Details

Time bar (total: 9.7s)

sample43.0ms

Algorithm
intervals
Results
18.0ms300×body80valid
5.0ms85×body80nan

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21829
34569
415579
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

localize13.0ms

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))

rewrite21.0ms

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))))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.4s

Counts
4 → 12
Calls
4 calls:
389.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
27.0ms
(/ (* M D) (* 2.0 d))
354.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
661.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify114.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0241207
1809207
24240207
35002207

prune162.0ms

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

localize13.0ms

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:
4.0ms
(/ (* M D) (* 2.0 d))
8.0ms
(/ (* (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:
34.0ms
(/ (* M D) (* 2.0 d))
675.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
359.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
715.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify31.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0295224
1954224
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

localize19.0ms

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:
5.0ms
(/ (* 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))
379.0ms
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))))
595.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
712.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify39.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0357309
11494309
25002309

prune240.0ms

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

localize15.0ms

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)

rewrite33.0ms

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:
4.0ms
(/ (* M D) (* 2.0 d))
17.0ms
(/ (* (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)

series1.8s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (* M D) (* 2.0 d))
691.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
367.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
721.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify36.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0357381
11198366
25002366

prune243.0ms

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

regimes434.0ms

Accuracy

22.1% (1.3b remaining)

Error of 8.4b against oracle of 7.1b and baseline of 8.8b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04129
14129

end0.0ms

sample1.2s

Algorithm
intervals
Results
573.0ms9316×body80valid
194.0ms3147×body80nan