Details

sample55.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
16.0ms	237×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	44	16
2	56	16
3	74	16
4	80	16
5	80	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

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))
0.5b	(* (log base) (log base))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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×	`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--` `div-inv`

Counts

4 → 108

Calls

4 calls:

13.0ms	(/ (- (* (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:

40.0ms	(/ (- (* (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))
147.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	444	1213
1	1816	1100
2	5001	1070

prune441.0ms

Pruning

11 alts after pruning (11 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` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

2.0ms

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

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

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

simplify51.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 4 (48.0ms)

Iter	Nodes	Cost
0	103	207
1	270	193
2	671	192
3	1907	190
4	5001	188

prune107.0ms

Pruning

14 alts after pruning (14 fresh and 0 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))

rewrite18.0ms

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×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

2 → 119

Calls

2 calls:

10.0ms	(/ 1 (/ (log base) (atan2 im re)))
3.0ms	(/ (log base) (atan2 im re))

series95.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ 1 (/ (log base) (atan2 im re)))
41.0ms	(/ (log base) (atan2 im re))

simplify40.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	335	999
1	1404	889
2	5001	788

prune209.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

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` `rec-exp` `1-exp` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `inv-pow`

Counts

2 → 73

Calls

2 calls:

10.0ms	(* (/ 1 (log base)) (atan2 im re))
3.0ms	(/ 1 (log base))

series211.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(* (/ 1 (log base)) (atan2 im re))
157.0ms	(/ 1 (log base))

simplify92.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	201	398
1	778	342
2	1905	307
3	4147	301
4	5002	301

prune126.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes210.0ms

Accuracy

0% (0.2b 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	10	3
1	10	3

end0.0ms

sample1.5s

Algorithm

intervals

Results

577.0ms	8140×	body	80	nan
562.0ms	8000×	body	80	valid