Details

Time bar (total: 1.5m)

sample734.0ms

Algorithm
intervals
Results
472.0ms1153×body80nan
161.0ms412×body80valid

simplify271.0ms

Calls
1 calls:
Slowest
271.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.0b

localize79.0ms

Local error

Found 4 expressions with local error:

12.7b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
10.2b
(sqrt (/ d h))
9.1b
(sqrt (/ d l))
5.8b
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
27×add-cbrt-cube add-exp-log
14×sqrt-div
10×frac-times
9×add-sqr-sqrt pow1 cbrt-undiv div-exp
8×sqrt-prod
7×*-un-lft-identity associate-*l/ prod-exp associate-*r/ add-cube-cbrt cbrt-unprod
4×flip3-- insert-posit16 flip-- add-log-exp
3×associate-*l* pow-prod-down div-inv associate-/l/
2×rem-sqrt-square pow1/2
1×clear-num associate-/r* frac-2neg times-frac associate-*r* associate-/r/ *-commutative associate-/l*
Calls
4 calls:
Slowest
35.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
21.0ms
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
1.0ms
(sqrt (/ d h))
1.0ms
(sqrt (/ d l))

series329.0ms

Calls
4 calls:
Slowest
189.0ms
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
69.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
39.0ms
(sqrt (/ d h))
33.0ms
(sqrt (/ d l))

simplify20.7s

Calls
66 calls:
Slowest
2.0s
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))) (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)))
1.7s
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)))
1.2s
(* (+ (* 1 1) (+ (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2)) (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))))) (sqrt h))
1.2s
(* (+ (* 1 1) (+ (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2)) (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))))) (sqrt l))
921.0ms
(* (+ (* 1 1) (+ (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2)) (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))))) (* (sqrt l) (sqrt h)))

prune1.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.9b

localize24.0ms

Local error

Found 4 expressions with local error:

10.8b
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
10.2b
(sqrt (/ d h))
9.1b
(sqrt (/ d l))
5.8b
(* (- 1 (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube sqrt-div add-exp-log
11×add-sqr-sqrt
9×frac-times pow1 *-un-lft-identity add-cube-cbrt
8×sqrt-prod
7×times-frac
6×associate-*l/ associate-*r/
5×associate-/r* div-inv
4×flip3-- insert-posit16 flip-- add-log-exp
3×cbrt-undiv div-exp associate-*l* pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square pow1/2
1×clear-num frac-2neg associate-*r* associate-/r/ *-commutative associate-/l* associate-/l/
Calls
4 calls:
Slowest
36.0ms
(* (- 1 (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))
19.0ms
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
1.0ms
(sqrt (/ d h))
1.0ms
(sqrt (/ d l))

series323.0ms

Calls
4 calls:
Slowest
208.0ms
(* (- 1 (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))
47.0ms
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
39.0ms
(sqrt (/ d l))
29.0ms
(sqrt (/ d h))

simplify22.2s

Calls
72 calls:
Slowest
1.6s
(* (+ (* 1 1) (+ (* (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d)))) (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))) (* 1 (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))))) (sqrt h))
1.5s
(/ (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.4s
(* (+ (* 1 1) (+ (* (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d)))) (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))) (* 1 (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))))) (sqrt l))
1.4s
(* (+ (* 1 1) (+ (* (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d)))) (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))) (* 1 (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))))) (* (sqrt l) (sqrt h)))
1.3s
(* (- (pow 1 3) (pow (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d)))) 3)) (* (sqrt (/ d l)) (sqrt d)))

prune1.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.5b

localize12.0ms

Local error

Found 4 expressions with local error:

10.8b
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
10.2b
(sqrt (/ d h))
10.2b
(sqrt (/ d h))
9.1b
(sqrt (/ d l))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
7×times-frac
6×div-inv
5×associate-/r*
4×pow1 insert-posit16 add-log-exp
3×cbrt-undiv rem-sqrt-square pow1/2 sqrt-div div-exp
1×clear-num frac-2neg associate-*l/ associate-/r/ associate-/l* associate-/l/
Calls
4 calls:
Slowest
7.0ms
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
1.0ms
(sqrt (/ d h))
0.0ms
(sqrt (/ d h))
0.0ms
(sqrt (/ d l))

series145.0ms

Calls
4 calls:
Slowest
52.0ms
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
38.0ms
(sqrt (/ d h))
33.0ms
(sqrt (/ d l))
22.0ms
(sqrt (/ d h))

simplify4.3s

Calls
52 calls:
Slowest
1.4s
(/ (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
999.0ms
(/ (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))))
243.0ms
(- (log (* (/ l h) 2)) (- (log (* M D)) (log (* 2 d))))
240.0ms
(/ 2 (/ (* M D) (* 2 d)))
180.0ms
(- (log (* (/ l h) 2)) (log (/ (* M D) (* 2 d))))

prune1.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.4b

localize42.0ms

Local error

Found 4 expressions with local error:

10.8b
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
10.7b
(cbrt (/ d h))
10.7b
(cbrt (/ d h))
10.2b
(sqrt (/ d h))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
8×cbrt-prod
7×times-frac
6×div-inv
5×associate-/r*
4×pow1 sqrt-prod insert-posit16 add-log-exp
3×cbrt-undiv div-exp
2×cbrt-div pow1/3
1×rem-sqrt-square clear-num frac-2neg pow1/2 sqrt-div associate-*l/ associate-/r/ associate-/l* associate-/l/
Calls
4 calls:
Slowest
7.0ms
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
1.0ms
(sqrt (/ d h))
0.0ms
(cbrt (/ d h))
0.0ms
(cbrt (/ d h))

series229.0ms

Calls
4 calls:
Slowest
74.0ms
(cbrt (/ d h))
68.0ms
(cbrt (/ d h))
58.0ms
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
28.0ms
(sqrt (/ d h))

simplify5.6s

Calls
50 calls:
Slowest
1.4s
(/ (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.0s
(/ (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))))
599.0ms
(exp (* 1/3 (- (log (/ -1 h)) (log (/ -1 d)))))
301.0ms
(- (log (* (/ l h) 2)) (- (log (* M D)) (log (* 2 d))))
234.0ms
(exp (* 1/3 (- (log (/ -1 h)) (log (/ -1 d)))))

prune2.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 13.4b

regimes1.6s

Accuracy

65.3% (2.4b remaining)

Error of 18.5b against oracle of 16.1b and baseline of 22.9b

bsearch1.8s

end0.0ms

sample23.1s

Algorithm
intervals
Results
16.0s38706×body80nan
5.2s12798×body80valid