Details

Time bar (total: 16.1s)

sample269.0ms

Algorithm
intervals
Results
140.0ms1244×body80nan
63.0ms410×body80valid

simplify31.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 27.1b

Counts
2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

6.9b
(* (* (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))))
10.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.5b
(pow (/ d h) (/ 1.0 2.0))
10.9b
(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))))
10.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
2.0ms
(pow (/ d h) (/ 1.0 2.0))
2.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
601.0ms
(* (* (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))))
711.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
63.0ms
(pow (/ d h) (/ 1.0 2.0))
63.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify62.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0554575
12108559
25002557

prune367.0ms

Filtered
61 candidates to 53 candidates (86.9%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New421961
Fresh000
Picked101
Done000
Total431962

Merged error: 10.1b

Counts
62 → 19

localize32.0ms

Local error

Found 4 expressions with local error:

6.9b
(* (* (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 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
9.4b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))
10.5b
(pow (/ d h) (/ 1.0 2.0))
10.9b
(pow (/ d l) (/ 1.0 2.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×associate-*l*
9×unpow-prod-down
8×div-inv
7×*-commutative sqr-pow
5×associate-*r/
4×times-frac
3×associate-*r*
2×distribute-rgt-in pow-to-exp sub-neg pow-unpow distribute-lft-in clear-num
1×flip3-- frac-2neg un-div-inv flip-- unswap-sqr
Counts
4 → 34
Calls
4 calls:
9.0ms
(* (* (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 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
8.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))
2.0ms
(pow (/ d h) (/ 1.0 2.0))
2.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
611.0ms
(* (* (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 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
706.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))
58.0ms
(pow (/ d h) (/ 1.0 2.0))
64.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0460559
11771545
25001524

prune290.0ms

Filtered
46 candidates to 38 candidates (82.6%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New321446
Fresh13518
Picked101
Done000
Total461965

Merged error: 9.6b

Counts
65 → 19

localize36.0ms

Local error

Found 4 expressions with local error:

6.2b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l))
6.9b
(* (* (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 2))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l)))))
10.5b
(pow (/ d h) (/ 1.0 2.0))
10.9b
(pow (/ d l) (/ 1.0 2.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
21×associate-*l*
17×times-frac
14×unpow-prod-down
12×neg-mul-1 *-commutative
9×div-inv associate-/l*
8×sqr-pow
4×associate-*r*
2×distribute-rgt-in pow-to-exp sub-neg pow-unpow distribute-lft-in associate-*r/
1×flip3-- frac-2neg distribute-frac-neg clear-num associate-/r* distribute-rgt-neg-out flip-- unswap-sqr
Counts
4 → 45
Calls
4 calls:
10.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l))
9.0ms
(* (* (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 2))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l)))))
2.0ms
(pow (/ d h) (/ 1.0 2.0))
2.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
672.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l))
624.0ms
(* (* (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 2))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l)))))
58.0ms
(pow (/ d h) (/ 1.0 2.0))
65.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0546712
12010687
25002687

prune348.0ms

Filtered
57 candidates to 49 candidates (86.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New461157
Fresh11718
Picked101
Done000
Total581876

Merged error: 7.6b

Counts
76 → 18

localize32.0ms

Local error

Found 4 expressions with local error:

10.5b
(pow (/ d h) (/ 1.0 2.0))
10.5b
(pow (/ d h) (/ 1.0 2.0))
10.9b
(pow (/ d l) (/ 1.0 2.0))
10.9b
(pow (/ d l) (/ 1.0 2.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
8×div-inv
4×pow-to-exp unpow-prod-down pow-unpow sqr-pow
Counts
4 → 16
Calls
4 calls:
2.0ms
(pow (/ d h) (/ 1.0 2.0))
2.0ms
(pow (/ d h) (/ 1.0 2.0))
2.0ms
(pow (/ d l) (/ 1.0 2.0))
3.0ms
(pow (/ d l) (/ 1.0 2.0))

series245.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ d h) (/ 1.0 2.0))
57.0ms
(pow (/ d h) (/ 1.0 2.0))
62.0ms
(pow (/ d l) (/ 1.0 2.0))
62.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 4 (49.0ms)

IterNodesCost
0115148
1269120
2820120
32405120
45002100

prune297.0ms

Filtered
28 candidates to 20 candidates (71.4%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New26228
Fresh21517
Picked101
Done000
Total291746

Merged error: 7.6b

Counts
46 → 17

regimes795.0ms

Accuracy

37.6% (9.1b remaining)

Error of 16.6b against oracle of 7.5b and baseline of 22.1b

bsearch770.0ms

Steps
ItersRangePoint
7
7.94742693071978e+186
8.718640230163806e+188
1.7042909891776182e+187
4
3.631715492995854e+82
6.027276772227959e+82
3.706576782971857e+82
11
-2.1991128365843992e-299
5.554464097013436e-298
-1.86853407285333e-310
3
-1.2333817938772057e+129
-8.987021278480719e+128
-9.614545652285346e+128

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0106125
1112125
2117125
3120125
4125125
5127125
6127125

end0.0ms

sample7.9s

Algorithm
intervals
Results
4.3s38284×body80nan
1.9s12748×body80valid