Details

sample57.0ms

Algorithm

intervals

Results

20.0ms	283×	body	80	nan
18.0ms	256×	body	80	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 32.9b

localize24.0ms

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)))

rewrite27.0ms

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))
12.0ms	(/ (- (* (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)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (atan2 im re) (log base))
36.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
147.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	444	1214
1	1816	1100
2	5001	1070

prune418.0ms

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)))

rewrite10.0ms

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))
6.0ms	(/ (atan2 im re) (log (/ 1 base)))

series152.0ms

Counts

2 → 6

Calls

2 calls:

117.0ms	(log (/ 1 base))
35.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify106.0ms

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

prune171.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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)))))
0.5b	(cbrt base)
0.5b	(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)))))
0.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.1s

Counts

4 → 12

Calls

4 calls:

552.0ms	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
224.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
178.0ms	(cbrt base)
188.0ms	(cbrt base)

simplify47.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (36.0ms)

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

prune488.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (atan2 im re) (+ (* (- 2) (log (exp (log (pow base 1/3))))) (log (/ 1 (cbrt base)))))
0.5b	(cbrt base)
4.0b	(exp (log (pow base 1/3)))
4.9b	(pow base 1/3)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log` `log-prod` `exp-sum`
6×	`unpow-prod-down` `add-cbrt-cube`
5×	`pow1`
4×	`exp-prod` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `associate-/r` `associate-/l`
2×	`associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow1/3` `pow1/3` `div-exp` `pow-exp` `clear-num` `log-pow` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 77

Calls

4 calls:

12.0ms	(/ (atan2 im re) (+ (* (- 2) (log (exp (log (pow base 1/3))))) (log (/ 1 (cbrt base)))))
0.0ms	(cbrt base)
2.0ms	(exp (log (pow base 1/3)))
1.0ms	(pow base 1/3)

series740.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (atan2 im re) (+ (* (- 2) (log (exp (log (pow base 1/3))))) (log (/ 1 (cbrt base)))))
180.0ms	(cbrt base)
180.0ms	(exp (log (pow base 1/3)))
173.0ms	(pow base 1/3)

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	333	763
1	1145	668
2	5002	612

prune300.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes226.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	34	13
2	35	13
3	35	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

565.0ms	8095×	body	80	nan
558.0ms	8000×	body	80	valid