Details

sample117.0ms

Algorithm

intervals

Results

36.0ms	282×	body	80	nan
32.0ms	152×	body	160	valid
30.0ms	101×	body	320	valid
0.0ms	3×	body	80	valid

simplify117.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 36.6b

localize18.0ms

Local error

Found 4 expressions with local error:

8.1b	(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))))))
31.5b	(sqrt (- (* g g) (* h h)))
31.5b	(sqrt (- (* g g) (* h h)))

rewrite44.0ms

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:

19.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* 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)))
4.0ms	(sqrt (- (* g g) (* h h)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

330.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
315.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	385	768
1	1378	726
2	5001	720

prune433.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 33.5b

localize19.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.5b	(sqrt (- (* g g) (* h h)))
31.5b	(sqrt (- (* g g) (* h h)))

rewrite27.0ms

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` `sqrt-div` `add-cbrt-cube`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

2.0ms	(- (* 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)))
4.0ms	(sqrt (- (* g g) (* h h)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
322.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	319	569
1	1259	537
2	5001	533

prune465.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 33.0b

localize21.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
4.8b	(- (* g g) (* h h))
31.5b	(sqrt (- (* g g) (* h h)))
31.5b	(sqrt (- (* g g) (* h h)))

rewrite14.0ms

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` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

2.0ms	(- (* g g) (* h h))
2.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
45.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify45.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	122	378
1	432	350
2	1459	350
3	5001	348

prune457.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 33.0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (- g) (sqrt (* (+ g h) (- g h))))
4.8b	(- (* g g) (* h h))
31.5b	(sqrt (- (* g g) (* h h)))
31.5b	(sqrt (* (+ g h) (- g h)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

7.0ms	(- (- g) (sqrt (* (+ g h) (- g h))))
3.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (* (+ g h) (- g h)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- g) (sqrt (* (+ g h) (- g h))))
30.0ms	(- (* g g) (* h h))
50.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (* (+ g h) (- g h)))

simplify40.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	287	498
1	1366	469
2	5001	467

prune408.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 32.7b

regimes839.0ms

Accuracy

85.7% (0.5b remaining)

Error of 30.8b against oracle of 30.3b and baseline of 33.6b

bsearch234.0ms

Steps

Iters	Range		Point
11	-1.5627956907882408e-164	-7.044561979089967e-184	-1.4401173585185467e-164

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	46
1	53	46

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.1s	3665×	body	320	valid
913.0ms	8043×	body	80	nan
873.0ms	4225×	body	160	valid
13.0ms	110×	body	80	valid