Details

analyze453.0ms (6.8%)

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
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)

sample3.2s (47.8%)

Results

1.7s	2123×	body	1024	valid
788.0ms	4604×	body	128	valid
460.0ms	1012×	body	512	valid
151.0ms	512×	body	256	valid
7.0ms	5×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
36×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

prune4.0ms (0.1%)

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)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x (cos.f64 y))
✓	0.2b	(*.f64 z (sin.f64 y))

series16.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(*.f64 x (cos.f64 y))
7.0ms	(*.f64 z (sin.f64 y))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

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

simplify110.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

573×	`distribute-rgt-neg-in_binary64`
544×	`fma-neg_binary64`
460×	`distribute-lft-neg-in_binary64`
415×	`associate-r_binary64`
322×	`neg-mul-1_binary64`

Counts

88 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	788
1	248	727
2	767	707
3	1769	707
4	3319	707
5	4769	707
6	4999	707
7	4915	707

prune62.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	65	9	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	9	75

Error

0.0b

Counts

75 → 9

Alt Table

Status	Error	Program
▶	0.4b	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	30.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	27.7b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.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 (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)))
	18.4b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.6b	(-.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))))
	0.6b	(-.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)))))
	15.2b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 z (sin.f64 y)))))

Compiler

Compiled 1454 to 549 computations (62.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series442.0ms (6.6%)

Counts

3 → 48

Calls

3 calls:

245.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
189.0ms	(cbrt.f64 (cos.f64 y))
8.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
19×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 81

Calls

3 calls:

9.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
5.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
1.0ms	(cbrt.f64 (cos.f64 y))

simplify138.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-def_binary64`
610×	`unswap-sqr_binary64`
426×	`fma-neg_binary64`
366×	`*-commutative_binary64`
361×	`log-prod_binary64`

Counts

129 → 133

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	129	1459
1	299	1232
2	1037	1167
3	1977	1123
4	4368	1105
5	4887	1105
6	4986	1105

prune275.0ms (4.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	219	8	227

Error

0.0b

Counts

227 → 8

Alt Table

Status	Error	Program
	0.6b	(-.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)))))
▶	0.3b	(-.f64 (.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))) (*.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)))
	18.4b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	30.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.6b	(-.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))))
	0.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	15.2b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 z (sin.f64 y)))))

Compiler

Compiled 5319 to 1485 computations (72.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 z (sin.f64 y))
✓	0.2b	(pow.f64 (cos.f64 y) 2)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
	0.3b	(cbrt.f64 (cos.f64 y))

series279.0ms (4.2%)

Counts

2 → 16

Calls

2 calls:

275.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
3.0ms	(pow.f64 (cos.f64 y) 2)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`cbrt-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`unpow-prod-down_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 38

Calls

2 calls:

2.0ms	(pow.f64 (cos.f64 y) 2)
1.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

simplify102.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-def_binary64`
425×	`sub-neg_binary64`
364×	`*-commutative_binary64`
346×	`distribute-rgt-neg-in_binary64`
305×	`cancel-sign-sub-inv_binary64`

Counts

54 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	592
1	150	484
2	388	480
3	1311	473
4	2994	473
5	4287	473
6	4536	473
7	4950	473
8	4861	473

prune133.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	118	8	126

Error

0.0b

Counts

126 → 8

Alt Table

Status	Error	Program
	0.6b	(-.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)))))
✓	0.3b	(-.f64 (.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))) (*.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)))
	18.4b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	30.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.6b	(-.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))))
▶	0.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	15.2b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (.f64 z (sin.f64 y)))))

Compiler

Compiled 2848 to 1344 computations (52.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series270.0ms (4.1%)

Counts

4 → 72

Calls

4 calls:

176.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
37.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
31.0ms	(cbrt.f64 z)
27.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite23.0ms (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:

9.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
5.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
4.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify116.0ms (1.7%)

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

prune230.0ms (3.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	189	7	196
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	191	13	204

Error

0.0b

Counts

204 → 13

Alt Table

Status	Error	Program
	15.2b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 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)))
	30.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.5b	(-.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))))
	0.6b	(-.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)))))
	35.3b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (sqrt.f64 (cbrt.f64 z)) (sqrt.f64 (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z)))) (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z)))) (.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.3b	(-.f64 (.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	1.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (exp.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (.f64 (cbrt.f64 z) (sin.f64 y))))
	21.0b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 z z) (.f64 (.f64 (.f64 (cbrt.f64 z) (sin.f64 y)) (.f64 (cbrt.f64 z) (sin.f64 y))) (.f64 (cbrt.f64 z) (sin.f64 y))))))
	18.4b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.6b	(-.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))))
	0.5b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (sin.f64 y)))))

Compiler

Compiled 4331 to 1175 computations (72.9% saved)

regimes514.0ms (7.7%)

Accuracy

Total 0.1b remaining (59.5%)

Threshold costs 0.1b (59.5%)

Counts

120 → 1

Compiler

Compiled 9420 to 5938 computations (37% 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	9	14
1	16	14
2	26	14
3	32	14
4	36	14
5	37	14
6	37	14

end210.0ms (3.2%)

Compiler: Compiled 321 to 172 computations (46.4% saved)

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

Details

analyze453.0ms (6.8%)

sample3.2s (47.8%)

simplify16.0ms (0.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series16.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify110.0ms (1.6%)

prune62.0ms (0.9%)

localize12.0ms (0.2%)

series442.0ms (6.6%)

rewrite19.0ms (0.3%)

simplify138.0ms (2.1%)

prune275.0ms (4.1%)

localize13.0ms (0.2%)

series279.0ms (4.2%)

rewrite5.0ms (0.1%)

simplify102.0ms (1.5%)

prune133.0ms (2%)

localize12.0ms (0.2%)

series270.0ms (4.1%)

rewrite23.0ms (0.3%)

simplify116.0ms (1.7%)

prune230.0ms (3.5%)

regimes514.0ms (7.7%)

simplify5.0ms (0.1%)

end210.0ms (3.2%)

Profiling

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14