Details

analyze360.0ms (5.3%)

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
37.4%	62.4%	0.1%	6
49.9%	49.9%	0.1%	7
62.4%	37.4%	0.1%	8
62.4%	37.4%	0.1%	9
71.8%	28.1%	0.1%	10
79.6%	20.3%	0.1%	11
79.6%	20.3%	0.1%	12
85%	14.8%	0.1%	13
89.3%	10.5%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample87.0ms (1.3%)

Algorithm

1×

intervals

Results

35.0ms	67×	body	1024	valid
13.0ms	148×	body	128	valid
7.0ms	28×	body	512	valid
5.0ms	13×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% 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)

localize8.0ms (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))

series22.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))

rewrite13.0ms (0.2%)

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:

12.0ms	(*.f64 z (sin.f64 y))
0.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

simplify87.0ms (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

prune46.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	57	8	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	8	66

Error

0.0b

Counts

66 → 8

Alt Table

Status	Error	Program
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	34.2b	(.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)))))
	1.4b	(.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)))))
▶	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	42.5b	(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)))))
	32.5b	(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 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	34.7b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1186 to 405 computations (65.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series23.0ms (0.3%)

Counts

2 → 40

Calls

2 calls:

15.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
7.0ms	(*.f64 (cos.f64 y) x)

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

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Rules

803×	`distribute-rgt-neg-in_binary64`
796×	`fma-def_binary64`
741×	`cancel-sign-sub-inv_binary64`
379×	`fma-neg_binary64`
324×	`*-commutative_binary64`

Counts

70 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	840
1	173	788
2	484	778
3	1314	771
4	3692	771
5	4945	771

prune58.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	64	9	73

Error

0.0b

Counts

73 → 9

Alt Table

Status	Error	Program
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (*.f64 (cos.f64 y) x))))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	34.2b	(.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)))))
	17.1b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))
	42.5b	(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)))))
	32.5b	(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 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	34.7b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1203 to 426 computations (64.6% saved)

localize11.0ms (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))

series1.2s (17.5%)

Counts

4 → 72

Calls

4 calls:

611.0ms	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
308.0ms	(cbrt.f64 (sin.f64 y))
257.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (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)))

rewrite28.0ms (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 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
8.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (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))

simplify132.0ms (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

prune214.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	225	2	227
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	228	8	236

Error

0.0b

Counts

236 → 8

Alt Table

Status	Error	Program
	2.4b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
▶	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (*.f64 (cos.f64 y) x))))
	34.2b	(.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)))))
	17.1b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))
	2.1b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y))))
	42.5b	(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)))))
	32.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 5377 to 1720 computations (68% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cos.f64 y) x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (*.f64 (cos.f64 y) x)))
✓	0.4b	(.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (*.f64 (cos.f64 y) x)))
✓	0.6b	(cbrt.f64 (*.f64 (cos.f64 y) x))

series1.3s (18.7%)

Counts

3 → 72

Calls

3 calls:

752.0ms

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

500.0ms

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

22.0ms

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

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

6.0ms

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

4.0ms

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

2.0ms

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

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-neg_binary64`
544×	`cancel-sign-sub-inv_binary64`
363×	`*-commutative_binary64`
339×	`fma-def_binary64`
332×	`distribute-rgt-neg-in_binary64`

Counts

151 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1975
1	377	1721
2	1168	1533
3	2763	1400
4	4882	1400
5	4961	1400

prune255.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	306	10	316

Error

0.0b

Counts

316 → 10

Alt Table

Status	Error	Program
	2.4b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	1.2b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x)))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))))) (cbrt.f64 (*.f64 (cos.f64 y) x))))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (*.f64 (cos.f64 y) x))))
✓	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) (cbrt.f64 (.f64 (cos.f64 y) x))) (cbrt.f64 (*.f64 (cos.f64 y) x))))
	34.2b	(.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)))))
	17.1b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))
	2.1b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y))))
	42.5b	(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)))))
	32.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 8100 to 1983 computations (75.5% saved)

regimes461.0ms (6.8%)

Accuracy

Total 0.1b remaining (65%)

Threshold costs 0.1b (65%)

Counts

106 → 1

Compiler

Compiled 7464 to 4330 computations (42% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	12
1	18	12
2	15	12

end0.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample2.3s (34.1%)

Algorithm

1×

intervals

Results

1.1s	1985×	body	1024	valid
412.0ms	4518×	body	128	valid
249.0ms	976×	body	512	valid
89.0ms	515×	body	256	valid
7.0ms	6×	body	2048	valid

Compiler

Compiled 267 to 128 computations (52.1% saved)

Details

analyze360.0ms (5.3%)

sample87.0ms (1.3%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series22.0ms (0.3%)

rewrite13.0ms (0.2%)

simplify87.0ms (1.3%)

prune46.0ms (0.7%)

localize8.0ms (0.1%)

series23.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify67.0ms (1%)

prune58.0ms (0.9%)

localize11.0ms (0.2%)

series1.2s (17.5%)

rewrite28.0ms (0.4%)

simplify132.0ms (1.9%)

prune214.0ms (3.1%)

localize11.0ms (0.2%)

series1.3s (18.7%)

rewrite18.0ms (0.3%)

simplify97.0ms (1.4%)

prune255.0ms (3.7%)

regimes461.0ms (6.8%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (34.1%)

Profiling