Details

sample53.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
17.0ms	252×	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

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: 34.6b

Counts

2 → 1

localize19.0ms

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))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

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)))
7.0ms	(* (atan2 im re) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
26.0ms	(* (atan2 im re) (log base))
147.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

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

prune411.0ms

Filtered

120 candidates to 79 candidates (65.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	12	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Merged error: 0.1b

Counts

121 → 12

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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:

6.0ms

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

series32.0ms

Counts

1 → 3

Calls

1 calls:

32.0ms

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

simplify52.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 4 (49.0ms)

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

prune91.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	28	6	34
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	34	12	46

Merged error: 0.0b

Counts

46 → 12

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (log base) (atan2 im re))
0.7b	(/ 1 (/ (log base) (atan2 im re)))

rewrite15.0ms

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:

4.0ms	(/ (log base) (atan2 im re))
6.0ms	(/ 1 (/ (log base) (atan2 im re)))

series89.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (log base) (atan2 im re))
47.0ms	(/ 1 (/ (log base) (atan2 im re)))

simplify41.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (30.0ms)

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

prune162.0ms

Filtered

125 candidates to 54 candidates (43.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	4	6	10
Picked	1	0	1
Done	0	1	1
Total	126	11	137

Merged error: 0.0b

Counts

137 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (log base)) (cbrt (log base)))
0.5b	(cbrt (log base))
0.5b	(cbrt (log base))
0.5b	(cbrt (log base))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`pow1`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`pow1/3` `swap-sqr` `log-pow`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (log base)) (cbrt (log base)))
1.0ms	(cbrt (log base))
1.0ms	(cbrt (log base))
1.0ms	(cbrt (log base))

series1.0s

Counts

4 → 12

Calls

4 calls:

268.0ms	(* (cbrt (log base)) (cbrt (log base)))
262.0ms	(cbrt (log base))
252.0ms	(cbrt (log base))
251.0ms	(cbrt (log base))

simplify87.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	121	487
1	430	416
2	2982	358
3	5001	351

prune175.0ms

Filtered

93 candidates to 56 candidates (60.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	93	11	104

Merged error: 0b

Counts

104 → 11

regimes175.0ms

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	6	3

end0.0ms

sample1.5s

Algorithm

intervals

Results

554.0ms	8000×	body	80	valid
527.0ms	8012×	body	80	nan