Details

sample62.0ms

Algorithm

intervals

Results

21.0ms	251×	body	80	nan
18.0ms	256×	body	80	valid

simplify10.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (atan2 im re) (log base))
0.4b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

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:

8.0ms	(* (atan2 im re) (log base))
30.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (atan2 im re) (log base))
38.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
138.0ms	(* (log base) (log base))
32.0ms	(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

prune416.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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:

5.0ms

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

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

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

simplify51.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 4 (48.0ms)

Iter	Nodes	Cost
0	103	207
1	270	193
2	671	192
3	1907	190
4	5001	188

prune88.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 74

Calls

2 calls:

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

series176.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(/ 1 (log base))
30.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	206	403
1	829	345
2	2677	303
3	5002	296

prune139.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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:

5.0ms

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

series30.0ms

Counts

1 → 3

Calls

1 calls:

30.0ms

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

simplify51.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 4 (48.0ms)

Iter	Nodes	Cost
0	103	207
1	270	193
2	671	192
3	1907	190
4	5001	188

prune63.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

regimes201.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b 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

sample1.6s

Algorithm

intervals

Results

575.0ms	8000×	body	80	valid
559.0ms	7772×	body	80	nan