Details

prune3.0m (43.2%)

sample1.9m (28.2%)

Algorithm
61×intervals
Results
27.1s253526×body80valid
22.4s29908×body1280valid
17.4s160881×body80nan
11.0s8697×body2560valid
10.8s20043×body640valid
6.8s3353×body5120valid
3.7s10008×body320valid
2.0s8979×body160valid
1.1s868×body10240exit
294.0ms625×body1280nan
228.0ms8256×pre80true
223.0ms603×body640nan
104.0ms370×body320nan
35.0ms192×body160nan

rewrite39.6s (9.6%)

Algorithm
117×rewrite-expression-head
Calls

437 calls:

25.5s
(* (/ NdChar (+ (pow 1.0 3) (pow (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 3))) (+ (* 1.0 1.0) (- (* (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (* 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
2.0s
(- (* (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (* 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
473.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
472.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
327.0ms
(exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))
Rules
25050×add-exp-log
16559×prod-exp
7796×pow-exp
7477×times-frac
6811×div-exp
6203×add-sqr-sqrt
6037×*-un-lft-identity
4848×add-cube-cbrt
4170×sqrt-prod
2800×pow-to-exp
2712×add-cbrt-cube
1306×pow1
1260×associate-*r*
1098×cbrt-unprod
937×pow-unpow
808×rec-exp 1-exp
799×associate-*l*
628×unpow-prod-down
588×cbrt-undiv
549×exp-prod
509×add-log-exp
447×cbrt-prod
443×associate-/l*
437×log1p-expm1-u expm1-log1p-u
384×distribute-lft-out associate-/r*
372×associate-*r/
363×pow-prod-down
345×div-inv
343×distribute-rgt-neg-in
338×prod-diff
330×unswap-sqr
304×distribute-lft-neg-in
293×log-pow
289×distribute-lft-out--
284×sqrt-div
215×difference-of-squares
207×flip-- flip3--
192×distribute-rgt-in distribute-lft-in
190×sqr-pow
170×frac-times
143×associate-/r/
141×*-commutative
132×associate-*l/
100×flip-+ clear-num flip3-+ frac-2neg
90×pow-pow
88×cube-div
85×exp-diff
83×pow1/3
77×div-sub
68×sqrt-pow1
67×cbrt-div
65×distribute-frac-neg
63×fma-def sub-neg
62×exp-neg
59×frac-sub
56×pow-prod-up neg-sub0
50×neg-mul-1
45×associate--l+
44×associate-/l/
41×pow1/2
39×swap-sqr
37×rem-sqrt-square
36×pow-sqr
34×log-div
33×log-prod
30×pow-plus
29×tan-quot
26×sum-log
25×fma-udef cos-sum
24×fma-neg
23×un-div-inv
21×pow2 cube-prod exp-sum
19×pow-sub +-commutative
17×unpow2
15×sub-div
14×hypot-def
11×rem-cube-cbrt
10×pow-neg frac-add
9×diff-log
8×rem-exp-log
7×unpow3 cube-mult
6×inv-pow pow-flip
5×associate-+l+ unsub-neg
4×sqrt-undiv associate-+r- associate-+r+ acos-asin asin-acos
3×log1p-udef log1p-expm1 unpow-prod-up hypot-udef sum-cubes rem-log-exp
2×distribute-rgt-neg-out distribute-neg-frac
1×e-exp-1 pow3 cos-diff mul0 distribute-rgt-out-- rem-cbrt-cube

regimes31.5s (7.7%)

Accuracy

Total 38.0b remaining (19%)

Threshold costs 4.3b (2.2%)

8.0b14.5%Toniolo and Linder, Equation (13)
5.6b76.7%Toniolo and Linder, Equation (7)
4.5b13%Henrywood and Agarwal, Equation (12)
4.4b-3.3%Toniolo and Linder, Equation (10-)
4.3b66.2%Henrywood and Agarwal, Equation (3)

series31.1s (7.6%)

Calls

437 calls:

2.4s
(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*))))))
2.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.2s
(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*)))))
374.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

simplify11.4s (2.8%)

Algorithm
177×egg-herbie

localize2.2s (0.5%)

bsearch1.5s (0.4%)

end0.0ms (0.0%)