Details

analyze512.0ms (6%)

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)

sample1.9s (21.9%)

Results

1.6s	8256×	body	128	valid
187.0ms	991×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify123.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1042×	`fma-def_binary64`
693×	`fma-neg_binary64`
662×	`cube-prod_binary64`
522×	`pow-sqr_binary64`
453×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	20
1	35	19
2	57	12
3	80	9
4	89	9
5	216	9
6	486	9
7	978	9
8	1296	9
9	1996	9
10	2287	9
11	3311	9
12	4367	9
13	4644	9
14	4721	9
15	4986	9
16	4826	9

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	34.9b	(/.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)))
▶	0.2b	(/.f64 (atan2.f64 im re) (log.f64 base))

Status

Error

Program

34.9b

(/.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)))

▶

0.2b

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

Compiler

Compiled 117 to 73 computations (37.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (atan2.f64 im re) (log.f64 base))

series421.0ms (4.9%)

Counts

1 → 8

Calls

1 calls:

421.0ms

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

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

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 → 33

Calls

1 calls:

2.0ms

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

simplify84.0ms (1%)

Algorithm

1×	egg-herbie

Rules

763×	`fma-neg_binary64`
574×	`neg-mul-1_binary64`
543×	`neg-sub0_binary64`
429×	`sub-neg_binary64`
336×	`div-sub_binary64`

Counts

41 → 35

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	663
1	108	615
2	213	585
3	384	585
4	1312	585
5	2948	585
6	3524	585
7	4593	585
8	4969	585

prune35.0ms (0.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	25	10	35
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	26	11	37

Error

0.0b

Counts

37 → 11

Alt Table

Status	Error	Program
	33.3b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	27.7b	(.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	27.5b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	34.9b	(/.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)))
▶	0.2b	(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	29.7b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	6.4b	(cbrt.f64 (/.f64 (.f64 (.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))

Compiler

Compiled 871 to 334 computations (61.7% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 1 base))
✓	0.2b	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))

series517.0ms (6%)

Counts

2 → 16

Calls

2 calls:

498.0ms	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))
19.0ms	(log.f64 (/.f64 1 base))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
15×	`log-pow_binary64`

Counts

2 → 72

Calls

2 calls:

5.0ms	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))
2.0ms	(log.f64 (/.f64 1 base))

simplify142.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1036×	`fma-neg_binary64`
547×	`associate-/l*_binary64`
547×	`div-sub_binary64`
358×	`sub-neg_binary64`
275×	`associate-/r*_binary64`

Counts

88 → 106

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	96	1237
1	152	1153
2	340	1147
3	899	1141
4	2347	1125
5	3114	1125
6	4104	1125
7	4547	1125
8	4997	1125
9	4829	1125

prune110.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	104	13	117

Error

0.0b

Counts

117 → 13

Alt Table

Status	Error	Program
	33.3b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	27.7b	(.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	27.5b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	29.1b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (sqrt.f64 (neg.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	34.9b	(/.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)))
	6.4b	(*.f64 -1 (cbrt.f64 (pow.f64 (neg.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))
	31.3b	(.f64 -1 (/.f64 (atan2.f64 im re) (.f64 (sqrt.f64 (neg.f64 (log.f64 base))) (sqrt.f64 (neg.f64 (log.f64 base))))))
	31.5b	(*.f64 -1 (/.f64 (atan2.f64 im re) (expm1.f64 (log1p.f64 (log.f64 (/.f64 1 base))))))
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
▶	0.4b	(.f64 -1 (/.f64 (atan2.f64 im re) (+.f64 (.f64 (log.f64 (cbrt.f64 base)) -2) (neg.f64 (log.f64 (cbrt.f64 base))))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))

Compiler

Compiled 2208 to 1169 computations (47.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (cbrt.f64 base))
✓	0.2b	(/.f64 (atan2.f64 im re) (+.f64 (*.f64 (log.f64 (cbrt.f64 base)) -2) (neg.f64 (log.f64 (cbrt.f64 base)))))
✓	0.3b	(+.f64 (*.f64 (log.f64 (cbrt.f64 base)) -2) (neg.f64 (log.f64 (cbrt.f64 base))))
✓	0.7b	(cbrt.f64 base)

series3.0s (34.6%)

Counts

4 → 72

Calls

4 calls:

1.7s	(/.f64 (atan2.f64 im re) (+.f64 (*.f64 (log.f64 (cbrt.f64 base)) -2) (neg.f64 (log.f64 (cbrt.f64 base)))))
611.0ms	(log.f64 (cbrt.f64 base))
598.0ms	(+.f64 (*.f64 (log.f64 (cbrt.f64 base)) -2) (neg.f64 (log.f64 (cbrt.f64 base))))
30.0ms	(cbrt.f64 base)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
12×	`log-prod_binary64`
9×	`times-frac_binary64`

Counts

4 → 85

Calls

4 calls:

6.0ms	(/.f64 (atan2.f64 im re) (+.f64 (*.f64 (log.f64 (cbrt.f64 base)) -2) (neg.f64 (log.f64 (cbrt.f64 base)))))
6.0ms	(+.f64 (*.f64 (log.f64 (cbrt.f64 base)) -2) (neg.f64 (log.f64 (cbrt.f64 base))))
1.0ms	(log.f64 (cbrt.f64 base))
1.0ms	(cbrt.f64 base)

simplify141.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

402×	`associate-l_binary64`
350×	`unsub-neg_binary64`
328×	`fma-def_binary64`
319×	`log-prod_binary64`
307×	`associate-r_binary64`

Counts

157 → 149

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	143	2594
1	309	1808
2	848	1662
3	3316	1660
4	4870	1660
5	4972	1659
6	4960	1659

prune179.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	191	3	194
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	199	8	207

Error

Counts

207 → 8

Alt Table

Status	Error	Program
	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	6.4b	(*.f64 -1 (cbrt.f64 (pow.f64 (neg.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))
	33.3b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	29.1b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (sqrt.f64 (neg.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	0.4b	(.f64 -1 (.f64 -1/3 (/.f64 (atan2.f64 im re) (log.f64 (pow.f64 base 1/3)))))
	0.4b	(.f64 -1 (/.f64 (atan2.f64 im re) (+.f64 (-.f64 (.f64 (log.f64 base) -2/3) (log.f64 (cbrt.f64 (sqrt.f64 base)))) (neg.f64 (log.f64 (cbrt.f64 (sqrt.f64 base)))))))
▶	0.3b	(.f64 -1 (/.f64 (atan2.f64 im re) (+.f64 (-.f64 (.f64 (log.f64 base) -2/3) (log.f64 (cbrt.f64 (pow.f64 base 2/3)))) (neg.f64 (log.f64 (cbrt.f64 (cbrt.f64 base)))))))

Compiler

Compiled 4420 to 1927 computations (56.4% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (pow.f64 base 2/3))
✓	0.6b	(cbrt.f64 (cbrt.f64 base))
	0.7b	(cbrt.f64 base)
✓	5.9b	(pow.f64 base 2/3)

series359.0ms (4.2%)

Counts

3 → 36

Calls

3 calls:

308.0ms	(cbrt.f64 (cbrt.f64 base))
27.0ms	(cbrt.f64 (pow.f64 base 2/3))
24.0ms	(pow.f64 base 2/3)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
6×	`unpow-prod-down_binary64`

Counts

3 → 52

Calls

3 calls:

1.0ms	(pow.f64 base 2/3)
1.0ms	(cbrt.f64 (pow.f64 base 2/3))
1.0ms	(cbrt.f64 (cbrt.f64 base))

simplify98.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-def_binary64`
596×	`unswap-sqr_binary64`
563×	`log-prod_binary64`
397×	`exp-prod_binary64`
301×	`log-pow_binary64`

Counts

88 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	703
1	136	665
2	287	650
3	920	616
4	2377	616
5	3673	616
6	4859	616
7	4827	616

prune112.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	96	8	104

Error

Counts

104 → 8

Alt Table

Status	Error	Program
	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	6.4b	(*.f64 -1 (cbrt.f64 (pow.f64 (neg.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))
	33.3b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	29.1b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (sqrt.f64 (neg.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	0.4b	(.f64 -1 (.f64 -1/3 (/.f64 (atan2.f64 im re) (log.f64 (pow.f64 base 1/3)))))
	0.4b	(.f64 -1 (/.f64 (atan2.f64 im re) (+.f64 (-.f64 (.f64 (log.f64 base) -2/3) (log.f64 (cbrt.f64 (sqrt.f64 base)))) (neg.f64 (log.f64 (cbrt.f64 (sqrt.f64 base)))))))
✓	0.3b	(.f64 -1 (/.f64 (atan2.f64 im re) (+.f64 (-.f64 (.f64 (log.f64 base) -2/3) (log.f64 (cbrt.f64 (pow.f64 base 2/3)))) (neg.f64 (log.f64 (cbrt.f64 (cbrt.f64 base)))))))

Compiler

Compiled 2678 to 1539 computations (42.5% saved)

regimes657.0ms (7.7%)

Accuracy

Total 0.3b remaining (89.9%)

Threshold costs 0.3b (89.9%)

Counts

125 → 1

Compiler

Compiled 11801 to 8201 computations (30.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	17	17
2	20	17
3	22	17
4	23	17
5	23	17

end133.0ms (1.6%)

Compiler: Compiled 163 to 115 computations (29.4% saved)

Details

analyze512.0ms (6%)

sample1.9s (21.9%)

simplify123.0ms (1.4%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series421.0ms (4.9%)

rewrite4.0ms (0%)

simplify84.0ms (1%)

prune35.0ms (0.4%)

localize9.0ms (0.1%)

series517.0ms (6%)

rewrite11.0ms (0.1%)

simplify142.0ms (1.7%)

prune110.0ms (1.3%)

localize11.0ms (0.1%)

series3.0s (34.6%)

rewrite18.0ms (0.2%)

simplify141.0ms (1.7%)

prune179.0ms (2.1%)

localize26.0ms (0.3%)

series359.0ms (4.2%)

rewrite7.0ms (0.1%)

simplify98.0ms (1.1%)

prune112.0ms (1.3%)

regimes657.0ms (7.7%)

simplify2.0ms (0%)

end133.0ms (1.6%)

Profiling