Details

analyze531.0ms (8.3%)

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)

sample2.9s (45%)

Results

1.5s	2123×	body	1024	valid
765.0ms	4604×	body	128	valid
418.0ms	1012×	body	512	valid
153.0ms	512×	body	256	valid
7.0ms	5×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (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
✓	0.0b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
✓	0.2b	(*.f64 z (sin.f64 y))

series22.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

14.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
8.0ms	(*.f64 z (sin.f64 y))

rewrite5.0ms (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)))

simplify84.0ms (1.3%)

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

prune45.0ms (0.7%)

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
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
▶	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.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)))))
	30.9b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.6b	(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))))
	15.3b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (*.f64 z (sin.f64 y)))))
	30.9b	(fma.f64 (.f64 x (.f64 y y)) -1/2 (fma.f64 y z x))

Compiler

Compiled 1113 to 378 computations (66% saved)

localize10.0ms (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)

series255.0ms (4%)

Counts

4 → 72

Calls

4 calls:

160.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
38.0ms	(cbrt.f64 z)
35.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
21.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite20.0ms (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 (1.8%)

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

prune195.0ms (3.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	189	7	196
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	191	12	203

Error

0.0b

Counts

203 → 12

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)))))
	35.3b	(fma.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))))
	30.9b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.6b	(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))))
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	0.8b	(fma.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))))
	30.9b	(fma.f64 (.f64 x (.f64 y y)) -1/2 (fma.f64 y z x))
	0.5b	(fma.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))))
▶	0.5b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (sin.f64 y)))))
	1.9b	(fma.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	(fma.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))))))
	15.3b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))

Compiler

Compiled 4345 to 1267 computations (70.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series251.0ms (3.9%)

Counts

2 → 48

Calls

2 calls:

230.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (sin.f64 y)))
20.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (sin.f64 y))))

rewrite15.0ms (0.2%)

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:

7.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (sin.f64 y))))
5.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (sin.f64 y)))

simplify107.0ms (1.7%)

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

prune303.0ms (4.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	189	13	202

Error

0.0b

Counts

202 → 13

Alt Table

Status	Error	Program
▶	0.5b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))) (sin.f64 y)))))
	30.9b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 z) (.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (sin.f64 y))))
	0.8b	(fma.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))))
	17.3b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 z) (.f64 (sin.f64 y) (cbrt.f64 (*.f64 z z)))))
	30.9b	(fma.f64 (.f64 x (.f64 y y)) -1/2 (fma.f64 y z x))
	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)))))
	35.3b	(fma.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))))
	0.6b	(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))))
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
✓	0.5b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (sin.f64 y)))))
	1.9b	(fma.f64 x (cos.f64 y) (.f64 (exp.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	15.3b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))

Compiler

Compiled 4287 to 1326 computations (69.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series561.0ms (8.8%)

Counts

2 → 24

Calls

2 calls:

303.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
258.0ms	(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))

simplify105.0ms (1.6%)

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

prune244.0ms (3.8%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	196	13	209

Error

0.0b

Counts

209 → 13

Alt Table

Status	Error	Program
✓	0.5b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))) (sin.f64 y)))))
	30.9b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 z) (.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (sin.f64 y))))
	0.8b	(fma.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))))
	17.3b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 z) (.f64 (sin.f64 y) (cbrt.f64 (*.f64 z z)))))
	30.9b	(fma.f64 (.f64 x (.f64 y y)) -1/2 (fma.f64 y z x))
	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)))))
	35.3b	(fma.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))))
	0.6b	(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))))
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
✓	0.5b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (sin.f64 y)))))
	1.9b	(fma.f64 x (cos.f64 y) (.f64 (exp.f64 (log.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	15.3b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))

Compiler

Compiled 5616 to 1623 computations (71.1% saved)

regimes415.0ms (6.5%)

Accuracy

Total 0.1b remaining (45.9%)

Threshold costs 0.1b (45.9%)

Counts

90 → 1

Compiler

Compiled 7500 to 4210 computations (43.9% saved)

simplify2.0ms (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

end167.0ms (2.6%)

Compiler: Compiled 287 to 150 computations (47.7% saved)

Details

analyze531.0ms (8.3%)

sample2.9s (45%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series22.0ms (0.3%)

rewrite5.0ms (0.1%)

simplify84.0ms (1.3%)

prune45.0ms (0.7%)

localize10.0ms (0.2%)

series255.0ms (4%)

rewrite20.0ms (0.3%)

simplify117.0ms (1.8%)

prune195.0ms (3.1%)

localize11.0ms (0.2%)

series251.0ms (3.9%)

rewrite15.0ms (0.2%)

simplify107.0ms (1.7%)

prune303.0ms (4.8%)

localize16.0ms (0.2%)

series561.0ms (8.8%)

rewrite4.0ms (0.1%)

simplify105.0ms (1.6%)

prune244.0ms (3.8%)

regimes415.0ms (6.5%)

simplify2.0ms (0%)

end167.0ms (2.6%)

Profiling