Details

Time bar (total: 23.7s)

sample100.0ms

Algorithm
intervals
Results
37.0ms303×body80valid
11.0ms88×body80nan

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28118
317718
444118
5257318
done500118

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize22.0ms

Local error

Found 4 expressions with local error:

1.5b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.4b
(/ (* M D) (* 2.0 d))
6.1b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
10.7b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
35×add-sqr-sqrt
27×prod-exp
23×add-cbrt-cube
19×div-exp associate-*r*
17×add-cube-cbrt *-un-lft-identity
14×times-frac
12×associate-*l*
10×pow-exp
8×unswap-sqr
7×pow1 unpow-prod-down sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 113
Calls
4 calls:
18.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
13.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
59.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.1s

Counts
4 → 12
Calls
4 calls:
572.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
46.0ms
(/ (* M D) (* 2.0 d))
600.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
921.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.6s

Counts
125 → 125
Iterations

Useful iterations: 2 (360.0ms)

IterNodesCost
02362311
16202115
230801929
done50011929

prune552.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize58.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
4.4b
(/ (* M D) (* 2.0 d))
6.1b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
6.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite360.0ms

Algorithm
rewrite-expression-head
Rules
609×add-exp-log
325×prod-exp
184×div-exp
75×pow-exp
54×add-cbrt-cube
45×associate-*r*
43×cbrt-unprod
42×times-frac
41×add-sqr-sqrt
36×cbrt-prod
33×add-cube-cbrt *-un-lft-identity
22×cbrt-undiv
15×pow-to-exp
10×associate-*l*
7×pow1 unpow-prod-down
6×unswap-sqr
4×associate-*r/ div-inv add-log-exp
3×sqrt-prod sqr-pow
2×sqrt-div *-commutative
1×frac-times rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ clear-num associate-/r* flip-- associate-/l*
Counts
4 → 242
Calls
4 calls:
196.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
20.0ms
(/ (* M D) (* 2.0 d))
9.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
103.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series2.1s

Counts
4 → 12
Calls
4 calls:
790.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
33.0ms
(/ (* M D) (* 2.0 d))
456.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
776.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify840.0ms

Counts
254 → 254
Iterations

Useful iterations: done (827.0ms)

IterNodesCost
04447867
114647094
done50005188

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize37.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
4.4b
(/ (* M D) (* 2.0 d))
4.4b
(/ (* M D) (* 2.0 d))
6.1b
(sqrt (- 1.0 (* (* (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) (cbrt l)))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
14×add-sqr-sqrt
12×div-exp
9×associate-*r* cbrt-unprod
8×cbrt-undiv add-cube-cbrt *-un-lft-identity
6×unpow-prod-down
5×pow1 pow-exp
4×add-log-exp
3×times-frac associate-*l* sqrt-prod div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip--
Counts
4 → 88
Calls
4 calls:
49.0ms
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
15.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(sqrt (- 1.0 (* (* (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) (cbrt l)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
546.0ms
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
31.0ms
(/ (* M D) (* 2.0 d))
37.0ms
(/ (* M D) (* 2.0 d))
609.0ms
(sqrt (- 1.0 (* (* (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) (cbrt l)))))

simplify1.2s

Counts
100 → 100
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01732440
14402036
221651788
done50001764

prune872.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize39.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
4.4b
(/ (* M D) (* 2.0 d))
4.4b
(* (* M D) (/ 1 (* 2.0 d)))
6.1b
(sqrt (- 1.0 (* (* (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (fabs (/ (cbrt h) (cbrt l))) (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)))) (/ (cbrt h) (cbrt l)))))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
82×add-exp-log
42×prod-exp
39×add-cbrt-cube
16×add-sqr-sqrt div-exp associate-*r* cbrt-unprod
10×pow1 add-cube-cbrt *-un-lft-identity
8×cbrt-undiv
6×unpow-prod-down
5×times-frac pow-exp
4×rec-exp 1-exp associate-*l* add-log-exp
3×pow-prod-down sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 107
Calls
4 calls:
28.0ms
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
13.0ms
(/ (* M D) (* 2.0 d))
69.0ms
(* (* M D) (/ 1 (* 2.0 d)))
6.0ms
(sqrt (- 1.0 (* (* (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (fabs (/ (cbrt h) (cbrt l))) (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)))) (/ (cbrt h) (cbrt l)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
598.0ms
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
39.0ms
(/ (* M D) (* 2.0 d))
53.0ms
(* (* M D) (/ 1 (* 2.0 d)))
693.0ms
(sqrt (- 1.0 (* (* (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (fabs (/ (cbrt h) (cbrt l))) (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)))) (/ (cbrt h) (cbrt l)))))

simplify3.0s

Counts
119 → 119
Iterations

Useful iterations: 2 (767.0ms)

IterNodesCost
02342772
16712495
243952140
done50002140

prune704.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.0b

regimes1.2s

Accuracy

0% (1.0b remaining)

Error of 8.2b against oracle of 7.2b and baseline of 8.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02950
13950
done3950

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.6s9277×body80valid
273.0ms3012×body80nan