Details

sample57.0ms

Algorithm

intervals

Results

20.0ms	266×	body	80	nan
18.0ms	256×	body	80	valid

simplify11.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 31.8b

Counts

2 → 1

localize18.0ms

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)))
0.3b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:

9.0ms	(/ (- (* (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))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
29.0ms	(* (atan2 im re) (log base))
151.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	444	1213
1	1816	1100
2	5001	1070

prune397.0ms

Filtered

120 candidates to 79 candidates (65.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	111	9	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	9	121

Merged error: 0.1b

Counts

121 → 9

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (/ 1 base))
0.3b	(/ (atan2 im re) (log (/ 1 base)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

27×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`log-pow`
13×	`log-prod`
12×	`pow1`
9×	`add-exp-log`
6×	`associate-/r*`
5×	`pow-flip` `inv-pow`
4×	`rem-log-exp` `add-cbrt-cube`
3×	`div-exp` `associate-/l*`
2×	`div-inv` `add-log-exp`
1×	`cbrt-undiv` `log-div` `rec-exp` `frac-2neg` `1-exp` `log-rec` `clear-num`

Counts

2 → 68

Calls

2 calls:

3.0ms	(log (/ 1 base))
4.0ms	(/ (atan2 im re) (log (/ 1 base)))

series154.0ms

Counts

2 → 6

Calls

2 calls:

119.0ms	(log (/ 1 base))
34.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify103.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	197	433
1	536	402
2	1518	386
3	3905	369
4	5001	369

prune163.0ms

Filtered

74 candidates to 42 candidates (56.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	67	7	74
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	70	13	83

Merged error: 0.0b

Counts

83 → 13

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ -1 (log base))
0.3b	(* (atan2 im re) (/ -1 (log base)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow`
4×	`associate-/r*`
3×	`associate-l` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 66

Calls

2 calls:

3.0ms	(/ -1 (log base))
7.0ms	(* (atan2 im re) (/ -1 (log base)))

series208.0ms

Counts

2 → 6

Calls

2 calls:

162.0ms	(/ -1 (log base))
46.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify36.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	205	380
1	1004	347
2	5001	307

prune170.0ms

Filtered

72 candidates to 45 candidates (62.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	72	13	85

Merged error: 0b

Counts

85 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
0.3b	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
0.6b	(cbrt (/ 1 base))
0.6b	(cbrt (/ 1 base))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

65×	`cbrt-prod`
63×	`times-frac`
58×	`*-un-lft-identity`
53×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`log-prod`
32×	`associate-+l+`
16×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
10×	`distribute-rgt-out`
9×	`pow1`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `div-inv`
5×	`distribute-lft1-in` `log-pow` `add-log-exp`
3×	`cbrt-div` `associate-/l*`
2×	`flip3-+` `pow1/3` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `log-div` `frac-2neg` `div-exp` `clear-num` `sum-log`

Counts

4 → 148

Calls

4 calls:

7.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
13.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
3.0ms	(cbrt (/ 1 base))
3.0ms	(cbrt (/ 1 base))

series723.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
265.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
180.0ms	(cbrt (/ 1 base))
178.0ms	(cbrt (/ 1 base))

simplify46.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	399	1452
1	1135	1288
2	5001	1146

prune542.0ms

Filtered

160 candidates to 126 candidates (78.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	156	4	160
Fresh	6	5	11
Picked	1	0	1
Done	1	0	1
Total	164	9	173

Merged error: 0b

Counts

173 → 9

regimes193.0ms

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	23	11
1	25	11
2	25	11

end0.0ms

sample1.5s

Algorithm

intervals

Results

566.0ms	8000×	body	80	valid
549.0ms	8146×	body	80	nan