Details

sample64.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
20.0ms	269×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize19.0ms

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))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite61.0ms

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:

32.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
9.0ms	(* (atan2 im re) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
31.0ms	(* (atan2 im re) (log base))
154.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (46.0ms)

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

prune415.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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

series161.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(log (/ 1 base))
43.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify100.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	197	434
1	514	402
2	1452	386
3	3804	373
4	5002	373

prune169.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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:

5.0ms	(/ -1 (log base))
19.0ms	(* (atan2 im re) (/ -1 (log base)))

series219.0ms

Counts

2 → 6

Calls

2 calls:

172.0ms	(/ -1 (log base))
47.0ms	(* (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

prune173.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ 1 base))
0.3b	(/ (atan2 im re) (cbrt (pow (log (/ 1 base)) 3)))
0.4b	(cbrt (pow (log (/ 1 base)) 3))
0.7b	(pow (log (/ 1 base)) 3)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

90×	`cbrt-prod`
72×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`log-pow`
36×	`unpow-prod-down` `cube-prod`
31×	`pow1`
21×	`associate-/r*`
13×	`log-prod` `pow-flip` `inv-pow`
12×	`add-exp-log`
6×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
4×	`rem-log-exp` `add-log-exp`
3×	`pow-unpow` `div-exp` `associate-/l*`
2×	`log-rec` `div-inv`
1×	`cbrt-undiv` `pow-to-exp` `log-div` `rec-exp` `pow-pow` `frac-2neg` `pow1/3` `1-exp` `cube-neg` `pow-exp` `clear-num` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 185

Calls

4 calls:

3.0ms	(log (/ 1 base))
17.0ms	(/ (atan2 im re) (cbrt (pow (log (/ 1 base)) 3)))
4.0ms	(cbrt (pow (log (/ 1 base)) 3))
5.0ms	(pow (log (/ 1 base)) 3)

series470.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(log (/ 1 base))
39.0ms	(/ (atan2 im re) (cbrt (pow (log (/ 1 base)) 3)))
124.0ms	(cbrt (pow (log (/ 1 base)) 3))
180.0ms	(pow (log (/ 1 base)) 3)

simplify52.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	364	1385
1	1475	1236
2	5001	1199

prune278.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

regimes259.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	6
1	22	6
2	24	6
3	24	6

end0.0ms

sample1.6s

Algorithm

intervals

Results

560.0ms	8000×	body	80	valid
559.0ms	7964×	body	80	nan