Details

analyze1.1s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 46.952782%

Guaranteed chance to sample good point: 88.149127%

sample37.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
2.0ms	18×	body	80	nan

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	44	16
2	56	16
3	74	16
4	80	16
5	80	16

prune6.0ms

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

Merged error: 35.1b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 108

Calls

4 calls:

8.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (atan2 im re) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (atan2 im re) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	441	1237
1	1738	1127
2	5001	1101

prune209.0ms

Filtered

75 candidates to 120 candidates (-60.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	12	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Merged error: 0.1b

Counts

121 → 12

localize18.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (/ (+ 0 (log base)) 1))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
93×	`*-un-lft-identity`
57×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`distribute-lft-out`
19×	`associate-/r*`
13×	`pow1`
12×	`log-pow`
8×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`div-exp` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
1×	`frac-2neg` `1-exp` `clear-num` `associate-/r/` `add-log-exp`

Counts

1 → 95

Calls

1 calls:

15.0ms

(/ (atan2 im re) (/ (+ 0 (log base)) 1))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(/ (atan2 im re) (/ (+ 0 (log base)) 1))

simplify68.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	355	941
1	1467	819
2	4142	698
3	5001	698

prune116.0ms

Filtered

37 candidates to 98 candidates (-164.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	95	15	110

Merged error: 0.0b

Counts

110 → 15

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (log base) (atan2 im re))
0.6b	(/ 1 (/ (log base) (atan2 im re)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `associate-/r*`
16×	`log-pow`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

2 → 119

Calls

2 calls:

3.0ms	(/ (log base) (atan2 im re))
6.0ms	(/ 1 (/ (log base) (atan2 im re)))

series27.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(/ (log base) (atan2 im re))
13.0ms	(/ 1 (/ (log base) (atan2 im re)))

simplify65.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	335	1003
1	1399	891
2	4997	788
3	5001	788

prune123.0ms

Filtered

57 candidates to 125 candidates (-119.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	5	8	13
Picked	1	0	1
Done	0	1	1
Total	124	16	140

Merged error: 0.0b

Counts

140 → 16

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1))) (cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1))))
4.2b	(cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1)))
4.2b	(cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1)))
4.2b	(cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

980×	`times-frac`
752×	`*-un-lft-identity`
582×	`cbrt-prod`
499×	`add-sqr-sqrt`
409×	`add-cube-cbrt`
198×	`distribute-lft-out`
119×	`swap-sqr`
110×	`pow1`
99×	`log-pow`
65×	`associate-r` `associate-l`
28×	`div-inv`
25×	`unswap-sqr`
9×	`pow1/3`
7×	`cbrt-div` `associate-/r/`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 508

Calls

4 calls:

76.0ms	(* (cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1))) (cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1))))
8.0ms	(cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1)))
8.0ms	(cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1)))
8.0ms	(cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1)))

series110.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1))) (cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1))))
23.0ms	(cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1)))
23.0ms	(cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1)))
23.0ms	(cbrt (/ (atan2 im re) (/ (+ 0 (log base)) 1)))

simplify128.0ms

Algorithm

egg-herbie

Counts

520 → 520

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	664	9629
1	2514	8931
2	5001	7669

prune673.0ms

Filtered

200 candidates to 520 candidates (-160.0%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	519	1	520
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	519	17	536

Merged error: 0.0b

Counts

536 → 17

regimes434.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	14	5
2	14	5

end0.0ms

analyze1.1s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 46.952782%

Guaranteed chance to sample good point: 88.149127%

sample1.0s

Algorithm

intervals

Results

782.0ms	8000×	body	80	valid
41.0ms	457×	body	80	nan

Details

analyze1.1s

sample37.0ms

simplify9.0ms

prune6.0ms

localize19.0ms

rewrite23.0ms

series42.0ms

simplify58.0ms

prune209.0ms

localize18.0ms

rewrite25.0ms

series19.0ms

simplify68.0ms

prune116.0ms

localize7.0ms

rewrite14.0ms

series27.0ms

simplify65.0ms

prune123.0ms

localize12.0ms

rewrite154.0ms

series110.0ms

simplify128.0ms

prune673.0ms

regimes434.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.1s

sample1.0s

Profiling