Details

simplify6.1m (38.7%)

sample3.3m (21.2%)

Algorithm
61×intervals
Results
44.3s253560×body80valid
41.4s29210×body1280valid
23.2s160234×body80nan
21.7s20401×body640valid
18.3s8958×body2560valid
11.7s3343×body5120valid
7.3s10108×body320valid
3.0s8732×body160valid
1.3s658×body10240exit
364.0ms586×body1280nan
328.0ms662×body640nan
251.0ms381×body320nan
160.0ms8256×pre80true
30.0ms155×body160nan

series2.4m (15.6%)

Calls

451 calls:

8.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.4s
(pow (exp (sqrt (/ (- (+ (+ Ev Vef) EAccept) mu) KbT))) (sqrt (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))

prune2.2m (14.1%)

rewrite1.2m (7.8%)

Algorithm
118×rewrite-expression-head
Calls

451 calls:

22.6s
(* (/ NaChar (+ (pow (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 3) (pow 1.0 3))) (+ (* 1.0 1.0) (- (* (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))) (* 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
2.9s
(- (* (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))) (* 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))
2.1s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (* (pow (/ 1 (cbrt (* (cbrt l) (cbrt l)))) (/ 1.0 2.0)) (pow (/ d (cbrt (cbrt l))) (/ 1.0 2.0))))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
1.8s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
90474×add-exp-log
67979×prod-exp
40074×pow-exp
26867×div-exp
15623×pow-to-exp
9960×times-frac
7533×add-sqr-sqrt
6793×*-un-lft-identity
5718×add-cube-cbrt
5157×sqrt-prod
4635×rec-exp 1-exp
2582×add-cbrt-cube
2174×unpow-prod-down
1500×associate-*l*
1332×associate-*r*
1138×pow1
1031×cbrt-unprod
704×associate-/r*
697×cbrt-prod
602×unswap-sqr
578×sqr-pow
564×add-log-exp
504×associate-*r/
470×pow-unpow
454×cbrt-undiv
355×associate-/l* distribute-lft-out
342×div-inv
341×pow-prod-down
287×associate-*l/
285×sqrt-div
258×distribute-lft-out--
239×frac-times
213×associate-/r/
201×div-sub
195×flip-+ flip3-+
171×difference-of-squares
169×exp-prod
164×flip3-- flip--
163×exp-diff
158×*-commutative
151×cube-prod
145×distribute-rgt-neg-in
110×tan-quot
105×distribute-rgt-in distribute-lft-in
100×pow-pow
98×unpow2
97×distribute-lft-neg-in
92×sqrt-pow1
87×clear-num frac-2neg
82×frac-sub
77×sub-neg
70×pow1/2
61×neg-sub0
59×rem-sqrt-square
55×associate-+r- unsub-neg
49×associate-/l/
48×pow1/3
40×sum-log
38×log-prod
36×cbrt-div
35×log-pow
28×+-commutative
27×pow-sub
23×associate--l+
21×swap-sqr
19×diff-log associate-+r+ sub-div
15×frac-add
14×associate--r+
13×neg-mul-1
10×cos-sum pow-flip
9×pow-prod-up unpow3 cube-mult
8×log-div
7×distribute-neg-frac
6×rem-cube-cbrt inv-pow pow-sqr
5×cos-diff
4×pow-neg un-div-inv rem-exp-log exp-sum rem-log-exp
3×pow2 sum-cubes distribute-frac-neg acos-asin
2×cube-div pow-plus associate--l- asin-acos
1×difference-cubes associate-+l+ sqrt-unprod neg-log distribute-rgt-out-- rem-square-sqrt mul0 rem-cbrt-cube exp-to-pow

regimes16.0s (1.7%)

Accuracy

Total 40.4b remaining (18.9%)

Threshold costs 5.1b (2.4%)

8.0b14.9%Toniolo and Linder, Equation (13)
6.4b73.4%Toniolo and Linder, Equation (7)
5.4b0%Henrywood and Agarwal, Equation (12)
4.3b31.8%Toniolo and Linder, Equation (10-)
3.7b51.3%Toniolo and Linder, Equation (10+)

bsearch4.3s (0.5%)

localize3.9s (0.4%)

end0.0ms (0.0%)