Details

simplify37.2m

Calls

13623 calls:

Slowest
3.9s
(/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l))
3.0s
(* (/ (* (* 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)))))
2.9s
(/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2)))) (* (* 2 2) 2)) (* (* l l) l))
2.9s
(* (* (/ (* (* (* 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)))
2.5s
(* (* (/ (* (* (* 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)))

prune3.7m

sample3.5m

Algorithm
54×intervals
Results
56.8s239188×body80valid
42.1s159760×body80nan
31.8s17516×body1280valid
20.9s8469×body10240exit
16.8s13976×body640valid
8.0s4991×body2560valid
6.5s7318×body320valid
5.7s2363×body5120valid
4.1s8068×body160valid
679.0ms651×body640nan
663.0ms609×body1280nan
614.0ms341×body320nan
113.0ms209×body160nan

series1.2m

Calls

393 calls:

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

rewrite31.3s

Algorithm
102×rewrite-expression-head
Calls

393 calls:

Slowest
5.0s
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J))) (cbrt J))
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J)))
1.3s
(/ NdChar (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1))
1.2s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.2s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
Rules
26539×times-frac
12531×add-sqr-sqrt
12355×*-un-lft-identity
11542×add-cube-cbrt
6058×add-exp-log
4399×add-cbrt-cube
2844×associate-*r*
2437×prod-exp
2044×div-exp
1682×sqrt-prod
1575×cbrt-undiv
1522×pow1
1506×cbrt-unprod
1446×sqrt-div
1359×associate-/r/
1324×frac-times
1265×div-inv
951×associate-*l*
869×associate-/l*
856×associate-*r/
756×associate-*l/
653×flip3-- flip--
619×associate-/r*
539×pow-prod-down
537×flip-+ flip3-+
445×add-log-exp
393×insert-posit16
306×pow-unpow
298×pow-exp
276×unswap-sqr
250×cbrt-prod
195×unpow-prod-down
194×distribute-lft-out--
193×difference-of-squares
185×sqrt-pow1
176×*-commutative
168×distribute-lft-out
153×swap-sqr
149×frac-add
135×pow-to-exp
109×distribute-rgt-neg-in
108×pow1/2 tan-quot
104×distribute-rgt-out-- 1-exp
101×distribute-lft-neg-in
83×rec-exp
82×frac-2neg clear-num
77×pow-prod-up
76×sqr-pow
61×sin-mult
58×cbrt-div
57×distribute-rgt-in distribute-lft-in
55×rem-sqrt-square
54×sub-neg
43×exp-prod
39×associate-/l/
34×pow-sqr
32×log-prod pow-plus
29×log-pow
27×pow-pow
22×pow1/3 div-sub
20×distribute-neg-frac
19×pow2
17×sum-log
16×cos-sum
15×+-commutative
12×exp-sum
11×frac-sub neg-mul-1
10×exp-diff cube-prod log-div
pow-flip pow-sub
associate-+l+ difference-of-sqr-1 cos-diff diff-log
sqr-sin inv-pow
associate-+r+ associate--l+ rem-log-exp asin-acos cube-div
associate-+r- cube-unmult rem-exp-log acos-asin
distribute-lft1-in sqrt-unprod sub-div exp-to-pow unpow2 rem-square-sqrt un-div-inv distribute-rgt-out
neg-sub0 sqrt-undiv distribute-frac-neg pow3 unpow3 sqrt-pow2 cube-mult associate--r-

regimes16.6s

Accuracy

Total 45.8b remaining (27.7%)

8.5b39.4%Henrywood and Agarwal, Equation (3)
8.5b9.5%Toniolo and Linder, Equation (13)
7.3b13.1%Maksimov and Kolovsky, Equation (3)
6.1b-23.5%Henrywood and Agarwal, Equation (12)
5.8b75.7%Toniolo and Linder, Equation (7)

localize5.5s

bsearch5.2s

end1.0ms