Details

sample51.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
14.0ms	220×	body	80	nan

simplify12.0ms

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: 30.3b

Counts

2 → 1

localize18.0ms

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))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

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))
3.0ms	(* (log base) (log base))
5.0ms	(sqrt (+ (* re re) (* im im)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- (* (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))
156.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (72.0ms)

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

prune103.0ms

Filtered

31 candidates to 20 candidates (64.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	26	5	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	5	32

Merged error: 0.1b

Counts

32 → 5

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 4

Calls

1 calls:

2.0ms

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

series38.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

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

simplify69.0ms

Algorithm

egg-herbie

Counts

7 → 7

Iterations

Useful iterations: 6 (66.0ms)

Iter	Nodes	Cost
0	33	28
1	46	26
2	84	26
3	140	26
4	354	26
5	963	26
6	5001	24

prune31.0ms

Filtered

7 candidates to 5 candidates (71.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	5	2	7
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	5	7	12

Merged error: 0.1b

Counts

12 → 7

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 13

Calls

2 calls:

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

series315.0ms

Counts

2 → 6

Calls

2 calls:

153.0ms	(/ 1 (log (/ 1 base)))
161.0ms	(* (atan2 im re) (/ 1 (log (/ 1 base))))

simplify134.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	43	40
1	123	38
2	326	37
3	746	30
4	2284	30
5	5001	30

prune42.0ms

Filtered

19 candidates to 8 candidates (42.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	19	0	19
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	19	7	26

Merged error: 0.1b

Counts

26 → 7

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (hypot im re)) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-/r/` `*-commutative` `associate-/l/`
1×	`pow2` `flip3--` `frac-2neg` `flip3-+` `div-sub` `clear-num` `flip--` `flip-+` `div-inv`

Counts

3 → 11

Calls

3 calls:

9.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot im re)) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
2.0ms	(* (atan2 im re) (log base))
3.0ms	(* (log base) (log base))

series214.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot im re)) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
27.0ms	(* (atan2 im re) (log base))
150.0ms	(* (log base) (log base))

simplify65.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	164	155
1	561	147
2	2159	136
3	5001	135

prune49.0ms

Filtered

20 candidates to 11 candidates (55.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	16	4	20
Fresh	4	0	4
Picked	1	0	1
Done	0	2	2
Total	21	6	27

Merged error: 0.0b

Counts

27 → 6

regimes158.0ms

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	14	5
1	16	5
2	16	5

end0.0ms

sample1.5s

Algorithm

intervals

Results

592.0ms	8000×	body	80	valid
564.0ms	8005×	body	80	nan