Details

analyze621.0ms (3.7%)

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)

sample2.6s (15.5%)

Results

2.3s	8256×	body	128	valid
203.0ms	1042×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify127.0ms (0.8%)

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%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.5b	(/.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)))
▶	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

Status

Error

Program

35.5b

(/.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)))

▶

0.3b

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

Compiler

Compiled 117 to 73 computations (37.6% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

series416.0ms (2.5%)

Counts

1 → 8

Calls

1 calls:

416.0ms

(/.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))

simplify91.0ms (0.5%)

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

prune38.0ms (0.2%)

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

0.1b

Counts

37 → 11

Alt Table

Status	Error	Program
	7.0b	(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))))
	1.5b	(.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))))
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	7.0b	(cbrt.f64 (.f64 (.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (atan2.f64 im re) (log.f64 base))) (/.f64 (atan2.f64 im re) (log.f64 base))))
	15.0b	(log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	29.7b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	35.5b	(/.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)))
▶	0.3b	(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
	32.5b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.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)))
	30.8b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))

Compiler

Compiled 871 to 330 computations (62.1% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 1 base))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))

series488.0ms (2.9%)

Counts

2 → 16

Calls

2 calls:

468.0ms	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))
20.0ms	(log.f64 (/.f64 1 base))

rewrite10.0ms (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:

3.0ms	(/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))
2.0ms	(log.f64 (/.f64 1 base))

simplify138.0ms (0.8%)

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

prune111.0ms (0.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	100	6	106
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	103	14	117

Error

0.0b

Counts

117 → 14

Alt Table

Status	Error	Program
	29.6b	(.f64 -1 (.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base)))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))))
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	0.6b	(*.f64 -1 (/.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (neg.f64 (log.f64 base)) 3))))
	32.0b	(.f64 -1 (.f64 (/.f64 1 (sqrt.f64 (neg.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (sqrt.f64 (neg.f64 (log.f64 base))))))
	7.0b	(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))))
	1.5b	(.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))))
	30.1b	(*.f64 -1 (exp.f64 (log.f64 (neg.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
▶	0.4b	(.f64 -1 (/.f64 (atan2.f64 im re) (+.f64 (log.f64 (.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))) (log.f64 (cbrt.f64 (/.f64 1 base))))))
	32.3b	(*.f64 -1 (/.f64 (atan2.f64 im re) (expm1.f64 (log1p.f64 (neg.f64 (log.f64 base))))))
	29.7b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	35.5b	(/.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)))
✓	0.3b	(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
	32.5b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	30.8b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))

Compiler

Compiled 2245 to 1211 computations (46.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))) (log.f64 (cbrt.f64 (/.f64 1 base))))
✓	0.3b	(/.f64 (atan2.f64 im re) (+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))) (log.f64 (cbrt.f64 (/.f64 1 base)))))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))
✓	0.5b	(cbrt.f64 (/.f64 1 base))

series5.4s (32.1%)

Counts

4 → 72

Calls

4 calls:

4.1s	(/.f64 (atan2.f64 im re) (+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))) (log.f64 (cbrt.f64 (/.f64 1 base)))))
1.2s	(+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))) (log.f64 (cbrt.f64 (/.f64 1 base))))
37.0ms	(*.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))
31.0ms	(cbrt.f64 (/.f64 1 base))

rewrite70.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`pow1_binary64`
154×	`log-pow_binary64`
142×	`times-frac_binary64`
136×	`*-un-lft-identity_binary64`
121×	`add-sqr-sqrt_binary64`

Counts

4 → 295

Calls

4 calls:

13.0ms	(/.f64 (atan2.f64 im re) (+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))) (log.f64 (cbrt.f64 (/.f64 1 base)))))
12.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))) (log.f64 (cbrt.f64 (/.f64 1 base))))
10.0ms	(*.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))
2.0ms	(cbrt.f64 (/.f64 1 base))

simplify217.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

482×	`associate-l_binary64`
414×	`fma-def_binary64`
371×	`associate-r_binary64`
323×	`log-prod_binary64`
321×	`distribute-rgt-in_binary64`

Counts

367 → 365

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	216	7400
1	385	5498
2	1099	5130
3	3765	4854
4	4956	4854
5	4782	4854

prune489.0ms (2.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	431	6	437
Fresh	10	2	12
Picked	1	0	1
Done	1	0	1
Total	443	8	451

Error

Counts

451 → 8

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 -1 (/.f64 (/.f64 (atan2.f64 im re) (log.f64 (cbrt.f64 (/.f64 1 base)))) (+.f64 2 1)))
	0.4b	(.f64 -1 (.f64 (/.f64 -1 (log.f64 base)) (atan2.f64 im re)))
	7.0b	(.f64 -1 (cbrt.f64 (/.f64 (.f64 (.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (.f64 (.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))) (log.f64 (cbrt.f64 (/.f64 1 base)))) (+.f64 (log.f64 (.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))) (log.f64 (cbrt.f64 (/.f64 1 base))))) (+.f64 (log.f64 (.f64 (cbrt.f64 (/.f64 1 base)) (cbrt.f64 (/.f64 1 base)))) (log.f64 (cbrt.f64 (/.f64 1 base))))))))
	0.4b	(*.f64 -1 (/.f64 (atan2.f64 im re) (+.f64 (log.f64 (pow.f64 base -1/3)) (log.f64 (pow.f64 base -2/3)))))
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	0.6b	(.f64 -1 (/.f64 (atan2.f64 im re) (/.f64 (.f64 1/3 (pow.f64 (neg.f64 (log.f64 base)) 3)) (.f64 1/3 (.f64 (log.f64 base) (log.f64 base))))))
	0.4b	(.f64 -1 (.f64 1/3 (/.f64 (atan2.f64 im re) (*.f64 -1/3 (log.f64 base)))))
	0.6b	(*.f64 -1 (/.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (neg.f64 (log.f64 base)) 3))))

Compiler

Compiled 12029 to 8417 computations (30% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (cbrt.f64 (/.f64 1 base)))
✓	0.3b	(/.f64 (/.f64 (atan2.f64 im re) (log.f64 (cbrt.f64 (/.f64 1 base)))) (+.f64 2 1))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 (cbrt.f64 (/.f64 1 base))))
	0.5b	(cbrt.f64 (/.f64 1 base))

series4.0s (23.7%)

Counts

3 → 84

Calls

3 calls:

1.8s	(/.f64 (atan2.f64 im re) (log.f64 (cbrt.f64 (/.f64 1 base))))
1.7s	(/.f64 (/.f64 (atan2.f64 im re) (log.f64 (cbrt.f64 (/.f64 1 base)))) (+.f64 2 1))
562.0ms	(log.f64 (cbrt.f64 (/.f64 1 base)))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

175×	`times-frac_binary64`
126×	`*-un-lft-identity_binary64`
86×	`add-sqr-sqrt_binary64`
86×	`add-cube-cbrt_binary64`
40×	`log-pow_binary64`

Counts

3 → 184

Calls

3 calls:

9.0ms	(/.f64 (/.f64 (atan2.f64 im re) (log.f64 (cbrt.f64 (/.f64 1 base)))) (+.f64 2 1))
2.0ms	(/.f64 (atan2.f64 im re) (log.f64 (cbrt.f64 (/.f64 1 base))))
2.0ms	(log.f64 (cbrt.f64 (/.f64 1 base)))

simplify223.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

408×	`associate-/r*_binary64`
397×	`associate-/l/_binary64`
303×	`times-frac_binary64`
297×	`distribute-rgt-neg-out_binary64`
280×	`associate-/l*_binary64`

Counts

268 → 274

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	256	6206
1	479	5776
2	1082	5167
3	2966	5153
4	4491	5151
5	4965	5151
6	4883	5151

prune276.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	307	3	310
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	311	7	318

Error

Counts

318 → 7

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 -1 (/.f64 (/.f64 (atan2.f64 im re) (log.f64 (cbrt.f64 (/.f64 1 base)))) (+.f64 2 1)))
	0.4b	(.f64 -1 (.f64 (/.f64 -1 (log.f64 base)) (atan2.f64 im re)))
	0.4b	(.f64 -1 (.f64 3 (/.f64 (atan2.f64 im re) (*.f64 -3 (log.f64 base)))))
	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 (log.f64 (pow.f64 base -1/3)) (log.f64 (pow.f64 base -2/3)))))
	0.4b	(.f64 -1 (/.f64 (/.f64 1 1/3) (.f64 (/.f64 -3 (atan2.f64 im re)) (log.f64 base))))
	0.6b	(*.f64 -1 (/.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (neg.f64 (log.f64 base)) 3))))

Compiler

Compiled 7621 to 5138 computations (32.6% saved)

regimes1.4s (8%)

Accuracy

Total 0.3b remaining (94.3%)

Threshold costs 0.3b (94.3%)

Counts

172 → 1

Compiler

Compiled 20971 to 15523 computations (26% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-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	12	14
1	17	14
2	20	14
3	23	14
4	26	14
5	27	14
6	26	14

end108.0ms (0.6%)

Compiler: Compiled 135 to 107 computations (20.7% saved)

Details

analyze621.0ms (3.7%)

sample2.6s (15.5%)

simplify127.0ms (0.8%)

prune5.0ms (0%)

localize5.0ms (0%)

series416.0ms (2.5%)

rewrite4.0ms (0%)

simplify91.0ms (0.5%)

prune38.0ms (0.2%)

localize8.0ms (0%)

series488.0ms (2.9%)

rewrite10.0ms (0.1%)

simplify138.0ms (0.8%)

prune111.0ms (0.7%)

localize12.0ms (0.1%)

series5.4s (32.1%)

rewrite70.0ms (0.4%)

simplify217.0ms (1.3%)

prune489.0ms (2.9%)

localize11.0ms (0.1%)

series4.0s (23.7%)

rewrite30.0ms (0.2%)

simplify223.0ms (1.3%)

prune276.0ms (1.6%)

regimes1.4s (8%)

simplify3.0ms (0%)

end108.0ms (0.6%)

Profiling