Details

sample76.0ms

Algorithm

intervals

Results

29.0ms	256×	body	80	valid
29.0ms	265×	body	80	nan

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize18.0ms

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))
28.0b	(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:

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)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (atan2 im re) (log base))
33.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
140.0ms	(* (log base) (log base))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	466	1254
1	1924	1122
2	5002	1081

prune432.0ms

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))

series31.0ms

Counts

1 → 3

Calls

1 calls:

31.0ms

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

simplify51.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 4 (48.0ms)

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

prune99.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `associate-/r*`
16×	`log-pow`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

2 → 123

Calls

2 calls:

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

series90.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ 1 (/ (log base) (atan2 im re)))
44.0ms	(/ (log base) (atan2 im re))

simplify42.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	339	1017
1	1408	907
2	5001	806

prune194.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`times-frac`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`associate-l`
15×	`add-exp-log`
12×	`pow1`
9×	`add-cbrt-cube`
7×	`log-pow`
4×	`div-exp` `prod-exp` `associate-/r*`
3×	`associate-r` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `1-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `inv-pow`

Counts

2 → 77

Calls

2 calls:

2.0ms	(/ 1 (log base))
10.0ms	(* (/ 1 (log base)) (atan2 im re))

series204.0ms

Counts

2 → 6

Calls

2 calls:

153.0ms	(/ 1 (log base))
51.0ms	(* (/ 1 (log base)) (atan2 im re))

simplify92.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	205	414
1	782	358
2	1909	323
3	4191	317
4	5003	317

prune130.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0b

regimes197.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	3

end0.0ms

sample2.0s

Algorithm

intervals

Results

913.0ms	8000×	body	80	valid
766.0ms	7750×	body	80	nan