Details

sample52.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
17.0ms	226×	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: 33.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 im re) (log base))
0.3b	(/ (- (* (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))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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:

4.0ms	(* (atan2 im re) (log base))
16.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 im re) (log base))
34.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
149.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (48.0ms)

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

prune417.0ms

Pruning

11 alts after pruning (11 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)))

rewrite7.0ms

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:

2.0ms	(log (/ 1 base))
3.0ms	(/ (atan2 im re) (log (/ 1 base)))

series152.0ms

Counts

2 → 6

Calls

2 calls:

113.0ms	(log (/ 1 base))
38.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify107.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	197	433
1	536	402
2	1518	386
3	3905	369
4	5001	369

prune174.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
0.3b	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

34×	`log-prod`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
22×	`associate-+r+`
21×	`cbrt-prod`
12×	`associate-+l+`
10×	`distribute-rgt-out` `log-pow`
9×	`pow1`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
5×	`pow-flip` `associate-/r*` `inv-pow` `add-log-exp`
3×	`log-rec` `associate-/l*`
2×	`flip3-+` `pow1/3` `associate-/r/` `flip-+` `div-inv`
1×	`cbrt-undiv` `+-commutative` `distribute-lft-neg-out` `associate-+r-` `log-div` `distribute-neg-out` `frac-2neg` `div-exp` `unsub-neg` `clear-num` `sum-log`

Counts

4 → 110

Calls

4 calls:

10.0ms	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
11.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.2s

Counts

4 → 12

Calls

4 calls:

562.0ms	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
222.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
186.0ms	(cbrt base)
183.0ms	(cbrt base)

simplify45.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	450	1197
1	1366	1030
2	5002	916

prune471.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (/ (atan2 im re) (log (cbrt base))) (+ (- 2) -1))
0.3b	(/ (atan2 im re) (log (cbrt base)))
0.6b	(cbrt base)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
177×	`*-un-lft-identity`
117×	`add-sqr-sqrt`
97×	`add-cube-cbrt`
50×	`log-pow`
40×	`distribute-lft-out`
28×	`pow1`
26×	`pow1/3`
22×	`associate-/l*`
20×	`difference-of-sqr--1` `distribute-rgt-neg-in`
11×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`cbrt-prod` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`flip3-+` `flip-+` `associate-/l/`

Counts

3 → 202

Calls

3 calls:

19.0ms	(/ (/ (atan2 im re) (log (cbrt base))) (+ (- 2) -1))
2.0ms	(/ (atan2 im re) (log (cbrt base)))
1.0ms	(cbrt base)

series370.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(/ (/ (atan2 im re) (log (cbrt base))) (+ (- 2) -1))
88.0ms	(/ (atan2 im re) (log (cbrt base)))
181.0ms	(cbrt base)

simplify83.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	588	2493
1	2375	2405
2	5001	2366

prune478.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes121.0ms

Accuracy

0% (0.4b 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	21	8
1	30	8
2	32	8
3	32	8

end0.0ms

sample1.5s

Algorithm

intervals

Results

571.0ms	7928×	body	80	nan
569.0ms	8000×	body	80	valid