Details

analyze1.0ms (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)

sample3.3s (44.9%)

Results

2.0s	3516×	body	1024	valid
509.0ms	1467×	body	512	valid
299.0ms	2497×	body	128	valid
205.0ms	212×	body	2048	valid
138.0ms	564×	body	256	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify85.0ms (1.2%)

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

2 alts after pruning (2 fresh and 0 done)

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

Error

27.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.3b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 53 to 38 computations (28.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
✓	3.0b	(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

series21.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

18.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
3.0ms	(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

rewrite75.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`prod-diff_binary64`
138×	`*-un-lft-identity_binary64`
138×	`add-sqr-sqrt_binary64`
134×	`add-cube-cbrt_binary64`
130×	`exp-sum_binary64`

Counts

2 → 210

Calls

2 calls:

17.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
11.0ms	(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

simplify208.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-neg_binary64`
353×	`associate-l_binary64`
348×	`cancel-sign-sub-inv_binary64`
337×	`associate-r_binary64`
312×	`distribute-rgt-in_binary64`

Counts

246 → 262

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	385	6318
1	601	5551
2	2210	4517
3	4561	4512
4	5041	4512

prune181.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	260	3	263

Error

0.1b

Counts

263 → 3

Alt Table

Status	Error	Program
✓	27.3b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	61.5b	(.f64 (.f64 1/2 (cos.f64 re)) (/.f64 (-.f64 (.f64 (exp.f64 (-.f64 0 im)) (exp.f64 (-.f64 0 im))) (.f64 (exp.f64 im) (exp.f64 im))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
▶	9.2b	(.f64 (cos.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))

Compiler

Compiled 10229 to 3847 computations (62.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3)))
✓	0.1b	(.f64 (cos.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
✓	0.1b	(*.f64 1/6 (pow.f64 im 3))

series33.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

25.0ms	(.f64 (cos.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
4.0ms	(-.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3)))
3.0ms	(*.f64 1/6 (pow.f64 im 3))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`prod-diff_binary64`
30×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`

Counts

3 → 115

Calls

3 calls:

7.0ms	(.f64 (cos.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
5.0ms	(*.f64 1/6 (pow.f64 im 3))
4.0ms	(-.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3)))

simplify104.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-neg_binary64`
674×	`fma-def_binary64`
290×	`cancel-sign-sub-inv_binary64`
206×	`associate-r_binary64`
200×	`distribute-rgt-in_binary64`

Counts

151 → 175

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	2805
1	452	2369
2	1443	2152
3	4472	2150
4	4877	2150

prune192.0ms (2.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	167	8	175
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	167	11	178

Error

0.0b

Counts

178 → 11

Alt Table

Status	Error	Program
✓	9.2b	(.f64 (cos.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	9.8b	(.f64 (cos.f64 re) (fma.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im)) (neg.f64 (cbrt.f64 im)) (*.f64 (pow.f64 im 3) -1/6)))
	9.8b	(.f64 (.f64 (cos.f64 re) (.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))) (cbrt.f64 (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3)))))
	21.1b	(*.f64 (cos.f64 re) (cbrt.f64 (pow.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) 3)))
▶	9.5b	(.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cbrt.f64 (cos.f64 re))))
✓	27.3b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	42.2b	(/.f64 (.f64 (cos.f64 re) (fma.f64 (pow.f64 im 6) -1/36 (.f64 im im))) (+.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3))))
	61.5b	(.f64 (.f64 1/2 (cos.f64 re)) (/.f64 (-.f64 (.f64 (exp.f64 (-.f64 0 im)) (exp.f64 (-.f64 0 im))) (.f64 (exp.f64 im) (exp.f64 im))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
	38.4b	(.f64 (sqrt.f64 (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cos.f64 re))) (sqrt.f64 (*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cos.f64 re))))
	9.9b	(.f64 (.f64 (cbrt.f64 (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cos.f64 re))) (cbrt.f64 (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cos.f64 re)))) (cbrt.f64 (*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cos.f64 re))))
	36.2b	(.f64 (.f64 (cos.f64 re) (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (-.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3)))))

Compiler

Compiled 3886 to 2431 computations (37.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series785.0ms (10.7%)

Counts

4 → 72

Calls

4 calls:

311.0ms	(*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cbrt.f64 (cos.f64 re)))
251.0ms	(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
197.0ms	(cbrt.f64 (cos.f64 re))
26.0ms	(.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cbrt.f64 (cos.f64 re))))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

9.0ms	(*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cbrt.f64 (cos.f64 re)))
8.0ms	(.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cbrt.f64 (cos.f64 re))))
5.0ms	(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
1.0ms	(cbrt.f64 (cos.f64 re))

simplify110.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

435×	`cancel-sign-sub-inv_binary64`
373×	`neg-mul-1_binary64`
365×	`associate-r_binary64`
330×	`associate-l_binary64`
284×	`unswap-sqr_binary64`

Counts

184 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	3669
1	567	2796
2	2390	2743
3	4145	2726
4	4972	2726

prune311.0ms (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	239	5	244
Fresh	5	3	8
Picked	1	0	1
Done	0	2	2
Total	245	10	255

Error

0.0b

Counts

255 → 10

Alt Table

Status	Error	Program
▶	9.5b	(.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 re))))))
✓	27.3b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
✓	9.2b	(.f64 (cos.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	9.8b	(.f64 (cos.f64 re) (fma.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im)) (neg.f64 (cbrt.f64 im)) (*.f64 (pow.f64 im 3) -1/6)))
	9.5b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))) (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) 4)) (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cbrt.f64 (cos.f64 re))))
	22.6b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 (cos.f64 re) 2/3))) (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cbrt.f64 (cos.f64 re))))
	22.6b	(.f64 (cbrt.f64 (cos.f64 re)) (.f64 (pow.f64 (cos.f64 re) 2/3) (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))
	9.5b	(.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))) (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) (cbrt.f64 (cbrt.f64 (cos.f64 re)))) (cbrt.f64 (cbrt.f64 (cos.f64 re))))))
	61.5b	(.f64 (.f64 1/2 (cos.f64 re)) (/.f64 (-.f64 (.f64 (exp.f64 (-.f64 0 im)) (exp.f64 (-.f64 0 im))) (.f64 (exp.f64 im) (exp.f64 im))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
	36.2b	(.f64 (.f64 (cos.f64 re) (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (-.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3)))))

Compiler

Compiled 6617 to 3208 computations (51.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 re))))
	0.2b	(*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))
	0.3b	(cbrt.f64 (cos.f64 re))
✓	0.7b	(expm1.f64 (cbrt.f64 (cos.f64 re)))

series367.0ms (5%)

Counts

2 → 24

Calls

2 calls:

184.0ms	(expm1.f64 (cbrt.f64 (cos.f64 re)))
183.0ms	(log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 re))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (cbrt.f64 (cos.f64 re)))
0.0ms	(log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 re))))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Rules

562×	`cancel-sign-sub-inv_binary64`
551×	`distribute-rgt-neg-in_binary64`
463×	`distribute-lft-neg-in_binary64`
443×	`sub-neg_binary64`
309×	`neg-mul-1_binary64`

Counts

46 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	440
1	148	405
2	404	395
3	1300	392
4	3119	392
5	4583	392
6	4947	392

prune440.0ms (6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	180	9	189

Error

0.0b

Counts

189 → 9

Alt Table

Status	Error	Program
	61.5b	(.f64 (.f64 1/2 (cos.f64 re)) (/.f64 (-.f64 (.f64 (exp.f64 (-.f64 0 im)) (exp.f64 (-.f64 0 im))) (.f64 (exp.f64 im) (exp.f64 im))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
	9.5b	(.f64 (exp.f64 (log.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re))))) (*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 re))))))
✓	9.2b	(.f64 (cos.f64 re) (-.f64 (neg.f64 im) (.f64 1/6 (pow.f64 im 3))))
	9.8b	(.f64 (cos.f64 re) (fma.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im)) (neg.f64 (cbrt.f64 im)) (*.f64 (pow.f64 im 3) -1/6)))
	9.5b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 (cos.f64 re)))) (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 re))) 4)) (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cbrt.f64 (cos.f64 re))))
	22.6b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 (cos.f64 re) 2/3))) (.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (cbrt.f64 (cos.f64 re))))
	22.6b	(.f64 (cbrt.f64 (cos.f64 re)) (.f64 (pow.f64 (cos.f64 re) 2/3) (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))
✓	27.3b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	36.2b	(.f64 (.f64 (cos.f64 re) (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (-.f64 (neg.f64 im) (*.f64 1/6 (pow.f64 im 3)))))

Compiler

Compiled 4891 to 2168 computations (55.7% saved)

regimes748.0ms (10.2%)

Accuracy

Total 0.1b remaining (69.8%)

Threshold costs 0.1b (69.8%)

Counts

102 → 3

Compiler

Compiled 12840 to 8688 computations (32.3% saved)

bsearch4.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
11×	`+-commutative_binary64`
10×	`sub-neg_binary64`
9×	`neg-mul-1_binary64`
8×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	73
1	49	71
2	80	71
3	103	71
4	113	71
5	117	71
6	118	71
7	115	71

end194.0ms (2.7%)

Compiler: Compiled 283 to 187 computations (33.9% saved)

Details

analyze1.0ms (0%)

sample3.3s (44.9%)

simplify85.0ms (1.2%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series21.0ms (0.3%)

rewrite75.0ms (1%)

simplify208.0ms (2.8%)

prune181.0ms (2.5%)

localize9.0ms (0.1%)

series33.0ms (0.4%)

rewrite24.0ms (0.3%)

simplify104.0ms (1.4%)

prune192.0ms (2.6%)

localize13.0ms (0.2%)

series785.0ms (10.7%)

rewrite29.0ms (0.4%)

simplify110.0ms (1.5%)

prune311.0ms (4.2%)

localize14.0ms (0.2%)

series367.0ms (5%)

rewrite1.0ms (0%)

simplify73.0ms (1%)

prune440.0ms (6%)

regimes748.0ms (10.2%)

bsearch4.0ms (0%)

simplify5.0ms (0.1%)

end194.0ms (2.7%)

Profiling