Details

Time bar (total: 8.6m)

sample709.0ms

Algorithm
intervals
Results
457.0ms1235×body80nan
155.0ms413×body80valid

simplify353.0ms

Calls
1 calls:
Slowest
353.0ms
(* (* (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: 28.1b

localize70.0ms

Local error

Found 4 expressions with local error:

13.8b
(pow (/ d h) (/ 1 2))
13.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.6b
(pow (/ d l) (/ 1 2))
8.1b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite3.6s

Algorithm
rewrite-expression-head
Rules
1111×add-sqr-sqrt
503×times-frac
475×unswap-sqr
364×associate-*r*
357×associate-*l*
337×unpow-prod-down
331×add-exp-log
294×*-un-lft-identity
179×prod-exp add-cube-cbrt
102×difference-of-squares
99×div-exp associate-*l/
81×frac-times
61×associate-/l*
60×associate-/r* pow-exp
42×sqr-pow
30×add-cbrt-cube
28×*-commutative
26×pow-unpow
22×unpow2
21×clear-num
20×frac-2neg
18×pow-to-exp
16×pow1
14×rec-exp 1-exp
13×cbrt-unprod
11×associate-*r/
10×div-inv
6×pow-prod-down
5×cbrt-undiv
4×insert-posit16 distribute-lft-out-- add-log-exp
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in un-div-inv
1×flip3-- flip--
Calls
4 calls:
Slowest
3.1s
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
402.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.0ms
(pow (/ d l) (/ 1 2))
5.0ms
(pow (/ d h) (/ 1 2))

series699.0ms

Calls
4 calls:
Slowest
360.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
138.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
111.0ms
(pow (/ d h) (/ 1 2))
89.0ms
(pow (/ d l) (/ 1 2))

simplify3.6m

Calls
844 calls:
Slowest
1.3s
(* (/ 1 2) (pow (/ (* (sqrt M) (sqrt D)) (* (cbrt (* 2 d)) (cbrt (* 2 d)))) 2))
1.2s
(- (sqrt 1) (* (* (/ (sqrt 1) (sqrt 2)) (pow (/ (* M D) (* 2 d)) (/ 2 2))) (sqrt (/ h l))))
1.1s
(* (* (* (cbrt 1) (cbrt 1)) (pow (/ (* M D) (* 2 d)) 2)) h)
1.1s
(* (/ 1 2) (pow (/ (* M 1) (* 2 (* (cbrt d) (cbrt d)))) 2))
1.0s
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))

prune15.0s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 10.0b

localize80.0ms

Local error

Found 4 expressions with local error:

13.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.6b
(pow (/ d l) (/ 1 2))
5.6b
(* (* (pow (/ (cbrt d) (cbrt h)) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
3.9b
(/ (* M D) (* 2 d))

rewrite3.7s

Algorithm
rewrite-expression-head
Rules
1329×add-sqr-sqrt
686×times-frac
537×unswap-sqr
501×associate-*l*
442×associate-*r*
387×unpow-prod-down
376×*-un-lft-identity
340×add-exp-log
261×add-cube-cbrt
183×prod-exp
102×div-exp difference-of-squares
99×associate-*l/
81×frac-times
73×associate-/l*
72×associate-/r*
68×cbrt-prod
58×pow-exp
54×*-commutative
47×sqr-pow
42×add-cbrt-cube
22×clear-num unpow2
21×frac-2neg
17×pow-to-exp cbrt-unprod
15×pow1
14×rec-exp 1-exp
13×pow-unpow
11×associate-*r/
9×cbrt-undiv div-inv
6×pow-prod-down
4×insert-posit16 distribute-lft-out-- add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in un-div-inv
1×pow-pow flip3-- flip--
Calls
4 calls:
Slowest
3.3s
(* (* (pow (/ (cbrt d) (cbrt h)) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
359.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
27.0ms
(/ (* M D) (* 2 d))
7.0ms
(pow (/ d l) (/ 1 2))

series1.5s

Calls
4 calls:
Slowest
1.3s
(* (* (pow (/ (cbrt d) (cbrt h)) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
115.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
75.0ms
(pow (/ d l) (/ 1 2))
29.0ms
(/ (* M D) (* 2 d))

simplify4.1m

Calls
1191 calls:
Slowest
1.4s
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))
1.1s
(* (* (sqrt (/ 1 2)) (sqrt (pow (/ (* M D) (* 2 d)) 2))) (/ (sqrt h) (sqrt l)))
1.0s
(* (/ 1 2) (pow (/ (* M 1) (* 2 (* (cbrt d) (cbrt d)))) 2))
1.0s
(* (* (* (* (pow (/ (cbrt d) (cbrt h)) (/ 1 2)) (pow (/ d l) (/ 1 2))) (* (pow (/ (cbrt d) (cbrt h)) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (pow (/ (cbrt d) (cbrt h)) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
955.0ms
(* (/ 1 2) (pow (/ (* (cbrt M) (cbrt M)) (* 2 (sqrt d))) 2))

prune21.4s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 6.9b

localize101.0ms

Local error

Found 4 expressions with local error:

16.2b
(sqrt (/ h l))
16.2b
(sqrt (/ h l))
12.6b
(pow (/ d l) (/ 1 2))
5.8b
(* (* (sqrt (/ 1 2)) (/ (* M D) (* 2 d))) (sqrt (/ h l)))

rewrite601.0ms

Algorithm
rewrite-expression-head
Rules
5085×sqrt-div
4968×frac-times
2915×associate-/l*
2895×associate-/r*
2701×add-sqr-sqrt
1892×*-un-lft-identity
1852×add-cube-cbrt
887×associate-*l*
836×associate-*r*
675×clear-num
665×frac-2neg
431×unswap-sqr
372×associate-*l/
325×times-frac
279×associate-*r/
226×*-commutative
154×sqrt-prod
32×add-exp-log
30×un-div-inv
29×add-cbrt-cube
15×prod-exp cbrt-unprod
13×pow-unpow unpow-prod-down
12×pow1
7×div-inv
5×div-exp
4×cbrt-undiv rem-sqrt-square insert-posit16 add-log-exp
3×pow-prod-down
2×sqrt-pow1 pow1/2 pow-exp
1×pow-to-exp pow-pow sqr-pow
Calls
4 calls:
Slowest
319.0ms
(* (* (sqrt (/ 1 2)) (/ (* M D) (* 2 d))) (sqrt (/ h l)))
5.0ms
(sqrt (/ h l))
5.0ms
(pow (/ d l) (/ 1 2))
4.0ms
(sqrt (/ h l))

series1.1s

Calls
4 calls:
Slowest
650.0ms
(sqrt (/ h l))
287.0ms
(* (* (sqrt (/ 1 2)) (/ (* M D) (* 2 d))) (sqrt (/ h l)))
111.0ms
(pow (/ d l) (/ 1 2))
78.0ms
(sqrt (/ h l))