Details

analyze680.0ms (12.5%)

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
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 32 to 21 computations (34.4% saved)

sample51.0ms (0.9%)

Algorithm

1×

intervals

Results

35.0ms	256×	body	128	valid
3.0ms	28×	body	128	nan

Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify125.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

662×	`cube-prod_binary64`
603×	`distribute-rgt-in_binary64`
522×	`pow-sqr_binary64`
453×	`associate-/l*_binary64`
447×	`sqr-pow_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	22
1	31	19
2	49	12
3	70	9
4	78	9
5	197	9
6	452	9
7	867	9
8	1025	9
9	1607	9
10	1898	9
11	2922	9
12	3978	9
13	4255	9
14	4332	9
15	4901	9
16	4825	9

prune4.0ms (0.1%)

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

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	32.1b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Status

Error

Program

▶

0.3b

(/.f64 (atan2.f64 im re) (log.f64 base))

32.1b

(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))

Compiler

Compiled 89 to 58 computations (34.8% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`

Counts

1 → 31

Calls

1 calls:

2.0ms

(/.f64 (atan2.f64 im re) (log.f64 base))

Compiler

Compiled 370 to 88 computations (76.2% saved)

series33.0ms (0.6%)

Error

0.3b

Counts

1 → 9

Calls

1 calls:

30.0ms

(/.f64 (atan2.f64 im re) (log.f64 base))

Compiler

Compiled 210 to 145 computations (31% saved)

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

649×	`neg-mul-1_binary64`
637×	`sub-neg_binary64`
613×	`neg-sub0_binary64`
350×	`distribute-neg-in_binary64`
336×	`div-sub_binary64`

Counts

40 → 13

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	610
1	106	572
2	211	572
3	380	572
4	1292	572
5	2872	572
6	3635	572
7	4521	572
8	4919	572

prune7.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	11	2	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	11	4	15

Error

0.2b

Counts

15 → 4

Alt Table

Status	Error	Program
	6.7b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	32.1b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
▶	1.7b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))

Compiler

Compiled 198 to 102 computations (48.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))
5.7b	(cbrt.f64 (atan2.f64 im re))
5.7b	(cbrt.f64 (atan2.f64 im re))
5.7b	(cbrt.f64 (atan2.f64 im re))

rewrite62.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 73

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))
1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 1604 to 235 computations (85.3% saved)

series100.0ms (1.8%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

28.0ms	(*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))
25.0ms	(cbrt.f64 (atan2.f64 im re))
23.0ms	(cbrt.f64 (atan2.f64 im re))
22.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 1044 to 565 computations (45.9% saved)

simplify104.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

819×	`log-prod_binary64`
569×	`distribute-rgt-in_binary64`
530×	`distribute-lft-in_binary64`
455×	`unswap-sqr_binary64`
355×	`*-commutative_binary64`

Counts

97 → 78

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	49	1042
1	79	961
2	243	929
3	560	909
4	1392	731
5	3016	731
6	4211	731
7	4772	731

prune50.0ms (0.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	74	8	82

Error

0.1b

Counts

82 → 8

Alt Table

Status	Error	Program
	6.7b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	28.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 im re))) (sqrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
▶	1.8b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 4)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	5.4b	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	28.4b	(.f64 (.f64 (*.f64 (pow.f64 (atan2.f64 im re) 1/6) (pow.f64 (atan2.f64 im re) 1/6)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	32.1b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
✓	1.7b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))

Compiler

Compiled 827 to 307 computations (62.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

5.7b	(cbrt.f64 (atan2.f64 im re))
5.7b	(cbrt.f64 (atan2.f64 im re))
5.7b	(cbrt.f64 (atan2.f64 im re))
5.7b	(cbrt.f64 (atan2.f64 im re))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))
1.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 1395 to 302 computations (78.4% saved)

series111.0ms (2%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

32.0ms	(cbrt.f64 (atan2.f64 im re))
26.0ms	(cbrt.f64 (atan2.f64 im re))
25.0ms	(cbrt.f64 (atan2.f64 im re))
25.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 1551 to 808 computations (47.9% saved)

simplify90.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

813×	`associate-/r/_binary64`
618×	`log-prod_binary64`
449×	`associate-l_binary64`
350×	`distribute-rgt-out_binary64`
295×	`associate-r_binary64`

Counts

68 → 44

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	580
1	27	552
2	54	552
3	112	552
4	344	536
5	1538	536
6	2826	536
7	3718	536
8	5193	536

prune19.0ms (0.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	43	9	52

Error

0.1b

Counts

52 → 9

Alt Table

Status	Error	Program
	29.0b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 4)) (/.f64 (.f64 (pow.f64 (atan2.f64 im re) 1/6) (pow.f64 (atan2.f64 im re) 1/6)) (log.f64 base)))
▶	5.4b	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	6.7b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	28.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 im re))) (sqrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
✓	1.8b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 4)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	28.4b	(.f64 (.f64 (*.f64 (pow.f64 (atan2.f64 im re) 1/6) (pow.f64 (atan2.f64 im re) 1/6)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	32.1b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
✓	1.7b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))

Compiler

Compiled 755 to 321 computations (57.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
0.4b	(/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base))
5.7b	(cbrt.f64 (atan2.f64 im re))
8.6b	(cbrt.f64 (pow.f64 (atan2.f64 im re) 2))

rewrite130.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

76×	`add-sqr-sqrt_binary64`
63×	`cbrt-prod_binary64`
58×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
42×	`add-cube-cbrt_binary64`

Counts

4 → 141

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
3.0ms	(/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base))
2.0ms	(cbrt.f64 (pow.f64 (atan2.f64 im re) 2))
1.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 3057 to 954 computations (68.8% saved)

series149.0ms (2.7%)

Error

0.1b

Counts

4 → 30

Calls

4 calls:

62.0ms	(/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base))
30.0ms	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
28.0ms	(cbrt.f64 (pow.f64 (atan2.f64 im re) 2))
24.0ms	(cbrt.f64 (atan2.f64 im re))

Compiler

Compiled 1110 to 755 computations (32% saved)

simplify152.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

608×	`div-sub_binary64`
599×	`associate-/l*_binary64`
350×	`times-frac_binary64`
339×	`associate-*l/_binary64`
329×	`log-prod_binary64`

Counts

171 → 132

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	3655
1	325	3198
2	1100	3194
3	3509	2972
4	3670	2686
5	5107	2686

prune54.0ms (1%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	125	7	132
Fresh	4	1	5
Picked	0	1	1
Done	0	3	3
Total	129	12	141

Error

0.1b

Counts

141 → 12

Alt Table

Status	Error	Program
	30.1b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2))) (cbrt.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)))) (*.f64 (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)) (cbrt.f64 (pow.f64 (atan2.f64 im re) 2/3))))
	5.3b	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (cbrt.f64 (/.f64 (atan2.f64 im re) (pow.f64 (log.f64 base) 3))))
	28.9b	(.f64 (.f64 (pow.f64 (atan2.f64 im re) 2/3) (*.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) (cbrt.f64 (cbrt.f64 (atan2.f64 im re))))) (/.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) (log.f64 base)))
	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	5.4b	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	28.4b	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 im re)) 2)) (/.f64 (pow.f64 (atan2.f64 im re) 2/3) (log.f64 base)))
	1.7b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	28.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 5/2) (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 im re))) (cbrt.f64 (log.f64 base))))
	28.8b	(.f64 (.f64 (*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2/3)) (cbrt.f64 (pow.f64 (atan2.f64 im re) 2/3))) (cbrt.f64 (pow.f64 (atan2.f64 im re) 2/3))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	30.1b	(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 im re))) (/.f64 (log.f64 base) (pow.f64 (atan2.f64 im re) 1/6))))
	1.8b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 im re))) 4)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	32.1b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Compiler

Compiled 1546 to 570 computations (63.1% saved)

regimes1.6s (30.2%)

Accuracy

Total 0.2b remaining (69.1%)

Threshold costs 0.2b (69.1%)

Compiler

Compiled 20859 to 11578 computations (44.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
1×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
2	18	14
3	21	14
4	24	14
5	25	14
6	24	14

end1.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

sample1.7s (30.8%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
113.0ms	980×	body	128	nan

Compiler

Compiled 335 to 201 computations (40% saved)

Details

analyze680.0ms (12.5%)

sample51.0ms (0.9%)

simplify125.0ms (2.3%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

rewrite22.0ms (0.4%)

series33.0ms (0.6%)

simplify100.0ms (1.8%)

prune7.0ms (0.1%)

localize9.0ms (0.2%)

rewrite62.0ms (1.1%)

series100.0ms (1.8%)

simplify104.0ms (1.9%)

prune50.0ms (0.9%)

localize16.0ms (0.3%)

rewrite31.0ms (0.6%)

series111.0ms (2%)

simplify90.0ms (1.7%)

prune19.0ms (0.3%)

localize12.0ms (0.2%)

rewrite130.0ms (2.4%)

series149.0ms (2.7%)

simplify152.0ms (2.8%)

prune54.0ms (1%)

regimes1.6s (30.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.7s (30.8%)

Profiling