Details

Time bar (total: 10.8s)

analyze2.3s

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
5.1%94.6%0.3%13
7%92.7%0.3%14

sample50.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
8.0ms97×body80nan
3.0ms41×body80invalid

simplify62.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
0526118

prune16.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 11.6b

Counts
2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
4.5b
(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
4.8b
(* M (/ D (* 2.0 d)))
10.4b
(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
55×add-exp-log
34×add-sqr-sqrt
26×associate-*r*
25×prod-exp
20×add-cbrt-cube
19×add-cube-cbrt *-un-lft-identity
14×times-frac
12×div-exp
11×associate-*l*
9×pow1
8×pow-exp
7×sqrt-prod cbrt-unprod unswap-sqr
4×sqrt-div associate-*r/ add-log-exp
3×cbrt-undiv *-commutative sqr-pow
2×pow-to-exp flip3-- pow-prod-down flip-- div-inv
1×unpow-prod-down rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 111
Calls
4 calls:
6.0ms
(* w0 (sqrt (- 1.0 (* (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
(* M (/ D (* 2.0 d)))
9.0ms
(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

series555.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
153.0ms
(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
6.0ms
(* M (/ D (* 2.0 d)))
217.0ms
(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

simplify68.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049811867
149811867

prune231.0ms

Filtered
82 candidates to 123 candidates (-50.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1176123
Fresh011
Picked101
Done000
Total1187125

Merged error: 7.0b

Counts
125 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
4.5b
(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
4.8b
(* M (/ D (* 2.0 d)))
8.1b
(* h (pow (* M (/ D (* 2.0 d))) 2.0))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
55×add-exp-log
24×prod-exp
20×add-sqr-sqrt add-cbrt-cube
14×*-un-lft-identity
13×div-exp
12×add-cube-cbrt associate-*r*
8×pow-exp
7×pow1
6×times-frac associate-*l* cbrt-unprod
5×sqrt-prod
4×cbrt-undiv add-log-exp
3×associate-/r* unswap-sqr
2×pow-to-exp sqrt-div *-commutative div-inv sqr-pow
1×unpow-prod-down rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num flip-- associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 95
Calls
4 calls:
6.0ms
(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
4.0ms
(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
7.0ms
(* M (/ D (* 2.0 d)))
6.0ms
(* h (pow (* M (/ D (* 2.0 d))) 2.0))

series395.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
124.0ms
(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
6.0ms
(* M (/ D (* 2.0 d)))
94.0ms
(* h (pow (* M (/ D (* 2.0 d))) 2.0))

simplify71.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049881463
149881463

prune190.0ms

Filtered
73 candidates to 107 candidates (-46.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1052107
Fresh246
Picked101
Done000
Total1086114

Merged error: 6.1b

Counts
114 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

4.2b
(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
4.5b
(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
4.8b
(* M (/ D (* 2.0 d)))
4.8b
(* M (/ D (* 2.0 d)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
24×add-cbrt-cube
23×add-sqr-sqrt
19×associate-*r*
18×prod-exp
15×*-un-lft-identity
13×add-cube-cbrt
9×pow1 associate-*l* cbrt-unprod
6×times-frac div-exp
5×sqrt-prod
4×cbrt-undiv pow-exp add-log-exp unswap-sqr
3×*-commutative
2×sqrt-div associate-*r/ pow-prod-down div-inv sqr-pow
1×pow-to-exp unpow-prod-down rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
6.0ms
(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
4.0ms
(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
8.0ms
(* M (/ D (* 2.0 d)))
7.0ms
(* M (/ D (* 2.0 d)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
125.0ms
(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
6.0ms
(* M (/ D (* 2.0 d)))
6.0ms
(* M (/ D (* 2.0 d)))

simplify50.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
050071379

prune244.0ms

Filtered
73 candidates to 108 candidates (-47.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1053108
Fresh145
Picked011
Done000
Total1068114

Merged error: 6.1b

Counts
114 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (* (* (* (cbrt h) (cbrt h)) (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (cbrt h))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
4.5b
(sqrt (- 1.0 (/ (* (* (* (cbrt h) (cbrt h)) (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (cbrt h))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
4.8b
(* M (/ D (* 2.0 d)))
4.8b
(* M (/ D (* 2.0 d)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
627×add-exp-log
404×prod-exp
149×div-exp
108×pow-exp
41×add-cbrt-cube
27×pow-to-exp
21×cbrt-unprod
20×add-sqr-sqrt
15×*-un-lft-identity
14×associate-*r*
13×add-cube-cbrt
10×cbrt-undiv
9×pow1 times-frac
6×associate-*l*
5×sqrt-prod
4×add-log-exp
3×associate-/r* div-inv
2×sqrt-div associate-*r/ pow-prod-down *-commutative unswap-sqr
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 clear-num flip-- associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 185
Calls
4 calls:
22.0ms
(/ (* (* (* (cbrt h) (cbrt h)) (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (cbrt h))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
4.0ms
(sqrt (- 1.0 (/ (* (* (* (cbrt h) (cbrt h)) (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (cbrt h))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
7.0ms
(* M (/ D (* 2.0 d)))
7.0ms
(* M (/ D (* 2.0 d)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (* (* (* (cbrt h) (cbrt h)) (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (cbrt h))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
135.0ms
(sqrt (- 1.0 (/ (* (* (* (cbrt h) (cbrt h)) (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (cbrt h))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
6.0ms
(* M (/ D (* 2.0 d)))
6.0ms
(* M (/ D (* 2.0 d)))

simplify84.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049913577
149913577

prune196.0ms

Filtered
74 candidates to 197 candidates (-166.2%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1961197
Fresh156
Picked101
Done011
Total1987205

Merged error: 6.1b

Counts
205 → 7

regimes1.9s

Accuracy

0% (1.5b remaining)

Error of 9.3b against oracle of 7.8b and baseline of 9.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02532
12532

end0.0ms

analyze2.2s

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
5.1%94.6%0.3%13
7%92.7%0.3%14

sample1.4s

Algorithm
intervals
Results
623.0ms8000×body80valid
247.0ms3153×body80nan
108.0ms1326×body80invalid

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