Details

sample1.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 45.410156%

Guaranteed chance to sample good point: 78.957961%

Results

34.0ms	135×	body	320	valid
19.0ms	116×	body	160	valid
3.0ms	31×	body	80	nan
0.0ms	5×	body	80	valid

simplify115.0ms

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

prune7.0ms

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: 33.6b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
8.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
27.1b	(sqrt (- (* g g) (* h h)))
27.1b	(sqrt (- (* g g) (* h h)))

rewrite32.0ms

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:

11.0ms	(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)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
69.0ms	(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 (33.0ms)

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

prune262.0ms

Filtered

64 candidates to 72 candidates (-12.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	53	19	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	19	73

Merged error: 29.0b

Counts

73 → 19

localize21.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (neg g) (sqrt (- (* g g) (* h h))))
8.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
27.1b	(sqrt (- (* g g) (* h h)))
27.1b	(sqrt (- (* g g) (* h h)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `distribute-lft-out--`
1×	`associate--l-` `cbrt-prod` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `pow1/3` `neg-log` `associate-*l/`

Counts

4 → 64

Calls

4 calls:

8.0ms	(- (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)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (neg g) (sqrt (- (* g g) (* h h))))
68.0ms	(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)))

simplify105.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	303	666
1	1038	629
2	4433	621
3	5001	621

prune251.0ms

Filtered

63 candidates to 76 candidates (-20.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	71	5	76
Fresh	4	14	18
Picked	1	0	1
Done	0	0	0
Total	76	19	95

Merged error: 28.7b

Counts

95 → 19

localize26.0ms

Local error

Found 4 expressions with local error:

27.1b	(sqrt (- (* g g) (* h h)))
27.1b	(sqrt (- (* g g) (* h h)))
27.1b	(sqrt (- (* g g) (* h h)))
27.1b	(sqrt (- (* g g) (* h h)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series28.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify58.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 4 (50.0ms)

Iter	Nodes	Cost
0	97	424
1	239	412
2	579	412
3	1808	412
4	5001	408

prune246.0ms

Filtered

64 candidates to 76 candidates (-18.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	76	19	95

Merged error: 28.7b

Counts

95 → 19

localize21.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (neg g) (sqrt (- (* g g) (* h h))))
8.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
27.1b	(sqrt (- (* g g) (* h h)))
27.1b	(sqrt (- (* g g) (* h h)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `distribute-lft-out--`
1×	`associate--l-` `cbrt-prod` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `pow1/3` `neg-log` `associate-*l/`

Counts

4 → 64

Calls

4 calls:

9.0ms	(- (neg g) (sqrt (- (* g g) (* h h))))
12.0ms	(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)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (neg g) (sqrt (- (* g g) (* h h))))
68.0ms	(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)))

simplify120.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	303	666
1	1038	629
2	4433	621
3	5001	621

prune138.0ms

Filtered

63 candidates to 76 candidates (-20.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	17	18
Picked	0	1	1
Done	0	0	0
Total	76	19	95

Merged error: 28.7b

Counts

95 → 19

regimes878.0ms

Accuracy

72.4% (0.8b remaining)

Error of 31.4b against oracle of 30.6b and baseline of 33.4b

bsearch114.0ms

Steps

Iters	Range		Point
9	1.1033801189897902e-166	1.5006279306300244e-157	1.5924999051122437e-162

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	46
1	45	46
2	45	46

end0.0ms

sample3.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 45.410156%

Guaranteed chance to sample good point: 78.957961%

Results

945.0ms	3737×	body	320	valid
695.0ms	4125×	body	160	valid
60.0ms	731×	body	80	nan
12.0ms	138×	body	80	valid

Details

sample1.3s

simplify115.0ms

prune7.0ms

localize18.0ms

rewrite32.0ms

series149.0ms

simplify42.0ms

prune262.0ms

localize21.0ms

rewrite28.0ms

series91.0ms

simplify105.0ms

prune251.0ms

localize26.0ms

rewrite16.0ms

series28.0ms

simplify58.0ms

prune246.0ms

localize21.0ms

rewrite29.0ms

series91.0ms

simplify120.0ms

prune138.0ms

regimes878.0ms

bsearch114.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling