Details

sample50.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
15.0ms	234×	body	80	nan

simplify12.0ms

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 (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

localize21.0ms

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)))

rewrite107.0ms

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:

57.0ms	(/ (- (* (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))
18.0ms	(sqrt (+ (* re re) (* im im)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
26.0ms	(* (atan2 im re) (log base))
150.0ms	(* (log base) (log base))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	564	5478
1	2081	5120
2	5001	5058

prune688.0ms

Filtered

339 candidates to 114 candidates (66.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	328	11	339
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	329	11	340

Merged error: 0.1b

Counts

340 → 11

localize9.0ms

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` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

3.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 4 (49.0ms)

Iter	Nodes	Cost
0	105	215
1	272	201
2	671	200
3	1918	198
4	5002	196

prune80.0ms

Filtered

36 candidates to 24 candidates (33.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	27	9	36
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	35	12	47

Merged error: 0.0b

Counts

47 → 12

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(expm1 (log1p (/ (atan2 im re) (log base))))
0.2b	(log1p (/ (atan2 im re) (log base)))
0.3b	(/ (atan2 im re) (log base))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-/r*` `log-pow` `log1p-expm1-u`
3×	`associate-/l*` `add-log-exp`
2×	`expm1-log1p`
1×	`cbrt-undiv` `log1p-udef` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `div-inv` `expm1-udef`

Counts

3 → 56

Calls

3 calls:

1.0ms	(expm1 (log1p (/ (atan2 im re) (log base))))
1.0ms	(log1p (/ (atan2 im re) (log base)))
3.0ms	(/ (atan2 im re) (log base))

series147.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(expm1 (log1p (/ (atan2 im re) (log base))))
59.0ms	(log1p (/ (atan2 im re) (log base)))
33.0ms	(/ (atan2 im re) (log base))

simplify54.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (49.0ms)

Iter	Nodes	Cost
0	134	363
1	314	331
2	720	327
3	1983	320
4	5002	314

prune130.0ms

Filtered

65 candidates to 39 candidates (40.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	65	12	77

Merged error: 0.0b

Counts

77 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (* (atan2 im re) (/ 1 (log base)))))
0.2b	(log1p (* (atan2 im re) (/ 1 (log base))))
0.3b	(/ 1 (log base))
0.3b	(* (atan2 im re) (/ 1 (log base)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt`
17×	`add-exp-log`
16×	`associate-r`
15×	`pow1`
11×	`add-cbrt-cube`
10×	`associate-*r/`
8×	`associate-/r*` `log-pow`
7×	`associate-/l*`
5×	`expm1-log1p-u` `log1p-expm1-u`
4×	`div-exp` `prod-exp` `add-log-exp`
3×	`associate-l` `clear-num` `un-div-inv` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `expm1-log1p` `frac-2neg` `1-exp` `cbrt-unprod` `div-inv`
1×	`log1p-udef` `pow-flip` `log1p-expm1` `pow-prod-down` `*-commutative` `inv-pow` `expm1-udef`

Counts

4 → 112

Calls

4 calls:

1.0ms	(expm1 (log1p (* (atan2 im re) (/ 1 (log base)))))
1.0ms	(log1p (* (atan2 im re) (/ 1 (log base))))
3.0ms	(/ 1 (log base))
9.0ms	(* (atan2 im re) (/ 1 (log base)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(expm1 (log1p (* (atan2 im re) (/ 1 (log base)))))
88.0ms	(log1p (* (atan2 im re) (/ 1 (log base))))
154.0ms	(/ 1 (log base))
36.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify51.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	248	616
1	903	534
2	2768	483
3	5001	469

prune169.0ms

Filtered

124 candidates to 67 candidates (46.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	123	13	136

Merged error: 0b

Counts

136 → 13

regimes215.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	6
1	13	6

end0.0ms

sample1.4s

Algorithm

intervals

Results

554.0ms	8000×	body	80	valid
528.0ms	7882×	body	80	nan