Details

sample69.0ms

Algorithm

intervals

Results

20.0ms	119×	body	320	valid
15.0ms	282×	body	80	nan
15.0ms	131×	body	160	valid
0.0ms	6×	body	80	valid

simplify126.0ms

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: 39.2b

localize21.0ms

Local error

Found 4 expressions with local error:

7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
8.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
33.1b	(sqrt (- (* g g) (* h h)))
33.1b	(sqrt (- (* g g) (* h h)))

rewrite35.0ms

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:

12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series732.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
317.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
52.0ms	(sqrt (- (* g g) (* h h)))

simplify46.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (37.0ms)

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

prune463.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 36.0b

localize19.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
33.1b	(sqrt (- (* g g) (* h h)))
33.1b	(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`
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:

4.0ms	(- (* g g) (* h h))
12.0ms	(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:

31.0ms	(- (* g g) (* h h))
328.0ms	(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)))

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

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

prune508.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 35.6b

localize20.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
4.8b	(- (* g g) (* h h))
33.1b	(sqrt (- (* g g) (* h h)))
33.1b	(sqrt (- (* g g) (* h h)))

rewrite22.0ms

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:

4.0ms	(- (* g g) (* h h))
7.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
52.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify52.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	135	422
1	482	394
2	1632	388
3	5001	378

prune489.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 35.6b

localize22.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
4.8b	(- (* g g) (* h h))
33.1b	(sqrt (- (* g g) (* h h)))
33.1b	(sqrt (- (* g g) (* h h)))

rewrite21.0ms

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:

4.0ms	(- (* g g) (* h h))
7.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
32.0ms	(- (* g g) (* h h))
52.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	135	420
1	482	394
2	1632	388
3	5001	380

prune422.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 35.6b

regimes876.0ms

Accuracy

77.4% (0.7b remaining)

Error of 31.6b against oracle of 31.0b and baseline of 33.8b

bsearch138.0ms

Steps

Iters	Range		Point
9	-7.812206201917273e-155	-8.851182119783336e-163	-8.030232010219059e-161

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	48
1	44	48

end0.0ms

sample1.9s

Algorithm

intervals

Results

627.0ms	3752×	body	320	valid
469.0ms	4100×	body	160	valid
409.0ms	7876×	body	80	nan
8.0ms	148×	body	80	valid