Details

Time bar (total: 17.4s)

sample229.0ms

Algorithm
intervals
Results
119.0ms1091×body80nan
54.0ms383×body80valid

simplify182.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

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))

rewrite26.0ms

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))
10.0ms
(* (* (/ 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:
617.0ms
(* (* (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))))
66.0ms
(pow (/ d h) (/ 1.0 2.0))
735.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
64.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify61.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0551575
12099559
25001557

prune367.0ms

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
31×*-commutative
26×associate-*r*
24×unpow-prod-down
20×div-inv
18×associate-*l*
10×sqr-pow
8×associate-/l*
3×associate-*l/ associate-/r* associate-/r/
2×distribute-rgt-in pow-to-exp sub-neg pow-unpow frac-2neg distribute-lft-in associate-*r/ clear-num
1×flip3-- flip-- unswap-sqr
Counts
4 → 63
Calls
4 calls:
9.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (/ 2.0 1.0) l))
10.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (/ 2.0 1.0) 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:
769.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (/ 2.0 1.0) l))
635.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (/ 2.0 1.0) l))))
63.0ms
(pow (/ d h) (/ 1.0 2.0))
97.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0616726
12471704
25001704

prune405.0ms

Filtered
75 candidates to 68 candidates (90.7%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New66975
Fresh7714
Picked101
Done000
Total741690

Merged error: 9.1b

Counts
90 → 16

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×unpow-prod-down associate-*l*
8×associate-*r*
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/
1×flip3-- flip-- unswap-sqr
Counts
4 → 29
Calls
4 calls:
5.0ms
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
9.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l) (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 2.0 1.0)))))
2.0ms
(pow (/ d h) (/ 1.0 2.0))
3.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
752.0ms
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
646.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l) (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 2.0 1.0)))))
66.0ms
(pow (/ d h) (/ 1.0 2.0))
60.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0417521
11525507
25002507

prune265.0ms

Filtered
41 candidates to 34 candidates (82.9%)
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New34741
Fresh51015
Picked011
Done000
Total391857

Merged error: 7.9b

Counts
57 → 18

localize35.0ms

Local error

Found 4 expressions with local error:

5.2b
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
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))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
8×unpow-prod-down
7×div-inv
6×associate-*r*
5×*-commutative
4×times-frac sqr-pow
3×pow-to-exp pow-unpow
Counts
4 → 19
Calls
4 calls:
5.0ms
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
3.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))
3.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))
3.0ms
(pow (/ d l) (/ 1.0 2.0))

series907.0ms

Counts
4 → 12
Calls
4 calls:
692.0ms
(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
83.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))
66.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))
65.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify72.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0226170
1662149
23240149
35001149

prune173.0ms

Filtered
31 candidates to 28 candidates (90.3%)
Pruning

20 alts after pruning (18 fresh and 2 done)

PrunedKeptTotal
New28331
Fresh11516
Picked011
Done011
Total292049

Merged error: 7.6b

Counts
49 → 20

regimes798.0ms

Accuracy

42.6% (8.8b remaining)

Error of 16.9b against oracle of 8.1b and baseline of 23.5b

bsearch1.4s

Steps
ItersRangePoint
4
9.983542155463539e+153
1.3705642339211417e+154
1.3482318403016823e+154
9
1.2354394788556486e-127
1.7334984255159758e-122
1.672891020029372e-122
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
088173
188173

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.1s37855×body80nan
1.8s12663×body80valid