Details

Time bar (total: 6.2m)

sample653.0ms

Algorithm
intervals
Results
386.0ms1220×body80nan
189.0ms401×body80valid

simplify382.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
381.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.8b

localize62.0ms

Local error

Found 4 expressions with local error:

12.3b
(sqrt (/ d l))
12.3b
(sqrt (/ d l))
11.8b
(sqrt (/ d h))
11.8b
(sqrt (/ d h))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
52×sqrt-prod
44×add-sqr-sqrt
40×times-frac
32×*-un-lft-identity add-cube-cbrt
8×pow1 rem-sqrt-square
4×sqrt-pow1 add-cbrt-cube pow1/2 sqrt-div add-exp-log insert-posit16 div-inv add-log-exp
Counts
4 → 104
Calls
4 calls:
Slowest
2.0ms
(sqrt (/ d l))
2.0ms
(sqrt (/ d l))
2.0ms
(sqrt (/ d h))
2.0ms
(sqrt (/ d h))

series285.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(sqrt (/ d l))
80.0ms
(sqrt (/ d l))
64.0ms
(sqrt (/ d h))
57.0ms
(sqrt (/ d h))

simplify1.4s

Counts
160 → 116
Calls
160 calls:
Slowest
81.0ms
(* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l)))
73.0ms
(* (* (sqrt (/ d h)) (sqrt (/ d h))) (sqrt (/ d h)))
59.0ms
(* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l)))
57.0ms
(* (* (sqrt (/ d h)) (sqrt (/ d h))) (sqrt (/ d h)))
51.0ms
(sqrt (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))))

prune2.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 20.4b

localize104.0ms

Local error

Found 4 expressions with local error:

12.3b
(sqrt (/ d l))
11.8b
(sqrt (/ d h))
11.8b
(sqrt (/ d h))
11.5b
(* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (/ h l))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
965×add-cbrt-cube add-exp-log
636×prod-exp cbrt-unprod
215×cbrt-undiv div-exp
49×frac-times
47×associate-*r/
41×add-sqr-sqrt
39×times-frac sqrt-prod
37×associate-*l/
36×pow1
35×sqrt-div
32×*-un-lft-identity add-cube-cbrt
22×pow-prod-down
13×associate-*r*
6×rem-sqrt-square
4×insert-posit16 div-inv add-log-exp
3×sqrt-pow1 pow1/2
1×associate-*l* *-commutative
Counts
4 → 359
Calls
4 calls:
Slowest
1.6s
(* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (/ h l))
2.0ms
(sqrt (/ d l))
2.0ms
(sqrt (/ d h))
2.0ms
(sqrt (/ d h))

series737.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
503.0ms
(* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (/ h l))
84.0ms
(sqrt (/ d h))
77.0ms
(sqrt (/ d h))
73.0ms
(sqrt (/ d l))

simplify1.7m

Counts
418 → 371
Calls
418 calls:
Slowest
1.9s
(* (* (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))))) (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))))) (/ (* (* h h) h) (* (* l l) l)))
1.9s
(* (* (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (/ h l)) (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (/ h l))) (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (/ h l)))
1.6s
(* (* (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l))) (* (* (sqrt (/ d h)) (sqrt (/ d h))) (sqrt (/ d h)))) (* (* (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))))) (* (* (/ h l) (/ h l)) (/ h l)))
1.6s
(* (* (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (* (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))))) (* (* (/ h l) (/ h l)) (/ h l)))
1.4s
(* (* (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))))) (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))))) (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))))) (* (* (/ h l) (/ h l)) (/ h l)))

prune10.1s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 12.1b

localize133.0ms

Local error

Found 4 expressions with local error:

12.3b
(sqrt (/ d l))
11.8b
(sqrt (/ d h))
11.8b
(sqrt (/ d h))
7.4b
(* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))))

rewrite708.0ms

Algorithm
rewrite-expression-head
Rules
2220×add-exp-log
1780×add-cbrt-cube
1400×prod-exp cbrt-unprod
572×cbrt-undiv div-exp
129×frac-times
75×associate-*r/
67×sqrt-div
63×associate-*l/
48×pow1
39×sqrt-prod
34×add-sqr-sqrt
31×pow-prod-down
30×times-frac
25×*-un-lft-identity add-cube-cbrt
6×rem-sqrt-square
4×insert-posit16 add-log-exp
3×sqrt-pow1 pow1/2 div-inv
1×associate-*r* associate-*l* *-commutative
Counts
4 → 650
Calls
4 calls:
Slowest
617.0ms
(* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))))
4.0ms
(sqrt (/ d l))
4.0ms
(sqrt (/ d h))
4.0ms
(sqrt (/ d h))

series790.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
583.0ms
(* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))))
80.0ms
(sqrt (/ d h))
65.0ms
(sqrt (/ d l))
62.0ms
(sqrt (/ d h))

simplify3.8m

Counts
739 → 662
Calls
739 calls:
Slowest
2.4s
(* (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l))) (* (* (sqrt (/ d h)) (sqrt (/ d h))) (sqrt (/ d h)))) (* (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))))
2.2s
(* (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))))
2.1s
(* (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))))
2.0s
(* (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l))) (* (* (sqrt (/ d h)) (sqrt (/ d h))) (sqrt (/ d h)))) (* (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))))
1.9s
(* (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))) (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))))) (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))))))

prune20.3s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 8.5b

localize126.0ms

Local error

Found 4 expressions with local error:

11.8b
(sqrt (/ d h))
11.8b
(sqrt (/ d h))
7.4b
(* (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))))
6.8b
(/ (* M D) (* 2 d))

rewrite849.0ms

Algorithm
rewrite-expression-head
Rules
3523×add-exp-log
2863×add-cbrt-cube
2287×prod-exp cbrt-unprod
862×cbrt-undiv div-exp
129×frac-times
107×associate-*r/
75×pow1
66×sqrt-div
63×associate-*l/
54×pow-prod-down
26×sqrt-prod
24×add-sqr-sqrt
21×times-frac
18×*-un-lft-identity add-cube-cbrt
4×rem-sqrt-square insert-posit16 add-log-exp
3×div-inv
2×sqrt-pow1 pow1/2
1×clear-num associate-/r* frac-2neg associate-*r* associate-*l* *-commutative associate-/l*
Counts
4 → 895
Calls
4 calls:
Slowest
748.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))))
15.0ms
(/ (* M D) (* 2 d))
5.0ms
(sqrt (/ d h))
4.0ms
(sqrt (/ d h))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
926.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))))
84.0ms
(sqrt (/ d h))
68.0ms
(sqrt (/ d h))
41.0ms
(/ (* M D) (* 2 d))