Details

Time bar (total: 9.7s)

sample46.0ms

Algorithm
intervals
Results
19.0ms292×body80valid
6.0ms98×body80nan

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 16.9b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

2.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b
(/ (* M D) (* 2.0 d))
13.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×*-commutative
8×times-frac
6×associate-*l*
5×unpow-prod-down associate-*r/
4×sqrt-div
3×clear-num div-inv
2×flip3-- frac-2neg associate-/r* flip-- associate-/l*
1×pow1/2 associate-*r* un-div-inv sqr-pow
Counts
4 → 29
Calls
4 calls:
3.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms
(/ (* M D) (* 2.0 d))
8.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
404.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
364.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms
(/ (* M D) (* 2.0 d))
676.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify117.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0238207
1794207
24224207
35002207

prune171.0ms

Filtered
41 candidates to 34 candidates (82.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New33841
Fresh000
Picked101
Done000
Total34842

Merged error: 9.4b

Counts
42 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (- h))
4.7b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) (- h)) (- l))
4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) (- h)) (- l))))
5.5b
(/ (* M D) (* 2.0 d))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
25×times-frac
21×*-commutative
18×associate-*l*
15×unpow-prod-down
13×neg-mul-1
11×associate-/l*
5×div-inv
3×associate-*r* associate-/r* sqr-pow
2×frac-2neg sqrt-div clear-num distribute-rgt-neg-out
1×flip3-- pow1/2 distribute-frac-neg flip--
Counts
4 → 46
Calls
4 calls:
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (- h))
10.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) (- h)) (- l))
2.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) (- h)) (- l))))
4.0ms
(/ (* M D) (* 2.0 d))

series1.8s

Counts
4 → 12
Calls
4 calls:
729.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (- h))
687.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) (- h)) (- l))
367.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) (- h)) (- l))))
27.0ms
(/ (* M D) (* 2.0 d))

simplify37.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0380365
11287362
25001360

prune277.0ms

Filtered
58 candidates to 53 candidates (91.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New53558
Fresh347
Picked101
Done000
Total57966

Merged error: 8.3b

Counts
66 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (- l) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h))))))
5.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h))
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
17×*-commutative
12×times-frac
6×associate-*l*
5×unpow-prod-down
4×associate-/r* associate-/l*
3×div-inv
2×frac-2neg sqrt-div clear-num
1×neg-mul-1 flip3-- pow1/2 associate-*r* distribute-rgt-neg-out flip-- sqr-pow
Counts
4 → 34
Calls
4 calls:
2.0ms
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (- l) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h))))))
8.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h))
4.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(/ (* M D) (* 2.0 d))

series1.2s

Counts
4 → 12
Calls
4 calls:
385.0ms
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (- l) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h))))))
728.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h))
32.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))

simplify38.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0324293
11313293
25002293

prune255.0ms

Filtered
46 candidates to 42 candidates (91.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New44246
Fresh178
Picked011
Done000
Total451055

Merged error: 8.3b

Counts
55 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) (- h))
4.7b
(/ M (/ (* 2.0 d) D))
4.7b
(/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (- h)) (- l))
4.9b
(sqrt (- 1.0 (/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (- h)) (- l))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
21×associate-*l*
20×associate-/r/
18×unpow-prod-down associate-/l*
14×neg-mul-1
10×times-frac
7×*-commutative
6×frac-2neg clear-num div-inv
3×associate-*r* sqr-pow
2×sqrt-div associate-/r* distribute-rgt-neg-out
1×flip3-- pow1/2 distribute-frac-neg flip--
Counts
4 → 47
Calls
4 calls:
7.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) (- h))
4.0ms
(/ M (/ (* 2.0 d) D))
9.0ms
(/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (- h)) (- l))
2.0ms
(sqrt (- 1.0 (/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (- h)) (- l))))

series1.8s

Counts
4 → 12
Calls
4 calls:
734.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) (- h))
29.0ms
(/ M (/ (* 2.0 d) D))
705.0ms
(/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (- h)) (- l))
318.0ms
(sqrt (- 1.0 (/ (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (- h)) (- l))))

simplify41.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0399381
11397378
25001372

prune245.0ms

Filtered
59 candidates to 51 candidates (86.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New57259
Fresh268
Picked101
Done011
Total60969

Merged error: 8.3b

Counts
69 → 9

regimes754.0ms

Accuracy

0% (2.3b remaining)

Error of 9.3b against oracle of 6.9b and baseline of 9.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02818
13618
24318
34318

end0.0ms

sample1.2s

Algorithm
intervals
Results
576.0ms9356×body80valid
188.0ms3083×body80nan