Details

sample69.0ms

Algorithm

intervals

Results

24.0ms	122×	body	320	valid
14.0ms	131×	body	160	valid
13.0ms	245×	body	80	nan
0.0ms	3×	body	80	valid

simplify128.0ms

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

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)))

rewrite48.0ms

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:

19.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
18.0ms	(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)))

series732.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
310.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (38.0ms)

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

prune474.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.9b

localize19.0ms

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)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def`
9×	`add-cube-cbrt`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1`
5×	`cbrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`distribute-lft-neg-in`
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-` `neg-mul-1` `flip3-+` `pow1/3` `neg-log` `associate-*l/` `flip-+`

Counts

4 → 79

Calls

4 calls:

13.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
321.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify42.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	336	679
1	1232	632
2	5001	628

prune550.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 31.7b

localize23.0ms

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)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-log-exp`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3--` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `flip3-+` `fma-neg` `diff-log` `prod-diff` `neg-log` `flip-+`

Counts

4 → 80

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
13.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
4.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
65.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
50.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify113.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	214	476
1	929	438
2	3969	427
3	5001	424

prune526.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.8b

localize27.0ms

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)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`fma-def` `sqrt-div` `add-log-exp`
9×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `frac-times` `distribute-rgt-neg-in` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-pow1`
2×	`pow1/2` `associate-r/` `associate-l/` `sum-log` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `neg-log`

Counts

4 → 83

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
13.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
4.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (* (+ g h) (- g h)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
59.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
52.0ms	(sqrt (- (* g g) (* h h)))
64.0ms	(sqrt (* (+ g h) (- g h)))

simplify45.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	318	522
1	1541	484
2	5002	477

prune495.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 30.8b

regimes732.0ms

Accuracy

75.9% (0.5b remaining)

Error of 31.3b against oracle of 30.8b and baseline of 32.9b

bsearch107.0ms

Steps

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	44
1	45	44
2	45	44

end0.0ms

sample1.8s

Algorithm

intervals

Results

620.0ms	3741×	body	320	valid
462.0ms	4141×	body	160	valid
403.0ms	7969×	body	80	nan
7.0ms	118×	body	80	valid