Details

sample73.0ms

Algorithm

intervals

Results

21.0ms	130×	body	320	valid
18.0ms	266×	body	80	nan
14.0ms	122×	body	160	valid
0.0ms	4×	body	80	valid

simplify130.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	21
1	125	21
2	317	21
3	648	21
4	1073	21
5	1417	21
6	1725	21
7	3333	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: 39.3b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
10.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
32.8b	(sqrt (- (* g g) (* h h)))
32.8b	(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` `expm1-log1p-u` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

12.0ms	(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)))

series737.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
324.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
52.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify52.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	403	826
1	1482	784
2	5001	777

prune465.0ms

Filtered

80 candidates to 75 candidates (93.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	61	19	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	19	81

Merged error: 34.5b

Counts

81 → 19

localize25.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.8b	(sqrt (- (* g g) (* h h)))
32.8b	(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` `flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

4.0ms	(- (* 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)))
5.0ms	(sqrt (- (* g g) (* h h)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
306.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	315	621
1	1278	588
2	5001	581

prune671.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	68	13	81
Fresh	13	5	18
Picked	1	0	1
Done	0	0	0
Total	82	18	100

Merged error: 33.9b

Counts

100 → 18

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
3.2b	(- (* g g) (* h h))
32.8b	(sqrt (- (* g g) (* h h)))
32.8b	(sqrt (- (* g g) (* h h)))

rewrite18.0ms

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` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

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)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
45.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify52.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	135	420
1	482	394
2	1632	388
3	5001	378

prune479.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	81	19	100

Merged error: 33.8b

Counts

100 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
3.2b	(- (* g g) (* h h))
32.8b	(sqrt (- (* g g) (* h h)))
32.8b	(sqrt (- (* g g) (* h h)))

rewrite18.0ms

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` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

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)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
35.0ms	(- (* g g) (* h h))
43.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	135	420
1	482	394
2	1632	388
3	5001	378

prune352.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	82	19	101

Merged error: 33.8b

Counts

101 → 19

regimes650.0ms

Accuracy

80.6% (0.6b remaining)

Error of 31.9b against oracle of 31.3b and baseline of 34.3b

bsearch181.0ms

Steps

Iters	Range		Point
12	9.882066756411172e-177	1.6329938810163285e-136	5.803774567702152e-156

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	55
1	54	55
2	58	55
3	61	55
4	61	55

end0.0ms

sample1.9s

Algorithm

intervals

Results

617.0ms	3791×	body	320	valid
443.0ms	4069×	body	160	valid
429.0ms	8105×	body	80	nan
10.0ms	140×	body	80	valid