Details

sample56.0ms

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)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

505×	`*-un-lft-identity`
216×	`add-sqr-sqrt`
207×	`associate-l`
169×	`times-frac`
145×	`distribute-lft-out`
133×	`pow1`
120×	`swap-sqr`
119×	`log-pow`
84×	`distribute-lft-out--`
58×	`unswap-sqr`
56×	`difference-of-squares`
43×	`add-cube-cbrt`
13×	`associate-/r` `associate-/l`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `sqrt-prod`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/`
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 → 293

Calls

4 calls:

45.0ms	(/ (- (* (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))
16.0ms	(sqrt (+ (* re re) (* im im)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
27.0ms	(* (atan2 im re) (log base))
145.0ms	(* (log base) (log base))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify97.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	551	5486
1	2018	5292
2	5002	5253

prune502.0ms

Filtered

305 candidates to 95 candidates (31.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	296	9	305
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	297	9	306

Merged error: 0.1b

Counts

306 → 9

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 78

Calls

2 calls:

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

series150.0ms

Counts

2 → 6

Calls

2 calls:

116.0ms	(log (/ 1 base))
34.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify109.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	210	469
1	591	433
2	1600	413
3	4409	390
4	5002	390

prune175.0ms

Filtered

84 candidates to 45 candidates (53.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	80	13	93

Merged error: 0.0b

Counts

93 → 13

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 77

Calls

2 calls:

3.0ms	(/ -1 (log base))
9.0ms	(* (atan2 im re) (/ -1 (log base)))

series209.0ms

Counts

2 → 6

Calls

2 calls:

163.0ms	(/ -1 (log base))
45.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify56.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	221	408
1	1148	375
2	5001	336

prune204.0ms

Filtered

83 candidates to 55 candidates (66.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	83	13	96

Merged error: 0b

Counts

96 → 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))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

132×	`*-un-lft-identity`
102×	`times-frac`
82×	`add-sqr-sqrt` `add-cube-cbrt`
65×	`cbrt-prod`
50×	`log-pow`
48×	`log-prod`
45×	`distribute-rgt-out` `associate-r`
44×	`pow1`
32×	`associate-+l+`
28×	`associate-/r*`
27×	`cbrt-div`
20×	`distribute-lft-out`
16×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
15×	`distribute-lft1-in`
12×	`pow1/3` `associate-/l*`
10×	`associate-l`
9×	`associate-+r-` `log-div`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `div-inv`
4×	`frac-2neg` `clear-num`
2×	`flip3-+` `sum-log` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `div-exp`

Counts

4 → 238

Calls

4 calls:

13.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
20.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
3.0ms	(cbrt (/ 1 base))
7.0ms	(cbrt (/ 1 base))

series704.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
259.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
176.0ms	(cbrt (/ 1 base))
172.0ms	(cbrt (/ 1 base))

simplify69.0ms

Algorithm

egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	484	2135
1	1663	1877
2	5002	1619

prune613.0ms

Filtered

250 candidates to 149 candidates (59.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	245	5	250
Fresh	8	3	11
Picked	1	0	1
Done	0	1	1
Total	254	9	263

Merged error: 0b

Counts

263 → 9

regimes206.0ms

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	25	13
1	27	13
2	27	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

578.0ms	8000×	body	80	valid
550.0ms	8146×	body	80	nan