Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	253×	body	80	nan
18.0ms	256×	body	80	valid

simplify13.0ms

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: 34.4b

localize22.0ms

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))
0.5b	(* (log base) (log base))
32.0b	(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:

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	(* (atan2 im re) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
32.0ms	(* (atan2 im re) (log base))
151.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	466	1255
1	1924	1122
2	5001	1081

prune441.0ms

Filtered

129 candidates to 89 candidates (69.0%)

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))

rewrite3.0ms

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` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

2.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 4 (50.0ms)

Iter	Nodes	Cost
0	105	215
1	272	201
2	673	200
3	1915	198
4	5002	196

prune123.0ms

Filtered

36 candidates to 24 candidates (66.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(log1p (/ (atan2 im re) (log base)))
0.2b	(expm1 (log1p (/ (atan2 im re) (log base))))
0.3b	(/ (atan2 im re) (log base))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-/r*` `log-pow`
3×	`log1p-expm1-u` `associate-/l*` `add-log-exp`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `div-inv` `expm1-udef`

Counts

3 → 55

Calls

3 calls:

0.0ms	(log1p (/ (atan2 im re) (log base)))
0.0ms	(expm1 (log1p (/ (atan2 im re) (log base))))
2.0ms	(/ (atan2 im re) (log base))

series153.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(log1p (/ (atan2 im re) (log base)))
56.0ms	(expm1 (log1p (/ (atan2 im re) (log base))))
37.0ms	(/ (atan2 im re) (log base))

simplify55.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (50.0ms)

Iter	Nodes	Cost
0	134	363
1	314	331
2	722	327
3	1980	320
4	5002	314

prune189.0ms

Filtered

64 candidates to 40 candidates (62.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (* (atan2 im re) (/ 1 (log base))))
0.2b	(expm1 (log1p (* (atan2 im re) (/ 1 (log base)))))
0.2b	(/ 1 (log base))
0.3b	(* (atan2 im re) (/ 1 (log base)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`times-frac`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`add-exp-log`
16×	`associate-r`
14×	`pow1`
11×	`add-cbrt-cube`
7×	`log-pow`
5×	`expm1-log1p-u`
4×	`div-exp` `prod-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`log1p-udef` `expm1-log1p` `pow-flip` `frac-2neg` `log1p-expm1` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow` `expm1-udef`

Counts

4 → 100

Calls

4 calls:

0.0ms	(log1p (* (atan2 im re) (/ 1 (log base))))
0.0ms	(expm1 (log1p (* (atan2 im re) (/ 1 (log base)))))
2.0ms	(/ 1 (log base))
9.0ms	(* (atan2 im re) (/ 1 (log base)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(log1p (* (atan2 im re) (/ 1 (log base))))
57.0ms	(expm1 (log1p (* (atan2 im re) (/ 1 (log base)))))
155.0ms	(/ 1 (log base))
36.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify50.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	241	591
1	884	511
2	2754	464
3	5001	450

prune210.0ms

Filtered

112 candidates to 61 candidates (54.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0b

regimes274.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	6
1	15	6
2	15	6

end0.0ms

sample1.5s

Algorithm

intervals

Results

578.0ms	8212×	body	80	nan
562.0ms	8000×	body	80	valid