Details

simplify40.1m

Calls

15285 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))))
2.2s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))
2.1s
(* (* (* h h) h) (* (/ (* (* M M) M) (/ (* (* 2 2) 2) (/ (* (* D D) D) (* (* d d) d)))) (/ (* (* M M) M) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d))))))
2.0s
(/ (* (* (/ 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))))
2.0s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))

prune4.4m

sample3.5m

Algorithm
54×intervals
Results
56.0s239410×body80valid
40.4s159066×body80nan
32.7s18031×body1280valid
20.2s8625×body10240exit
17.8s13625×body640valid
7.9s5032×body2560valid
7.6s7334×body320valid
7.1s2331×body5120valid
4.0s7945×body160valid
998.0ms564×body1280nan
633.0ms618×body640nan
236.0ms363×body320nan
65.0ms181×body160nan

series1.2m

Calls

384 calls:

Slowest
1.8s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))

rewrite20.5s

Algorithm
104×rewrite-expression-head
Calls

384 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))
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))
1.8s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.8s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
908.0ms
(* (cbrt (+ 1 (exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT)))) (cbrt (+ 1 (exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT)))))
Rules
23998×times-frac
12228×add-sqr-sqrt
11858×*-un-lft-identity
11195×add-cube-cbrt
5867×add-exp-log
3500×add-cbrt-cube
2996×sqrt-prod
2426×prod-exp
2007×div-exp
1339×associate-*l*
1336×cbrt-undiv
1307×pow1
1277×div-inv
1119×associate-/l*
1118×cbrt-unprod
926×prod-diff
726×associate-*r*
699×associate-/r/
659×associate-/r*
522×difference-of-squares
413×pow-unpow
412×add-log-exp associate-*r/
384×expm1-log1p-u insert-posit16 log1p-expm1-u
361×pow-prod-down
259×cbrt-prod
234×associate-*l/
232×frac-times
221×pow-exp
220×unswap-sqr
191×1-exp rec-exp
190×unpow-prod-down
174×flip3-- flip--
160×exp-prod
134×distribute-lft-out--
124×*-commutative
117×pow-prod-up
111×sqrt-div
110×distribute-rgt-in distribute-lft-in
104×distribute-lft-out
103×swap-sqr
101×frac-2neg clear-num
90×frac-sub
85×pow-to-exp
84×sqrt-pow1
70×distribute-lft-neg-in distribute-rgt-neg-in
69×pow-plus
68×pow-sqr
65×pow1/3
60×sqr-pow
59×pow1/2
50×rem-sqrt-square
46×associate--l+
42×pow2
38×sub-neg fma-udef
36×fma-neg
35×tan-quot
34×fma-def
30×pow-pow associate-/l/
24×flip-+ flip3-+
21×cbrt-div
18×div-sub
17×cos-sum
16×difference-of-sqr-1
14×pow-flip
12×inv-pow frac-add
10×neg-mul-1
pow-sub
un-div-inv
sum-log +-commutative diff-log
sin-sum
remove-posit16 exp-diff pow3 hypot-udef rem-exp-log acos-asin
neg-sub0 associate-+r- unpow2 distribute-frac-neg cos-diff
expm1-udef exp-neg sqrt-unprod distribute-neg-frac asin-acos rem-square-sqrt
expm1-log1p mul0 sin-mult sqr-sin rem-cbrt-cube sin-diff

regimes15.7s

Accuracy

Total 39.3b remaining (29%)

11.6b-17%Toniolo and Linder, Equation (13)
6.4b-12.5%Henrywood and Agarwal, Equation (12)
6.1b20.5%Henrywood and Agarwal, Equation (13)
5.4b77.3%Toniolo and Linder, Equation (7)
4.7b-18.4%Maksimov and Kolovsky, Equation (3)

localize5.5s

bsearch2.1s

end1.0ms