Details

Time bar (total: 17.1s)

sample226.0ms

Algorithm
intervals
Results
116.0ms1091×body80nan
54.0ms383×body80valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
272017
3500117

prune4.0ms

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: 25.5b

Counts
2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

6.6b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
9.5b
(pow (/ d h) (/ 1.0 2.0))
12.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.6b
(pow (/ d l) (/ 1.0 2.0))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l*
15×associate-*l/
9×frac-times unpow-prod-down associate-*r* clear-num div-inv
8×frac-2neg *-commutative
7×sqr-pow
5×associate-*r/
4×times-frac
2×distribute-rgt-in pow-to-exp sub-neg pow-unpow distribute-lft-in
1×flip3-- un-div-inv flip-- unswap-sqr
Counts
4 → 49
Calls
4 calls:
10.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
2.0ms
(pow (/ d h) (/ 1.0 2.0))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
2.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
631.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
65.0ms
(pow (/ d h) (/ 1.0 2.0))
715.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
60.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify59.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0554575
12108559
25002557

prune340.0ms

Filtered
61 candidates to 53 candidates (86.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New461561
Fresh000
Picked101
Done000
Total471562

Merged error: 10.4b

Counts
62 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

6.3b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
6.6b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
9.5b
(pow (/ d h) (/ 1.0 2.0))
13.6b
(pow (/ d l) (/ 1.0 2.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
33×associate-*l*
32×times-frac
31×*-commutative
20×associate-*r*
19×unpow-prod-down
10×div-inv associate-/l*
9×sqr-pow
2×distribute-rgt-in pow-to-exp sub-neg pow-unpow distribute-lft-in associate-*r/ associate-/r*
1×flip3-- frac-2neg clear-num flip-- unswap-sqr
Counts
4 → 57
Calls
4 calls:
10.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
9.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
2.0ms
(pow (/ d h) (/ 1.0 2.0))
2.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
724.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
657.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
60.0ms
(pow (/ d h) (/ 1.0 2.0))
66.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0595659
12049645
25002645

prune374.0ms

Filtered
69 candidates to 62 candidates (89.9%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New581169
Fresh9514
Picked101
Done000
Total681684

Merged error: 9.1b

Counts
84 → 16

localize37.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.6b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (/ (* 1.0 (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) 2.0) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
9.5b
(pow (/ d h) (/ 1.0 2.0))
13.6b
(pow (/ d l) (/ 1.0 2.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×associate-*l*
9×unpow-prod-down
7×*-commutative div-inv sqr-pow
4×times-frac
2×distribute-rgt-in pow-to-exp sub-neg pow-unpow distribute-lft-in associate-*r/ associate-*r*
1×flip3-- flip-- unswap-sqr
Counts
4 → 29
Calls
4 calls:
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
10.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (/ (* 1.0 (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) 2.0) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
2.0ms
(pow (/ d h) (/ 1.0 2.0))
3.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
703.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
617.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (/ (* 1.0 (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) 2.0) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
61.0ms
(pow (/ d h) (/ 1.0 2.0))
238.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0441529
11610515
25001514

prune257.0ms

Filtered
41 candidates to 34 candidates (82.9%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New35641
Fresh51015
Picked011
Done000
Total401757

Merged error: 7.9b

Counts
57 → 17

localize38.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
9.5b
(pow (/ d h) (/ (/ 1.0 2.0) 2))
9.5b
(pow (/ d h) (/ (/ 1.0 2.0) 2))
13.6b
(pow (/ d l) (/ 1.0 2.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×unpow-prod-down
7×div-inv
6×associate-*l*
5×*-commutative
4×times-frac sqr-pow
3×pow-to-exp pow-unpow
Counts
4 → 19
Calls
4 calls:
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
3.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))
3.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))
2.0ms
(pow (/ d l) (/ 1.0 2.0))

series917.0ms

Counts
4 → 12
Calls
4 calls:
726.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
66.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))
65.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))
60.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify77.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0246178
1734157
23547157
35002157

prune181.0ms

Filtered
31 candidates to 28 candidates (90.3%)
Pruning

19 alts after pruning (17 fresh and 2 done)

PrunedKeptTotal
New28331
Fresh11415
Picked011
Done011
Total291948

Merged error: 7.6b

Counts
48 → 19

regimes765.0ms

Accuracy

38.5% (9.4b remaining)

Error of 17.6b against oracle of 8.2b and baseline of 23.5b

bsearch1.4s

Steps
ItersRangePoint
4
9.983542155463539e+153
1.3705642339211417e+154
1.3482318403016823e+154
8
1.945727474439915e-104
6.421977964855124e-102
4.4873787195281464e-102
10
-1.1560362044200962e-298
1.370484824164856e-306
-5.947329688418974e-309
7
-5.0093397021035504e-64
-2.5569140972568866e-66
-3.610070899996603e-66
9
-1.062337529556331e+204
-1.1270786676968276e+198
-2.5139383191211987e+200

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
098166
198166

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.1s37855×body80nan
1.8s12663×body80valid