Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune3.0ms

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: 31.4b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sqrt-div`
3×	`flip3-+` `flip-+`
2×	`log-div` `pow1/2` `div-sub`
1×	`+-commutative` `frac-2neg` `clear-num` `log-pow` `div-inv` `associate-/l*`

Counts

3 → 12

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
5.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* re re) (* im im))
136.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify123.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	120	142
1	360	138
2	892	136
3	3575	136
4	5001	136

prune72.0ms

Filtered

21 candidates to 17 candidates (81.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	16	5	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	6	22

Merged error: 7.8b

Counts

22 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(/ 1 (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))))
0.6b	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

4×	`clear-num` `associate-/r/`
3×	`frac-2neg` `pow1/2` `associate-/r*` `div-inv`
2×	`flip3-+` `sqrt-div` `log-pow` `flip-+`
1×	`+-commutative` `remove-double-div` `inv-pow`

Counts

4 → 20

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
6.0ms	(/ 1 (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))))
2.0ms	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
134.0ms	(/ 1 (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))))
139.0ms	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	138	147
1	437	141
2	1356	138
3	5001	136

prune94.0ms

Filtered

32 candidates to 24 candidates (75.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	28	10	38

Merged error: 7.7b

Counts

38 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (log 10.0) (/ 1 (log (sqrt (+ (* re re) (* im im)))))))
0.3b	(/ 1 (log (sqrt (+ (* re re) (* im im)))))
0.6b	(* (log 10.0) (/ 1 (log (sqrt (+ (* re re) (* im im))))))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-*r/`
6×	`clear-num` `associate-/r*` `associate-/r/`
4×	`frac-2neg` `pow1/2` `un-div-inv` `div-inv`
3×	`log-pow`
2×	`sqrt-div` `associate-r` `*-commutative` `inv-pow`
1×	`flip3-+` `flip-+`

Counts

4 → 29

Calls

4 calls:

4.0ms	(/ 1 (* (log 10.0) (/ 1 (log (sqrt (+ (* re re) (* im im)))))))
2.0ms	(/ 1 (log (sqrt (+ (* re re) (* im im)))))
3.0ms	(* (log 10.0) (/ 1 (log (sqrt (+ (* re re) (* im im))))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ 1 (* (log 10.0) (/ 1 (log (sqrt (+ (* re re) (* im im)))))))
81.0ms	(/ 1 (log (sqrt (+ (* re re) (* im im)))))
134.0ms	(* (log 10.0) (/ 1 (log (sqrt (+ (* re re) (* im im))))))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	146	140
1	431	136
2	1106	130
3	2933	127
4	5002	127

prune91.0ms

Filtered

41 candidates to 25 candidates (61.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	39	12	51

Merged error: 7.7b

Counts

51 → 12

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (/ (log 10.0) (log (* -1 re))))
0.3b	(/ (log 10.0) (log (* -1 re)))

rewrite10.0ms

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 10.0) (log (* -1 re))))
6.0ms	(/ (log 10.0) (log (* -1 re)))

series582.0ms

Counts

2 → 6

Calls

2 calls:

279.0ms	(/ 1 (/ (log 10.0) (log (* -1 re))))
303.0ms	(/ (log 10.0) (log (* -1 re)))

simplify73.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	61	64
1	132	59
2	345	58
3	886	53
4	2223	53
5	5002	53

prune26.0ms

Filtered

18 candidates to 9 candidates (50.0%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	16	2	18
Fresh	1	7	8
Picked	0	1	1
Done	0	3	3
Total	17	13	30

Merged error: 7.7b

Counts

30 → 13

regimes575.0ms

Accuracy

53.8% (11.2b remaining)

Error of 19.1b against oracle of 7.9b and baseline of 32.1b

bsearch63.0ms

Steps

Iters	Range		Point
6	5.4636796240070045e+45	3.1545612030570996e+46	3.110542402831786e+46
8	-224.79902743150487	-0.2390566333155073	-222.33808009768373

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	16
1	30	16

end0.0ms

sample504.0ms

Algorithm

intervals

Results

355.0ms

8000×

body

valid