Details

sample55.0ms

Algorithm

intervals

Results

20.0ms	245×	body	80	nan
18.0ms	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize20.0ms

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)))
0.4b	(* (atan2 im re) (log base))
0.6b	(* (log base) (log base))
31.6b	(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×	`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:

10.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (atan2 im re) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
28.0ms	(* (atan2 im re) (log base))
153.0ms	(* (log base) (log base))
41.0ms	(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

prune480.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

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×	`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:

3.0ms	(log (/ 1 base))
4.0ms	(/ (atan2 im re) (log (/ 1 base)))

series158.0ms

Counts

2 → 6

Calls

2 calls:

123.0ms	(log (/ 1 base))
36.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify106.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (35.0ms)

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

prune188.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

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:

3.0ms	(/ -1 (log base))
8.0ms	(* (atan2 im re) (/ -1 (log base)))

series218.0ms

Counts

2 → 6

Calls

2 calls:

173.0ms	(/ -1 (log base))
45.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

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

prune193.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
84×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`log-pow`
38×	`pow1`
25×	`associate-/r*`
21×	`add-exp-log`
18×	`pow-flip` `inv-pow`
13×	`log-prod`
10×	`div-exp` `add-cbrt-cube`
9×	`associate-/l*`
7×	`div-inv`
4×	`cbrt-undiv` `rem-log-exp`
3×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `frac-2neg` `log-rec` `clear-num`
1×	`div-sub` `distribute-frac-neg` `associate-/r/`

Counts

3 → 188

Calls

3 calls:

3.0ms	(log (/ 1 base))
8.0ms	(/ 1 (/ (log (/ 1 base)) (atan2 im re)))
6.0ms	(/ (log (/ 1 base)) (atan2 im re))

series219.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(log (/ 1 base))
49.0ms	(/ 1 (/ (log (/ 1 base)) (atan2 im re)))
47.0ms	(/ (log (/ 1 base)) (atan2 im re))

simplify54.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	501	1610
1	2007	1420
2	5001	1268

prune314.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes188.0ms

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	12	5
1	18	5
2	20	5
3	20	5

end0.0ms

sample1.5s

Algorithm

intervals

Results

572.0ms	8000×	body	80	valid
532.0ms	7800×	body	80	nan