Details

sample97.0ms

Algorithm

intervals

Results

25.0ms	122×	body	320	valid
24.0ms	286×	body	80	nan
17.0ms	126×	body	160	valid
1.0ms	8×	body	80	valid

simplify117.0ms

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	5001	21

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 36.4b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

7.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
9.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(sqrt (- (* g g) (* h h)))

rewrite35.0ms

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)) (- (neg g) (sqrt (- (* g g) (* h h))))))
11.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
66.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	386	766
1	1391	724
2	5002	718

prune673.0ms

Filtered

72 candidates to 64 candidates (11.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	52	20	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	20	73

Merged error: 32.3b

Counts

73 → 20

localize20.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
9.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(sqrt (- (* g g) (* h h)))

rewrite27.0ms

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))
14.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series87.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
66.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	321	569
1	1271	537
2	5002	533

prune736.0ms

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	69	22	91

Merged error: 31.8b

Counts

91 → 22

localize21.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
3.4b	(- (* g g) (* h h))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(sqrt (- (* g g) (* h h)))

rewrite16.0ms

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))
3.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
6.0ms	(- (* g g) (* h h))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify50.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	123	378
1	439	350
2	1491	350
3	5003	348

prune623.0ms

Filtered

70 candidates to 54 candidates (22.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	20	21
Picked	1	0	1
Done	0	0	0
Total	70	22	92

Merged error: 31.8b

Counts

92 → 22

localize22.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
9.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(sqrt (- (* g g) (* h h)))

rewrite24.0ms

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:

3.0ms	(- (* g g) (* h h))
11.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
67.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	321	575
1	1264	541
2	5001	537

prune518.0ms

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	21	21
Picked	0	1	1
Done	0	0	0
Total	71	22	93

Merged error: 31.8b

Counts

93 → 22

regimes1.2s

Accuracy

77.7% (0.7b remaining)

Error of 32.3b against oracle of 31.6b and baseline of 34.6b

bsearch217.0ms

Steps

Iters	Range		Point
11	-3.763177598489959e-144	-7.7833088808868e-172	-1.3102379320493951e-160

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	40
1	39	40

end0.0ms

sample2.5s

Algorithm

intervals

Results

776.0ms	3764×	body	320	valid
561.0ms	4082×	body	160	valid
552.0ms	8073×	body	80	nan
11.0ms	154×	body	80	valid

Details

sample97.0ms

simplify117.0ms

prune6.0ms

localize17.0ms

rewrite35.0ms

series151.0ms

simplify42.0ms

prune673.0ms

localize20.0ms

rewrite27.0ms

series87.0ms

simplify39.0ms

prune736.0ms

localize21.0ms

rewrite16.0ms

series27.0ms

simplify50.0ms

prune623.0ms

localize22.0ms

rewrite24.0ms

series88.0ms

simplify37.0ms

prune518.0ms

regimes1.2s

bsearch217.0ms

simplify1.0ms

end0.0ms

sample2.5s

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