Details

sample68.0ms

Algorithm

intervals

Results

20.0ms	123×	body	320	valid
17.0ms	131×	body	160	valid
10.0ms	207×	body	80	nan
0.0ms	2×	body	80	valid

simplify123.0ms

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: 37.8b

localize18.0ms

Local error

Found 4 expressions with local error:

7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite88.0ms

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:

32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
34.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
10.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series641.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
277.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
39.0ms	(sqrt (- (* g g) (* h h)))

simplify45.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (36.0ms)

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

prune445.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.8b

localize20.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite67.0ms

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:

10.0ms	(- (* g g) (* h h))
30.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (* g g) (* h h))
281.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
40.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (32.0ms)

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

prune494.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 32.6b

localize20.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
3.6b	(- (* g g) (* h h))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite43.0ms

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:

8.0ms	(- (* g g) (* h h))
8.0ms	(- (* g g) (* h h))
11.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
26.0ms	(- (* g g) (* h h))
43.0ms	(sqrt (- (* g g) (* h h)))
40.0ms	(sqrt (- (* g g) (* h h)))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (43.0ms)

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

prune484.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 32.6b

localize25.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
3.6b	(- (* g g) (* h h))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite39.0ms

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:

8.0ms	(- (* g g) (* h h))
8.0ms	(- (* g g) (* h h))
11.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (* g g) (* h h))
32.0ms	(- (* g g) (* h h))
39.0ms	(sqrt (- (* g g) (* h h)))
44.0ms	(sqrt (- (* g g) (* h h)))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (43.0ms)

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

prune405.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 32.6b

regimes845.0ms

Accuracy

59% (1.3b remaining)

Error of 32.1b against oracle of 30.8b and baseline of 33.9b

bsearch141.0ms

Steps

Iters	Range		Point
9	-1.1653015587115658e-160	-2.7714262171513926e-167	-1.5872522339816564e-162

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	67
1	50	67
2	51	67
3	59	67
4	67	67
5	67	67

end0.0ms

sample1.9s

Algorithm

intervals

Results

594.0ms	3680×	body	320	valid
440.0ms	4135×	body	160	valid
401.0ms	7897×	body	80	nan
10.0ms	185×	body	80	valid