Details

simplify6.5m (39.6%)

sample3.4m (20.4%)

Algorithm
61×intervals
Results
47.5s253418×body80valid
37.7s29403×body1280valid
26.7s160338×body80nan
20.2s20091×body640valid
17.4s8792×body2560valid
11.5s3435×body5120valid
7.8s10024×body320valid
3.6s8958×body160valid
1.4s669×body10240exit
786.0ms591×body1280nan
281.0ms610×body640nan
240.0ms8256×pre80true
104.0ms352×body320nan
39.0ms188×body160nan

series3.2m (19.5%)

Calls

447 calls:

16.2s
(/ (- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
7.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))
7.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

prune2.3m (13.7%)

rewrite39.9s (4.0%)

Algorithm
119×rewrite-expression-head
Calls

447 calls:

2.1s
(exp (cbrt (pow (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT) 3)))
1.8s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.7s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.5s
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
1.0s
(exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))
Rules
52734×add-exp-log
37646×prod-exp
33359×times-frac
24362×pow-exp
18022×div-exp
16813×add-sqr-sqrt
16644×*-un-lft-identity
15304×add-cube-cbrt
10824×pow-to-exp
10587×sqrt-prod
6724×unpow-prod-down
3092×rec-exp 1-exp
2500×add-cbrt-cube
2147×sqr-pow
1553×associate-*r*
1196×pow1
1037×cbrt-prod
963×cbrt-unprod
947×associate-*l*
909×prod-diff
723×div-inv
689×distribute-lft-out--
627×pow-unpow
610×associate-/l*
559×cbrt-undiv
545×difference-of-squares
509×add-log-exp
507×cube-prod
448×log1p-expm1-u
447×expm1-log1p-u
375×associate-/r*
339×distribute-rgt-neg-in
338×associate-*r/
324×pow-prod-down
308×distribute-lft-neg-in
291×exp-prod
273×associate-*l/
255×associate-/r/
227×unswap-sqr
195×frac-times
187×sqrt-div
186×flip3-- flip--
160×sin-sum
138×distribute-lft-out
130×distribute-rgt-in distribute-lft-in
129×cos-sum
125×*-commutative
121×tan-quot
111×sqrt-pow1
103×fma-neg
92×frac-2neg clear-num
89×cube-div
88×fma-def
80×pow1/2
74×pow-pow
68×pow1/3
64×rem-sqrt-square
56×sub-neg
53×cbrt-div
49×pow-prod-up
42×associate--l+
39×unpow3 cube-mult
38×swap-sqr neg-mul-1
36×associate-/l/
35×div-sub frac-sub
31×flip-+ flip3-+ pow-sqr unpow2
24×fma-udef
23×rem-cube-cbrt
22×associate--r+
21×pow-plus diff-log
16×pow2
13×hypot-def log-prod
12×pow-sub
11×exp-diff
10×log-pow neg-sub0
9×+-commutative sum-log
6×rem-exp-log acos-asin rem-cbrt-cube
4×pow-neg asin-acos frac-add hypot-udef neg-log exp-sum
3×sqrt-undiv cos-diff unsub-neg distribute-frac-neg rem-log-exp associate-+r-
2×inv-pow associate--l- pow-flip associate--r- associate-+r+ distribute-neg-frac sin-diff
1×expm1-udef sqrt-pow2 un-div-inv sqrt-unprod exp-neg expm1-log1p rem-square-sqrt sub-div mul0 cube-neg exp-to-pow

regimes15.6s (1.6%)

Accuracy

Total 37.7b remaining (20.2%)

Threshold costs 3.8b (2%)

7.9b18.4%Toniolo and Linder, Equation (13)
5.9b75.5%Toniolo and Linder, Equation (7)
5.6b4%Henrywood and Agarwal, Equation (12)
5.0b-41.3%Henrywood and Agarwal, Equation (13)
4.8b48.7%Toniolo and Linder, Equation (10-)

bsearch6.3s (0.6%)

localize5.1s (0.5%)

end0.0ms (0.0%)