Details

analyze451.0ms (6.6%)

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)

sample3.1s (44.8%)

Results

1.6s	2015×	body	1024	valid
844.0ms	4667×	body	128	valid
455.0ms	1081×	body	512	valid
140.0ms	487×	body	256	valid
8.0ms	6×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12
3	16	12

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series25.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

17.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
8.0ms	(*.f64 z (sin.f64 y))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 z (sin.f64 y))
0.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

simplify96.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
465×	`distribute-rgt-neg-in_binary64`
379×	`distribute-lft-neg-in_binary64`
307×	`distribute-rgt-in_binary64`
280×	`*-commutative_binary64`

Counts

90 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	972
1	183	913
2	538	901
3	1443	900
4	2915	900
5	4952	900
6	5012	900

prune41.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	59	6	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	7	66

Error

0.1b

Counts

66 → 7

Alt Table

Status	Error	Program
	22.2b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	32.2b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	41.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
▶	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	30.9b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1151 to 384 computations (66.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
✓	0.3b	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
✓	0.6b	(cbrt.f64 (sin.f64 y))

series1.1s (15.8%)

Counts

4 → 72

Calls

4 calls:

638.0ms	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
243.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
185.0ms	(cbrt.f64 (sin.f64 y))
10.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 102

Calls

4 calls:

9.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))
6.0ms	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
5.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
1.0ms	(cbrt.f64 (sin.f64 y))

simplify131.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

601×	`unswap-sqr_binary64`
518×	`fma-neg_binary64`
478×	`*-commutative_binary64`
394×	`cancel-sign-sub-inv_binary64`
368×	`log-prod_binary64`

Counts

174 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	173	2226
1	429	1857
2	1367	1728
3	2548	1694
4	4453	1676
5	4953	1676
6	5033	1676

prune168.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	224	3	227
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	225	9	234

Error

0.0b

Counts

234 → 9

Alt Table

Status	Error	Program
	22.2b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	3.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
▶	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))) (cbrt.f64 (sin.f64 y))))
	32.2b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	41.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	30.9b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	22.2b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))) (sin.f64 y))))

Compiler

Compiled 5476 to 1745 computations (68.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series70.0ms (1%)

Counts

2 → 24

Calls

2 calls:

39.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
30.0ms	(cbrt.f64 z)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 55

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune262.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	251	9	260

Error

0.0b

Counts

260 → 9

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
▶	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))) (cbrt.f64 (sin.f64 y))))
	22.2b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	3.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
✓	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))) (cbrt.f64 (sin.f64 y))))
	32.2b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	41.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	30.9b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 7701 to 1969 computations (74.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series564.0ms (8.3%)

Counts

2 → 24

Calls

2 calls:

305.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
259.0ms	(cbrt.f64 (cbrt.f64 z))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
1.0ms	(cbrt.f64 (cbrt.f64 z))

simplify104.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

693×	`sqr-pow_binary64`
622×	`fma-def_binary64`
548×	`unswap-sqr_binary64`
376×	`distribute-rgt-in_binary64`
318×	`*-commutative_binary64`

Counts

51 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	474
1	78	474
2	138	474
3	283	468
4	779	450
5	1271	450
6	1449	450
7	1730	450
8	2156	450
9	2689	450
10	3638	450
11	4799	450
12	4840	450

prune268.0ms (3.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	207	9	216

Error

0.0b

Counts

216 → 9

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
✓	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))) (cbrt.f64 (sin.f64 y))))
	22.2b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	3.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
✓	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))) (cbrt.f64 (sin.f64 y))))
	32.2b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	41.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	30.9b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 7857 to 1675 computations (78.7% saved)

regimes207.0ms (3%)

Accuracy

Total 0.1b remaining (48.4%)

Threshold costs 0.1b (48.4%)

Counts

40 → 1

Compiler

Compiled 3316 to 1734 computations (47.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

end127.0ms (1.9%)

Compiler: Compiled 235 to 114 computations (51.5% saved)

Details

analyze451.0ms (6.6%)

sample3.1s (44.8%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series25.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify96.0ms (1.4%)

prune41.0ms (0.6%)

localize12.0ms (0.2%)

series1.1s (15.8%)

rewrite27.0ms (0.4%)

simplify131.0ms (1.9%)

prune168.0ms (2.5%)

localize15.0ms (0.2%)

series70.0ms (1%)

rewrite7.0ms (0.1%)

simplify68.0ms (1%)

prune262.0ms (3.8%)

localize20.0ms (0.3%)

series564.0ms (8.3%)

rewrite4.0ms (0.1%)

simplify104.0ms (1.5%)

prune268.0ms (3.9%)

regimes207.0ms (3%)

simplify3.0ms (0%)

end127.0ms (1.9%)

Profiling