Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 15 to 12 computations (20% saved)

sample4.2s (46.2%)

Results

2.6s	3586×	body	1024	valid
611.0ms	1382×	body	512	valid
391.0ms	2468×	body	128	valid
213.0ms	187×	body	2048	valid
187.0ms	633×	body	256	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify118.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

626×	`associate-/l*_binary64`
509×	`div-sub_binary64`
462×	`times-frac_binary64`
386×	`sub-neg_binary64`
367×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	22	18
2	49	18
3	111	18
4	208	17
5	362	17
6	692	17
7	1513	17
8	3726	17
9	4287	17
10	4857	17
11	4749	17

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

30.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.0b	(*.f64 (cos.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 51 to 34 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cos.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im))))
✓	3.2b	(fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im)))

series37.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

28.0ms	(*.f64 (cos.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im))))
9.0ms	(fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im)))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

8.0ms	(*.f64 (cos.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im))))
1.0ms	(fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im)))

simplify132.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

528×	`fma-def_binary64`
448×	`associate-l_binary64`
436×	`sub-neg_binary64`
372×	`associate-r_binary64`
187×	`associate--r+_binary64`

Counts

68 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	1448
1	335	1322
2	1104	1296
3	4070	1296
4	4976	1296
5	4945	1296

prune91.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	2	73

Error

0.1b

Counts

73 → 2

Alt Table

Status	Error	Program
▶	7.6b	(neg.f64 (+.f64 (.f64 (cos.f64 re) im) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
✓	30.0b	(*.f64 (cos.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im))))

Status

Error

Program

▶

7.6b

(neg.f64 (+.f64 (*.f64 (cos.f64 re) im) (+.f64 (*.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3))) (*.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))

✓

30.0b

(*.f64 (cos.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 1457 to 807 computations (44.6% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 re) (pow.f64 im 3))
✓	0.1b	(*.f64 (cos.f64 re) im)
✓	0.2b	(.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3)))
✓	0.3b	(.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5)))

series113.0ms (1.2%)

Counts

4 → 16

Calls

4 calls:

38.0ms	(.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5)))
33.0ms	(.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3)))
28.0ms	(*.f64 (cos.f64 re) (pow.f64 im 3))
14.0ms	(*.f64 (cos.f64 re) im)

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`
18×	`prod-exp_binary64`
17×	`associate-r_binary64`

Counts

4 → 95

Calls

4 calls:

5.0ms	(.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5)))
5.0ms	(*.f64 (cos.f64 re) (pow.f64 im 3))
5.0ms	(.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3)))
3.0ms	(*.f64 (cos.f64 re) im)

simplify121.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-neg_binary64`
476×	`fma-def_binary64`
346×	`cancel-sign-sub-inv_binary64`
312×	`associate-r_binary64`
258×	`associate-l_binary64`

Counts

111 → 164

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	196	1704
1	473	1481
2	1687	1413
3	3569	1412
4	4870	1410
5	4924	1410

prune236.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	159	5	164
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	159	7	166

Error

0.0b

Counts

166 → 7

Alt Table

Status	Error	Program
✓	7.6b	(neg.f64 (+.f64 (.f64 (cos.f64 re) im) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
✓	30.0b	(*.f64 (cos.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im))))
	46.2b	(neg.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (cos.f64 re)) (sqrt.f64 im)) (.f64 (sqrt.f64 (cos.f64 re)) (sqrt.f64 im))) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
	8.4b	(neg.f64 (+.f64 (.f64 (.f64 (cos.f64 re) (pow.f64 (cbrt.f64 im) 2)) (cbrt.f64 im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5))))))
	28.8b	(neg.f64 (+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 re) (cos.f64 re)) (cos.f64 re)) (.f64 (.f64 im im) im))) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
▶	7.9b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
	38.4b	(neg.f64 (+.f64 (.f64 (.f64 (cos.f64 re) (sqrt.f64 im)) (sqrt.f64 im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5))))))

Compiler

Compiled 5218 to 3121 computations (40.2% saved)

localize39.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (cbrt.f64 (cos.f64 re)) im))
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
	0.3b	(.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5)))
✓	0.3b	(cbrt.f64 (cos.f64 re))

series792.0ms (8.7%)

Counts

3 → 48

Calls

3 calls:

424.0ms	(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
354.0ms	(cbrt.f64 (cos.f64 re))
14.0ms	(.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (cbrt.f64 (cos.f64 re)) im))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
17×	`add-exp-log_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 79

Calls

3 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (cbrt.f64 (cos.f64 re)) im))
6.0ms	(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
1.0ms	(cbrt.f64 (cos.f64 re))

simplify132.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

903×	`fma-neg_binary64`
804×	`fma-def_binary64`
419×	`*-commutative_binary64`
369×	`sub-neg_binary64`
229×	`cancel-sign-sub-inv_binary64`

Counts

127 → 121

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	126	1274
1	281	1120
2	945	1074
3	1893	1046
4	3942	922
5	4995	922
6	4927	922

prune401.0ms (4.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	202	8	210

Error

0.0b

Counts

210 → 8

Alt Table

Status	Error	Program
✓	7.6b	(neg.f64 (+.f64 (.f64 (cos.f64 re) im) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
✓	30.0b	(*.f64 (cos.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im))))
	46.2b	(neg.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (cos.f64 re)) (sqrt.f64 im)) (.f64 (sqrt.f64 (cos.f64 re)) (sqrt.f64 im))) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
	8.4b	(neg.f64 (+.f64 (.f64 (.f64 (cos.f64 re) (pow.f64 (cbrt.f64 im) 2)) (cbrt.f64 im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5))))))
▶	8.1b	(neg.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re)))) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re))))) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re))))) (.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
	28.8b	(neg.f64 (+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 re) (cos.f64 re)) (cos.f64 re)) (.f64 (.f64 im im) im))) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
✓	7.9b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
	38.4b	(neg.f64 (+.f64 (.f64 (.f64 (cos.f64 re) (sqrt.f64 im)) (sqrt.f64 im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5))))))

Compiler

Compiled 7957 to 3877 computations (51.3% saved)

localize39.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re)))) (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re)))))
	0.3b	(.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5)))
	0.3b	(cbrt.f64 (cos.f64 re))
✓	0.3b	(cbrt.f64 (cbrt.f64 (cos.f64 re)))

series638.0ms (7%)

Counts

2 → 24

Calls

2 calls:

327.0ms	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re)))) (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re)))))
311.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 re)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`pow1_binary64`
49×	`pow-prod-up_binary64`
45×	`pow1/3_binary64`
33×	`pow-sqr_binary64`
32×	`pow-prod-down_binary64`

Counts

2 → 92

Calls

2 calls:

16.0ms	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re)))) (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re)))))
1.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 re)))

simplify153.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
511×	`sub-neg_binary64`
488×	`unswap-sqr_binary64`
376×	`distribute-rgt-neg-in_binary64`
360×	`cancel-sign-sub-inv_binary64`

Counts

116 → 96

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	92	1069
1	175	858
2	403	842
3	1117	810
4	3050	806
5	4340	806
6	4469	806
7	4948	806
8	4876	806

prune848.0ms (9.3%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	423	8	431

Error

0.0b

Counts

431 → 8

Alt Table

Status	Error	Program
✓	7.6b	(neg.f64 (+.f64 (.f64 (cos.f64 re) im) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
✓	30.0b	(*.f64 (cos.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 1/2 (exp.f64 im))))
	46.2b	(neg.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (cos.f64 re)) (sqrt.f64 im)) (.f64 (sqrt.f64 (cos.f64 re)) (sqrt.f64 im))) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
	8.4b	(neg.f64 (+.f64 (.f64 (.f64 (cos.f64 re) (pow.f64 (cbrt.f64 im) 2)) (cbrt.f64 im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5))))))
✓	8.1b	(neg.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re)))) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re))))) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re))))) (.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
	28.8b	(neg.f64 (+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 re) (cos.f64 re)) (cos.f64 re)) (.f64 (.f64 im im) im))) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
✓	7.9b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (.f64 (cbrt.f64 (cos.f64 re)) im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (*.f64 (cos.f64 re) (pow.f64 im 5))))))
	38.4b	(neg.f64 (+.f64 (.f64 (.f64 (cos.f64 re) (sqrt.f64 im)) (sqrt.f64 im)) (+.f64 (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3))) (.f64 1/120 (.f64 (cos.f64 re) (pow.f64 im 5))))))

Compiler

Compiled 24846 to 8426 computations (66.1% saved)

regimes612.0ms (6.7%)

Accuracy

Total 0.2b remaining (83.2%)

Threshold costs 0.2b (83.2%)

Counts

53 → 3

Compiler

Compiled 9696 to 6072 computations (37.4% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
15×	`+-commutative_binary64`
13×	`sub-neg_binary64`
12×	`neg-mul-1_binary64`
11×	`neg-sub0_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	85
1	56	85
2	78	83
3	109	83
4	132	83
5	143	83
6	149	83
7	151	83
8	149	83

end233.0ms (2.6%)

Compiler: Compiled 366 to 215 computations (41.3% saved)

Details

analyze3.0ms (0%)

sample4.2s (46.2%)

simplify118.0ms (1.3%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series37.0ms (0.4%)

rewrite10.0ms (0.1%)

simplify132.0ms (1.5%)

prune91.0ms (1%)

localize30.0ms (0.3%)

series113.0ms (1.2%)

rewrite23.0ms (0.3%)

simplify121.0ms (1.3%)

prune236.0ms (2.6%)

localize39.0ms (0.4%)

series792.0ms (8.7%)

rewrite23.0ms (0.3%)

simplify132.0ms (1.5%)

prune401.0ms (4.4%)

localize39.0ms (0.4%)

series638.0ms (7%)

rewrite28.0ms (0.3%)

simplify153.0ms (1.7%)

prune848.0ms (9.3%)

regimes612.0ms (6.7%)

bsearch5.0ms (0.1%)

simplify14.0ms (0.2%)

end233.0ms (2.6%)

Profiling