Details

sample68.0ms

Algorithm

intervals

Results

21.0ms	122×	body	320	valid
15.0ms	131×	body	160	valid
13.0ms	243×	body	80	nan
0.0ms	3×	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: 36.2b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.8b	(sqrt (- (* g g) (* h h)))
31.8b	(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` `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:

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

series718.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
312.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify50.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	403	824
1	1484	782
2	5001	775

prune412.0ms

Filtered

80 candidates to 73 candidates (91.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	67	13	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	13	81

Merged error: 33.9b

Counts

81 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
6.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.8b	(sqrt (- (* g g) (* h h)))
31.8b	(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` `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)))
4.0ms	(sqrt (- (* g g) (* h h)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
305.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	315	619
1	1280	588
2	5002	581

prune413.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	78	16	94

Merged error: 33.1b

Counts

94 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
31.8b	(sqrt (- (* g g) (* h h)))
31.8b	(sqrt (- (* g g) (* h h)))

rewrite22.0ms

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))
8.0ms	(- (* 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:

29.0ms	(- (* g g) (* h h))
31.0ms	(- (* g g) (* h h))
51.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify51.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	135	422
1	482	394
2	1632	388
3	5001	378

prune373.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	82	16	98

Merged error: 33.1b

Counts

98 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
6.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.8b	(sqrt (- (* g g) (* h h)))
31.8b	(sqrt (- (* g g) (* h h)))

rewrite31.0ms

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))))))
8.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* g g) (* h h))
301.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
44.0ms	(sqrt (- (* g g) (* h h)))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	315	619
1	1280	588
2	5002	581

prune329.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	14	14
Picked	1	0	1
Done	0	1	1
Total	80	17	97

Merged error: 33.1b

Counts

97 → 17

regimes579.0ms

Accuracy

0% (1.2b remaining)

Error of 32.3b against oracle of 31.1b and baseline of 32.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	23
1	25	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

619.0ms	3721×	body	320	valid
456.0ms	4120×	body	160	valid
431.0ms	7892×	body	80	nan
11.0ms	159×	body	80	valid