Details

series1.8m (35.6%)

Calls

437 calls:

5.3s
(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*)))))
5.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.0s
(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*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.4s
(* (* (* 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*))))

sample1.4m (27.3%)

Algorithm
61×intervals
Results
15.4s29350×body1280valid
15.3s253224×body80valid
9.2s158091×body80nan
8.6s8786×body2560valid
7.2s20641×body640valid
5.2s3346×body5120valid
2.3s9945×body320valid
1.3s9119×body160valid
401.0ms677×body10240exit
139.0ms617×body1280nan
113.0ms615×body640nan
101.0ms8256×pre80true
46.0ms340×body320nan
17.0ms195×body160nan

prune50.0s (16.5%)

rewrite36.4s (12.0%)

Algorithm
115×rewrite-expression-head
Calls

437 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))
2.8s
(* (* (* (* (* (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))
945.0ms
(* (* (* (* (/ (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))
860.0ms
(/ (sqrt NdChar) (/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar)))
Rules
37962×add-exp-log
26552×prod-exp
15080×pow-exp
11515×div-exp
6958×pow-to-exp
4072×add-sqr-sqrt
3725×*-un-lft-identity
3646×times-frac
2946×add-cube-cbrt
2481×add-cbrt-cube
1834×sqrt-prod
1385×pow1
1134×1-exp
1094×rec-exp
1074×associate-*r* associate-*r/
1053×cbrt-unprod
943×sqrt-div
918×unpow-prod-down
724×frac-times
714×cbrt-prod
683×associate-*l*
549×add-log-exp
506×associate-*l/
475×flip3-- flip--
451×pow-prod-down
429×cbrt-div
406×cbrt-undiv
384×associate-/l*
355×pow-unpow
327×associate-/r*
325×unswap-sqr
286×sqr-pow
263×distribute-lft-out
246×flip-+ flip3-+ associate-/r/
231×difference-of-squares
228×div-inv
178×distribute-lft-out--
151×*-commutative
141×cube-div
140×distribute-rgt-neg-in
115×unpow2
108×distribute-lft-neg-in
100×pow1/3
99×sqrt-pow1
94×clear-num frac-2neg
75×tan-quot
72×distribute-rgt-in distribute-lft-in
64×pow-prod-up frac-sub
62×pow1/2
60×swap-sqr
58×sub-neg pow-pow
56×rem-sqrt-square
54×sum-log
46×pow-sqr
38×frac-add
33×associate-/l/
31×+-commutative
30×associate--l+
28×pow-plus
23×div-sub
22×pow2
21×neg-sub0
20×pow-sub
19×pow-neg
16×exp-diff log-div
12×neg-mul-1
11×cube-prod
10×un-div-inv associate-+r+
distribute-neg-frac
diff-log neg-log rem-cube-cbrt exp-prod
unpow3 cube-mult exp-sum log-prod
log-pow associate-+l-
associate-+l+ inv-pow unsub-neg pow-flip associate-+r-
distribute-frac-neg acos-asin cos-sum associate--r+
rem-exp-log unpow1/3 sqrt-unprod cos-diff rem-square-sqrt mul0 rem-cbrt-cube

simplify11.9s (3.9%)

Algorithm
175×egg-herbie

regimes10.2s (3.3%)

Accuracy

Total 44.2b remaining (20.5%)

Threshold costs 5.4b (2.5%)

8.0b21.4%Toniolo and Linder, Equation (13)
6.3b3.8%Henrywood and Agarwal, Equation (12)
5.9b8.7%Toniolo and Linder, Equation (10+)
5.0b78.6%Toniolo and Linder, Equation (7)
3.6b0%Toniolo and Linder, Equation (10-)

localize2.2s (0.7%)

bsearch2.0s (0.7%)

end1.0ms (0.0%)