Details

analyze369.0ms (7%)

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)

sample70.0ms (1.3%)

Algorithm

1×

intervals

Results

37.0ms	72×	body	1024	valid
11.0ms	138×	body	128	valid
8.0ms	32×	body	512	valid
2.0ms	13×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 28 to 20 computations (28.6% 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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(-.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))

series14.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

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

rewrite7.0ms (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:

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

simplify102.0ms (1.9%)

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

prune54.0ms (1%)

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

0.1b

Counts

75 → 9

Alt Table

Status	Error	Program
▶	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)))
	24.2b	(-.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)))))
	33.1b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	25.1b	(-.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 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	31.3b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.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))))
	15.2b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.7b	(-.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)))))

Compiler

Compiled 1454 to 557 computations (61.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series427.0ms (8%)

Counts

3 → 48

Calls

3 calls:

236.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
182.0ms	(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)))

rewrite19.0ms (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))

simplify104.0ms (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

prune289.0ms (5.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	213	5	218
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	215	12	227

Error

0.0b

Counts

227 → 12

Alt Table

Status	Error	Program
	15.3b	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (sqrt.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))))
▶	0.3b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	24.2b	(-.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)))))
	25.1b	(-.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)))
	0.5b	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (cbrt.f64 (cbrt.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)))) (expm1.f64 (log1p.f64 (cbrt.f64 (cos.f64 y))))) (.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))))
	31.3b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	15.2b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.7b	(-.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)))))
	15.2b	(-.f64 (.f64 (.f64 x (expm1.f64 (log1p.f64 (pow.f64 (cos.f64 y) 2/3)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))

Compiler

Compiled 5513 to 1607 computations (70.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

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)

simplify118.0ms (2.2%)

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

prune231.0ms (4.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	138	11	149

Error

0.0b

Counts

149 → 11

Alt Table

Status	Error	Program
	15.3b	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))) (cbrt.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)) (expm1.f64 (log1p.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))))
	0.4b	(-.f64 (.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (cbrt.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
	0.7b	(-.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)))))
	15.2b	(-.f64 (.f64 (.f64 x (expm1.f64 (log1p.f64 (pow.f64 (cos.f64 y) 2/3)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	25.1b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (pow.f64 (cos.f64 y) 2)) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.5b	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (cbrt.f64 (cbrt.f64 (cos.f64 y))))) (*.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))))
	31.3b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	24.2b	(-.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)))))

Compiler

Compiled 3475 to 1672 computations (51.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series598.0ms (11.3%)

Counts

2 → 24

Calls

2 calls:

428.0ms	(log1p.f64 (cbrt.f64 (cos.f64 y)))
170.0ms	(expm1.f64 (log1p.f64 (cbrt.f64 (cos.f64 y))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-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:

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

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

748×	`distribute-rgt-neg-in_binary64`
636×	`fma-def_binary64`
539×	`associate-l_binary64`
454×	`unswap-sqr_binary64`
442×	`associate-r_binary64`

Counts

46 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	411
1	120	380
2	294	374
3	866	370
4	3194	370
5	4908	370
6	5160	370

prune145.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Error

0.0b

Counts

111 → 10

Alt Table

Status	Error	Program
	0.3b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (log.f64 (exp.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (cos.f64 y))))))) (*.f64 z (sin.f64 y)))
	24.2b	(-.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)))))
	0.4b	(-.f64 (.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (cbrt.f64 (cos.f64 y)))) (*.f64 z (sin.f64 y)))
	0.7b	(-.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)))))
	15.2b	(-.f64 (.f64 (.f64 x (expm1.f64 (log1p.f64 (pow.f64 (cos.f64 y) 2/3)))) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	25.1b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (pow.f64 (cos.f64 y) 2)) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.5b	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (cbrt.f64 (cbrt.f64 (cos.f64 y))))) (*.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))))
	31.3b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.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 2608 to 1293 computations (50.4% saved)

regimes405.0ms (7.6%)

Accuracy

Total 0.1b remaining (58.4%)

Threshold costs 0.1b (58.4%)

Counts

87 → 1

Compiler

Compiled 7148 to 4534 computations (36.6% saved)

simplify3.0ms (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

end1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample2.2s (41.2%)

Algorithm

1×

intervals

Results

999.0ms	2023×	body	1024	valid
401.0ms	4505×	body	128	valid
242.0ms	945×	body	512	valid
96.0ms	522×	body	256	valid
6.0ms	5×	body	2048	valid

Compiler

Compiled 258 to 154 computations (40.3% 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

analyze369.0ms (7%)

sample70.0ms (1.3%)

simplify16.0ms (0.3%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series14.0ms (0.3%)

rewrite7.0ms (0.1%)

simplify102.0ms (1.9%)

prune54.0ms (1%)

localize10.0ms (0.2%)

series427.0ms (8%)

rewrite19.0ms (0.4%)

simplify104.0ms (2%)

prune289.0ms (5.4%)

localize13.0ms (0.3%)

series11.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify118.0ms (2.2%)

prune231.0ms (4.3%)

localize17.0ms (0.3%)

series598.0ms (11.3%)

rewrite1.0ms (0%)

simplify74.0ms (1.4%)

prune145.0ms (2.7%)

regimes405.0ms (7.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.2s (41.2%)

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