Details

analyze1.2s (15.3%)

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
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12
76.5%	23.4%	0.1%	13
81.9%	17.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.4s (29.8%)

Results

1.1s	1400×	body	1024	valid
963.0ms	5872×	body	128	valid
284.0ms	669×	body	512	valid
94.0ms	313×	body	256	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	22	12
3	26	12
4	26	12

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series23.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

19.0ms	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
4.0ms	(+.f64 x (sin.f64 y))

rewrite53.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

838×	`log1p-expm1-u_binary64`
838×	`expm1-log1p-u_binary64`
564×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
81×	`add-log-exp_binary64`

Counts

2 → 60

Calls

2 calls:

51.0ms	(+.f64 x (sin.f64 y))
51.0ms	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	167	18
2	2097	18
3	6179	18
0	0	0
1	0	0

simplify87.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-def_binary64`
473×	`sub-neg_binary64`
443×	`unswap-sqr_binary64`
356×	`distribute-rgt-neg-in_binary64`
355×	`cancel-sign-sub-inv_binary64`

Counts

120 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	544
1	100	542
2	244	535
3	703	531
4	2177	531
5	3696	531
6	4608	531
7	4922	531

prune58.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	3	82

Error

0.0b

Counts

82 → 3

Alt Table

Status	Error	Program
▶	1.4b	(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2))
	29.8b	(pow.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2)
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 1130 to 380 computations (66.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2)
✓	0.6b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))

series880.0ms (10.8%)

Counts

3 → 108

Calls

3 calls:

477.0ms

(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2)

389.0ms

(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))

14.0ms

(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2))

rewrite142.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

622×	`prod-diff_binary64`
479×	`fma-udef_binary64`
233×	`fma-def_binary64`
198×	`expm1-udef_binary64`
198×	`log1p-udef_binary64`

Counts

3 → 82

Calls

3 calls:

140.0ms

(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2))

140.0ms

(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2)

140.0ms

(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	230	41
2	2605	41
3	4807	41
4	4929	41
5	4992	41
6	4918	41
0	0	0
1	0	0

simplify118.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

773×	`times-frac_binary64`
550×	`fma-def_binary64`
505×	`associate-/r*_binary64`
473×	`associate-/l*_binary64`
233×	`*-commutative_binary64`

Counts

190 → 209

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	601	7014
1	2043	6698
2	5587	6698

prune334.0ms (4.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	366	2	368
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	366	5	371

Error

0.0b

Counts

371 → 5

Alt Table

Status	Error	Program
✓	1.4b	(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2))
	15.6b	(fma.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
▶	1.7b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) 3) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2))
	29.8b	(pow.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2)
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 18361 to 8925 computations (51.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2)
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	0.6b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))
✓	0.8b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) 3)

series968.0ms (11.9%)

Counts

2 → 72

Calls

2 calls:

566.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) 3)
401.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

rewrite114.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

616×	`prod-diff_binary64`
453×	`fma-udef_binary64`
344×	`fma-def_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`

Counts

2 → 47

Calls

2 calls:

112.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
112.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	230	29
2	2676	29
3	4797	29
4	4886	29
5	4946	29
0	0	0
1	0	0

simplify162.0ms (2%)

Algorithm

1×	egg-herbie

Rules

789×	`times-frac_binary64`
580×	`fma-def_binary64`
479×	`associate-/l*_binary64`
209×	`*-commutative_binary64`
135×	`sqr-pow_binary64`

Counts

119 → 157

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	539	6633
1	2004	6404
2	5006	6404

prune580.0ms (7.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	389	0	389
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	389	5	394

Error

0.0b

Counts

394 → 5

Alt Table

Status	Error	Program
✓	1.4b	(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2))
▶	15.6b	(fma.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
✓	1.7b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) 3) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2))
	29.8b	(pow.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2)
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 27464 to 14786 computations (46.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series48.0ms (0.6%)

Counts

3 → 64

Calls

3 calls:

31.0ms	(fma.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
15.0ms	(*.f64 z (sqrt.f64 (cos.f64 y)))
2.0ms	(sqrt.f64 (cos.f64 y))

rewrite65.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
501×	`log-prod_binary64`
235×	`fma-def_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`

Counts

3 → 75

Calls

3 calls:

63.0ms	(fma.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
63.0ms	(sqrt.f64 (cos.f64 y))
63.0ms	(*.f64 z (sqrt.f64 (cos.f64 y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	206	27
2	2536	25
3	5480	25
0	0	0
1	0	0

simplify105.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

703×	`distribute-rgt-neg-in_binary64`
595×	`distribute-lft-neg-in_binary64`
454×	`sub-neg_binary64`
413×	`fma-neg_binary64`
366×	`neg-mul-1_binary64`

Counts

139 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	55	681
1	151	673
2	433	663
3	1404	663
4	3035	663
5	4604	663
6	4991	663

prune137.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	176	6	182

Error

0.0b

Counts

182 → 6

Alt Table

Status	Error	Program
✓	1.4b	(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2))
	15.6b	(fma.f64 (*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 1/4) 2)) (sqrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
✓	1.7b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) 3) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2))
	15.6b	(fma.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 y)))) (+.f64 x (sin.f64 y)))
	29.8b	(pow.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2)
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 3116 to 905 computations (71% saved)

regimes421.0ms (5.2%)

Accuracy

Total 0.0b remaining (49%)

Threshold costs 0.0b (49%)

Counts

69 → 1

Compiler

Compiled 4720 to 2978 computations (36.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

end107.0ms (1.3%)

Compiler: Compiled 135 to 80 computations (40.7% saved)

Details

analyze1.2s (15.3%)

sample2.4s (29.8%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series23.0ms (0.3%)

rewrite53.0ms (0.6%)

simplify87.0ms (1.1%)

prune58.0ms (0.7%)

localize12.0ms (0.1%)

series880.0ms (10.8%)

rewrite142.0ms (1.7%)

simplify118.0ms (1.4%)

prune334.0ms (4.1%)

localize15.0ms (0.2%)

series968.0ms (11.9%)

rewrite114.0ms (1.4%)

simplify162.0ms (2%)

prune580.0ms (7.1%)

localize10.0ms (0.1%)

series48.0ms (0.6%)

rewrite65.0ms (0.8%)

simplify105.0ms (1.3%)

prune137.0ms (1.7%)

regimes421.0ms (5.2%)

simplify5.0ms (0.1%)

end107.0ms (1.3%)

Profiling