Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	194×	body	80	valid
6.0ms	26×	body	2560	valid
4.0ms	23×	body	1280	valid
3.0ms	256×	pre	80	true
1.0ms	8×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

52.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.0ms	(+ (* (* 4.0 p) p) (* x x))
53.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
40.0ms	(+ (* (* 4.0 p) p) (* x x))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify88.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	242	529
1	853	492
2	2977	488
3	5002	487

prune188.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize27.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	500
1	283	484
2	827	484
3	2050	484
4	5001	484

prune408.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.2b

localize26.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	500
1	283	484
2	827	484
3	2050	484
4	5001	484

prune485.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.2b

localize29.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.1b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
18.1b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
16.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
135.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
133.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	170	560
1	527	530
2	2131	526
3	5001	514

prune442.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.2b

regimes387.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	36
1	31	36

end0.0ms

sample856.0ms

Algorithm

intervals

Results

209.0ms	6035×	body	80	valid
183.0ms	812×	body	2560	valid
107.0ms	616×	body	1280	valid
95.0ms	8000×	pre	80	true
42.0ms	300×	body	640	valid
15.0ms	153×	body	320	valid
6.0ms	84×	body	160	valid