Details

sample72.0ms

Algorithm

intervals

Results

24.0ms	125×	body	320	valid
14.0ms	128×	body	160	valid
12.0ms	237×	body	80	nan
0.0ms	3×	body	80	valid

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 39.3b

localize18.0ms

Local error

Found 4 expressions with local error:

7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
34.3b	(sqrt (- (* g g) (* h h)))
34.3b	(sqrt (- (* g g) (* h h)))

rewrite86.0ms

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:

33.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
322.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	385	766
1	1380	724
2	5002	718

prune389.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 36.4b

localize24.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
34.3b	(sqrt (- (* g g) (* h h)))
34.3b	(sqrt (- (* g g) (* h h)))

rewrite61.0ms

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:

10.0ms	(- (* g g) (* h h))
32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
316.0ms	(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)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	297	569
1	1188	537
2	5001	533

prune387.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 36.0b

localize26.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
34.3b	(sqrt (- (* g g) (* h h)))
34.3b	(sqrt (- (* g g) (* h h)))

rewrite62.0ms

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:

8.0ms	(- (* g g) (* h h))
35.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
317.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
52.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune401.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 36.0b

localize26.0ms

Local error

Found 4 expressions with local error:

34.3b	(sqrt (- (* g g) (* h h)))
34.3b	(sqrt (- (* g g) (* h h)))
34.3b	(sqrt (- (* g g) (* h h)))
34.3b	(sqrt (- (* g g) (* h h)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

11.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))
52.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify53.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	96	424
1	234	412
2	572	412
3	1471	412
4	5002	412

prune456.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 36.0b

regimes559.0ms

Accuracy

80.2% (0.6b remaining)

Error of 31.9b against oracle of 31.3b and baseline of 34.1b

bsearch165.0ms

Steps

Iters	Range		Point
11	1.9768890383181146e-169	4.542022577868292e-150	4.794897658246635e-160

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	41
1	48	41
2	48	41

end0.0ms

sample1.9s

Algorithm

intervals

Results

599.0ms	3684×	body	320	valid
446.0ms	4168×	body	160	valid
395.0ms	7797×	body	80	nan
8.0ms	148×	body	80	valid