Details

sample70.0ms

Algorithm

intervals

Results

20.0ms	119×	body	320	valid
17.0ms	132×	body	160	valid
14.0ms	255×	body	80	nan
0.0ms	5×	body	80	valid

simplify122.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	21
1	125	21
2	317	21
3	648	21
4	1073	21
5	1417	21
6	1725	21
7	3333	21
8	5002	21

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: 36.8b

Counts

2 → 1

localize17.0ms

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)))

rewrite34.0ms

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))))))
12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
6.0ms	(sqrt (- (* g g) (* h h)))

series725.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
310.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify66.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	617	1026
1	2787	1026
2	5002	1026

prune398.0ms

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)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

5.0ms	(- (* g g) (* h h))
9.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
304.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
236.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify51.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	451	630
1	2105	627
2	5003	624

prune319.0ms

Filtered

61 candidates to 44 candidates (72.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	50	11	61
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	59	18	77

Merged error: 30.7b

Counts

77 → 18

localize21.0ms

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)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 42

Calls

4 calls:

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

series154.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
47.0ms	(sqrt (- (* g g) (* h h)))
43.0ms	(sqrt (- (* g g) (* h h)))

simplify88.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	92	234
1	321	228
2	816	222
3	2639	196
4	5002	196

prune233.0ms

Filtered

54 candidates to 28 candidates (51.9%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	53	19	72

Merged error: 30.6b

Counts

72 → 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)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 42

Calls

4 calls:

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

series157.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
35.0ms	(- (* g g) (* h h))
43.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify84.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	92	234
1	321	228
2	816	222
3	2639	196
4	5002	196

prune177.0ms

Filtered

54 candidates to 28 candidates (51.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	3	14	17
Picked	1	0	1
Done	0	1	1
Total	56	17	73

Merged error: 30.6b

Counts

73 → 17

regimes604.0ms

Accuracy

61.6% (0.5b remaining)

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

bsearch293.0ms

Steps

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

simplify1.0ms

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

642.0ms	3794×	body	320	valid
463.0ms	4048×	body	160	valid
450.0ms	8099×	body	80	nan
9.0ms	158×	body	80	valid