Details

sample60.0ms

Algorithm

intervals

Results

21.0ms	287×	body	80	nan
19.0ms	256×	body	80	valid

simplify14.0ms

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 (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (* (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))
0.6b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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--` `hypot-def` `div-inv`

Counts

4 → 117

Calls

4 calls:

13.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
7.0ms	(* (atan2 im re) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series254.0ms

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)))
27.0ms	(* (atan2 im re) (log base))
152.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	466	1254
1	1924	1122
2	5001	1081

prune455.0ms

Filtered

129 candidates to 89 candidates (69.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `log-div` `rec-exp` `frac-2neg` `1-exp` `log-rec` `clear-num`

Counts

2 → 72

Calls

2 calls:

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

series153.0ms

Counts

2 → 6

Calls

2 calls:

114.0ms	(log (/ 1 base))
39.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify110.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	201	449
1	540	418
2	1522	402
3	3981	385
4	5002	385

prune181.0ms

Filtered

78 candidates to 46 candidates (59.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 70

Calls

2 calls:

2.0ms	(/ -1 (log base))
9.0ms	(* (atan2 im re) (/ -1 (log base)))

series206.0ms

Counts

2 → 6

Calls

2 calls:

165.0ms	(/ -1 (log base))
40.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify38.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	209	396
1	1008	363
2	5001	323

prune189.0ms

Filtered

76 candidates to 49 candidates (64.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0b

localize18.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-def` `frac-2neg` `div-exp` `unsub-neg` `clear-num` `sum-log`

Counts

4 → 119

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:

543.0ms	(+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base))))
226.0ms	(/ (atan2 im re) (+ (* (- 2) (log (cbrt base))) (log (/ 1 (cbrt base)))))
174.0ms	(cbrt base)
178.0ms	(cbrt base)

simplify47.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	490	1205
1	1500	1048
2	5002	921

prune487.0ms

Filtered

131 candidates to 117 candidates (89.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes169.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	9
1	21	9
2	21	9

end0.0ms

sample1.6s

Algorithm

intervals

Results

590.0ms	7901×	body	80	nan
589.0ms	8000×	body	80	valid