Details

analyze1.7s (8.4%)

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
0%	93.7%	6.3%	7
0%	93.7%	6.3%	8
0%	90.5%	9.5%	9
0%	90.5%	9.5%	10
0%	89%	11%	11
0%	89%	11%	12
0%	88.2%	11.8%	13
0%	88.2%	11.8%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample14.8s (75.3%)

Results

8.9s	4088×	body	8192	exit
3.4s	4983×	body	1024	valid
727.0ms	1784×	body	512	valid
610.0ms	1028×	body	1024	invalid
409.0ms	421×	body	2048	valid
199.0ms	703×	body	256	valid
188.0ms	543×	body	512	invalid
72.0ms	261×	body	256	invalid
60.0ms	376×	body	128	invalid
54.0ms	365×	body	128	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify82.0ms (0.4%)

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

58.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	58.6b	(.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)

localize8.0ms (0%)

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)))
✓	4.3b	(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

series22.0ms (0.1%)

Counts

2 → 36

Calls

2 calls:

20.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
2.0ms	(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

rewrite64.0ms (0.3%)

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)))
10.0ms	(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

simplify192.0ms (1%)

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

prune143.0ms (0.7%)

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
▶	0.5b	(neg.f64 (+.f64 (.f64 (cos.f64 re) im) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
✓	58.6b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	60.3b	(exp.f64 (+.f64 (log.f64 (*.f64 1/2 (cos.f64 re))) (log.f64 (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

Compiler

Compiled 10209 to 3835 computations (62.4% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

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

series45.0ms (0.2%)

Counts

3 → 12

Calls

3 calls:

19.0ms	(.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3)))
18.0ms	(*.f64 (cos.f64 re) (pow.f64 im 3))
8.0ms	(*.f64 (cos.f64 re) im)

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
12×	`add-cbrt-cube_binary64`
11×	`prod-exp_binary64`

Counts

3 → 74

Calls

3 calls:

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

simplify108.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-neg_binary64`
443×	`*-commutative_binary64`
358×	`fma-def_binary64`
274×	`distribute-rgt-neg-in_binary64`
261×	`cancel-sign-sub-inv_binary64`

Counts

86 → 127

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	1257
1	336	1102
2	1177	1062
3	2719	1055
4	4782	1029
5	4979	1029
6	4932	1029

prune109.0ms (0.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	121	6	127
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	121	9	130

Error

0.1b

Counts

130 → 9

Alt Table

Status	Error	Program
▶	1.8b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (.f64 (cos.f64 re) im))) (cbrt.f64 (.f64 (cos.f64 re) im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	39.0b	(neg.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 im (cos.f64 re)) 3)) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
✓	0.5b	(neg.f64 (+.f64 (.f64 (cos.f64 re) im) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
✓	58.6b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	1.9b	(neg.f64 (+.f64 (.f64 (.f64 (cos.f64 re) (pow.f64 (cbrt.f64 im) 2)) (cbrt.f64 im)) (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3)))))
	16.5b	(neg.f64 (+.f64 (.f64 (sqrt.f64 (cos.f64 re)) (.f64 (sqrt.f64 (cos.f64 re)) im)) (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3)))))
	38.7b	(neg.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (cos.f64 re)) (sqrt.f64 im)) (.f64 (sqrt.f64 (cos.f64 re)) (sqrt.f64 im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	30.7b	(neg.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 re) im)) (sqrt.f64 (.f64 (cos.f64 re) im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	60.3b	(exp.f64 (+.f64 (log.f64 (*.f64 1/2 (cos.f64 re))) (log.f64 (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

Compiler

Compiled 2931 to 1663 computations (43.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (.f64 (cos.f64 re) im))) (cbrt.f64 (*.f64 (cos.f64 re) im)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (*.f64 (cos.f64 re) im)))
✓	0.6b	(cbrt.f64 (*.f64 (cos.f64 re) im))

series1.2s (6.2%)

Counts

3 → 72

Calls

3 calls:

746.0ms

(*.f64 (cbrt.f64 (*.f64 (cos.f64 re) im)) (cbrt.f64 (*.f64 (cos.f64 re) im)))

457.0ms

(cbrt.f64 (*.f64 (cos.f64 re) im))

20.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 re) im)) (cbrt.f64 (*.f64 (cos.f64 re) im))) (cbrt.f64 (*.f64 (cos.f64 re) im)))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 re) im)) (cbrt.f64 (*.f64 (cos.f64 re) im))) (cbrt.f64 (*.f64 (cos.f64 re) im)))

4.0ms

(*.f64 (cbrt.f64 (*.f64 (cos.f64 re) im)) (cbrt.f64 (*.f64 (cos.f64 re) im)))

4.0ms

(cbrt.f64 (*.f64 (cos.f64 re) im))

simplify96.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-neg_binary64`
515×	`cancel-sign-sub-inv_binary64`
364×	`*-commutative_binary64`
340×	`fma-def_binary64`
319×	`distribute-rgt-neg-in_binary64`

Counts

151 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	158	1975
1	378	1721
2	1157	1533
3	2707	1398
4	4805	1398
5	4921	1398

prune146.0ms (0.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	237	11	248

Error

0.0b

Counts

248 → 11

Alt Table

Status	Error	Program
	16.5b	(neg.f64 (+.f64 (.f64 (sqrt.f64 (cos.f64 re)) (.f64 (sqrt.f64 (cos.f64 re)) im)) (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3)))))
	3.3b	(neg.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 im (cos.f64 re)))) 8) (cbrt.f64 (cbrt.f64 (.f64 (cos.f64 re) im)))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
✓	1.8b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (.f64 (cos.f64 re) im))) (cbrt.f64 (.f64 (cos.f64 re) im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	39.0b	(neg.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 im (cos.f64 re)) 3)) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
✓	0.5b	(neg.f64 (+.f64 (.f64 (cos.f64 re) im) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
✓	58.6b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
▶	1.8b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (.f64 (cos.f64 re) im))) (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	28.1b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (cos.f64 re) (/.f64 -1 im)) 2)) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 (.f64 (cos.f64 re) im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	1.9b	(neg.f64 (+.f64 (.f64 (.f64 (cos.f64 re) (pow.f64 (cbrt.f64 im) 2)) (cbrt.f64 im)) (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3)))))
	30.7b	(neg.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 re) im)) (sqrt.f64 (.f64 (cos.f64 re) im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	60.3b	(exp.f64 (+.f64 (log.f64 (*.f64 1/2 (cos.f64 re))) (log.f64 (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

Compiler

Compiled 7919 to 3259 computations (58.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (.f64 (cos.f64 re) im))) (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 im)))
	0.5b	(.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (*.f64 (cos.f64 re) im)))
	0.6b	(cbrt.f64 (*.f64 (cos.f64 re) im))
✓	0.6b	(cbrt.f64 im)

series55.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

32.0ms	(cbrt.f64 im)
22.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (.f64 (cos.f64 re) im))) (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 im)))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64`
14×	`pow1_binary64`
13×	`pow-prod-down_binary64`
13×	`pow1/3_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 41

Calls

2 calls:

12.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (.f64 (cos.f64 re) im))) (*.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 im)))
1.0ms	(cbrt.f64 im)

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

956×	`fma-neg_binary64`
524×	`cancel-sign-sub-inv_binary64`
432×	`fma-def_binary64`
411×	`*-commutative_binary64`
354×	`unswap-sqr_binary64`

Counts

77 → 62

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	86	973
1	205	880
2	716	872
3	1505	866
4	3222	516
5	4336	516
6	4887	516

prune125.0ms (0.6%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	182	3	185
Fresh	1	6	7
Picked	0	1	1
Done	0	3	3
Total	183	13	196

Error

0.0b

Counts

196 → 13

Alt Table

Status	Error	Program
✓	0.5b	(neg.f64 (+.f64 (.f64 (cos.f64 re) im) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	28.1b	(neg.f64 (+.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 im (cos.f64 re)) 2)) (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	28.1b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (cos.f64 re) (/.f64 -1 im)) 2)) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 (.f64 (cos.f64 re) im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	2.4b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 im (cos.f64 re)))) (cbrt.f64 (cbrt.f64 (.f64 im (cos.f64 re))))) (cbrt.f64 (cbrt.f64 (.f64 im (cos.f64 re)))))) (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	16.5b	(neg.f64 (+.f64 (.f64 (sqrt.f64 (cos.f64 re)) (.f64 (sqrt.f64 (cos.f64 re)) im)) (.f64 1/6 (.f64 (cos.f64 re) (pow.f64 im 3)))))
	3.3b	(neg.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 im (cos.f64 re)))) 8) (cbrt.f64 (cbrt.f64 (.f64 (cos.f64 re) im)))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
✓	1.8b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (.f64 (cos.f64 re) im))) (cbrt.f64 (.f64 (cos.f64 re) im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	39.0b	(neg.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 im (cos.f64 re)) 3)) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
✓	58.6b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
✓	1.8b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (.f64 (cos.f64 re) im))) (.f64 (cbrt.f64 (cos.f64 re)) (cbrt.f64 im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	2.1b	(neg.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 re) im)) (cbrt.f64 (.f64 (cos.f64 re) im))) (.f64 (cbrt.f64 (cos.f64 re)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 im) (cbrt.f64 im))) (cbrt.f64 (cbrt.f64 im))))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	30.7b	(neg.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 re) im)) (sqrt.f64 (.f64 (cos.f64 re) im))) (.f64 1/6 (*.f64 (cos.f64 re) (pow.f64 im 3)))))
	60.3b	(exp.f64 (+.f64 (log.f64 (*.f64 1/2 (cos.f64 re))) (log.f64 (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))))

Compiler

Compiled 6219 to 2506 computations (59.7% saved)

regimes376.0ms (1.9%)

Accuracy

Total 0.8b remaining (91.4%)

Threshold costs 0.8b (91.4%)

Counts

58 → 1

Compiler

Compiled 8345 to 5388 computations (35.4% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	23	22
2	44	20
3	61	20
4	71	20
5	76	20
6	77	20
7	76	20

end219.0ms (1.1%)

Compiler: Compiled 367 to 231 computations (37.1% saved)

Details

analyze1.7s (8.4%)

sample14.8s (75.3%)

simplify82.0ms (0.4%)

prune3.0ms (0%)

localize8.0ms (0%)

series22.0ms (0.1%)

rewrite64.0ms (0.3%)

simplify192.0ms (1%)

prune143.0ms (0.7%)

localize9.0ms (0%)

series45.0ms (0.2%)

rewrite15.0ms (0.1%)

simplify108.0ms (0.5%)

prune109.0ms (0.6%)

localize12.0ms (0.1%)

series1.2s (6.2%)

rewrite19.0ms (0.1%)

simplify96.0ms (0.5%)

prune146.0ms (0.7%)

localize19.0ms (0.1%)

series55.0ms (0.3%)

rewrite15.0ms (0.1%)

simplify78.0ms (0.4%)

prune125.0ms (0.6%)

regimes376.0ms (1.9%)

simplify6.0ms (0%)

end219.0ms (1.1%)

Profiling