Details

series1.7m (33.3%)

Calls

437 calls:

5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))))
5.0s
(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)) (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.5s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.4m (28.9%)

Algorithm
61×intervals
Results
15.9s29584×body1280valid
15.8s254654×body80valid
9.8s161103×body80nan
9.0s8804×body2560valid
7.4s20531×body640valid
5.5s3356×body5120valid
2.4s9809×body320valid
1.2s8729×body160valid
455.0ms838×body10240exit
144.0ms597×body1280nan
109.0ms595×body640nan
105.0ms8256×pre80true
47.0ms349×body320nan
16.0ms172×body160nan

prune50.9s (17.0%)

rewrite34.1s (11.4%)

Algorithm
116×rewrite-expression-head
Calls

437 calls:

2.0s
(* (* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(/ (/ 1 (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ 1 NdChar))
1.0s
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
948.0ms
(* (* (* (* (/ (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))
874.0ms
(/ 1 (/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) NdChar))
Rules
31116×add-exp-log
21611×prod-exp
10474×pow-exp
8752×div-exp
4962×pow-to-exp
4640×times-frac
4365×add-sqr-sqrt
4280×*-un-lft-identity
3230×add-cube-cbrt
2549×add-cbrt-cube
1282×pow1
1276×associate-*r/
1189×sqrt-prod
1126×cbrt-unprod
1034×associate-*r*
864×pow-unpow rec-exp 1-exp
737×associate-*l*
648×frac-times
623×cbrt-prod
539×unpow-prod-down
530×add-log-exp
460×pow-prod-down
458×cbrt-undiv
447×distribute-lft-out
444×associate-*l/
407×flip3-- flip--
350×flip-+ flip3-+
336×frac-add
315×sqrt-div
299×unswap-sqr
289×associate-/l*
280×div-inv
256×associate-/r*
183×difference-of-squares
179×sqr-pow
164×associate-/r/
146×*-commutative
131×distribute-lft-out--
128×swap-sqr
105×exp-prod
94×pow1/3
81×cbrt-div
80×clear-num frac-2neg sqrt-pow1
78×distribute-rgt-neg-in
71×tan-quot
68×distribute-rgt-in distribute-lft-in
60×pow1/2
56×rem-sqrt-square sub-neg
49×pow-pow
45×div-sub
38×frac-sub
36×sum-log
33×unpow2
30×associate-/l/
29×+-commutative
26×associate--l+
13×distribute-lft-neg-in pow-sub neg-sub0
11×pow-prod-up pow-sqr
10×log-pow pow-flip
9×diff-log exp-diff associate-+r+ cube-prod
8×inv-pow
7×log-prod
6×pow-plus unsub-neg pow2 associate-+r-
5×cube-div un-div-inv rem-exp-log
4×neg-log associate-+l+ distribute-neg-frac sqrt-undiv associate-+l- pow-neg
3×rem-cube-cbrt unpow3 cube-mult acos-asin
2×asin-acos exp-sum cos-sum rem-log-exp
1×difference-cubes sqrt-unprod cos-diff rem-square-sqrt neg-mul-1 mul0

simplify11.9s (4.0%)

regimes10.3s (3.5%)

Accuracy

Total 40.2b remaining (19.2%)

Threshold costs 5.6b (2.7%)

7.8b14.6%Toniolo and Linder, Equation (13)
6.8b12.7%Toniolo and Linder, Equation (10+)
5.2b-19.9%Henrywood and Agarwal, Equation (12)
5.2b78.3%Toniolo and Linder, Equation (7)
3.3b51%Toniolo and Linder, Equation (10-)

bsearch3.4s (1.1%)

localize2.5s (0.8%)

end1.0ms (0.0%)