Details

series1.7m (33.8%)

Calls

438 calls:

5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.6s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.4m (28.3%)

Algorithm
61×intervals
Results
15.8s29584×body1280valid
15.7s254654×body80valid
9.8s161103×body80nan
8.9s8804×body2560valid
7.2s20531×body640valid
5.4s3356×body5120valid
2.4s9809×body320valid
1.4s8729×body160valid
439.0ms838×body10240exit
137.0ms597×body1280nan
109.0ms595×body640nan
101.0ms8256×pre80true
52.0ms349×body320nan
16.0ms172×body160nan

prune51.8s (17.1%)

rewrite34.4s (11.4%)

Algorithm
116×rewrite-expression-head
Calls

438 calls:

1.9s
(* (* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(/ (/ 1 (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ 1 NdChar))
1.1s
(/ 1 (/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) NdChar))
1.0s
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* (* t (* (cbrt (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))) (cbrt (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))))) (cbrt (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))))) (- 1.0 (* v v))))
980.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
31125×add-exp-log
21634×prod-exp
10482×pow-exp
8730×div-exp
4966×pow-to-exp
4751×times-frac
4463×add-sqr-sqrt
4339×*-un-lft-identity
3290×add-cube-cbrt
2570×add-cbrt-cube
1766×associate-*r/
1389×pow1
1273×sqrt-prod
1159×cbrt-unprod
1033×associate-*r*
870×pow-unpow
855×1-exp rec-exp
769×frac-times
761×associate-*l*
644×cbrt-prod
607×unpow-prod-down
548×flip3-- flip--
540×sqrt-div
529×add-log-exp
526×pow-prod-down
504×associate-*l/
452×cbrt-undiv
444×distribute-lft-out
386×cbrt-div
335×frac-add
324×flip-+ flip3-+
306×unswap-sqr
297×associate-/l*
287×div-inv
262×associate-/r*
244×associate-/r/
205×sqr-pow
192×difference-of-squares
145×*-commutative
134×distribute-lft-out--
129×swap-sqr
105×exp-prod
98×pow1/3
81×clear-num frac-2neg
77×distribute-rgt-neg-in
73×sqrt-pow1
71×tan-quot
61×distribute-rgt-in distribute-lft-in
55×sub-neg
54×pow1/2
53×pow-pow
52×rem-sqrt-square
44×div-sub
39×cube-div frac-sub
34×sum-log
33×associate-/l/ unpow2
28×+-commutative
26×associate--l+
20×pow-prod-up pow-sqr
13×distribute-lft-neg-in pow-sub
12×neg-sub0
11×cube-prod
10×diff-log log-pow
9×exp-diff pow-plus associate-+r+
7×rem-cube-cbrt inv-pow pow-flip pow2 log-prod
6×unsub-neg associate-+r-
5×un-div-inv rem-exp-log unpow3 cube-mult sqrt-undiv
4×associate-+l+ pow-neg
3×neg-log distribute-rgt-out-- distribute-neg-frac acos-asin associate-+l-
2×cos-sum asin-acos exp-sum rem-log-exp
1×difference-cubes sqrt-unprod cos-diff rem-square-sqrt sub-div neg-mul-1 mul0 rem-cbrt-cube

simplify11.8s (3.9%)

regimes10.7s (3.5%)

Accuracy

Total 40.1b remaining (19.1%)

Threshold costs 5.4b (2.6%)

7.8b14.5%Toniolo and Linder, Equation (13)
6.8b12.7%Toniolo and Linder, Equation (10+)
5.2b-19.9%Henrywood and Agarwal, Equation (12)
5.2b78.3%Toniolo and Linder, Equation (7)
3.3b51%Toniolo and Linder, Equation (10-)

bsearch3.5s (1.1%)

localize2.3s (0.8%)

end1.0ms (0.0%)