Details

series1.7m (33.4%)

Calls

439 calls:

4.7s
(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*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.4s
(* (* (* 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*))))

sample1.4m (28.2%)

Algorithm
61×intervals
Results
15.6s29350×body1280valid
15.5s253224×body80valid
9.5s158091×body80nan
8.8s8786×body2560valid
7.5s20641×body640valid
5.3s3346×body5120valid
2.4s9945×body320valid
1.3s9119×body160valid
418.0ms677×body10240exit
147.0ms617×body1280nan
115.0ms615×body640nan
104.0ms8256×pre80true
46.0ms340×body320nan
18.0ms195×body160nan

prune52.0s (17.2%)

rewrite37.0s (12.2%)

Algorithm
115×rewrite-expression-head
Calls

439 calls:

2.8s
(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.7s
(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar))
916.0ms
(* (* (* (* (/ (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))
840.0ms
(/ (sqrt NdChar) (/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar)))
Rules
53651×add-exp-log
39642×prod-exp
27304×pow-exp
18793×div-exp
12563×pow-to-exp
4213×add-sqr-sqrt
4107×1-exp
4061×rec-exp
3832×*-un-lft-identity
3809×times-frac
3052×add-cube-cbrt
2482×add-cbrt-cube
1927×sqrt-prod
1271×pow1
1057×cbrt-unprod associate-*r*
1032×associate-*r/
960×unpow-prod-down
752×associate-*l*
735×cbrt-prod
663×sqrt-div
549×add-log-exp
548×frac-times
485×cbrt-div
443×associate-*l/
424×cbrt-undiv
415×pow-prod-down
390×associate-/l*
389×flip3-- flip--
368×pow-unpow
343×associate-/r*
327×unswap-sqr
297×flip-+ flip3-+ associate-/r/
289×sqr-pow
259×distribute-lft-out
250×difference-of-squares
244×div-inv
180×distribute-lft-out--
148×*-commutative
139×distribute-rgt-neg-in
123×sqrt-pow1
118×pow1/3
115×unpow2
108×distribute-lft-neg-in
95×frac-2neg clear-num
84×swap-sqr
75×tan-quot
71×pow1/2
66×distribute-rgt-in distribute-lft-in
61×frac-sub
60×pow-pow
58×sub-neg
55×rem-sqrt-square
51×sum-log
40×pow-prod-up
36×cube-div
35×associate-/l/
31×frac-add
29×+-commutative
28×pow-sqr
24×div-sub
22×associate--l+
20×pow-sub neg-sub0
19×pow-neg
16×exp-diff pow-plus log-div
14×cube-prod
12×neg-mul-1 pow2
10×associate-+r+
diff-log un-div-inv
exp-prod distribute-neg-frac
neg-log
rem-cube-cbrt inv-pow sub-div pow-flip unpow3 cube-mult exp-sum log-prod
distribute-rgt-out-- log-pow associate--r+
associate-+l+ associate-+r- unsub-neg associate-+l-
cos-sum sqrt-unprod rem-square-sqrt distribute-frac-neg acos-asin
sqrt-pow2 rem-exp-log unpow1/3 pow3 cos-diff mul0 rem-cbrt-cube

simplify12.9s (4.3%)

Algorithm
175×egg-herbie

regimes10.0s (3.3%)

Accuracy

Total 47.8b remaining (21.7%)

Threshold costs 4.3b (2%)

7.9b23.3%Toniolo and Linder, Equation (13)
5.9b8.7%Toniolo and Linder, Equation (10+)
5.7b0%Henrywood and Agarwal, Equation (12)
5.4b0%Maksimov and Kolovsky, Equation (3)
5.0b78.6%Toniolo and Linder, Equation (7)

localize2.3s (0.8%)

bsearch2.1s (0.7%)

end0.0ms (0.0%)