Details

simplify1.1hr

Calls

23251 calls:

Slowest
2.6s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))))) (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))))) (* (* (cos k) (cos k)) (cos k))))
2.3s
(* (* (* h h) h) (* (* (/ 1 l) (/ 1 l)) (* (/ 1 l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))))
2.2s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.9s
(/ (* (* (/ 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))))))
1.9s
(sqrt (+ (* 1 1) (+ (* (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d))) (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))) (* 1 (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))))))

prune4.3m

sample3.5m

Algorithm
57×intervals
Results
56.2s239252×body80valid
39.6s144380×body80nan
35.1s21278×body1280valid
19.7s8373×body10240exit
18.9s14802×body640valid
8.5s5892×body2560valid
6.2s2443×body5120valid
5.9s7738×body320valid
4.6s8248×body160valid
673.0ms565×body1280nan
596.0ms616×body640nan
454.0ms8256×pre80true
263.0ms385×body320nan
78.0ms200×body160nan

series1.3m

Calls

410 calls:

Slowest
2.0s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))
1.9s
(sqrt (* (* (cbrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))) (cbrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))) (cbrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
1.6s
(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
(* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))

rewrite22.1s

Algorithm
110×rewrite-expression-head
Calls

410 calls:

Slowest
1.7s
(+ (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
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (/ d D) (* (/ d D) (/ c0 h))) w))
1.0s
(+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1)
923.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
852.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
Rules
47459×times-frac
22115×add-sqr-sqrt
21776×*-un-lft-identity
20765×add-cube-cbrt
8833×associate-*r/
6298×frac-times cbrt-div
5203×flip3-- flip--
5139×frac-sub
4478×add-exp-log
4142×associate-*r*
3842×cbrt-prod
3773×add-cbrt-cube
2340×sqrt-div
2209×div-inv
2182×sqrt-prod
1746×div-exp
1735×pow1
1659×associate-*l/
1603×cbrt-undiv
1406×prod-diff
1370×prod-exp
1251×associate-/l*
1219×associate-*l*
1173×cbrt-unprod
840×associate-/r*
744×associate-/r/
714×difference-of-squares
528×pow-prod-down
477×unpow-prod-down
470×add-log-exp
414×expm1-log1p-u
410×log1p-expm1-u insert-posit16
298×pow-prod-up
237×distribute-lft-out--
231×pow1/3
230×pow-unpow
225×unswap-sqr
219×sqr-pow
194×sqrt-pow1
192×distribute-rgt-neg-in
191×distribute-lft-out
188×distribute-lft-neg-in
157×pow-sqr
131×*-commutative
127×swap-sqr
115×pow1/2 fma-neg
113×pow-plus
107×frac-2neg clear-num
93×distribute-rgt-in distribute-lft-in
75×pow-exp
69×pow2
64×rem-sqrt-square
48×pow-to-exp
47×fma-udef
46×1-exp rec-exp
42×associate-/l/
40×sub-neg
37×fma-def
34×tan-quot
33×associate--l+
32×flip-+ unpow2 flip3-+
25×cos-sum
24×diff-log
23×pow-pow
22×associate--r+
21×div-sub
20×neg-mul-1
19×log-pow exp-prod
15×hypot-udef
14×hypot-def
12×pow-flip sqrt-unprod
10×log-prod inv-pow
pow-sub
sum-log
+-commutative
log1p-udef
neg-sub0 expm1-udef log1p-expm1 neg-log distribute-neg-frac frac-add
expm1-log1p associate-+r- rem-log-exp distribute-rgt-out-- asin-acos rem-square-sqrt sin-mult
associate-+r+ distribute-frac-neg cube-unmult associate--l- rem-exp-log acos-asin associate--r-
sqrt-undiv mul0 exp-sum pow3 difference-of-sqr-1 sub-div sqr-sin cos-diff expm1-def

regimes16.0s

Accuracy

Total 34.5b remaining (27.4%)

Threshold costs 3.8b (3%)

7.9b47.2%Henrywood and Agarwal, Equation (3)
6.9b14.7%Henrywood and Agarwal, Equation (13)
5.9b74.8%Toniolo and Linder, Equation (7)
4.5b-11.9%Maksimov and Kolovsky, Equation (3)
4.3b30.4%Henrywood and Agarwal, Equation (12)

localize5.6s

bsearch4.4s

end1.0ms