Details

sample67.0ms

Algorithm

intervals

Results

20.0ms	119×	body	320	valid
15.0ms	132×	body	160	valid
14.0ms	255×	body	80	nan
0.0ms	5×	body	80	valid

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	43	21
1	122	21
2	299	21
3	591	21
4	931	21
5	1162	21
6	1388	21
7	2798	21
8	5002	21

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: 36.8b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

8.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
11.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.4b	(sqrt (- (* g g) (* h h)))
29.4b	(sqrt (- (* g g) (* h h)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-div`
20×	`frac-times`
16×	`*-commutative`
12×	`associate-/r*`
10×	`associate-*l/`
8×	`flip3--` `sqrt-prod` `flip--` `difference-of-squares`
6×	`cbrt-prod` `frac-2neg` `flip3-+` `clear-num` `flip-+`
4×	`sqrt-div` `associate-*r/`
2×	`pow1/2` `pow1/3` `associate-l` `div-inv`

Counts

4 → 56

Calls

4 calls:

9.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
312.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify65.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	606	1032
1	2678	1032
2	5001	1032

prune404.0ms

Filtered

68 candidates to 62 candidates (91.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	52	16	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	16	69

Merged error: 31.8b

Counts

69 → 16

localize23.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* g g) (* h h))
8.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.4b	(sqrt (- (* g g) (* h h)))
29.4b	(sqrt (- (* g g) (* h h)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

17×	`cbrt-div`
16×	`*-commutative`
12×	`difference-of-squares`
10×	`frac-times`
8×	`sqrt-prod`
6×	`flip3-+` `associate-/r*` `flip-+`
5×	`associate-*l/`
4×	`sqrt-div`
3×	`cbrt-prod` `flip3--` `frac-2neg` `clear-num` `flip--`
2×	`pow1/2` `associate-*r/`
1×	`sub-neg` `pow1/3` `associate-l` `div-inv`

Counts

4 → 43

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
9.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
321.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify50.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	440	610
1	2012	606
2	5002	606

prune325.0ms

Filtered

55 candidates to 42 candidates (76.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	45	10	55
Fresh	7	8	15
Picked	1	0	1
Done	0	0	0
Total	53	18	71

Merged error: 30.7b

Counts

71 → 18

localize19.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* g g) (* h h))
2.4b	(- (* g g) (* h h))
29.4b	(sqrt (- (* g g) (* h h)))
29.4b	(sqrt (- (* g g) (* h h)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-commutative` `difference-of-squares`
8×	`sqrt-prod`
4×	`flip3--` `sqrt-div` `flip--`
2×	`sub-neg` `pow1/2`

Counts

4 → 30

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
5.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
32.0ms	(- (* g g) (* h h))
52.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify80.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	83	188
1	274	180
2	673	180
3	2286	180
4	5001	180

prune228.0ms

Filtered

42 candidates to 24 candidates (57.1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	41	19	60

Merged error: 30.6b

Counts

60 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* g g) (* h h))
2.4b	(- (* g g) (* h h))
29.4b	(sqrt (- (* g g) (* h h)))
29.4b	(sqrt (- (* g g) (* h h)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-commutative` `difference-of-squares`
8×	`sqrt-prod`
4×	`flip3--` `sqrt-div` `flip--`
2×	`sub-neg` `pow1/2`

Counts

4 → 30

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
4.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
36.0ms	(- (* g g) (* h h))
44.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify80.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	83	188
1	274	180
2	673	180
3	2286	180
4	5001	180

prune156.0ms

Filtered

42 candidates to 24 candidates (57.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	3	14	17
Picked	1	0	1
Done	0	1	1
Total	44	17	61

Merged error: 30.6b

Counts

61 → 17

regimes625.0ms

Accuracy

61.6% (0.5b remaining)

Error of 31.3b against oracle of 30.8b and baseline of 32.0b

bsearch312.0ms

Steps

Iters	Range		Point
10	7.424835646178562e-156	3.9734604320333723e-140	5.531706596038948e-148
11	-1.006330366555798e-157	-1.5871482242209944e-186	-3.503330331902463e-160

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	41
1	43	41

end0.0ms

sample1.9s

Algorithm

intervals

Results

618.0ms	3794×	body	320	valid
452.0ms	4048×	body	160	valid
436.0ms	8099×	body	80	nan
9.0ms	158×	body	80	valid