Details

simplify46.7m

Calls

15124 calls:

Slowest
3.5s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))
3.2s
(* (* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (/ (* h h) (* (* 1 1) 1))) (/ h (* (* l l) l)))
3.2s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D)))) (* (* h h) h))
3.0s
(* (* (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* M M) M))) (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* M M) M)))) (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)))
2.9s
(/ (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D))) (/ (* (* h h) h) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D)))))

prune4.4m

sample3.4m

Algorithm
53×intervals
Results
56.2s231092×body80valid
42.2s160852×body80nan
28.4s15467×body1280valid
20.2s8572×body10240exit
15.6s11903×body640valid
6.7s4942×body2560valid
6.3s6027×body320valid
5.8s2323×body5120valid
4.1s7357×body160valid
762.0ms610×body1280nan
525.0ms635×body640nan
241.0ms357×body320nan
82.0ms217×body160nan

series1.3m

Calls

400 calls:

Slowest
3.3s
(sqrt (+ (pow (* (* U t) (* n 2)) 1) (* (* (* (* (/ l Om) n) U) (- (* l -2) (* (* (/ l Om) n) (- U U*)))) 2)))
1.7s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (- (* (- U U*) (* (/ l Om) n))))))))
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))

rewrite28.6s

Algorithm
103×rewrite-expression-head
Calls

400 calls:

Slowest
1.4s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
Rules
40428×times-frac
16066×add-sqr-sqrt
15885×add-exp-log
15824×*-un-lft-identity
15295×add-cube-cbrt
7658×prod-exp
7327×add-cbrt-cube
5980×div-exp
4551×cbrt-prod
3670×sqrt-prod
3197×cbrt-unprod
2996×cbrt-undiv
2452×div-inv
1516×associate-/r/
1337×pow1
1032×associate-/l*
803×associate-/r*
751×pow-exp associate-*r*
738×1-exp
665×sqrt-div
645×associate-*l*
600×associate-*r/
478×rec-exp
465×add-log-exp
437×associate-*l/
428×pow-prod-down
403×flip-+ flip3-+
400×insert-posit16
369×frac-times
263×unpow-prod-down
246×difference-of-squares
241×pow-unpow
223×pow-to-exp
194×unswap-sqr
165×flip3-- flip--
163×frac-add
161×swap-sqr
145×*-commutative
119×distribute-lft-out
115×sqrt-pow1
114×tan-quot
105×distribute-rgt-out--
102×distribute-lft-out--
90×frac-2neg clear-num
85×pow1/2
83×sqr-pow
71×exp-prod
70×sin-mult
65×cbrt-div
60×rem-sqrt-square
53×distribute-rgt-neg-in
49×distribute-lft-neg-in pow1/3
48×distribute-rgt-in pow-prod-up distribute-lft-in
47×sub-neg
46×associate-/l/
29×pow-plus pow-sqr
28×pow-pow
25×div-sub
24×pow2 diff-log
21×log-pow
18×frac-sub
14×unpow2
12×pow-flip sum-log
11×associate-+r+ difference-of-sqr-1
10×associate--l+ +-commutative inv-pow sqr-sin
log-prod un-div-inv
sub-div neg-mul-1 pow-sub
exp-sum cos-sum
neg-sub0 neg-log associate--r+ asin-acos rem-exp-log
associate-+l+ remove-posit16 acos-asin cos-diff
associate--l- associate-+r- cube-unmult distribute-frac-neg rem-log-exp distribute-neg-frac associate--r-
exp-diff sqrt-undiv pow3 sqrt-unprod exp-neg rem-square-sqrt rem-cbrt-cube

regimes15.9s

Accuracy

Total 53.1b remaining (40%)

17.2b-4.4%Henrywood and Agarwal, Equation (13)
9.1b7%Toniolo and Linder, Equation (13)
8.7b-1.8%Maksimov and Kolovsky, Equation (3)
6.4b73.5%Toniolo and Linder, Equation (7)
4.1b0%Henrywood and Agarwal, Equation (12)

localize6.4s

bsearch4.5s

end1.0ms