Details

simplify30.7m

Calls

11057 calls:

Slowest
3.3s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))
2.6s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.4s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))
2.4s
(* (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))
2.4s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* (/ h l) (/ h l)) (/ h l)))

sample3.6m

Algorithm
55×intervals
Results
59.6s245507×body80valid
38.5s161835×body80nan
36.5s19664×body1280valid
24.0s16055×body640valid
20.6s8538×body10240exit
7.4s8085×body320valid
7.4s5001×body2560valid
5.3s2346×body5120valid
4.2s8351×body160valid
763.0ms585×body1280nan
482.0ms615×body640nan
204.0ms380×body320nan
64.0ms182×body160nan

prune3.6m

series1.4m

Calls

400 calls:

Slowest
3.2s
(sqrt (+ (pow (* (* U t) (* n 2)) 1) (* (* (* (* (/ l Om) n) U) (- (* l -2) (* (* (/ l Om) n) (- U U*)))) 2)))
2.0s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (- (* (- U U*) (* (/ l Om) n))))))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.7s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.7s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

rewrite27.8s

Algorithm
104×rewrite-expression-head
Calls

400 calls:

Slowest
4.6s
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
1.1s
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (cbrt J)))
970.0ms
(* E (exp (exp (/ (+ (- (+ Ev Vef) mu) EAccept) KbT))))
575.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)))
444.0ms
(+ (sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M))) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h))
Rules
7653×times-frac
6560×add-exp-log
4889×add-sqr-sqrt
4628×*-un-lft-identity
4211×add-cbrt-cube
3999×add-cube-cbrt
2893×prod-exp
2072×div-exp
1603×cbrt-unprod
1523×pow1
1440×cbrt-undiv
1124×sqrt-prod
772×associate-/l*
717×associate-*r*
671×associate-*l*
643×cbrt-prod
633×associate-/r/
515×div-inv
514×pow-prod-down
477×associate-*r/
460×add-log-exp
454×sqrt-div
400×insert-posit16
394×pow-exp
356×associate-*l/
351×frac-times
343×associate-/r*
304×pow-unpow
292×flip-+ flip3-+
279×unpow-prod-down
265×unswap-sqr
212×difference-of-squares
190×frac-add
161×distribute-lft-out
158×distribute-lft-out--
154×pow1/3 *-commutative
150×swap-sqr
149×pow-to-exp
133×sqrt-pow1
129×exp-prod
127×flip3-- flip--
117×1-exp
116×pow-prod-up
112×tan-quot
101×rec-exp
88×pow1/2
86×sqr-pow
76×pow-sqr
75×frac-2neg clear-num
73×cbrt-div
70×rem-sqrt-square
52×sin-mult
50×pow-plus
49×distribute-lft-neg-in distribute-rgt-neg-in associate-/l/
43×distribute-rgt-in distribute-lft-in
42×sub-neg
38×pow2
33×pow-pow
28×div-sub
27×distribute-rgt-out--
22×sum-log
21×+-commutative
16×log-pow
15×exp-diff
12×log-prod
11×frac-sub log-div
10×cube-prod cos-sum
pow-flip pow-sub
inv-pow neg-mul-1 unpow2 rem-exp-log
associate-+l+ exp-sum associate--l+ associate-+l- cube-div diff-log
cos-diff
remove-posit16 associate-+r- associate-+r+ pow3 sqr-sin
un-div-inv rem-log-exp
neg-sub0 distribute-frac-neg distribute-neg-frac
cube-unmult exp-neg unpow3 sqrt-unprod sub-div sqrt-pow2 asin-acos rem-square-sqrt cube-mult acos-asin associate--r- e-exp-1

regimes15.2s

Accuracy

Total 37.6b remaining (23%)

8.5b13.2%Toniolo and Linder, Equation (13)
8.1b5.9%Maksimov and Kolovsky, Equation (3)
5.5b77.4%Toniolo and Linder, Equation (7)
4.9b0%Henrywood and Agarwal, Equation (12)
3.1b0%Henrywood and Agarwal, Equation (13)

localize5.7s

bsearch4.3s

end1.0ms