Details

sample69.0ms

Algorithm

intervals

Results

23.0ms	136×	body	320	valid
14.0ms	269×	body	80	nan
13.0ms	117×	body	160	valid
0.0ms	3×	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	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: 37.0b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.6b	(sqrt (- (* g g) (* h h)))
29.6b	(sqrt (- (* g g) (* h h)))

rewrite34.0ms

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:

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

series726.0ms

Counts

4 → 12

Calls

4 calls:

309.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
321.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (35.0ms)

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

prune431.0ms

Filtered

72 candidates to 64 candidates (88.9%)

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: 30.9b

Counts

73 → 21

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- g) (sqrt (- (* g g) (* h h))))
8.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.6b	(sqrt (- (* g g) (* h h)))
29.6b	(sqrt (- (* g g) (* h h)))

rewrite35.0ms

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:

13.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
12.0ms	(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)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
316.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify127.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	333	666
1	1140	629
2	4928	620
3	5002	620

prune455.0ms

Filtered

76 candidates to 64 candidates (84.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	9	11	20
Picked	1	0	1
Done	0	0	0
Total	78	19	97

Merged error: 30.4b

Counts

97 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* g g) (* h h))
1.4b	(- (- g) (sqrt (- (* g g) (* h h))))
29.6b	(sqrt (- (* g g) (* h h)))
29.6b	(sqrt (- (* g g) (* h h)))

rewrite22.0ms

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:

4.0ms	(- (* g g) (* h h))
9.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
65.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
47.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify100.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	189	469
1	768	442
2	3242	436
3	5002	435

prune412.0ms

Filtered

75 candidates to 58 candidates (77.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	4	14	18
Picked	1	0	1
Done	0	0	0
Total	76	18	94

Merged error: 30.3b

Counts

94 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- g) (sqrt (- (* g g) (* h h))))
8.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.6b	(sqrt (- (* g g) (* h h)))
29.6b	(sqrt (- (* g g) (* h h)))

rewrite35.0ms

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:

13.0ms	(- (- 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)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
321.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
53.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify125.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	333	668
1	1140	631
2	4928	620
3	5002	620

prune380.0ms

Filtered

76 candidates to 64 candidates (84.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	0	17	17
Picked	1	0	1
Done	0	0	0
Total	75	19	94

Merged error: 30.3b

Counts

94 → 19

regimes782.0ms

Accuracy

83.9% (0.5b remaining)

Error of 31.6b against oracle of 31.1b and baseline of 34.4b

bsearch178.0ms

Steps

Iters	Range		Point
11	-7.10145127998849e-172	-2.0422538931777442e-197	-6.779846107637631e-172

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	42
1	40	42

end0.0ms

sample1.9s

Algorithm

intervals

Results

628.0ms	3732×	body	320	valid
474.0ms	4124×	body	160	valid
440.0ms	8068×	body	80	nan
8.0ms	144×	body	80	valid