Details

sample82.0ms

Algorithm

intervals

Results

23.0ms	110×	body	320	valid
21.0ms	257×	body	80	nan
19.0ms	137×	body	160	valid
1.0ms	9×	body	80	valid

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 38.4b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

6.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.3b	(sqrt (- (* g g) (* h h)))
31.3b	(sqrt (- (* g g) (* h h)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

14.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
13.0ms	(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)))

series860.0ms

Counts

4 → 12

Calls

4 calls:

444.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
322.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	385	766
1	1380	724
2	5002	718

prune398.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	55	17	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	17	73

Merged error: 33.5b

Counts

73 → 17

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.3b	(sqrt (- (* g g) (* h h)))
31.3b	(sqrt (- (* g g) (* h h)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
13.0ms	(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)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
319.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	319	569
1	1259	537
2	5001	533

prune384.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	64	7	71
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	69	19	88

Merged error: 32.9b

Counts

88 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
3.6b	(- (* g g) (* h h))
31.3b	(sqrt (- (* g g) (* h h)))
31.3b	(sqrt (- (* g g) (* h h)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

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)))

series159.0ms

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)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify49.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	122	378
1	432	350
2	1459	350
3	5001	348

prune368.0ms

Filtered

70 candidates to 54 candidates (77.1%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	68	21	89

Merged error: 32.9b

Counts

89 → 21

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.3b	(sqrt (- (* g g) (* h h)))
31.3b	(sqrt (- (* g g) (* h h)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
13.0ms	(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)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
322.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify40.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	319	569
1	1259	537
2	5001	533

prune278.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	2	17	19
Picked	1	0	1
Done	1	0	1
Total	72	20	92

Merged error: 32.9b

Counts

92 → 20

regimes675.0ms

Accuracy

0% (1.3b remaining)

Error of 32.2b against oracle of 30.9b and baseline of 32.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	23
1	25	23

end0.0ms

sample2.3s

Algorithm

intervals

Results

785.0ms	3784×	body	320	valid
568.0ms	8212×	body	80	nan
565.0ms	4063×	body	160	valid
11.0ms	153×	body	80	valid

Details

sample82.0ms

simplify120.0ms

prune4.0ms

localize17.0ms

rewrite36.0ms

series860.0ms

simplify44.0ms

prune398.0ms

localize19.0ms

rewrite26.0ms

series444.0ms

simplify39.0ms

prune384.0ms

localize22.0ms

rewrite17.0ms

series159.0ms

simplify49.0ms

prune368.0ms

localize19.0ms

rewrite26.0ms

series448.0ms

simplify40.0ms

prune278.0ms

regimes675.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

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