39	14
5	40	14
6	39	14

end1.0ms (0%)

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

sample3.5s (45.2%)

Algorithm

1×

intervals

Results

1.3s	1331×	body	1024	valid
974.0ms	5750×	body	128	valid
345.0ms	632×	body	512	valid
93.0ms	285×	body	256	valid
5.0ms	2×	body	2048	valid

Compiler

Compiled 202 to 118 computations (41.6% 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

analyze423.0ms (5.5%)

sample54.0ms (0.7%)

simplify20.0ms (0.3%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series13.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify132.0ms (1.7%)

prune67.0ms (0.9%)

localize11.0ms (0.1%)

series247.0ms (3.2%)

rewrite22.0ms (0.3%)

simplify117.0ms (1.5%)

prune177.0ms (2.3%)

localize14.0ms (0.2%)

series551.0ms (7.2%)

rewrite14.0ms (0.2%)

simplify108.0ms (1.4%)

prune213.0ms (2.8%)

localize11.0ms (0.1%)

series525.0ms (6.8%)

rewrite38.0ms (0.5%)

simplify156.0ms (2%)

prune368.0ms (4.8%)

regimes907.0ms (11.8%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample3.5s (45.2%)

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