Details

sample69.0ms

Algorithm

intervals

Results

20.0ms	122×	body	320	valid
18.0ms	131×	body	160	valid
13.0ms	245×	body	80	nan
0.0ms	3×	body	80	valid

simplify116.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize18.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.1b	(sqrt (- (* g g) (* h h)))
29.1b	(sqrt (- (* g g) (* h h)))

rewrite44.0ms

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:

16.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(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)))

series920.0ms

Counts

4 → 12

Calls

4 calls:

511.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
314.0ms	(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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (35.0ms)

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

prune403.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.9b

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b	(+ (- g) (sqrt (- (* g g) (* h h))))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.1b	(sqrt (- (* g g) (* h h)))
29.1b	(sqrt (- (* g g) (* h h)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
5×	`cbrt-div`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `sum-log` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `cbrt-prod` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `pow1/3` `neg-log` `associate-*l/` `flip-+`

Counts

4 → 61

Calls

4 calls:

11.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
16.0ms	(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)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
300.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
47.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify122.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	317	623
1	1131	584
2	4793	575
3	5001	575

prune425.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.8b

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
2.7b	(+ (- g) (sqrt (- (* g g) (* h h))))
29.1b	(sqrt (- (* g g) (* h h)))
29.1b	(sqrt (- (* g g) (* h h)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `distribute-rgt-neg-in` `flip3-+` `diff-log` `neg-log` `flip-+`

Counts

4 → 60

Calls

4 calls:

2.0ms	(- (* g g) (* h h))
11.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
60.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
46.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify109.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	195	428
1	832	397
2	3469	387
3	5001	386

prune396.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.8b

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
2.7b	(+ (- g) (sqrt (- (* g g) (* h h))))
29.1b	(sqrt (- (* g g) (* h h)))
29.1b	(sqrt (* (+ g h) (- g h)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqrt-div` `add-log-exp`
9×	`*-un-lft-identity`
8×	`pow1`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `flip3--` `sqrt-prod` `flip--`
4×	`add-exp-log` `frac-times` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`pow1/2` `associate-r/` `associate-l/` `sum-log` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `diff-log` `pow-prod-down` `neg-log`

Counts

4 → 63

Calls

4 calls:

2.0ms	(- (* g g) (* h h))
15.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
4.0ms	(sqrt (- (* g g) (* h h)))
6.0ms	(sqrt (* (+ g h) (- g h)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
60.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
48.0ms	(sqrt (- (* g g) (* h h)))
55.0ms	(sqrt (* (+ g h) (- g h)))

simplify41.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	293	474
1	1423	440
2	5001	434

prune356.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 30.8b

regimes745.0ms

Accuracy

65.5% (0.5b remaining)

Error of 31.3b against oracle of 30.8b and baseline of 32.3b

bsearch112.0ms

Steps

Iters	Range		Point
7	8.939753670236078e-162	2.2583535890233448e-160	3.224313048166206e-161

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	48
1	56	48
2	56	48

end0.0ms

sample1.9s

Algorithm

intervals

Results

618.0ms	3741×	body	320	valid
471.0ms	4141×	body	160	valid
403.0ms	7969×	body	80	nan
7.0ms	118×	body	80	valid