Details

sample115.0ms

Algorithm

intervals

Results

38.0ms	130×	body	320	valid
32.0ms	285×	body	80	nan
25.0ms	126×	body	160	valid

simplify129.0ms

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: 35.3b

localize17.0ms

Local error

Found 4 expressions with local error:

6.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(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:

18.0ms	(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))))))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series752.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
328.0ms	(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)))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	403	824
1	1484	782
2	5001	775

prune467.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.0b

localize25.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(sqrt (- (* g g) (* h h)))

rewrite31.0ms

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:

3.0ms	(- (* g g) (* h h))
17.0ms	(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)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
338.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(sqrt (- (* g g) (* h h)))
53.0ms	(sqrt (- (* g g) (* h h)))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (36.0ms)

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

prune501.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.5b

localize20.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
6.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(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` `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:

3.0ms	(- (* 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)))
5.0ms	(sqrt (- (* g g) (* h h)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
316.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
52.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	315	619
1	1280	588
2	5002	581

prune507.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 31.5b

localize21.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
2.8b	(- (* g g) (* h h))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(sqrt (- (* g g) (* h h)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
3.0ms	(- (* g g) (* h h))
9.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
32.0ms	(- (* g g) (* h h))
53.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	135	420
1	482	394
2	1632	388
3	5001	378

prune417.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 31.4b

regimes673.0ms

Accuracy

78% (0.6b remaining)

Error of 31.8b against oracle of 31.2b and baseline of 33.9b

bsearch134.0ms

Steps

Iters	Range		Point
7	-2.4247465927111454e-163	-3.205736453704625e-165	-2.3907293248482188e-163

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	53
1	45	53

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	3695×	body	320	valid
815.0ms	4156×	body	160	valid
803.0ms	8029×	body	80	nan
16.0ms	149×	body	80	valid