Details

sample55.0ms

Algorithm

intervals

Results

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

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	16
1	52	16
2	68	16
3	88	16
4	102	16
5	106	16
6	106	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

localize23.0ms

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)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

505×	`*-un-lft-identity`
266×	`add-sqr-sqrt`
207×	`associate-l`
169×	`times-frac`
145×	`distribute-lft-out`
133×	`pow1`
130×	`swap-sqr`
119×	`log-pow`
84×	`distribute-lft-out--`
68×	`unswap-sqr`
56×	`difference-of-squares`
43×	`add-cube-cbrt`
26×	`hypot-def`
13×	`associate-/r` `associate-/l`
12×	`log-prod` `*-commutative`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `sqrt-prod`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `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 → 327

Calls

4 calls:

55.0ms	(/ (- (* (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))
17.0ms	(sqrt (+ (* re re) (* im im)))

series257.0ms

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))
152.0ms	(* (log base) (log base))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify104.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	575	5478
1	2130	5116
2	5001	5056

prune578.0ms

Filtered

339 candidates to 114 candidates (33.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	331	8	339
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	332	8	340

Merged error: 0.1b

Counts

340 → 8

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×	`expm1-log1p-u` `frac-2neg` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `1-exp`

Counts

2 → 82

Calls

2 calls:

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

series160.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(log (/ 1 base))
42.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify111.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	214	486
1	573	449
2	1553	429
3	4452	410
4	5001	410

prune200.0ms

Filtered

88 candidates to 50 candidates (56.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 0.0b

Counts

96 → 12

localize9.0ms

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` `expm1-log1p-u` `frac-2neg` `div-exp` `prod-exp` `un-div-inv` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`pow-prod-down` `*-commutative`

Counts

2 → 81

Calls

2 calls:

3.0ms	(/ -1 (log base))
8.0ms	(* (atan2 im re) (/ -1 (log base)))

series216.0ms

Counts

2 → 6

Calls

2 calls:

173.0ms	(/ -1 (log base))
43.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify41.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	225	424
1	1152	391
2	5001	352

prune211.0ms

Filtered

87 candidates to 59 candidates (67.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	88	11	99

Merged error: 0b

Counts

99 → 11

localize13.0ms

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))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

135×	`*-un-lft-identity`
102×	`times-frac`
87×	`add-sqr-sqrt`
85×	`add-cube-cbrt`
65×	`cbrt-prod`
52×	`log-pow`
50×	`associate-r`
48×	`log-prod`
45×	`pow1` `distribute-rgt-out`
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`
14×	`fma-def`
13×	`pow1/3` `associate-l`
12×	`associate-/l*`
9×	`associate-+r-` `log-div`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `div-inv`
4×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u`
2×	`flip3-+` `sum-log` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `div-exp` `*-commutative` `unswap-sqr`

Counts

4 → 260

Calls

4 calls:

12.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
24.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
3.0ms	(cbrt (/ 1 base))
3.0ms	(cbrt (/ 1 base))

series731.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (atan2 im re) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
268.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
184.0ms	(cbrt (/ 1 base))
179.0ms	(cbrt (/ 1 base))

simplify67.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	540	2186
1	1702	1897
2	5001	1619

prune891.0ms

Filtered

272 candidates to 170 candidates (62.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	269	3	272
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	274	9	283

Merged error: 0b

Counts

283 → 9

regimes200.0ms

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	12
1	29	12
2	29	12

end0.0ms

sample1.5s

Algorithm

intervals

Results

582.0ms	8000×	body	80	valid
569.0ms	8146×	body	80	nan