Details

sample82.0ms

Algorithm

intervals

Results

26.0ms	124×	body	320	valid
18.0ms	226×	body	80	nan
18.0ms	128×	body	160	valid
0.0ms	4×	body	80	valid

simplify114.0ms

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: 34.4b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

7.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
8.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))

rewrite39.0ms

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:

17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- 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)))

series896.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
496.0ms	(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)))

simplify47.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	385	766
1	1380	724
2	5001	718

prune408.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	50	22	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	22	73

Merged error: 30.0b

Counts

73 → 22

localize20.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
7.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(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`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
14.0ms	(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)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
305.0ms	(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)))

simplify40.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	319	569
1	1259	537
2	5001	533

prune395.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	1	20	21
Picked	1	0	1
Done	0	0	0
Total	69	24	93

Merged error: 29.1b

Counts

93 → 24

localize22.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
7.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(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`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
14.0ms	(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)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
304.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
44.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	319	569
1	1259	537
2	5001	533

prune389.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	23	23
Picked	1	0	1
Done	0	0	0
Total	69	26	95

Merged error: 29.1b

Counts

95 → 26

localize20.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
8.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(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` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

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)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
299.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
43.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	297	571
1	1186	537
2	5001	533

prune279.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	25	25
Picked	0	1	1
Done	0	0	0
Total	70	27	97

Merged error: 29.1b

Counts

97 → 27

regimes961.0ms

Accuracy

77.9% (0.7b remaining)

Error of 32.1b against oracle of 31.4b and baseline of 34.4b

bsearch193.0ms

Steps

Iters	Range		Point
11	-6.75625382863954e-179	-1.2407175660568655e-205	-6.62242747948638e-179

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	40
1	39	40

end0.0ms

sample2.3s

Algorithm

intervals

Results

781.0ms	3720×	body	320	valid
574.0ms	8156×	body	80	nan
573.0ms	4136×	body	160	valid
10.0ms	144×	body	80	valid