Details

simplify16.0m (55.4%)

prune6.3m (21.7%)

sample3.8m (13.3%)

Algorithm
60×intervals
Results
1.0m255123×body80valid
41.1s159862×body80nan
39.8s23364×body1280valid
21.5s16743×body640valid
20.5s8679×body10240exit
7.7s5810×body2560valid
7.0s8484×body320valid
7.0s2495×body5120valid
4.3s8536×body160valid
645.0ms620×body1280nan
557.0ms8256×pre80true
472.0ms614×body640nan
196.0ms335×body320nan
137.0ms202×body160nan

series1.3m (4.5%)

Calls

444 calls:

2.1s
(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* n (/ 1 (/ Om l))) (- U* U)))))))))
2.0s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
2.0s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))
2.0s
(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))))
1.3s
(* (* (/ (sqrt 2) (sin k)) (/ (/ (sqrt 2) (+ (* (/ k t) (/ k t)) 2)) (* t (/ (tan k) (/ l t))))) (/ l t))

rewrite1.0m (3.5%)

Algorithm
114×rewrite-expression-head
Calls

444 calls:

16.3s
(* (/ (/ (/ (/ 2 (sin k)) (/ t l)) (/ t l)) (/ k t)) (/ (/ (/ (cos k) t) (sin k)) (/ k t)))
8.3s
(sqrt (- 1 (/ (/ M (/ d D)) (/ (/ l h) (/ (/ M (/ d D)) 4)))))
1.7s
(+ (/ (+ Vef (- (+ mu EDonor) Ec)) KbT) (+ (/ (+ Vef (- (+ mu EDonor) Ec)) KbT) (/ (+ Vef (- (+ mu EDonor) Ec)) KbT)))
786.0ms
(* (exp (exp (/ (+ Vef (- (+ mu EDonor) Ec)) KbT))) E)
729.0ms
(* (* (sqrt (/ d l)) (/ (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) (* l 2))) h)
Rules
369844×times-frac
143202×add-sqr-sqrt
142915×*-un-lft-identity
140161×add-cube-cbrt
30863×associate-*l*
19814×div-inv
8442×add-exp-log
7999×add-cbrt-cube
3655×div-exp
3534×cbrt-undiv
2944×sqrt-prod
2896×associate-/l*
2848×prod-exp
2730×cbrt-unprod
2338×pow1
1598×associate-*r*
1378×distribute-lft-out
915×associate-/r*
914×cbrt-prod
827×pow-prod-down
788×associate-/r/
542×add-log-exp
519×sqrt-div
502×difference-of-squares
461×distribute-lft-out--
453×unswap-sqr
444×insert-posit16
400×associate-*r/
359×frac-times
343×flip-+ flip3-+
309×associate-*l/
240×unpow-prod-down
233×pow-prod-up
204×flip3-- flip--
195×cbrt-div
164×*-commutative
144×swap-sqr
143×pow-sqr
132×frac-add
125×distribute-rgt-in distribute-lft-in
120×sqrt-pow1
114×pow-unpow
113×pow-plus
99×pow1/2
96×frac-2neg clear-num
89×sqr-pow
85×associate-/l/
78×sub-neg
77×pow2
76×rem-sqrt-square
59×pow-exp
53×difference-of-sqr-1
52×distribute-rgt-out
50×sin-mult
40×distribute-rgt1-in
37×pow-to-exp
36×1-exp rec-exp
34×pow-pow
33×distribute-lft1-in
32×sum-log
30×pow1/3
27×+-commutative
23×div-sub
22×unpow-prod-up
19×diff-log
16×log-div
14×log-pow
13×tan-quot
11×associate-+r-
9×exp-diff
8×pow-flip log-prod frac-sub inv-pow un-div-inv pow-sub
7×associate-+r+ exp-prod
6×exp-sum asin-acos associate-+l-
5×sqr-sin rem-log-exp
4×associate-+l+ remove-posit16 pow3
3×cube-unmult sub-div acos-asin
2×associate--l+ associate--r+ unpow2 cos-sum e-exp-1
1×cos-mult sqrt-undiv unpow1/2 sqrt-unprod sqrt-pow2 rem-square-sqrt rem-cbrt-cube cos-diff associate--r-

regimes17.4s (1.0%)

Accuracy

Total 36.9b remaining (19%)

Threshold costs 4.2b (2.2%)

8.3b25.6%Toniolo and Linder, Equation (13)
6.3b53%Henrywood and Agarwal, Equation (3)
5.4b76.9%Toniolo and Linder, Equation (7)
4.0b9.3%Henrywood and Agarwal, Equation (12)
3.7b0%Henrywood and Agarwal, Equation (13)

localize6.8s (0.4%)

bsearch2.7s (0.2%)

end2.0ms (0.0%)