Details

series1.9m (37.0%)

Calls

439 calls:

6.0s
(log (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
5.1s
(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 (/ 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*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

sample1.4m (27.0%)

Algorithm
61×intervals
Results
15.8s254654×body80valid
15.7s29584×body1280valid
9.7s161103×body80nan
8.8s8804×body2560valid
7.2s20531×body640valid
5.4s3356×body5120valid
2.3s9809×body320valid
1.2s8729×body160valid
426.0ms838×body10240exit
140.0ms597×body1280nan
111.0ms8256×pre80true
106.0ms595×body640nan
48.0ms349×body320nan
16.0ms172×body160nan

prune55.1s (17.5%)

rewrite30.3s (9.6%)

Algorithm
117×rewrite-expression-head
Calls

439 calls:

1.8s
(* (* (* (* (* (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))
994.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* (* t (* (cbrt (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))) (cbrt (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))))) (cbrt (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))))) (- 1.0 (* v v))))
951.0ms
(* (* (* (* (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))
875.0ms
(* (* (* (* (/ (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))
Rules
30706×add-exp-log
21349×prod-exp
10440×pow-exp
8663×div-exp
4950×pow-to-exp
4306×times-frac
4186×add-sqr-sqrt
4169×*-un-lft-identity
3268×add-cube-cbrt
2431×add-cbrt-cube
1380×pow1
1023×cbrt-unprod
991×associate-*r/
930×pow-unpow
845×1-exp
843×rec-exp
799×associate-*r*
690×sqrt-prod
683×unpow-prod-down
642×associate-*l*
527×sqrt-div
496×add-log-exp
486×pow-prod-down
439×log1p-expm1-u expm1-log1p-u
414×frac-times
408×cbrt-undiv
383×distribute-lft-out
380×cbrt-prod
347×associate-*l/
339×prod-diff
334×cbrt-div
331×associate-/r*
316×flip3-- flip--
295×div-inv
294×associate-/l*
232×unswap-sqr
225×sqr-pow
200×difference-of-squares
196×associate-/r/
157×flip-+ flip3-+
144×*-commutative
141×distribute-rgt-in distribute-lft-in
132×sqrt-pow1
131×distribute-lft-out--
115×distribute-rgt-neg-in
109×exp-prod
90×clear-num frac-2neg
76×pow1/2
69×pow1/3
68×tan-quot
62×fma-def
60×pow-pow
55×cube-prod
52×distribute-lft-neg-in
48×rem-sqrt-square
47×sub-neg
46×unpow2 swap-sqr
45×div-sub frac-sub
43×associate-/l/ log-prod
38×cube-div
37×fma-udef
36×pow-prod-up
32×associate--l+
28×pow-sqr
27×cos-sum fma-neg
20×exp-sum
19×sum-log
16×exp-neg unpow3 cube-mult +-commutative distribute-rgt-neg-out
14×pow-sub hypot-def
12×log-pow
11×un-div-inv
10×exp-diff neg-sub0
9×pow-plus
8×diff-log inv-pow frac-add pow-flip log-rec mul-1-neg
7×pow2
6×rem-cube-cbrt rem-exp-log associate-+r- unsub-neg
4×sub-div acos-asin neg-mul-1 pow-neg rem-log-exp
3×hypot-udef
2×sqrt-pow2 associate-+l+ associate-+r+ sqrt-unprod expm1-log1p rem-square-sqrt asin-acos distribute-rgt-out-- rem-cbrt-cube expm1-udef log-div
1×sqrt-undiv cos-diff mul0

simplify12.0s (3.8%)

regimes10.2s (3.2%)

Accuracy

Total 38.8b remaining (21%)

Threshold costs 5.6b (3%)

7.8b14.5%Toniolo and Linder, Equation (13)
6.8b12.7%Toniolo and Linder, Equation (10+)
5.2b-19.9%Henrywood and Agarwal, Equation (12)
5.1b78.3%Toniolo and Linder, Equation (7)
3.3b51%Toniolo and Linder, Equation (10-)

bsearch3.6s (1.1%)

localize2.3s (0.7%)

end1.0ms (0.0%)