Details

analyze504.0ms (8.4%)

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 (53.5%)

Results

1.6s	2015×	body	1024	valid
883.0ms	4667×	body	128	valid
541.0ms	1081×	body	512	valid
147.0ms	487×	body	256	valid
9.0ms	6×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify17.0ms (0.3%)

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

prune2.0ms (0%)

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)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

8.0ms	(*.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:

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

simplify95.0ms (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

prune55.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	66	8	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	8	75

Error

0.0b

Counts

75 → 8

Alt Table

Status	Error	Program
	29.1b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	22.1b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	0.5b	(-.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)))))
	14.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	0.5b	(-.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)))
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	31.7b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1418 to 533 computations (62.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
✓	0.2b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(cbrt.f64 (cos.f64 y))

series454.0ms (7.6%)

Counts

3 → 48

Calls

3 calls:

249.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
197.0ms	(cbrt.f64 (cos.f64 y))
7.0ms	(.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:

8.0ms	(.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))

simplify112.0ms (1.9%)

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

prune238.0ms (4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	217	9	226

Error

0.0b

Counts

226 → 9

Alt Table

Status	Error	Program
	0.5b	(-.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)))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	29.1b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (cos.f64 y) (cos.f64 y))) (cos.f64 y))) (.f64 z (sin.f64 y)))
▶	0.3b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	22.1b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	14.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.5b	(-.f64 (.f64 x (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
	31.7b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))

Compiler

Compiled 5359 to 1521 computations (71.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
✓	0.2b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))

series13.0ms (0.2%)

Counts

2 → 28

Calls

2 calls:

9.0ms	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
3.0ms	(pow.f64 (cos.f64 y) 2)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
11×	`prod-exp_binary64`
6×	`associate-r_binary64`
6×	`add-cbrt-cube_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 47

Calls

2 calls:

7.0ms	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify117.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-neg_binary64`
576×	`unswap-sqr_binary64`
435×	`sqr-pow_binary64`
433×	`fma-def_binary64`
336×	`*-commutative_binary64`

Counts

75 → 76

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	110	1034
1	253	880
2	787	833
3	1566	815
4	3415	635
5	3980	617
6	4678	617
7	4942	617
8	4901	617

prune169.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	137	9	146

Error

0.0b

Counts

146 → 9

Alt Table

Status	Error	Program
	0.5b	(-.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)))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.3b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	22.1b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	29.1b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (pow.f64 (cos.f64 y) 2)) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	14.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.5b	(-.f64 (.f64 x (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
	31.7b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))

Compiler

Compiled 3315 to 1580 computations (52.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.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))

series244.0ms (4.1%)

Counts

2 → 36

Calls

2 calls:

237.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
7.0ms	(.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`cbrt-prod_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 41

Calls

2 calls:

6.0ms	(.f64 (.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

simplify129.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
495×	`fma-def_binary64`
412×	`unswap-sqr_binary64`
387×	`cancel-sign-sub-inv_binary64`
342×	`log-prod_binary64`

Counts

77 → 71

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	103	1073
1	237	917
2	780	880
3	1509	872
4	3224	715
5	3868	697
6	4385	697
7	4688	697
8	4928	697

prune151.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	125	9	134

Error

0.0b

Counts

134 → 9

Alt Table

Status	Error	Program
	0.5b	(-.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)))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.3b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	22.1b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	29.1b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (pow.f64 (cos.f64 y) 2)) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	14.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.5b	(-.f64 (.f64 x (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
	31.7b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))

Compiler

Compiled 2756 to 1260 computations (54.3% saved)

regimes225.0ms (3.8%)

Accuracy

Total 0.1b remaining (51.5%)

Threshold costs 0.1b (51.5%)

Counts

55 → 1

Compiler

Compiled 4200 to 2546 computations (39.4% saved)

simplify4.0ms (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	11	14
1	20	14
2	29	14
3	35	14
4	39	14
5	40	14
6	39	14

end148.0ms (2.5%)

Compiler: Compiled 209 to 123 computations (41.1% 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

analyze504.0ms (8.4%)

sample3.2s (53.5%)

simplify17.0ms (0.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series15.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify95.0ms (1.6%)

prune55.0ms (0.9%)

localize11.0ms (0.2%)

series454.0ms (7.6%)

rewrite19.0ms (0.3%)

simplify112.0ms (1.9%)

prune238.0ms (4%)

localize13.0ms (0.2%)

series13.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify117.0ms (1.9%)

prune169.0ms (2.8%)

localize14.0ms (0.2%)

series244.0ms (4.1%)

rewrite9.0ms (0.2%)

simplify129.0ms (2.1%)

prune151.0ms (2.5%)

regimes225.0ms (3.8%)

simplify4.0ms (0.1%)

end148.0ms (2.5%)

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