Details

Time bar (total: 1.7m)

sample574.0ms

Algorithm
intervals
Results
374.0ms1147×body80nan
148.0ms395×body80valid

simplify301.0ms

Calls
1 calls:
Slowest
301.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.9b

localize69.0ms

Local error

Found 4 expressions with local error:

13.4b
(sqrt (/ d l))
12.6b
(sqrt (/ d h))
11.1b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
8.0b
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite31.0ms

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
17.0ms
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
12.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
1.0ms
(sqrt (/ d l))
0.0ms
(sqrt (/ d h))

series338.0ms

Calls
4 calls:
Slowest
204.0ms
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
86.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
25.0ms
(sqrt (/ d h))
22.0ms
(sqrt (/ d l))

simplify21.3s

Calls
66 calls:
Slowest
2.1s
(/ (* (* (* (/ (* 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) 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 l))
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))
968.0ms
(* (+ (* 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)))

prune1.7s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 17.3b

localize27.0ms

Local error

Found 4 expressions with local error:

13.4b
(sqrt (/ d l))
12.6b
(sqrt (/ d h))
8.0b
(* (- 1 (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)) (* (sqrt (/ d l)) (sqrt (/ d h))))
6.1b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2))

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 prod-exp associate-*r/ add-cube-cbrt cbrt-unprod
6×associate-*l/
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* *-commutative associate-/l*
Calls
4 calls:
Slowest
28.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2))
27.0ms
(* (- 1 (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)) (* (sqrt (/ d l)) (sqrt (/ d h))))
1.0ms
(sqrt (/ d l))
1.0ms
(sqrt (/ d h))

series315.0ms

Calls
4 calls:
Slowest
187.0ms
(* (- 1 (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)) (* (sqrt (/ d l)) (sqrt (/ d h))))
58.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2))
35.0ms
(sqrt (/ d l))
35.0ms
(sqrt (/ d h))

simplify22.4s

Calls
66 calls:
Slowest
3.1s
(/ (* (/ (* (* (* 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 2) (* l 2)) (* l 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 2) (* l 2)) (* l 2)))
1.4s
(/ (* (* (* (/ (* 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 2) (* l 2)) (* l 2)))
974.0ms
(* (+ (* 1 1) (+ (* (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h) (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)) (* 1 (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)))) (* (sqrt l) (sqrt h)))
968.0ms
(* (- (pow 1 3) (pow (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h) 3)) (* (sqrt (/ d l)) (sqrt (/ d h))))

prune1.8s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 15.4b

localize28.0ms

Local error

Found 4 expressions with local error:

13.4b
(sqrt (/ d l))
13.4b
(sqrt (/ d l))
12.6b
(sqrt (/ d h))
8.0b
(* (- 1 (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)) (* (* (sqrt (sqrt (/ d l))) (sqrt (sqrt (/ d l)))) (sqrt (/ d h))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-div
29×frac-times
17×associate-*l/
16×associate-*r/
13×pow1 add-cbrt-cube add-exp-log
12×sqrt-prod
11×add-sqr-sqrt
8×*-un-lft-identity flip3-- add-cube-cbrt flip--
6×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×rem-sqrt-square pow1/2 associate-*l* div-inv
1×associate-*r* *-commutative
Calls
4 calls:
Slowest
52.0ms
(* (- 1 (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)) (* (* (sqrt (sqrt (/ d l))) (sqrt (sqrt (/ d l)))) (sqrt (/ d h))))
1.0ms
(sqrt (/ d l))
1.0ms
(sqrt (/ d l))
1.0ms
(sqrt (/ d h))

series281.0ms

Calls
4 calls:
Slowest
184.0ms
(* (- 1 (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)) (* (* (sqrt (sqrt (/ d l))) (sqrt (sqrt (/ d l)))) (sqrt (/ d h))))
37.0ms
(sqrt (/ d l))
36.0ms
(sqrt (/ d l))
24.0ms
(sqrt (/ d h))

simplify26.4s

Calls
79 calls:
Slowest
1.1s
(* (- (* 1 1) (* (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h) (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h))) (* (* (sqrt (sqrt d)) (sqrt (sqrt d))) (sqrt d)))
979.0ms
(* (- (pow 1 3) (pow (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h) 3)) (* (* (sqrt (sqrt d)) (sqrt (sqrt (/ d l)))) (sqrt d)))
957.0ms
(* (+ (* 1 1) (+ (* (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h) (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)) (* 1 (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)))) (* (sqrt (sqrt l)) (sqrt h)))
879.0ms
(* (+ (* 1 1) (+ (* (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h) (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)) (* 1 (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h)))) (* (sqrt (sqrt l)) (sqrt h)))
874.0ms
(* (- (* 1 1) (* (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h) (* (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* l 2)) h))) (* (* (sqrt (sqrt d)) (sqrt (sqrt (/ d l)))) (sqrt (/ d h))))

prune2.1s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 15.4b

localize14.0ms

Local error

Found 4 expressions with local error:

13.4b
(sqrt (/ d l))
13.4b
(sqrt (/ d l))
12.6b
(sqrt (/ d h))
12.6b
(sqrt (/ d h))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-prod
12×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
4×pow1 rem-sqrt-square add-cbrt-cube pow1/2 sqrt-div add-exp-log insert-posit16 div-inv add-log-exp
Calls
4 calls:
Slowest
1.0ms
(sqrt (/ d h))
1.0ms
(sqrt (/ d l))
0.0ms
(sqrt (/ d h))
0.0ms
(sqrt (/ d l))

series116.0ms

Calls
4 calls:
Slowest
36.0ms
(sqrt (/ d l))
30.0ms
(sqrt (/ d l))
27.0ms
(sqrt (/ d h))
23.0ms
(sqrt (/ d h))

simplify95.0ms

Calls
36 calls:
Slowest
9.0ms
(sqrt (* (cbrt (/ d l)) (cbrt (/ d l))))
9.0ms
(sqrt (* (cbrt (/ d h)) (cbrt (/ d h))))
8.0ms
(sqrt (sqrt (/ d h)))
7.0ms
(sqrt (sqrt (/ d l)))
6.0ms
(sqrt (sqrt (/ d h)))

prune1.5s

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 15.4b

regimes1.6s

Accuracy

60.6% (3.7b remaining)

Error of 18.4b against oracle of 14.7b and baseline of 24.1b

bsearch481.0ms

end0.0ms

sample23.2s

Algorithm
intervals
Results
14.9s38500×body80nan
6.5s12809×body80valid