Details

analyze428.0ms (7.5%)

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)

sample2.3s (40.7%)

Results

930.0ms	1323×	body	1024	valid
892.0ms	5877×	body	128	valid
331.0ms	686×	body	512	valid
103.0ms	368×	body	256	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

230×	`fma-def_binary64`
171×	`fma-neg_binary64`
66×	`cancel-sign-sub-inv_binary64`
44×	`associate--r+_binary64`
44×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	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 4 expressions with local error:

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

series30.0ms (0.5%)

Counts

4 → 88

Calls

4 calls:

19.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
6.0ms	(*.f64 z (sin.f64 y))
4.0ms	(+.f64 x (cos.f64 y))
1.0ms	(cos.f64 y)

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64`
9×	`add-cube-cbrt_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 70

Calls

4 calls:

9.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
3.0ms	(*.f64 z (sin.f64 y))
2.0ms	(+.f64 x (cos.f64 y))
1.0ms	(cos.f64 y)

simplify95.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-neg_binary64`
528×	`fma-def_binary64`
418×	`associate-l_binary64`
386×	`associate-r_binary64`
267×	`cancel-sign-sub-inv_binary64`

Counts

158 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	1750
1	389	1683
2	1120	1631
3	3858	1621
4	4733	1621
5	4889	1621

prune116.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	129	9	138

Error

0.0b

Counts

138 → 9

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	26.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
	20.8b	(-.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)))))
	13.5b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	32.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	0.4b	(-.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))))
	31.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	42.8b	(log.f64 (/.f64 (exp.f64 (+.f64 x (cos.f64 y))) (exp.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 2343 to 791 computations (66.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series230.0ms (4%)

Counts

4 → 72

Calls

4 calls:

136.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
35.0ms	(cbrt.f64 z)
34.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
25.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
3.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify110.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-def_binary64`
720×	`fma-neg_binary64`
501×	`cancel-sign-sub-inv_binary64`
496×	`*-commutative_binary64`
395×	`unswap-sqr_binary64`

Counts

175 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1734
1	311	1507
2	1181	1430
3	2385	1407
4	4566	1395
5	4973	1395
6	4943	1395

prune204.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	195	10	205

Error

0.0b

Counts

205 → 10

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 2) (cbrt.f64 (cbrt.f64 z)))) (.f64 (cbrt.f64 z) (sin.f64 y))))
	26.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
	13.5b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	32.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
▶	0.4b	(-.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))))
	3.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 (.f64 z (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y))))))
	0.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (sin.f64 y))) (cbrt.f64 (.f64 (cbrt.f64 z) (sin.f64 y)))) (cbrt.f64 (*.f64 (cbrt.f64 z) (sin.f64 y))))))
	31.8b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	42.8b	(log.f64 (/.f64 (exp.f64 (+.f64 x (cos.f64 y))) (exp.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 4448 to 1247 computations (72% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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))

series779.0ms (13.6%)

Counts

4 → 72

Calls

4 calls:

463.0ms	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
181.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
128.0ms	(cbrt.f64 (sin.f64 y))
6.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))

rewrite25.0ms (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))

simplify120.0ms (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

prune282.0ms (4.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	224	3	227
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	228	9	237

Error

Counts

237 → 9

Alt Table

Status	Error	Program
	13.5b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	32.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (.f64 (cbrt.f64 (sqrt.f64 (sin.f64 y))) (pow.f64 (sin.f64 y) 1/6)) (*.f64 (cbrt.f64 (sqrt.f64 (sin.f64 y))) (pow.f64 (sin.f64 y) 1/6)))) (cbrt.f64 (sin.f64 y))))
	1.0b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
	32.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
▶	0.8b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y))))
	26.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	3.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 (.f64 z (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y))))))
	42.8b	(log.f64 (/.f64 (exp.f64 (+.f64 x (cos.f64 y))) (exp.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 5616 to 1769 computations (68.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 y) 2)
✓	0.3b	(.f64 (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)))
	0.6b	(cbrt.f64 (sin.f64 y))
✓	12.4b	(cbrt.f64 (pow.f64 (sin.f64 y) 2))

series205.0ms (3.6%)

Counts

3 → 40

Calls

3 calls:

193.0ms	(cbrt.f64 (pow.f64 (sin.f64 y) 2))
6.0ms	(.f64 (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)))
5.0ms	(pow.f64 (sin.f64 y) 2)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`

Counts

3 → 61

Calls

3 calls:

6.0ms	(.f64 (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)))
2.0ms	(pow.f64 (sin.f64 y) 2)
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 y) 2))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-neg_binary64`
646×	`fma-def_binary64`
323×	`*-commutative_binary64`
277×	`cancel-sign-sub-inv_binary64`
166×	`associate-+l+_binary64`

Counts

101 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1408
1	340	1189
2	1039	1141
3	2077	1133
4	4356	1133
5	4890	1133

prune156.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	130	9	139

Error

Counts

139 → 9

Alt Table

Status	Error	Program
	13.5b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	1.0b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3)) (cbrt.f64 (sin.f64 y))))
	32.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.8b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y))))
	32.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sqrt.f64 (sin.f64 y)))) (cbrt.f64 (sqrt.f64 (sin.f64 y)))))
	26.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	3.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 (.f64 z (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y))))))
	42.8b	(log.f64 (/.f64 (exp.f64 (+.f64 x (cos.f64 y))) (exp.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 3034 to 1440 computations (52.5% saved)

regimes309.0ms (5.4%)

Accuracy

Total 0.0b remaining (68.8%)

Threshold costs 0.0b (68.8%)

Counts

71 → 1

Compiler

Compiled 5324 to 3258 computations (38.8% 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

end128.0ms (2.2%)

Compiler: Compiled 191 to 122 computations (36.1% saved)

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14

Details

analyze428.0ms (7.5%)

sample2.3s (40.7%)

simplify21.0ms (0.4%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series30.0ms (0.5%)

rewrite17.0ms (0.3%)

simplify95.0ms (1.7%)

prune116.0ms (2%)

localize10.0ms (0.2%)

series230.0ms (4%)

rewrite21.0ms (0.4%)

simplify110.0ms (1.9%)

prune204.0ms (3.5%)

localize13.0ms (0.2%)

series779.0ms (13.6%)

rewrite25.0ms (0.4%)

simplify120.0ms (2.1%)

prune282.0ms (4.9%)

localize13.0ms (0.2%)

series205.0ms (3.6%)

rewrite11.0ms (0.2%)

simplify74.0ms (1.3%)

prune156.0ms (2.7%)

regimes309.0ms (5.4%)

simplify3.0ms (0%)

end128.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14