Details

simplify4.0m (32.6%)

sample3.4m (27.4%)

Algorithm
61×intervals
Results
45.6s254380×body80valid
38.7s29480×body1280valid
27.6s160993×body80nan
19.4s19902×body640valid
18.9s8950×body2560valid
12.0s3339×body5120valid
6.9s9701×body320valid
4.0s8766×body160valid
1.2s711×body10240exit
351.0ms596×body1280nan
325.0ms8256×pre80true
291.0ms612×body640nan
152.0ms370×body320nan
78.0ms193×body160nan

series2.4m (19.4%)

Calls

436 calls:

7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.4s
(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*)))))
7.4s
(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*))))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.0s
(* (* (* 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*)))))

prune1.4m (10.9%)

rewrite46.6s (6.3%)

Algorithm
115×rewrite-expression-head
Calls

436 calls:

2.1s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.5s
(cbrt (pow (- (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0) 3))
1.4s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.4s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.3s
(- (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0)
Rules
50605×add-exp-log
35642×prod-exp
22002×pow-exp
16996×div-exp
10437×pow-to-exp
3803×add-sqr-sqrt
3493×*-un-lft-identity
3267×times-frac
2749×add-cube-cbrt
2410×add-cbrt-cube
2035×1-exp rec-exp
1155×pow1
1104×sqrt-prod
1027×unpow-prod-down
966×cbrt-unprod
937×associate-*r*
806×associate-*l*
636×cbrt-prod
570×add-log-exp
455×associate-*r/
409×cbrt-undiv
395×associate-/l*
356×pow-prod-down
340×pow-unpow
337×unswap-sqr
332×associate-*l/
309×sqrt-div
302×associate-/r*
292×sqr-pow
251×distribute-lft-out--
248×div-inv
242×frac-times
202×difference-of-squares
201×flip3-- flip--
191×distribute-lft-out
181×associate-/r/
176×flip-+ flip3-+
154×*-commutative distribute-rgt-neg-in
136×distribute-lft-neg-in
122×sqrt-pow1
94×tan-quot
89×frac-2neg clear-num
87×cbrt-div
85×cube-prod
84×div-sub
83×pow1/2 distribute-rgt-in distribute-lft-in
82×unpow2
71×sub-neg
64×rem-sqrt-square
48×associate-/l/ sum-log
46×pow-sub
43×pow-pow
41×pow1/3
34×swap-sqr
33×frac-sub
32×frac-add +-commutative
24×diff-log
21×log-div
19×exp-diff neg-sub0
18×pow-prod-up associate--l+
16×exp-prod log-prod neg-mul-1
15×unpow3 cube-mult
14×cube-div
12×pow-sqr log-pow
11×rem-cube-cbrt
10×pow-neg associate-+l+ distribute-neg-frac
associate-+r+ neg-log associate--r+
asin-acos exp-sum rem-cbrt-cube
cos-sum un-div-inv
pow-plus associate-+l-
cos-diff distribute-rgt-out-- distribute-frac-neg associate--r- pow2
rem-exp-log associate--l- sqrt-unprod inv-pow pow-flip rem-square-sqrt rem-log-exp
associate-+r- sub-div unsub-neg acos-asin mul0

regimes17.0s (2.3%)

Accuracy

Total 38.5b remaining (18.4%)

Threshold costs 4.7b (2.2%)

7.3b18.3%Toniolo and Linder, Equation (13)
6.7b72.4%Toniolo and Linder, Equation (7)
6.4b0%Henrywood and Agarwal, Equation (12)
6.2b13.6%Toniolo and Linder, Equation (10-)
3.6b53.3%Toniolo and Linder, Equation (10+)

localize4.4s (0.6%)

bsearch3.7s (0.5%)

end0.0ms (0.0%)