Details

Time bar (total: 9.8s)

sample42.0ms

Algorithm
intervals
Results
17.0ms300×body80valid
5.0ms85×body80nan

simplify52.0ms

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: 15.3b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b
(/ (* M D) (* 2.0 d))
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
10.4b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite17.0ms

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)))))
4.0ms
(/ (* M D) (* 2.0 d))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
8.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
394.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
27.0ms
(/ (* M D) (* 2.0 d))
357.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
690.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify110.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0238207
1794207
24142207
35001207

prune170.0ms

Filtered
41 candidates to 34 candidates (82.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New34741
Fresh000
Picked101
Done000
Total35742

Merged error: 7.0b

Counts
42 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2.0 d))
4.1b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.2b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
16×*-commutative
12×times-frac associate-*l*
10×unpow-prod-down associate-/l*
4×div-inv
2×frac-2neg sqrt-div clear-num associate-/r* sqr-pow
1×flip3-- pow1/2 flip--
Counts
4 → 32
Calls
4 calls:
5.0ms
(/ (* M D) (* 2.0 d))
9.0ms
(/ (* (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)))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.8s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
700.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
387.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
723.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify29.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0292224
1945224
25001224

prune195.0ms

Filtered
44 candidates to 40 candidates (90.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New40444
Fresh426
Picked101
Done000
Total45651

Merged error: 6.8b

Counts
51 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2.0 d))
4.2b
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))))
4.6b
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
5.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
16×*-commutative
12×times-frac associate-*l*
10×unpow-prod-down associate-/r*
4×div-inv
2×frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×flip3-- pow1/2 flip--
Counts
4 → 32
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
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)))))
7.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.7s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
374.0ms
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))))
604.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
724.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify37.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0354309
11484309
25002309

prune283.0ms

Filtered
44 candidates to 42 candidates (95.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New42244
Fresh145
Picked101
Done000
Total44650

Merged error: 6.8b

Counts
50 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2.0 d))
4.1b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
4.2b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
21×*-commutative
18×associate-*l* associate-/l*
16×times-frac
15×unpow-prod-down
8×associate-*r*
5×div-inv
3×sqr-pow
2×frac-2neg sqrt-div clear-num associate-/r*
1×flip3-- pow1/2 flip--
Counts
4 → 40
Calls
4 calls:
5.0ms
(/ (* M D) (* 2.0 d))
19.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
2.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.9s

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (* M D) (* 2.0 d))
781.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
378.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
719.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify33.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0354381
11189366
25001366

prune252.0ms

Filtered
52 candidates to 47 candidates (90.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New50252
Fresh145
Picked101
Done000
Total52658

Merged error: 6.8b

Counts
58 → 6

regimes312.0ms

Accuracy

0% (3.1b remaining)

Error of 10.2b against oracle of 7.1b and baseline of 10.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02816
12816

end0.0ms

sample1.2s

Algorithm
intervals
Results
552.0ms9316×body80valid
188.0ms3147×body80nan