Details

sample55.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
18.0ms	270×	body	80	nan

simplify10.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.9b

Counts

2 → 1

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)))
0.3b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

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:

9.0ms	(/ (- (* (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))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
33.0ms	(* (atan2 im re) (log base))
152.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (46.0ms)

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

prune432.0ms

Filtered

120 candidates to 79 candidates (65.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	109	11	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Merged error: 0.1b

Counts

121 → 11

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

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

Counts

1 → 39

Calls

1 calls:

4.0ms

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

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

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

simplify85.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	118	300
1	349	280
2	1031	275
3	2871	272
4	5001	272

prune116.0ms

Filtered

42 candidates to 26 candidates (61.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	33	9	42
Fresh	6	4	10
Picked	0	1	1
Done	0	0	0
Total	39	14	53

Merged error: 0.0b

Counts

53 → 14

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
76×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`log-pow`
35×	`pow1`
25×	`associate-/r*`
17×	`pow-flip` `inv-pow`
15×	`add-exp-log`
9×	`add-cbrt-cube` `associate-/l*`
8×	`div-exp`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`log-div` `div-sub` `distribute-frac-neg` `log-rec` `associate-/r/`

Counts

2 → 153

Calls

2 calls:

8.0ms	(/ 1 (/ (log (/ 1 base)) (atan2 im re)))
6.0ms	(/ (log (/ 1 base)) (atan2 im re))

series94.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ 1 (/ (log (/ 1 base)) (atan2 im re)))
40.0ms	(/ (log (/ 1 base)) (atan2 im re))

simplify50.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	423	1449
1	1800	1277
2	5001	1138

prune241.0ms

Filtered

159 candidates to 67 candidates (42.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	153	6	159
Fresh	8	4	12
Picked	0	1	1
Done	0	1	1
Total	161	12	173

Merged error: 0.0b

Counts

173 → 12

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`prod-exp`
5×	`cbrt-unprod`
4×	`div-exp` `associate-/r*` `log-pow`
3×	`associate-r` `pow-prod-down` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `add-log-exp`
1×	`distribute-lft-neg-out` `pow-flip` `frac-2neg` `mul-1-neg` `associate-r/` `associate-l` `clear-num` `un-div-inv` `-commutative` `div-inv` `inv-pow`

Counts

2 → 60

Calls

2 calls:

3.0ms	(/ 1 (log base))
8.0ms	(* (* -1 (/ 1 (log base))) (atan2 im re))

series218.0ms

Counts

2 → 6

Calls

2 calls:

155.0ms	(/ 1 (log base))
62.0ms	(* (* -1 (/ 1 (log base))) (atan2 im re))

simplify89.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	238	339
1	1089	289
2	4749	264
3	5002	254

prune96.0ms

Filtered

66 candidates to 31 candidates (47.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	2	7	9
Picked	0	1	1
Done	0	2	2
Total	66	12	78

Merged error: 0.0b

Counts

78 → 12

regimes213.0ms

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

sample1.7s

Algorithm

intervals

Results

741.0ms	8118×	body	80	nan
572.0ms	8000×	body	80	valid