Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
17.0ms	266×	body	80	nan

simplify13.0ms

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

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: 27.4b

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)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
25.4b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-commutative`
5×	`hypot-def`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l/`
1×	`+-commutative` `pow2` `flip3--` `frac-2neg` `pow1/2` `div-sub` `clear-num` `flip--` `div-inv`

Counts

4 → 19

Calls

4 calls:

10.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
2.0ms	(* (atan2 im re) (log base))
2.0ms	(* (log base) (log base))
5.0ms	(sqrt (+ (* re re) (* im im)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
31.0ms	(* (atan2 im re) (log base))
147.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	228	210
1	741	201
2	2617	188
3	5002	187

prune114.0ms

Filtered

31 candidates to 20 candidates (64.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 0.2b

Counts

32 → 7

localize11.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ (atan2 im re) (log base))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

1×	`frac-2neg` `clear-num` `div-inv`

Counts

1 → 3

Calls

1 calls:

3.0ms

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

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

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

simplify43.0ms

Algorithm

egg-herbie

Counts

6 → 6

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	32	23
1	41	23
2	64	23
3	139	20
4	751	20
5	5002	20

prune57.0ms

Filtered

6 candidates to 4 candidates (66.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	4	2	6
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	5	8	13

Merged error: 0.1b

Counts

13 → 8

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (log base))
0.3b	(* (atan2 im re) (/ 1 (log base)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-*r/` `clear-num`
2×	`frac-2neg` `un-div-inv` `div-inv`
1×	`associate-r` `*-commutative` `inv-pow`

Counts

2 → 11

Calls

2 calls:

2.0ms	(/ 1 (log base))
3.0ms	(* (atan2 im re) (/ 1 (log base)))

series177.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(/ 1 (log base))
31.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify47.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 5 (40.0ms)

Iter	Nodes	Cost
0	39	35
1	90	35
2	181	32
3	340	28
4	1524	28
5	5002	25

prune36.0ms

Filtered

17 candidates to 6 candidates (35.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	17	8	25

Merged error: 0.1b

Counts

25 → 8

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`clear-num`
3×	`frac-2neg` `associate-/r/` `div-inv`
1×	`associate-/r*` `remove-double-div` `inv-pow`

Counts

2 → 12

Calls

2 calls:

3.0ms	(/ 1 (/ (log base) (atan2 im re)))
2.0ms	(/ (log base) (atan2 im re))

series90.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ 1 (/ (log base) (atan2 im re)))
44.0ms	(/ (log base) (atan2 im re))

simplify40.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (12.0ms)

Iter	Nodes	Cost
0	52	56
1	112	53
2	336	45
3	1214	43
4	5001	43

prune27.0ms

Filtered

18 candidates to 9 candidates (50.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	16	2	18
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	16	10	26

Merged error: 0.1b

Counts

26 → 10

regimes182.0ms

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

560.0ms	8000×	body	80	valid
540.0ms	8159×	body	80	nan