Details

Time bar (total: 25.1s)

sample70.0ms

Algorithm
intervals
Results
23.0ms297×body80valid
8.0ms97×body80nan

simplify4.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01718
13618
28118
317618
442218
5117418
6457018
done500018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.8b
(/ (* M D) (* 2.0 d))
12.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite84.0ms

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)))))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
16.0ms
(/ (* M D) (* 2.0 d))
40.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.1s

Counts
4 → 12
Calls
4 calls:
637.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
531.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
39.0ms
(/ (* M D) (* 2.0 d))
926.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.3s

Counts
125 → 125
Iterations

Useful iterations: 2 (376.0ms)

IterNodesCost
02362311
15772083
222621927
done50001927

prune608.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.6b

localize32.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
4.0b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
4.8b
(/ (* M D) (* 2.0 d))
7.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite362.0ms

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:
235.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
5.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
13.0ms
(/ (* M D) (* 2.0 d))
88.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series2.6s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
575.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
48.0ms
(/ (* M D) (* 2.0 d))
878.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify829.0ms

Counts
254 → 254
Iterations

Useful iterations: done (813.0ms)

IterNodesCost
04447867
111106986
done50005154

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize31.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
4.0b
(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)))))
4.8b
(/ (* M D) (* 2.0 d))
4.8b
(/ (* M D) (* 2.0 d))

rewrite96.0ms

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:
30.0ms
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
10.0ms
(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)))))
25.0ms
(/ (* M D) (* 2.0 d))
25.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
792.0ms
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
664.0ms
(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)))))
35.0ms
(/ (* M D) (* 2.0 d))
49.0ms
(/ (* M D) (* 2.0 d))

simplify1.4s

Counts
100 → 100
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01732440
14182030
218101788
done50001764

prune656.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize42.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
4.0b
(sqrt (- 1.0 (* (* (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (* (cbrt (fabs (/ (cbrt h) (cbrt l)))) (cbrt (fabs (/ (cbrt h) (cbrt l))))) (* (cbrt (fabs (/ (cbrt h) (cbrt l)))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))))) (/ (cbrt h) (cbrt l)))))
4.8b
(/ (* M D) (* 2.0 d))
4.8b
(/ (* M D) (* 2.0 d))

rewrite90.0ms

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:
43.0ms
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
10.0ms
(sqrt (- 1.0 (* (* (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (* (cbrt (fabs (/ (cbrt h) (cbrt l)))) (cbrt (fabs (/ (cbrt h) (cbrt l))))) (* (cbrt (fabs (/ (cbrt h) (cbrt l)))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))))) (/ (cbrt h) (cbrt l)))))
20.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
682.0ms
(* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
775.0ms
(sqrt (- 1.0 (* (* (* (fabs (/ (cbrt h) (cbrt l))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (* (cbrt (fabs (/ (cbrt h) (cbrt l)))) (cbrt (fabs (/ (cbrt h) (cbrt l))))) (* (cbrt (fabs (/ (cbrt h) (cbrt l)))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))))) (/ (cbrt h) (cbrt l)))))
54.0ms
(/ (* M D) (* 2.0 d))
31.0ms
(/ (* M D) (* 2.0 d))

simplify1.7s

Counts
100 → 100
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01762831
14312570
218812127
done50001859

prune678.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.8b

regimes1.4s

Accuracy

0% (1.6b remaining)

Error of 8.7b against oracle of 7.1b and baseline of 8.7b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02865
13665
done3665

end0.0ms

sample1.9s

Algorithm
intervals
Results
697.0ms9267×body80valid
250.0ms3186×body80nan