Details

Time bar (total: 55.8s)

sample98.0ms

Algorithm
intervals
Results
57.0ms293×body80valid
20.0ms101×body80nan

simplify154.0ms

Calls
1 calls:
Slowest
154.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize58.0ms

Local error

Found 4 expressions with local error:

12.7b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
5.2b
(/ (* M D) (* 2 d))
5.2b
(/ (* M D) (* 2 d))
3.3b
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
26×add-cbrt-cube add-exp-log
11×cbrt-undiv div-exp
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac
5×div-inv
4×pow1 prod-exp cbrt-unprod insert-posit16 add-log-exp
3×clear-num frac-2neg sqrt-prod associate-/l* associate-/l/
2×sqrt-div
1×frac-times rem-sqrt-square flip3-- pow1/2 associate-*l/ associate-*r/ associate-/r/ flip--
Calls
4 calls:
Slowest
11.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
3.0ms
(/ (* M D) (* 2 d))
3.0ms
(/ (* M D) (* 2 d))
2.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))

series420.0ms

Calls
4 calls:
Slowest
228.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
132.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
31.0ms
(/ (* M D) (* 2 d))
29.0ms
(/ (* M D) (* 2 d))

simplify11.9s

Calls
52 calls:
Slowest
2.0s
(/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
1.1s
(/ (* (* (* (/ (* 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) (/ l h)) (/ l h)))
989.0ms
(/ (* (* (* (/ (* 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) (/ l h)) (/ l h)))
576.0ms
(- (+ (log (/ (* M D) (* 2 d))) (log (/ (* M D) (* 2 d)))) (log (/ l h)))
472.0ms
(sqrt (- (pow 1 3) (pow (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h)) 3)))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize17.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* M D) (* 2 d))
5.2b
(/ (* M D) (* 2 d))
5.1b
(/ (/ (* M D) (* 2 d)) l)
4.8b
(/ (/ (* M D) (* 2 d)) (/ 1 h))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
28×times-frac
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt div-inv
13×add-cbrt-cube add-exp-log
12×associate-/l*
6×associate-/r*
5×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×associate-/l/
1×associate-/r/
Calls
4 calls:
Slowest
12.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
10.0ms
(/ (/ (* M D) (* 2 d)) l)
7.0ms
(/ (* M D) (* 2 d))
3.0ms
(/ (* M D) (* 2 d))

series192.0ms

Calls
4 calls:
Slowest
58.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
53.0ms
(/ (/ (* M D) (* 2 d)) l)
45.0ms
(/ (* M D) (* 2 d))
35.0ms
(/ (* M D) (* 2 d))

simplify9.0s

Calls
78 calls:
Slowest
745.0ms
(/ (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
583.0ms
(/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
572.0ms
(* 1/2 (/ (* M (* D h)) d))
417.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
366.0ms
(* 1/2 (/ (* M (* D h)) d))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize33.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* M D) (* 2 d))
5.1b
(/ (/ (* M D) (* 2 d)) l)
5.1b
(/ (* 2 d) (* M D))
4.8b
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
23×times-frac
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt div-inv
15×add-exp-log
12×associate-/l*
10×add-cbrt-cube
6×associate-/r* div-exp associate-/r/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
3×cbrt-undiv
2×rec-exp associate-/l/
Calls
4 calls:
Slowest
11.0ms
(/ (/ (* M D) (* 2 d)) l)
7.0ms
(/ (* 2 d) (* M D))
7.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))
7.0ms
(/ (* M D) (* 2 d))

series186.0ms

Calls
4 calls:
Slowest
70.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) (/ 1 h))
51.0ms
(/ (/ (* M D) (* 2 d)) l)
32.0ms
(/ (* M D) (* 2 d))
32.0ms
(/ (* 2 d) (* M D))

simplify15.0s

Calls
76 calls:
Slowest
588.0ms
(/ (cbrt (/ 1 (/ (* 2 d) (* M D)))) (cbrt (/ 1 h)))
566.0ms
(/ (sqrt (/ 1 (/ (* 2 d) (* M D)))) (cbrt (/ 1 h)))
551.0ms
(/ (* (cbrt (/ 1 (/ (* 2 d) (* M D)))) (cbrt (/ 1 (/ (* 2 d) (* M D))))) 1)
536.0ms
(/ (* (cbrt (/ 1 (/ (* 2 d) (* M D)))) (cbrt (/ 1 (/ (* 2 d) (* M D))))) 1)
513.0ms
(/ (sqrt (/ 1 (/ (* 2 d) (* M D)))) (sqrt (/ 1 h)))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize41.0ms

Local error

Found 4 expressions with local error:

14.1b
(cbrt (/ l h))
14.1b
(cbrt (/ l h))
14.1b
(cbrt (/ l h))
6.0b
(/ (/ (* M D) (* 2 d)) (* (cbrt (/ l h)) (cbrt (/ l h))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log
12×cbrt-prod add-cbrt-cube
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×cbrt-div times-frac
6×cbrt-undiv div-exp div-inv
5×associate-/l*
4×pow1 insert-posit16 add-log-exp
3×pow1/3 associate-/r/
2×prod-exp cbrt-unprod
1×frac-times clear-num associate-/r* frac-2neg associate-*l/ associate-*r/ associate-/l/
Calls
4 calls:
Slowest
18.0ms
(/ (/ (* M D) (* 2 d)) (* (cbrt (/ l h)) (cbrt (/ l h))))
1.0ms
(cbrt (/ l h))
1.0ms
(cbrt (/ l h))
1.0ms
(cbrt (/ l h))

series398.0ms

Calls
4 calls:
Slowest
168.0ms
(/ (/ (* M D) (* 2 d)) (* (cbrt (/ l h)) (cbrt (/ l h))))
86.0ms
(cbrt (/ l h))
74.0ms
(cbrt (/ l h))
70.0ms
(cbrt (/ l h))

simplify7.1s

Calls
54 calls:
Slowest
920.0ms
(/ (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (* (cbrt (/ l h)) (cbrt (/ l h))) (* (cbrt (/ l h)) (cbrt (/ l h)))) (* (cbrt (/ l h)) (cbrt (/ l h)))))
700.0ms
(/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (* (cbrt (/ l h)) (cbrt (/ l h))) (* (cbrt (/ l h)) (cbrt (/ l h)))) (* (cbrt (/ l h)) (cbrt (/ l h)))))
590.0ms
(/ (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (/ l h) (/ l h)))
465.0ms
(/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (/ l h) (/ l h)))
350.0ms
(/ (/ (* M D) (* 2 d)) (cbrt (/ l h)))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

regimes1.4s

Accuracy

-90.4% (1.9b remaining)

Error of 8.8b against oracle of 6.9b and baseline of 7.9b

bsearch230.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.8s9304×body80valid
773.0ms3107×body80nan