Details

sample52.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
16.0ms	234×	body	80	nan

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 (100.0%)

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: 34.6b

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)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
32.0b	(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:

41.0ms	(/ (- (* (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))
19.0ms	(sqrt (+ (* re re) (* im im)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
32.0ms	(* (atan2 im re) (log base))
152.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify100.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	540	5487
1	1986	5294
2	5001	5252

prune444.0ms

Filtered

305 candidates to 95 candidates (68.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	294	11	305
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	295	11	306

Merged error: 0.1b

Counts

306 → 11

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

3.0ms

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

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 4 (49.0ms)

Iter	Nodes	Cost
0	103	207
1	270	193
2	669	192
3	1910	190
4	5001	188

prune77.0ms

Filtered

34 candidates to 22 candidates (35.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	24	10	34
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	32	13	45

Merged error: 0.0b

Counts

45 → 13

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`times-frac`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
16×	`associate-r`
15×	`add-exp-log`
13×	`pow1`
10×	`associate-*r/`
9×	`add-cbrt-cube`
8×	`associate-/r*` `log-pow`
7×	`associate-/l*`
4×	`div-exp` `prod-exp`
3×	`associate-l` `clear-num` `un-div-inv` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `frac-2neg` `1-exp` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

2 → 85

Calls

2 calls:

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

series195.0ms

Counts

2 → 6

Calls

2 calls:

161.0ms	(/ 1 (log base))
33.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify50.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	213	428
1	848	368
2	2691	322
3	5001	315

prune127.0ms

Filtered

91 candidates to 42 candidates (53.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	91	13	104

Merged error: 0.0b

Counts

104 → 13

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (log base) (atan2 im re))
0.4b	(/ 1 (/ (log base) (atan2 im re)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
63×	`*-un-lft-identity`
62×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-/r*`
21×	`pow1`
18×	`log-pow`
15×	`add-exp-log`
13×	`associate-/l*`
10×	`associate-/r/`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv`
4×	`cbrt-undiv` `clear-num`
3×	`frac-2neg` `remove-double-div`
2×	`rec-exp` `1-exp` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

2 → 131

Calls

2 calls:

4.0ms	(/ (log base) (atan2 im re))
7.0ms	(/ 1 (/ (log base) (atan2 im re)))

series96.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (log base) (atan2 im re))
50.0ms	(/ 1 (/ (log base) (atan2 im re)))

simplify42.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	341	1026
1	1424	914
2	5001	807

prune127.0ms

Filtered

137 candidates to 59 candidates (56.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	139	11	150

Merged error: 0.0b

Counts

150 → 11

regimes182.0ms

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	11	3
1	13	3
2	13	3

end0.0ms

sample1.5s

Algorithm

intervals

Results

574.0ms	8000×	body	80	valid
533.0ms	7882×	body	80	nan