Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 45.410156%

Guaranteed chance to sample good point: 83.184258%

Results

34.0ms	117×	body	320	valid
23.0ms	132×	body	160	valid
3.0ms	29×	body	80	nan
1.0ms	7×	body	80	valid

simplify116.0ms

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

prune4.0ms

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: 33.9b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
8.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(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:

15.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (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)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
62.0ms	(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	773
1	1381	731
2	5002	725

prune263.0ms

Filtered

66 candidates to 72 candidates (-9.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	51	21	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	21	73

Merged error: 28.6b

Counts

73 → 21

localize18.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (neg g) (sqrt (- (* g g) (* h h))))
8.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h))))))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite31.0ms

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`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-*r/` `flip-+` `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)))
5.0ms	(sqrt (- (* g g) (* h h)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (neg g) (sqrt (- (* g g) (* h h))))
64.0ms	(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)))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	335	666
1	1151	629
2	5001	620

prune260.0ms

Filtered

64 candidates to 76 candidates (-18.8%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	73	24	97

Merged error: 27.9b

Counts

97 → 24

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* g g) (* h h))
1.8b	(- (neg g) (sqrt (- (* g g) (* h h))))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
9.0ms	(- (neg g) (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:

5.0ms	(- (* g g) (* h h))
8.0ms	(- (neg g) (sqrt (- (* g g) (* h h))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify101.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	190	469
1	775	442
2	3391	436
3	5001	435

prune247.0ms

Filtered

58 candidates to 75 candidates (-29.3%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	1	22	23
Picked	1	0	1
Done	0	0	0
Total	74	25	99

Merged error: 27.8b

Counts

99 → 25

localize23.0ms

Local error

Found 4 expressions with local error:

26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite17.0ms

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)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify56.0ms

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

prune138.0ms

Filtered

64 candidates to 76 candidates (-18.8%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	24	24
Picked	0	1	1
Done	0	0	0
Total	76	25	101

Merged error: 27.8b

Counts

101 → 25

regimes969.0ms

Accuracy

0% (1.5b remaining)

Error of 31.7b against oracle of 30.2b and baseline of 31.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	40
1	29	40

end0.0ms

sample3.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 45.410156%

Guaranteed chance to sample good point: 83.184258%

Results

988.0ms	3715×	body	320	valid
737.0ms	4141×	body	160	valid
68.0ms	764×	body	80	nan
13.0ms	144×	body	80	valid

Details

sample1.1s

simplify116.0ms

prune4.0ms

localize17.0ms

rewrite36.0ms

series142.0ms

simplify42.0ms

prune263.0ms

localize18.0ms

rewrite31.0ms

series86.0ms

simplify40.0ms

prune260.0ms

localize19.0ms

rewrite21.0ms

series28.0ms

simplify101.0ms

prune247.0ms

localize23.0ms

rewrite17.0ms

series30.0ms

simplify56.0ms

prune138.0ms

regimes969.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.2s

Profiling