Details

analyze519.0ms (8.8%)

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 (52%)

Results

1.5s	1999×	body	1024	valid
843.0ms	4628×	body	128	valid
481.0ms	1055×	body	512	valid
175.0ms	570×	body	256	valid
6.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify16.0ms (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

prune4.0ms (0.1%)

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

series15.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

8.0ms	(*.f64 z (sin.f64 y))
7.0ms	(*.f64 x (cos.f64 y))

rewrite9.0ms (0.2%)

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:

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

simplify96.0ms (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

prune68.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	64	10	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	10	75

Error

0.1b

Counts

75 → 10

Alt Table

Status	Error	Program
	24.3b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.6b	(-.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)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	16.4b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	0.4b	(-.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)))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	0.9b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	33.2b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	24.3b	(-.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)))
	31.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 1494 to 575 computations (61.5% saved)

localize14.0ms (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))

series419.0ms (7.1%)

Counts

3 → 48

Calls

3 calls:

235.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
176.0ms	(cbrt.f64 (cos.f64 y))
8.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite24.0ms (0.4%)

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))

simplify117.0ms (2%)

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

prune207.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	220	8	228

Error

0.0b

Counts

228 → 8

Alt Table

Status	Error	Program
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
▶	0.2b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	24.3b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.6b	(-.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)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	16.4b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	33.2b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	31.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 5309 to 1489 computations (72% saved)

localize14.0ms (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))

series11.0ms (0.2%)

Counts

2 → 28

Calls

2 calls:

8.0ms	(.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)

rewrite16.0ms (0.3%)

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:

12.0ms	(.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)

simplify113.0ms (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

prune172.0ms (2.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	134	11	145

Error

0.0b

Counts

145 → 11

Alt Table

Status	Error	Program
	16.4b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	0.3b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (log1p.f64 (expm1.f64 (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))))
✓	0.2b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	33.2b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	16.4b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (pow.f64 (cos.f64 y) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)) 1/3)) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	24.3b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.6b	(-.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)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	16.4b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (.f64 (pow.f64 (cos.f64 y) 1/6) (pow.f64 (cos.f64 y) 1/6))) (.f64 z (sin.f64 y)))
	31.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 3417 to 1656 computations (51.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 y))))
	0.2b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.6b	(expm1.f64 (cbrt.f64 (cos.f64 y)))

series346.0ms (5.8%)

Counts

2 → 24

Calls

2 calls:

175.0ms	(expm1.f64 (cbrt.f64 (cos.f64 y)))
170.0ms	(log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 y))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

1.0ms	(expm1.f64 (cbrt.f64 (cos.f64 y)))
0.0ms	(log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 y))))

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

572×	`cancel-sign-sub-inv_binary64`
533×	`distribute-rgt-neg-in_binary64`
450×	`distribute-lft-neg-in_binary64`
438×	`sub-neg_binary64`
306×	`neg-mul-1_binary64`

Counts

46 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	440
1	147	403
2	406	390
3	1291	386
4	3106	386
5	4570	386
6	4927	386

prune148.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	100	11	111

Error

0.0b

Counts

111 → 11

Alt Table

Status	Error	Program
	16.4b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
✓	0.3b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (log1p.f64 (expm1.f64 (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))))
✓	0.2b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	33.2b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	16.4b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (pow.f64 (cos.f64 y) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)) 1/3)) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
	24.3b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.6b	(-.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)))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	16.4b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (.f64 (pow.f64 (cos.f64 y) 1/6) (pow.f64 (cos.f64 y) 1/6))) (.f64 z (sin.f64 y)))
	31.4b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 2636 to 1313 computations (50.2% saved)

regimes230.0ms (3.9%)

Accuracy

Total 0.1b remaining (57.5%)

Threshold costs 0.1b (57.5%)

Counts

57 → 1

Compiler

Compiled 4356 to 2806 computations (35.6% saved)

simplify3.0ms (0%)

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	9	14
1	16	14
2	26	14
3	32	14
4	36	14
5	37	14
6	37	14

end178.0ms (3%)

Compiler: Compiled 260 to 161 computations (38.1% 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

analyze519.0ms (8.8%)

sample3.1s (52%)

simplify16.0ms (0.3%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series15.0ms (0.3%)

rewrite9.0ms (0.2%)

simplify96.0ms (1.6%)

prune68.0ms (1.1%)

localize14.0ms (0.2%)

series419.0ms (7.1%)

rewrite24.0ms (0.4%)

simplify117.0ms (2%)

prune207.0ms (3.5%)

localize14.0ms (0.2%)

series11.0ms (0.2%)

rewrite16.0ms (0.3%)

simplify113.0ms (1.9%)

prune172.0ms (2.9%)

localize17.0ms (0.3%)

series346.0ms (5.8%)

rewrite2.0ms (0%)

simplify78.0ms (1.3%)

prune148.0ms (2.5%)

regimes230.0ms (3.9%)

simplify3.0ms (0%)

end178.0ms (3%)

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