Details

analyze551.0ms (7.3%)

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
0%	99.9%	0.1%	6
37.4%	62.4%	0.1%	7
43.7%	56.2%	0.1%	8
43.7%	56.2%	0.1%	9
65.5%	34.3%	0.1%	10
70.2%	29.6%	0.1%	11
70.2%	29.6%	0.1%	12
81.9%	17.9%	0.1%	13
84.6%	15.2%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample3.1s (41.4%)

Results

1.6s	2168×	body	1024	valid
821.0ms	4560×	body	128	valid
437.0ms	1021×	body	512	valid
196.0ms	500×	body	256	valid
15.0ms	7×	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

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 44 to 25 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series14.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

7.0ms	(*.f64 z (cos.f64 y))
7.0ms	(*.f64 x (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:

4.0ms	(*.f64 x (sin.f64 y))
3.0ms	(*.f64 z (cos.f64 y))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
499×	`distribute-rgt-neg-in_binary64`
417×	`distribute-lft-neg-in_binary64`
415×	`associate-r_binary64`
282×	`sub-neg_binary64`

Counts

88 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	788
1	247	727
2	766	707
3	1731	707
4	3197	707
5	4852	707
6	4957	707

prune53.0ms (0.7%)

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
	32.9b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.8b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (cos.f64 y))) (cbrt.f64 (.f64 z (cos.f64 y)))) (cbrt.f64 (.f64 z (cos.f64 y)))))
▶	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (cbrt.f64 (.f64 x (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	19.1b	(+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 y) x) 3)) (.f64 z (cos.f64 y)))
	17.6b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	34.0b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y))))
	0.8b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cos.f64 y))))
	0.7b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	25.8b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))

Compiler

Compiled 1440 to 553 computations (61.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (cos.f64 y))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (cbrt.f64 (.f64 x (sin.f64 y)))) (cbrt.f64 (*.f64 x (sin.f64 y))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (cbrt.f64 (*.f64 x (sin.f64 y))))
✓	5.4b	(cbrt.f64 (*.f64 x (sin.f64 y)))

series1.2s (15.7%)

Counts

3 → 72

Calls

3 calls:

722.0ms

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

437.0ms

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

22.0ms

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

rewrite18.0ms (0.2%)

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:

7.0ms

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

5.0ms

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

2.0ms

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

simplify101.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
455×	`cancel-sign-sub-inv_binary64`
355×	`*-commutative_binary64`
346×	`fma-def_binary64`
297×	`exp-prod_binary64`

Counts

151 → 135

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	170	2539
1	412	2016
2	1170	1679
3	2730	1440
4	4576	1398
5	4937	1398

prune189.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	225	10	235

Error

0.0b

Counts

235 → 10

Alt Table

Status	Error	Program
	0.8b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cos.f64 y))))
	33.2b	(+.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 x (sin.f64 y)))) (sqrt.f64 (.f64 x (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	32.9b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.8b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (cos.f64 y))) (cbrt.f64 (.f64 z (cos.f64 y)))) (cbrt.f64 (.f64 z (cos.f64 y)))))
▶	0.6b	(+.f64 (.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	19.1b	(+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 y) x) 3)) (.f64 z (cos.f64 y)))
	17.6b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	34.0b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y))))
	0.7b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	25.8b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))

Compiler

Compiled 6596 to 1734 computations (73.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 (sin.f64 y))
✓	0.7b	(cbrt.f64 x)
	5.4b	(cbrt.f64 (*.f64 x (sin.f64 y)))

series237.0ms (3.2%)

Counts

3 → 36

Calls

3 calls:

164.0ms	(cbrt.f64 (sin.f64 y))
40.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
33.0ms	(cbrt.f64 x)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`cbrt-prod_binary64`
21×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`

Counts

3 → 68

Calls

3 calls:

4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 (sin.f64 y))
1.0ms	(cbrt.f64 x)

simplify94.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

854×	`log-prod_binary64`
572×	`unswap-sqr_binary64`
476×	`fma-neg_binary64`
371×	`cancel-sign-sub-inv_binary64`
327×	`*-commutative_binary64`

Counts

104 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	831
1	184	769
2	504	729
3	1287	711
4	3021	615
5	4130	615
6	4626	615
7	4900	615

prune172.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	166	11	177

Error

0.0b

Counts

177 → 11

Alt Table

Status	Error	Program
	34.0b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y))))
	0.7b	(+.f64 (.f64 (.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x)))) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	0.8b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cos.f64 y))))
	33.2b	(+.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 x (sin.f64 y)))) (sqrt.f64 (.f64 x (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	32.9b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.8b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (cos.f64 y))) (cbrt.f64 (.f64 z (cos.f64 y)))) (cbrt.f64 (.f64 z (cos.f64 y)))))
✓	0.6b	(+.f64 (.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	19.1b	(+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 y) x) 3)) (.f64 z (cos.f64 y)))
	17.6b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
▶	0.7b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	25.8b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))

Compiler

Compiled 5376 to 1415 computations (73.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series834.0ms (11.1%)

Counts

3 → 60

Calls

3 calls:

598.0ms

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

228.0ms

(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))

7.0ms

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

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`pow1_binary64`
23×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
19×	`add-exp-log_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 89

Calls

3 calls:

9.0ms

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

6.0ms

(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))

5.0ms

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

simplify92.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-neg_binary64`
694×	`fma-def_binary64`
396×	`*-commutative_binary64`
361×	`unswap-sqr_binary64`
302×	`cancel-sign-sub-inv_binary64`

Counts

149 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	2021
1	363	1792
2	1121	1656
3	2111	1610
4	4432	1610
5	4918	1610

prune196.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	224	9	233

Error

0.0b

Counts

233 → 9

Alt Table

Status	Error	Program
	3.5b	(+.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	17.6b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	32.9b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.8b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (cos.f64 y))) (cbrt.f64 (.f64 z (cos.f64 y)))) (cbrt.f64 (.f64 z (cos.f64 y)))))
✓	0.6b	(+.f64 (.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	34.0b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y))))
	0.8b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cos.f64 y))))
	25.8b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	3.1b	(+.f64 (.f64 (.f64 x (expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2))))) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))

Compiler

Compiled 5363 to 1646 computations (69.3% saved)

regimes360.0ms (4.8%)

Accuracy

Total 0.1b remaining (60.6%)

Threshold costs 0.1b (60.6%)

Counts

87 → 1

Compiler

Compiled 6928 to 4250 computations (38.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	14
1	20	14
2	17	14

end132.0ms (1.8%)

Compiler: Compiled 208 to 125 computations (39.9% saved)

Details

analyze551.0ms (7.3%)

sample3.1s (41.4%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series14.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify74.0ms (1%)

prune53.0ms (0.7%)

localize12.0ms (0.2%)

series1.2s (15.7%)

rewrite18.0ms (0.2%)

simplify101.0ms (1.3%)

prune189.0ms (2.5%)

localize16.0ms (0.2%)

series237.0ms (3.2%)

rewrite8.0ms (0.1%)

simplify94.0ms (1.2%)

prune172.0ms (2.3%)

localize12.0ms (0.2%)

series834.0ms (11.1%)

rewrite24.0ms (0.3%)

simplify92.0ms (1.2%)

prune196.0ms (2.6%)

regimes360.0ms (4.8%)

simplify2.0ms (0%)

end132.0ms (1.8%)

Profiling