Details

sample2.4m (37.2%)

Algorithm
61×intervals
Results
31.0s253725×body80valid
26.4s29606×body1280valid
21.5s160562×body80nan
15.0s20452×body640valid
13.2s8769×body2560valid
7.5s3397×body5120valid
4.9s9882×body320valid
2.6s9060×body160valid
866.0ms970×body10240exit
429.0ms358×body320nan
272.0ms652×body1280nan
230.0ms649×body640nan
189.0ms8256×pre80true
55.0ms174×body160nan

series1.9m (29.4%)

Calls

447 calls:

5.7s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.5s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.4s
(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 l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

prune55.4s (14.3%)

rewrite41.5s (10.7%)

Algorithm
116×rewrite-expression-head
Calls

447 calls:

2.4s
(/ (/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
1.7s
(* (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))) (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
1.1s
(* (* (* (* (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))
998.0ms
(* (exp 1.0) (exp (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))
955.0ms
(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
Rules
36071×add-exp-log
25390×prod-exp
12149×pow-exp
10037×div-exp
5466×pow-to-exp
3835×add-sqr-sqrt
3507×*-un-lft-identity
3442×times-frac
2831×add-cube-cbrt
2721×add-cbrt-cube
1398×sqrt-prod
1325×rec-exp 1-exp
1274×pow1
1216×cbrt-unprod
1007×associate-*r*
948×unpow-prod-down
884×associate-*l*
668×associate-*r/
552×add-log-exp
536×pow-unpow
491×cbrt-prod
484×cbrt-undiv
409×pow-prod-down
358×sqrt-div
326×unswap-sqr
297×associate-*l/
296×associate-/l* associate-/r*
279×distribute-lft-out
273×frac-times
267×sqr-pow
246×associate-/r/
242×div-inv
225×flip3-- flip--
200×flip-+ flip3-+
172×difference-of-squares
153×*-commutative
132×cube-prod
114×sqrt-pow1
98×distribute-rgt-in distribute-lft-in
92×tan-quot
87×clear-num frac-2neg
84×sub-neg
83×pow1/2
81×distribute-lft-out-- unpow2
80×rem-sqrt-square
76×distribute-rgt-neg-in
64×exp-prod
59×pow1/3
57×log-pow
55×frac-sub
54×swap-sqr pow-pow
52×distribute-lft-neg-in
34×sum-log
32×cbrt-div
31×associate-/l/ log-prod associate--l+
27×+-commutative div-sub
24×frac-add
22×pow-prod-up pow-sub
19×pow-sqr
18×exp-diff diff-log
16×cos-sum pow-neg log-div
14×cube-div
13×neg-sub0
10×associate-+r+
pow2
pow-plus rem-exp-log cos-diff
un-div-inv exp-sum rem-log-exp
pow-flip
rem-cube-cbrt unpow3 cube-mult asin-acos
inv-pow unpow1/2 neg-mul-1 associate-+r-
exp-to-pow
sqrt-unprod unsub-neg acos-asin associate--r-
difference-cubes sqrt-pow2 rem-square-sqrt sub-div mul0 rem-cbrt-cube

simplify11.9s (3.1%)

regimes11.8s (3.0%)

Accuracy

Total 53.0b remaining (24.4%)

Threshold costs 3.6b (1.7%)

11.7b12.7%Toniolo and Linder, Equation (13)
7.1b17.6%Toniolo and Linder, Equation (10+)
6.3b-3.6%Given's Rotation SVD example
5.4b77.5%Toniolo and Linder, Equation (7)
4.8b37.8%Henrywood and Agarwal, Equation (3)

bsearch5.1s (1.3%)

localize3.4s (0.9%)

end0.0ms (0.0%)