Details

Time bar (total: 3.9m)

sample3.7s

Algorithm
intervals
Results
1.9s1280×body80nan
639.0ms399×body80valid

simplify357.0ms

Calls
1 calls:
Slowest
357.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.0b

localize79.0ms

Local error

Found 4 expressions with local error:

12.6b
(sqrt (/ d l))
12.4b
(sqrt (/ d h))
10.8b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
6.0b
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite162.0ms

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
92.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
63.0ms
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
1.0ms
(sqrt (/ d l))
1.0ms
(sqrt (/ d h))

series674.0ms

Calls
4 calls:
Slowest
279.0ms
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
251.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
100.0ms
(sqrt (/ d l))
44.0ms
(sqrt (/ d h))

simplify47.7s

Calls
66 calls:
Slowest
5.7s
(/ (* (* (* (/ (* 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)))
5.2s
(/ (* (* (* (/ (* 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)))
3.0s
(* (- (pow 1 3) (pow (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2)) 3)) (* (sqrt (/ d l)) (sqrt d)))
2.7s
(* (- (* 1 1) (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2)) (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2)))) (* (sqrt d) (sqrt (/ d h))))
2.3s
(* (+ (* 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))

prune2.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 15.1b

localize36.0ms

Local error

Found 4 expressions with local error:

12.6b
(sqrt (/ d l))
12.4b
(sqrt (/ d h))
8.0b
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
6.0b
(* (- 1 (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite72.0ms

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
41.0ms
(* (- 1 (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))
13.0ms
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
9.0ms
(sqrt (/ d l))
1.0ms
(sqrt (/ d h))

series409.0ms

Calls
4 calls:
Slowest
262.0ms
(* (- 1 (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))
63.0ms
(/ (* (/ l h) 2) (/ (* M D) (* 2 d)))
45.0ms
(sqrt (/ d l))
39.0ms
(sqrt (/ d h))

simplify42.7s

Calls
72 calls:
Slowest
3.7s
(/ (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
3.1s
(* (+ (* 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))
2.7s
(* (+ (* 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))
2.6s
(* (- (* 1 1) (* (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d)))) (/ (/ (* M D) (* 2 d)) (/ (* (/ l h) 2) (/ (* M D) (* 2 d)))))) (* (sqrt d) (sqrt d)))
2.6s
(* (+ (* 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 l) (sqrt h)))

prune3.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 14.5b

localize53.0ms

Local error

Found 4 expressions with local error:

12.6b
(sqrt (/ d l))
12.4b
(sqrt (/ d h))
6.7b
(/ (* l 2) (* (/ (* M D) (* 2 d)) h))
6.0b
(* (- 1 (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
14×sqrt-div
11×add-cbrt-cube add-exp-log
9×add-sqr-sqrt frac-times pow1
8×sqrt-prod
7×*-un-lft-identity add-cube-cbrt
6×associate-*l/ associate-*r/
4×flip3-- insert-posit16 flip-- add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod div-inv
2×rem-sqrt-square pow1/2
1×cbrt-undiv clear-num associate-/r* frac-2neg times-frac div-exp associate-*r* associate-/r/ *-commutative associate-/l*
Calls
4 calls:
Slowest
51.0ms
(/ (* l 2) (* (/ (* M D) (* 2 d)) h))
47.0ms
(* (- 1 (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))) (* (sqrt (/ d l)) (sqrt (/ d h))))
7.0ms
(sqrt (/ d l))
1.0ms
(sqrt (/ d h))

series413.0ms

Calls
4 calls:
Slowest
251.0ms
(* (- 1 (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))) (* (sqrt (/ d l)) (sqrt (/ d h))))
69.0ms
(/ (* l 2) (* (/ (* M D) (* 2 d)) h))
59.0ms
(sqrt (/ d l))
35.0ms
(sqrt (/ d h))

simplify49.3s

Calls
55 calls:
Slowest
5.4s
(/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* (* (/ (* M D) (* 2 d)) h) (* (/ (* M D) (* 2 d)) h)) (* (/ (* M D) (* 2 d)) h)))
4.9s
(* (+ (* 1 1) (+ (* (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h))) (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))) (* 1 (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))))) (* (sqrt l) (sqrt h)))
4.1s
(* (+ (* 1 1) (+ (* (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h))) (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))) (* 1 (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))))) (sqrt l))
3.8s
(* (+ (* 1 1) (+ (* (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h))) (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))) (* 1 (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))))) (sqrt h))
2.3s
(* (- (pow 1 3) (pow (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h))) 3)) (* (sqrt (/ d l)) (sqrt (/ d h))))

prune4.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.8b

localize49.0ms

Local error

Found 4 expressions with local error:

12.6b
(sqrt (/ d l))
12.4b
(sqrt (/ d h))
6.7b
(/ (* l 2) (* (/ (* M D) (* 2 d)) h))
4.6b
(* (/ (* M D) (* 2 d)) h)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×sqrt-prod
7×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
5×associate-*l*
4×pow1 insert-posit16 div-inv add-log-exp
2×rem-sqrt-square times-frac pow1/2 sqrt-div associate-*l/
1×cbrt-undiv clear-num associate-/r* frac-2neg div-exp associate-/r/ *-commutative associate-/l*
Calls
4 calls:
Slowest
13.0ms
(/ (* l 2) (* (/ (* M D) (* 2 d)) h))
10.0ms
(* (/ (* M D) (* 2 d)) h)
4.0ms
(sqrt (/ d l))
1.0ms
(sqrt (/ d h))

series389.0ms

Calls
4 calls:
Slowest
139.0ms
(/ (* l 2) (* (/ (* M D) (* 2 d)) h))
106.0ms
(* (/ (* M D) (* 2 d)) h)
69.0ms
(sqrt (/ d l))
60.0ms
(sqrt (/ d h))

simplify9.0s

Calls
34 calls:
Slowest
4.1s
(/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* (* (/ (* M D) (* 2 d)) h) (* (/ (* M D) (* 2 d)) h)) (* (/ (* M D) (* 2 d)) h)))
1.4s
(- (log (* l 2)) (log (* (/ (* M D) (* 2 d)) h)))
726.0ms
(/ l (/ (* M D) (* 2 d)))
602.0ms
(* 1/2 (/ (* M (* D h)) d))
569.0ms
(* 1/2 (/ (* M (* D h)) d))

prune2.6s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 12.8b

regimes6.1s

Accuracy

64.7% (2.9b remaining)

Error of 17.2b against oracle of 14.3b and baseline of 22.5b

bsearch2.1s

end0.0ms

sample1.0m

Algorithm
intervals
Results
38.4s38782×body80nan
11.3s12771×body80valid