Details

analyze508.0ms (8.5%)

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)

sample2.9s (48.7%)

Results

1.5s	2034×	body	1024	valid
750.0ms	4720×	body	128	valid
403.0ms	1024×	body	512	valid
179.0ms	476×	body	256	valid
3.0ms	2×	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

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 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
✓	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(*.f64 x (cos.f64 y))

series30.0ms (0.5%)

Counts

3 → 84

Calls

3 calls:

15.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
8.0ms	(*.f64 x (cos.f64 y))
7.0ms	(*.f64 z (sin.f64 y))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`

Counts

3 → 56

Calls

3 calls:

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

simplify85.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary64`
513×	`fma-def_binary64`
401×	`sub-neg_binary64`
272×	`distribute-rgt-neg-in_binary64`
257×	`*-commutative_binary64`

Counts

140 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	1548
1	342	1505
2	1070	1476
3	2342	1476
4	4338	1476
5	4932	1476

prune105.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	100	10	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Error

0.0b

Counts

111 → 10

Alt Table

Status	Error	Program
	24.4b	(-.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)))))
	28.2b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	16.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	29.9b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (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)))
▶	0.1b	(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
	25.2b	(-.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)))
	31.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (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))))
	27.2b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))

Compiler

Compiled 2024 to 683 computations (66.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

15.0ms

(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

867×	`fma-neg_binary64`
806×	`cancel-sign-sub-inv_binary64`
392×	`associate-l_binary64`
384×	`fma-def_binary64`
326×	`associate-r_binary64`

Counts

46 → 28

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	656
1	90	627
2	214	627
3	626	623
4	2397	623
5	4589	623
6	5113	623

prune67.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	65	10	75

Error

0.0b

Counts

75 → 10

Alt Table

Status	Error	Program
	24.4b	(-.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)))))
	28.2b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	16.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	29.9b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (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)))
✓	0.1b	(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
	25.2b	(-.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)))
	31.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (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))))
	27.2b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))

Compiler

Compiled 1273 to 505 computations (60.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))

series1.0s (17%)

Counts

4 → 72

Calls

4 calls:

589.0ms	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
245.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
172.0ms	(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)))

rewrite26.0ms (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 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))
5.0ms	(.f64 z (.f64 (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))

simplify125.0ms (2.1%)

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

prune231.0ms (3.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	224	3	227
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	225	12	237

Error

0.0b

Counts

237 → 12

Alt Table

Status	Error	Program
	24.4b	(-.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)))))
	3.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
	28.2b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	16.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	29.9b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (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)))
✓	0.1b	(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
	0.7b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))) (cbrt.f64 (sin.f64 y))))
	25.2b	(-.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)))
	31.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	27.2b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (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)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y))))))

Compiler

Compiled 5732 to 1821 computations (68.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.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)))) (log1p.f64 (expm1.f64 (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))

series8.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y)))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-cbrt-cube_binary64`
6×	`cbrt-unprod_binary64`
6×	`prod-exp_binary64`

Counts

1 → 23

Calls

1 calls:

9.0ms

(*.f64 (*.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y)))))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

835×	`fma-def_binary64`
367×	`fma-neg_binary64`
334×	`unswap-sqr_binary64`
301×	`*-commutative_binary64`
300×	`unsub-neg_binary64`

Counts

47 → 40

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	74	881
1	194	421
2	607	411
3	1056	407
4	1918	393
5	3246	393
6	4534	393
7	4961	393

prune227.0ms (3.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	222	12	234

Error

0.0b

Counts

234 → 12

Alt Table

Status	Error	Program
	24.4b	(-.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)))))
	3.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
	28.2b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sin.f64 y))))
	16.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	29.9b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (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)))
✓	0.1b	(fma.f64 x (cos.f64 y) (neg.f64 (*.f64 z (sin.f64 y))))
	0.7b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))) (cbrt.f64 (sin.f64 y))))
	25.2b	(-.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)))
	31.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	27.2b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (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)))) (log1p.f64 (expm1.f64 (cbrt.f64 (sin.f64 y))))))

Compiler

Compiled 5871 to 1719 computations (70.7% saved)

regimes248.0ms (4.2%)

Accuracy

Total 0.1b remaining (61.7%)

Threshold costs 0.1b (61.7%)

Counts

58 → 1

Compiler

Compiled 4220 to 2586 computations (38.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	23	30
2	31	30
3	35	30
4	36	30
5	36	30

end149.0ms (2.5%)

Compiler: Compiled 277 to 158 computations (43% 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

analyze508.0ms (8.5%)

sample2.9s (48.7%)

simplify16.0ms (0.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series30.0ms (0.5%)

rewrite10.0ms (0.2%)

simplify85.0ms (1.4%)

prune105.0ms (1.8%)

localize8.0ms (0.1%)

series15.0ms (0.3%)

rewrite1.0ms (0%)

simplify69.0ms (1.1%)

prune67.0ms (1.1%)

localize12.0ms (0.2%)

series1.0s (17%)

rewrite26.0ms (0.4%)

simplify125.0ms (2.1%)

prune231.0ms (3.9%)

localize14.0ms (0.2%)

series8.0ms (0.1%)

rewrite10.0ms (0.2%)

simplify76.0ms (1.3%)

prune227.0ms (3.8%)

regimes248.0ms (4.2%)

simplify4.0ms (0.1%)

end149.0ms (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