Details

Time bar (total: 1.7m)

sample680.0ms

Algorithm
intervals
Results
446.0ms1281×body80nan
167.0ms402×body80valid

simplify323.0ms

Calls
1 calls:
Slowest
323.0ms
(* (* (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: 24.8b

localize71.0ms

Local error

Found 4 expressions with local error:

14.0b
(sqrt (/ d l))
11.6b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
10.6b
(sqrt (/ d h))
8.6b
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite56.0ms

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
27.0ms
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
25.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
1.0ms
(sqrt (/ d l))
1.0ms
(sqrt (/ d h))

series501.0ms

Calls
4 calls:
Slowest
280.0ms
(* (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
110.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ l h) 2))
59.0ms
(sqrt (/ d l))
52.0ms
(sqrt (/ d h))

simplify21.0s

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)))
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)))
1.2s
(* (+ (* 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))
1.1s
(* (+ (* 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))
978.0ms
(* (+ (* 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)))

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 17.3b

localize29.0ms

Local error

Found 4 expressions with local error:

14.0b
(sqrt (/ d l))
10.6b
(sqrt (/ d h))
10.3b
(/ (/ (* M D) (* 2 d)) (/ l h))
8.6b
(* (- 1 (* (/ (/ (* M D) (* 2 d)) (/ l h)) (/ (/ (* M D) (* 2 d)) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
25×times-frac
20×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
14×add-cbrt-cube sqrt-div add-exp-log div-inv
9×frac-times pow1
8×sqrt-prod
6×associate-*r/
5×associate-*l/ associate-/l*
4×associate-/r* 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/
Calls
4 calls:
Slowest
19.0ms
(* (- 1 (* (/ (/ (* M D) (* 2 d)) (/ l h)) (/ (/ (* M D) (* 2 d)) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
13.0ms
(/ (/ (* M D) (* 2 d)) (/ l h))
1.0ms
(sqrt (/ d l))
1.0ms
(sqrt (/ d h))

series531.0ms

Calls
4 calls:
Slowest
300.0ms
(* (- 1 (* (/ (/ (* M D) (* 2 d)) (/ l h)) (/ (/ (* M D) (* 2 d)) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
83.0ms
(sqrt (/ d h))
81.0ms
(/ (/ (* M D) (* 2 d)) (/ l h))
67.0ms
(sqrt (/ d l))

simplify18.3s

Calls
103 calls:
Slowest
865.0ms
(* (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) (/ l h)) (/ (/ (* M D) (* 2 d)) 2)) 3)) (* (sqrt (/ d l)) (sqrt (/ d h))))
791.0ms
(* (- (* 1 1) (* (* (/ (/ (* M D) (* 2 d)) (/ l h)) (/ (/ (* M D) (* 2 d)) 2)) (* (/ (/ (* M D) (* 2 d)) (/ l h)) (/ (/ (* M D) (* 2 d)) 2)))) (* (sqrt (/ d l)) (sqrt (/ d h))))
785.0ms
(/ (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (/ l h) (/ l h)) (/ l h)))
772.0ms
(* (+ (* 1 1) (+ (* (* (/ (/ (* M D) (* 2 d)) (/ l h)) (/ (/ (* M D) (* 2 d)) 2)) (* (/ (/ (* M D) (* 2 d)) (/ l h)) (/ (/ (* M D) (* 2 d)) 2))) (* 1 (* (/ (/ (* M D) (* 2 d)) (/ l h)) (/ (/ (* M D) (* 2 d)) 2))))) (* (sqrt l) (sqrt h)))
764.0ms
(* (- 1 (* (/ (/ (* M D) (* 2 d)) (/ l h)) (/ (/ (* M D) (* 2 d)) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))

prune2.1s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 16.9b

localize32.0ms

Local error

Found 4 expressions with local error:

14.0b
(sqrt (/ d l))
10.6b
(sqrt (/ d h))
8.6b
(* (- 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
5.5b
(/ (* M D) (* 2 d))

rewrite39.0ms

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-*r/
5×associate-*l/
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* *-commutative associate-/l*
Calls
4 calls:
Slowest
29.0ms
(* (- 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
6.0ms
(/ (* M D) (* 2 d))
1.0ms
(sqrt (/ d l))
1.0ms
(sqrt (/ d h))

series522.0ms

Calls
4 calls:
Slowest
343.0ms
(* (- 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
80.0ms
(sqrt (/ d l))
68.0ms
(sqrt (/ d h))
32.0ms
(/ (* M D) (* 2 d))

simplify12.9s

Calls
54 calls:
Slowest
1.1s
(* (- (pow 1 3) (pow (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2)) 3)) (* (sqrt (/ d l)) (sqrt (/ d h))))
850.0ms
(* (+ (* 1 1) (+ (* (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2)) (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2))) (* 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2))))) (* (sqrt l) (sqrt h)))
813.0ms
(* (- (pow 1 3) (pow (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2)) 3)) (* (sqrt (/ d l)) (sqrt d)))
760.0ms
(* (- (pow 1 3) (pow (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2)) 3)) (* (sqrt d) (sqrt (/ d h))))
749.0ms
(* (+ (* 1 1) (+ (* (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2)) (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2))) (* 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ (* M D) (* 2 d)) 2))))) (sqrt h))

prune1.8s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 15.7b

localize19.0ms

Local error

Found 4 expressions with local error:

14.0b
(sqrt (/ d l))
10.6b
(sqrt (/ d h))
8.6b
(* (- 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
5.5b
(/ (* M D) (* 2 d))

rewrite19.0ms

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-*r/
5×associate-*l/
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* *-commutative associate-/l*
Calls
4 calls:
Slowest
14.0ms
(* (- 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
3.0ms
(/ (* M D) (* 2 d))
1.0ms
(sqrt (/ d l))
0.0ms
(sqrt (/ d h))

series500.0ms

Calls
4 calls:
Slowest
319.0ms
(* (- 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2))) (* (sqrt (/ d l)) (sqrt (/ d h))))
68.0ms
(sqrt (/ d l))
65.0ms
(sqrt (/ d h))
48.0ms
(/ (* M D) (* 2 d))

simplify11.8s

Calls
54 calls:
Slowest
765.0ms
(* (- (pow 1 3) (pow (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2)) 3)) (* (sqrt (/ d l)) (sqrt (/ d h))))
741.0ms
(* (+ (* 1 1) (+ (* (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2)) (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2))) (* 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2))))) (sqrt l))
687.0ms
(* (+ (* 1 1) (+ (* (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2)) (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2))) (* 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2))))) (sqrt h))
675.0ms
(* (- (pow 1 3) (pow (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2)) 3)) (* (sqrt d) (sqrt (/ d h))))
671.0ms
(* (+ (* 1 1) (+ (* (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2)) (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2))) (* 1 (* (/ (/ (/ (* M D) (* 2 d)) l) (/ 1 h)) (/ (/ 1 (/ (* 2 d) (* M D))) 2))))) (* (sqrt l) (sqrt h)))

prune1.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 15.7b

regimes1.6s

Accuracy

64.1% (2.9b remaining)

Error of 16.8b against oracle of 13.8b and baseline of 22.0b

bsearch2.8s

end0.0ms

sample23.2s

Algorithm
intervals
Results
14.6s37967×body80nan
6.8s12823×body80valid