Details

simplify39.5m

Calls

14278 calls:

Slowest
3.7s
(/ (/ (* (/ (* (* (* 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
(/ (/ (* (/ (* (* (* 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))
2.5s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (* (* (cos k) (cos k)) (cos k))))
2.2s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
2.0s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))

prune4.0m

sample3.7m

Algorithm
55×intervals
Results
1.0m245091×body80valid
41.2s159760×body80nan
37.4s19518×body1280valid
20.1s15712×body640valid
19.8s8469×body10240exit
7.5s4991×body2560valid
6.9s8179×body320valid
5.7s8502×body160valid
5.3s2363×body5120valid
1.1s609×body1280nan
596.0ms651×body640nan
169.0ms341×body320nan
75.0ms209×body160nan

series1.3m

Calls

382 calls:

Slowest
2.4s
(sqrt (* 2 (* U (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
2.4s
(sqrt (* 2 (* U (* n (- (fma (* l (/ l Om)) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
2.3s
(sqrt (* 2 (* U (* n (- (fma (* l (/ l Om)) -2 t) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))))
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))))
1.6s
(* (* (* (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 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))

regimes16.0s

Accuracy

Total 39.0b remaining (26.6%)

8.5b39.4%Henrywood and Agarwal, Equation (3)
6.1b18.8%Henrywood and Agarwal, Equation (13)
5.7b13.2%Toniolo and Linder, Equation (13)
5.3b77%Toniolo and Linder, Equation (7)
4.7b0%Henrywood and Agarwal, Equation (12)

rewrite15.6s

Algorithm
103×rewrite-expression-head
Calls

382 calls:

Slowest
1.8s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.4s
(/ NdChar (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1))
781.0ms
(* (cbrt (- (- Ec (+ (+ Vef mu) EDonor)))) (cbrt (- (- Ec (+ (+ Vef mu) EDonor)))))
694.0ms
(cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2)))) (+ m n))) M))
410.0ms
(* U (* (- U U*) (* (* (/ l Om) n) (* (/ l Om) n))))
Rules
10757×times-frac
6596×add-sqr-sqrt
6377×add-exp-log
6296×*-un-lft-identity
5626×add-cube-cbrt
4143×add-cbrt-cube
2477×prod-exp
2370×div-exp
1629×cbrt-undiv
1563×sqrt-prod
1300×cbrt-unprod
1181×pow1
1164×frac-times
1110×sqrt-div
1045×associate-/l*
858×associate-*r*
713×associate-*l*
706×div-inv
655×associate-*r/
631×associate-*l/
629×prod-diff
618×associate-/r/
592×flip3-- flip--
589×cbrt-prod
529×associate-/r*
414×add-log-exp
401×pow-prod-down
385×expm1-log1p-u
382×log1p-expm1-u insert-posit16
353×unpow-prod-down
344×pow-exp
265×unswap-sqr
248×pow-unpow
236×difference-of-squares
231×distribute-rgt-in distribute-lft-in
179×distribute-lft-out--
162×pow-to-exp
148×sqrt-pow1
143×distribute-lft-out
140×1-exp
138×rec-exp
131×swap-sqr
122×*-commutative
113×sqr-pow
109×distribute-rgt-neg-in
103×frac-2neg clear-num
101×distribute-lft-neg-in
95×pow1/3
93×cbrt-div
79×fma-neg
68×pow1/2
48×pow-prod-up sub-neg
41×fma-udef
34×pow-sqr
31×associate-/l/
30×exp-prod
29×rem-sqrt-square tan-quot
25×cos-sum
23×associate--l+
20×distribute-neg-frac
19×pow-pow
18×log-pow
17×div-sub
14×pow-flip
12×pow2 pow-plus
11×neg-mul-1 diff-log
10×flip-+ fma-def flip3-+
asin-acos pow-sub
difference-of-sqr-1 inv-pow
log-prod
un-div-inv
sum-log log1p-expm1 +-commutative log1p-udef
frac-sub distribute-rgt-out-- cos-diff associate--r-
expm1-log1p expm1-udef associate-+r- mul0 sqrt-unprod sub-div hypot-udef rem-square-sqrt rem-log-exp frac-add
neg-sub0 exp-diff cube-unmult exp-to-pow rem-exp-log distribute-frac-neg acos-asin

localize5.1s

bsearch3.1s

end1.0ms