Details

analyze434.0ms (9%)

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 (48%)

Results

953.0ms	5909×	body	128	valid
904.0ms	1260×	body	1024	valid
285.0ms	714×	body	512	valid
101.0ms	371×	body	256	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify22.0ms (0.5%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series24.0ms (0.5%)

Counts

3 → 84

Calls

3 calls:

12.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))
6.0ms	(+.f64 x (cos.f64 y))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 61

Calls

3 calls:

5.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
5.0ms	(*.f64 z (sin.f64 y))
2.0ms	(+.f64 x (cos.f64 y))

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-neg_binary64`
503×	`fma-def_binary64`
418×	`associate-l_binary64`
386×	`associate-r_binary64`
239×	`cancel-sign-sub-inv_binary64`

Counts

145 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1641
1	369	1578
2	1084	1530
3	3795	1520
4	4687	1520
5	4866	1520

prune78.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	114	6	120

Error

0.0b

Counts

120 → 6

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	19.4b	(-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3)) (fma.f64 (cos.f64 y) (-.f64 (cos.f64 y) x) (.f64 x x))) (.f64 z (sin.f64 y)))
	34.4b	(-.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (cos.f64 y)) (*.f64 z (sin.f64 y)))
	29.6b	(-.f64 (log1p.f64 (expm1.f64 (+.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
	31.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
▶	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1999 to 623 computations (68.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
✓	0.3b	(*.f64 (cbrt.f64 z) (sin.f64 y))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series252.0ms (5.2%)

Counts

4 → 72

Calls

4 calls:

157.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
37.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
35.0ms	(cbrt.f64 z)
23.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite25.0ms (0.5%)

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:

8.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
7.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify119.0ms (2.5%)

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

prune157.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	196	6	202

Error

Counts

202 → 6

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	19.4b	(-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3)) (fma.f64 (cos.f64 y) (-.f64 (cos.f64 y) x) (.f64 x x))) (.f64 z (sin.f64 y)))
▶	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	34.4b	(-.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (cos.f64 y)) (*.f64 z (sin.f64 y)))
	29.6b	(-.f64 (log1p.f64 (expm1.f64 (+.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
	31.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 4244 to 1145 computations (73% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.5b	(.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z))))
	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z)))

series75.0ms (1.6%)

Counts

2 → 24

Calls

2 calls:

38.0ms	(cbrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z)))
37.0ms	(.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z))))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`cbrt-prod_binary64`
6×	`associate-l_binary64`
6×	`add-cube-cbrt_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 39

Calls

2 calls:

6.0ms	(cbrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z)))
4.0ms	(.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z))))

simplify91.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

411×	`distribute-rgt-in_binary64`
396×	`associate-+l+_binary64`
394×	`log-prod_binary64`
377×	`distribute-lft-in_binary64`
364×	`unswap-sqr_binary64`

Counts

63 → 71

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	480
1	94	432
2	244	400
3	647	400
4	1316	379
5	3447	379
6	4338	379
7	4970	379
8	4788	379

prune158.0ms (3.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	225	6	231

Error

Counts

231 → 6

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
▶	19.4b	(-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3)) (fma.f64 (cos.f64 y) (-.f64 (cos.f64 y) x) (.f64 x x))) (.f64 z (sin.f64 y)))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	34.4b	(-.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (cos.f64 y)) (*.f64 z (sin.f64 y)))
	29.6b	(-.f64 (log1p.f64 (expm1.f64 (+.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
	31.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 6166 to 1516 computations (75.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(fma.f64 (cos.f64 y) (-.f64 (cos.f64 y) x) (*.f64 x x))
✓	0.4b	(pow.f64 (cos.f64 y) 3)
✓	18.7b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3)) (fma.f64 (cos.f64 y) (-.f64 (cos.f64 y) x) (*.f64 x x)))

series171.0ms (3.5%)

Counts

3 → 52

Calls

3 calls:

148.0ms	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3)) (fma.f64 (cos.f64 y) (-.f64 (cos.f64 y) x) (*.f64 x x)))
12.0ms	(pow.f64 (cos.f64 y) 3)
11.0ms	(fma.f64 (cos.f64 y) (-.f64 (cos.f64 y) x) (*.f64 x x))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
20×	`distribute-lft-out_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

3 → 90

Calls

3 calls:

13.0ms	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3)) (fma.f64 (cos.f64 y) (-.f64 (cos.f64 y) x) (*.f64 x x)))
2.0ms	(pow.f64 (cos.f64 y) 3)
0.0ms	(fma.f64 (cos.f64 y) (-.f64 (cos.f64 y) x) (*.f64 x x))

simplify113.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

441×	`unswap-sqr_binary64`
294×	`associate-+r+_binary64`
229×	`fma-def_binary64`
207×	`+-commutative_binary64`
196×	`fma-neg_binary64`

Counts

142 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	319	5179
1	893	4864
2	3905	4848
3	5147	4848

prune169.0ms (3.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	160	6	166

Error

Counts

166 → 6

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
✓	19.4b	(-.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3)) (fma.f64 (cos.f64 y) (-.f64 (cos.f64 y) x) (.f64 x x))) (.f64 z (sin.f64 y)))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	34.4b	(-.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (cos.f64 y)) (*.f64 z (sin.f64 y)))
	29.6b	(-.f64 (log1p.f64 (expm1.f64 (+.f64 x (cos.f64 y)))) (*.f64 z (sin.f64 y)))
	31.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))

Compiler

Compiled 7139 to 3312 computations (53.6% saved)

regimes334.0ms (6.9%)

Accuracy

Total 0.0b remaining (28.7%)

Threshold costs 0.0b (28.7%)

Counts

80 → 1

Compiler

Compiled 6388 to 3958 computations (38% 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	9	14
1	16	14
2	26	14
3	32	14
4	36	14
5	37	14
6	37	14

end87.0ms (1.8%)

Compiler: Compiled 135 to 83 computations (38.5% 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

analyze434.0ms (9%)

sample2.3s (48%)

simplify22.0ms (0.5%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series24.0ms (0.5%)

rewrite15.0ms (0.3%)

simplify97.0ms (2%)

prune78.0ms (1.6%)

localize12.0ms (0.2%)

series252.0ms (5.2%)

rewrite25.0ms (0.5%)

simplify119.0ms (2.5%)

prune157.0ms (3.3%)

localize18.0ms (0.4%)

series75.0ms (1.6%)

rewrite12.0ms (0.3%)

simplify91.0ms (1.9%)

prune158.0ms (3.3%)

localize15.0ms (0.3%)

series171.0ms (3.5%)

rewrite22.0ms (0.5%)

simplify113.0ms (2.3%)

prune169.0ms (3.5%)

regimes334.0ms (6.9%)

simplify3.0ms (0.1%)

end87.0ms (1.8%)

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