Details

Time bar (total: 5.4m)

sample111.0ms

Algorithm
intervals
Results
61.0ms296×body80valid
21.0ms117×body80nan

simplify234.0ms

Calls
1 calls:
Slowest
234.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize45.0ms

Local error

Found 4 expressions with local error:

9.8b
(* (/ h l) (/ (* M D) (* 2 d)))
6.0b
(/ (* M D) (* 2 d))
6.0b
(/ (* M D) (* 2 d))
4.4b
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
1355×add-sqr-sqrt
672×times-frac
492×unswap-sqr
436×associate-*r*
421×*-un-lft-identity
357×add-cube-cbrt
305×associate-*l*
243×frac-times
230×associate-/l*
228×associate-/r*
118×sqrt-prod
112×difference-of-squares
97×*-commutative
69×add-cbrt-cube add-exp-log
41×clear-num
40×frac-2neg
27×associate-*r/
26×prod-exp cbrt-unprod
21×cbrt-undiv div-exp
9×associate-*l/
7×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×un-div-inv distribute-lft-out--
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down flip--
Calls
4 calls:
Slowest
1.6s
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
82.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
40.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))

series395.0ms

Calls
4 calls:
Slowest
196.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
104.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
50.0ms
(/ (* M D) (* 2 d))
45.0ms
(/ (* M D) (* 2 d))

simplify3.0m

Calls
1482 calls:
Slowest
10.7s
(sqrt (+ 1 (* (* (sqrt (/ h l)) (/ (* (sqrt M) (sqrt D)) (sqrt (* 2 d)))) (/ (sqrt (* M D)) (* (sqrt 2) (sqrt d))))))
10.4s
(* (/ h (sqrt l)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d)))))
1.4s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.3s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.3s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))

prune17.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize54.0ms

Local error

Found 4 expressions with local error:

6.0b
(/ (* M D) (* 2 d))
4.4b
(sqrt (- 1 (* (/ (* (* (cbrt h) (cbrt h)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))) (* (/ l (cbrt h)) (cbrt (* 2 d)))) (/ (* M D) (* 2 d)))))
4.2b
(/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))
4.1b
(/ (* (* (cbrt h) (cbrt h)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))) (* (/ l (cbrt h)) (cbrt (* 2 d))))

rewrite2.1m

Algorithm
rewrite-expression-head
Rules
477636×add-sqr-sqrt
241521×unswap-sqr
225737×times-frac
170355×cbrt-prod
84457×associate-*r*
56637×*-un-lft-identity
56203×associate-*l*
40073×add-cube-cbrt
28790×swap-sqr
28017×sqrt-prod
28012×difference-of-squares
16099×*-commutative
2015×add-cbrt-cube
1501×cbrt-unprod
1103×div-inv
1088×associate-/l*
980×cbrt-undiv
220×add-exp-log
191×associate-/r*
99×prod-exp
79×associate-/l/
76×div-exp associate-*r/
12×associate-*l/ associate-/r/
6×clear-num
5×pow1 frac-2neg
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×un-div-inv
2×sqrt-div distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Calls
4 calls:
Slowest
1.8m
(sqrt (- 1 (* (/ (* (* (cbrt h) (cbrt h)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))) (* (/ l (cbrt h)) (cbrt (* 2 d)))) (/ (* M D) (* 2 d)))))
677.0ms
(/ (* (* (cbrt h) (cbrt h)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))) (* (/ l (cbrt h)) (cbrt (* 2 d))))
84.0ms
(/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))
32.0ms
(/ (* M D) (* 2 d))

series1.2s

Calls
4 calls:
Slowest
591.0ms
(sqrt (- 1 (* (/ (* (* (cbrt h) (cbrt h)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))) (* (/ l (cbrt h)) (cbrt (* 2 d)))) (/ (* M D) (* 2 d)))))
273.0ms
(/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))
239.0ms
(/ (* (* (cbrt h) (cbrt h)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))) (* (/ l (cbrt h)) (cbrt (* 2 d))))
48.0ms
(/ (* M D) (* 2 d))