Details

simplify33.4m

Calls

13116 calls:

Slowest
2.4s
(/ (* (* (/ 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))))
2.3s
(/ (* (* (/ 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) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
2.1s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 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))))))
2.0s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.9s
(* (/ (* (* (/ 1 (sqrt (fma (* v -6) v 2))) (/ 1 (sqrt (fma (* v -6) v 2)))) (/ 1 (sqrt (fma (* v -6) v 2)))) (* (* (- 1 (* v v)) (- 1 (* v v))) (* (* t t) t))) (/ (* (* (/ (fma -5 (* v v) 1) (cbrt (- 1 (* v v)))) (/ (fma -5 (* v v) 1) (cbrt (- 1 (* v v))))) (/ (fma -5 (* v v) 1) (cbrt (- 1 (* v v))))) (* (* PI PI) PI)))

prune4.1m

sample3.3m

Algorithm
54×intervals
Results
58.5s239338×body80valid
36.9s159684×body80nan
30.3s17567×body1280valid
19.2s8277×body10240exit
17.7s13961×body640valid
7.6s4981×body2560valid
6.3s2452×body5120valid
5.8s7249×body320valid
3.8s7923×body160valid
674.0ms620×body1280nan
582.0ms652×body640nan
184.0ms359×body320nan
94.0ms174×body160nan

series1.2m

Calls

386 calls:

Slowest
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (/ (* (/ n (/ Om l)) (- U U*)) (/ Om l)))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))
1.4s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))

rewrite26.5s

Algorithm
103×rewrite-expression-head
Calls

386 calls:

Slowest
2.0s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
2.0s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
2.0s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.8s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.7s
(* NaChar (/ 1 (log (* E (exp (exp (/ (- Ev (- (- mu Vef) EAccept)) KbT)))))))
Rules
29708×times-frac
14628×add-sqr-sqrt
14246×*-un-lft-identity
13477×add-cube-cbrt
9086×cbrt-prod
8939×add-exp-log
6415×associate-*l*
4364×prod-exp
3305×add-cbrt-cube
3101×div-exp
1550×pow1
1201×cbrt-undiv
1063×cbrt-unprod
1022×div-inv
968×sqrt-prod
901×associate-/l*
842×prod-diff
769×associate-*r*
718×pow-exp
633×associate-/r/
553×1-exp
519×sqrt-pow1
470×pow-unpow
438×add-log-exp
429×pow-prod-down
386×expm1-log1p-u insert-posit16 log1p-expm1-u
377×difference-of-squares
354×associate-/r*
329×associate-*r/
310×pow-prod-up
276×pow1/2
266×associate-*l/
263×rec-exp
245×unpow-prod-down
235×unswap-sqr
224×distribute-lft-out--
214×frac-times
195×pow-to-exp
178×distribute-rgt-in distribute-lft-in
152×distribute-rgt-neg-in
150×distribute-lft-neg-in
142×pow-sqr
138×distribute-lft-out *-commutative
123×flip3-- flip--
89×fma-neg
88×sqrt-div
84×frac-2neg clear-num swap-sqr
69×cos-sum
64×sqr-pow
58×pow1/3
57×pow-plus
49×fma-def
47×sub-neg
46×cbrt-div
45×fma-udef
44×pow-pow rem-sqrt-square
42×frac-sub associate--l+
39×pow2
36×tan-quot
30×flip-+ flip3-+
28×associate-/l/
19×div-sub
18×pow-flip neg-mul-1 unpow2
14×sum-log diff-log
12×associate--r+ inv-pow
10×+-commutative
frac-add
un-div-inv
pow-sub
exp-sum sqrt-unprod distribute-neg-frac log-pow
neg-sub0 pow3
distribute-frac-neg hypot-udef distribute-rgt-out-- acos-asin cos-diff
associate-+l+ associate-+r- neg-log rem-square-sqrt rem-cbrt-cube sin-mult
sqrt-undiv mul0 sub-div associate--l- sqr-sin asin-acos associate--r- e-exp-1 distribute-rgt-out

regimes15.6s

Accuracy

Total 45.9b remaining (33.8%)

9.4b12.8%Toniolo and Linder, Equation (13)
9.1b33.6%Henrywood and Agarwal, Equation (3)
6.3b6.8%Henrywood and Agarwal, Equation (12)
6.2b16.1%Henrywood and Agarwal, Equation (13)
5.5b76.4%Toniolo and Linder, Equation (7)

localize5.8s

bsearch2.2s

end1.0ms