Details

sample80.0ms

Algorithm

intervals

Results

22.0ms	108×	body	320	valid
20.0ms	263×	body	80	nan
19.0ms	144×	body	160	valid
0.0ms	4×	body	80	valid

simplify128.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 35.3b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

8.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
11.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(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:

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

series715.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
304.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
48.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify48.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (39.0ms)

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

prune431.0ms

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: 30.5b

Counts

81 → 19

localize20.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
8.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite25.0ms

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`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
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))
11.0ms	(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)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
313.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	337	619
1	1359	588
2	5001	580

prune422.0ms

Filtered

81 candidates to 70 candidates (86.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	81	19	100

Merged error: 30.3b

Counts

100 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
8.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite25.0ms

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`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
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))
11.0ms	(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)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
320.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	337	619
1	1359	588
2	5001	580

prune412.0ms

Filtered

81 candidates to 70 candidates (86.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	81	19	100

Merged error: 30.3b

Counts

100 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
11.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite29.0ms

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))
15.0ms	(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)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
310.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (32.0ms)

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

prune338.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	18	18
Picked	1	0	1
Done	0	0	0
Total	79	21	100

Merged error: 30.3b

Counts

100 → 21

regimes734.0ms

Accuracy

65.2% (1.1b remaining)

Error of 31.7b against oracle of 30.6b and baseline of 33.7b

bsearch185.0ms

Steps

Iters	Range		Point
11	-1.1605235990288052e-153	-2.1832910633573214e-179	-2.130585112571416e-160

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	55
1	53	55
2	54	55
3	62	55
4	70	55
5	70	55

end0.0ms

sample2.3s

Algorithm

intervals

Results

771.0ms	3729×	body	320	valid
565.0ms	4116×	body	160	valid
546.0ms	7940×	body	80	nan
11.0ms	155×	body	80	valid