Details

sample57.0ms

Algorithm

intervals

Results

19.0ms	249×	body	80	nan
19.0ms	256×	body	80	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 34.3b

localize21.0ms

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))
0.5b	(* (log base) (log base))
32.3b	(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:

16.0ms	(/ (- (* (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)))

series248.0ms

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))
146.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (46.0ms)

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

prune468.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

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))

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(/ (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

prune127.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(log1p (expm1 (/ (atan2 im re) (log base))))
0.2b	(expm1 (/ (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×	`associate-/r*` `log-pow` `log1p-expm1-u`
3×	`expm1-log1p-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 (expm1 (/ (atan2 im re) (log base))))
0.0ms	(expm1 (/ (atan2 im re) (log base)))
2.0ms	(/ (atan2 im re) (log base))

series155.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(log1p (expm1 (/ (atan2 im re) (log base))))
63.0ms	(expm1 (/ (atan2 im re) (log base)))
33.0ms	(/ (atan2 im re) (log base))

simplify121.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	140	361
1	354	331
2	879	328
3	3484	315
4	5001	315

prune215.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.4b	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`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` `associate-/l`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `hypot-udef` `flip3--` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `flip-+` `div-inv`

Counts

4 → 109

Calls

4 calls:

0.0ms	(hypot re im)
13.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (atan2 im re) (log base))
5.0ms	(* (log base) (log base))

series276.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot re im)
38.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
27.0ms	(* (atan2 im re) (log base))
167.0ms	(* (log base) (log base))

simplify51.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	396	1034
1	1698	917
2	5001	875

prune369.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes223.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	5

end0.0ms

sample1.6s

Algorithm

intervals

Results

607.0ms	8018×	body	80	nan
598.0ms	8000×	body	80	valid