Details

sample69.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
23.0ms	246×	body	80	nan

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize25.0ms

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))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

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:

8.0ms	(* (atan2 im re) (log base))
28.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (atan2 im re) (log base))
32.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
146.0ms	(* (log base) (log base))
32.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	466	1254
1	1924	1122
2	5002	1083

prune901.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `log-pow`
9×	`pow1`
6×	`associate-/r*`
4×	`pow-flip` `inv-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 → 41

Calls

1 calls:

7.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify91.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	120	310
1	351	290
2	1033	285
3	2903	282
4	5002	282

prune179.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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:

18.0ms	(* (atan2 im re) (/ -1 (log base)))
5.0ms	(/ -1 (log base))

series199.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(* (atan2 im re) (/ -1 (log base)))
161.0ms	(/ -1 (log base))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

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

prune244.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (atan2 im re) (log base))
0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (* 1 (hypot re im))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`pow1`
12×	`log-prod`
9×	`add-exp-log` `times-frac` `add-cbrt-cube`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `flip3--` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `flip-+` `div-inv`

Counts

3 → 99

Calls

3 calls:

9.0ms	(* (atan2 im re) (log base))
31.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (* 1 (hypot re im))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))

series209.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* (atan2 im re) (log base))
32.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (* 1 (hypot re im))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
146.0ms	(* (log base) (log base))

simplify56.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	383	1055
1	1708	936
2	5001	888

prune607.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes273.0ms

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	14	5
1	16	5
2	16	5

end0.0ms

sample1.9s

Algorithm

intervals

Results

816.0ms	8000×	body	80	valid
736.0ms	8038×	body	80	nan