Details

prune11.4m (40.9%)

simplify9.8m (35.4%)

sample3.9m (14.1%)

Algorithm
59×intervals
Results
1.1m255909×body80valid
41.8s161464×body80nan
39.9s23832×body1280valid
22.0s16563×body640valid
18.9s8488×body10240exit
9.2s5782×body2560valid
7.2s8381×body320valid
6.0s2514×body5120valid
4.2s8712×body160valid
1.1s631×body640nan
608.0ms603×body1280nan
324.0ms8256×pre80true
294.0ms366×body320nan
73.0ms201×body160nan

series1.5m (5.2%)

Calls

442 calls:

Slowest
2.3s
(sqrt (* (* (* U n) 2) (- t (* (/ l Om) (- (* 2 l) (- (* (* (/ n (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) (- U U*))))))))
2.2s
(sqrt (* (* (* U n) 2) (- t (* (/ l Om) (- (* 2 l) (- (* (* n (/ l Om)) (- U U*))))))))
2.2s
(sqrt (* (* (* U n) 2) (- t (* (/ l Om) (- (* 2 l) (- (* (* n (/ l Om)) (- U U*))))))))
2.1s
(sqrt (* (* (* U n) 2) (- t (* (/ l Om) (- (* 2 l) (- (* (* n (/ l Om)) (- U U*))))))))
2.0s
(sqrt (* (* (* U n) 2) (- t (* (/ l Om) (- (* 2 l) (- (* (* n (/ l Om)) (- U U*))))))))

rewrite39.2s (2.4%)

Algorithm
113×rewrite-expression-head
Calls

442 calls:

Slowest
2.6s
(* (cbrt (/ (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1) NdChar)) (cbrt (/ (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1) NdChar)))
1.5s
(* (sqrt (+ 1 (exp (/ (- (+ (+ EAccept Vef) Ev) mu) KbT)))) (sqrt (+ 1 (exp (/ (- (+ (+ EAccept Vef) Ev) mu) KbT)))))
1.1s
(cbrt (* (* (/ (/ (* M D) (* d 2)) (/ l (/ (* M D) (* d 2)))) h) (* (* (/ (/ (* M D) (* d 2)) (/ l (/ (* M D) (* d 2)))) h) (* (/ (/ (* M D) (* d 2)) (/ l (/ (* M D) (* d 2)))) h))))
659.0ms
(/ NdChar (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1))
649.0ms
(/ 1 (/ (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1) NdChar))
Rules
374612×times-frac
137996×add-sqr-sqrt
137479×*-un-lft-identity
135420×add-cube-cbrt
30516×sqrt-prod
19539×div-inv
14270×add-exp-log
10078×cbrt-prod
8963×associate-/l*
7722×prod-exp
5309×add-cbrt-cube
4524×div-exp
4209×associate-/r/
3935×tan-quot
2518×pow-exp
2501×associate-*r/
2370×cbrt-undiv
1855×cbrt-unprod
1558×associate-/r*
1536×pow1
1231×frac-times
1202×associate-*r*
1193×associate-*l*
1119×frac-add
1098×cbrt-div
1003×pow-to-exp
868×associate-*l/
652×flip-+ flip3-+
629×distribute-lft-out
568×add-log-exp
529×pow-prod-down
512×distribute-lft-out--
483×unswap-sqr
479×sqrt-div
442×insert-posit16
431×unpow-prod-down
409×swap-sqr
353×pow-unpow
294×difference-of-squares
268×associate-/l/
193×flip3-- flip--
191×sqr-pow
160×1-exp
150×rec-exp
149×*-commutative
130×sqrt-pow1
101×cos-mult
97×frac-2neg clear-num
90×pow1/2
74×pow1/3
70×sub-neg
65×distribute-rgt-in sin-mult distribute-lft-in
60×rem-sqrt-square
54×sin-cos-mult
52×pow-prod-up
42×sum-log
37×log-pow
36×pow-sqr
30×+-commutative
29×frac-sub pow-plus
28×diff-log
27×pow-pow
26×associate--l+ div-sub
25×pow2
24×exp-prod
20×pow-flip
19×distribute-lft-neg-in distribute-rgt-neg-in pow-sub
16×rem-log-exp
13×log-prod exp-sum
11×sqrt-undiv
10×inv-pow cos-sum
9×cos-diff pow-neg
8×difference-of-sqr-1
7×neg-sub0
6×associate-+l+ sqrt-unprod
5×associate--l- acos-asin
4×distribute-rgt-out-- associate--r+
3×associate-+r+ cube-unmult sqr-sin un-div-inv neg-mul-1 rem-exp-log rem-square-sqrt
2×exp-diff distribute-lft1-in log-div pow3 sub-div unpow2 asin-acos rem-cbrt-cube distribute-rgt-out

regimes22.3s (1.3%)

Accuracy

Total 55.1b remaining (28.9%)

Threshold costs 3.1b (1.6%)

12.1b-9.2%Henrywood and Agarwal, Equation (13)
9.1b39.4%Henrywood and Agarwal, Equation (3)
7.8b9.6%Maksimov and Kolovsky, Equation (3)
7.0b71.1%Toniolo and Linder, Equation (7)
4.2b0%Toniolo and Linder, Equation (13)

localize8.3s (0.5%)

bsearch3.3s (0.2%)

end1.0ms (0.0%)