Details

sample70.0ms

Algorithm

intervals

Results

23.0ms	125×	body	320	valid
14.0ms	129×	body	160	valid
14.0ms	264×	body	80	nan
0.0ms	2×	body	80	valid

simplify124.0ms

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: 35.3b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite35.0ms

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

series930.0ms

Counts

4 → 12

Calls

4 calls:

507.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
327.0ms	(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)))

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

prune443.0ms

Filtered

80 candidates to 73 candidates (91.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	63	17	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	17	81

Merged error: 31.9b

Counts

81 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(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)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
308.0ms	(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)))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (34.0ms)

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

prune409.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	81	17	98

Merged error: 31.6b

Counts

98 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(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))
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)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
315.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (35.0ms)

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

prune395.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	81	17	98

Merged error: 31.6b

Counts

98 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
8.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite30.0ms

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))
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)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
321.0ms	(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 (36.0ms)

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

prune347.0ms

Filtered

81 candidates to 70 candidates (86.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	81	17	98

Merged error: 31.6b

Counts

98 → 17

regimes582.0ms

Accuracy

78.6% (0.6b remaining)

Error of 31.5b against oracle of 30.9b and baseline of 33.7b

bsearch167.0ms

Steps

Iters	Range		Point
10	1.6147928685964824e-179	6.96600622823193e-162	6.838979032133652e-162

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	48
1	54	48
2	58	48
3	61	48
4	61	48

end0.0ms

sample1.9s

Algorithm

intervals

Results

606.0ms	3756×	body	320	valid
454.0ms	4097×	body	160	valid
425.0ms	7961×	body	80	nan
8.0ms	147×	body	80	valid