Date:Tuesday, February 25th, 2020
Commit:7c13946c on findroot
Hostname:warfa with Racket 7.5
Seed:2020056
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

series1.7m (36.2%)

Calls

452 calls:

5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (pow l 1.0) (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.3m (27.9%)

Algorithm
61×intervals
Results
15.7s29517×body1280valid
15.4s253719×body80valid
9.8s159891×body80nan
8.9s8828×body2560valid
7.1s20160×body640valid
5.2s3336×body5120valid
2.2s9513×body320valid
1.3s8943×body160valid
453.0ms741×body10240exit
160.0ms676×body1280nan
111.0ms8256×pre80true
110.0ms586×body640nan
49.0ms342×body320nan
18.0ms197×body160nan

prune56.8s (19.8%)

rewrite17.9s (6.2%)

Algorithm
117×rewrite-expression-head
Calls

452 calls:

561.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
553.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
546.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
458.0ms
(/ 1 (/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) NdChar))
448.0ms
(* (* (* (/ (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
36699×add-exp-log
25963×prod-exp
13607×pow-exp
10650×div-exp
6977×times-frac
5901×add-sqr-sqrt
5735×pow-to-exp
5413×*-un-lft-identity
4585×add-cube-cbrt
3957×sqrt-prod
2877×add-cbrt-cube
2056×1-exp rec-exp
1653×associate-*l*
1387×unpow-prod-down
1268×pow1
1225×cbrt-unprod
809×associate-*r*
750×associate-*r/
564×cbrt-undiv
559×add-log-exp
544×associate-/l*
458×cbrt-prod
434×sqr-pow
417×pow-prod-down
397×sqrt-div
378×pow-unpow
369×frac-times
368×associate-/r*
333×associate-*l/
321×difference-of-squares
305×unswap-sqr
298×div-inv
274×flip3-- flip--
272×distribute-lft-out
216×distribute-lft-out--
205×flip-+ flip3-+
199×cube-prod
174×associate-/r/
151×*-commutative
116×distribute-rgt-neg-in
97×frac-2neg clear-num
90×frac-sub
87×distribute-rgt-in distribute-lft-in
86×exp-prod
83×sqrt-pow1
82×tan-quot
79×associate-/l/
69×distribute-lft-neg-in
67×sub-neg
63×pow1/2 pow1/3
60×rem-sqrt-square
56×pow-pow
50×frac-add
43×cbrt-div
40×log-pow
37×div-sub
34×sum-log
33×unpow2
31×log-prod
30×associate--l+
28×+-commutative
21×diff-log
18×swap-sqr
15×neg-sub0
14×pow-sub
10×pow-prod-up unpow3 pow-sqr
9×rem-cube-cbrt cube-mult neg-mul-1
8×cos-sum exp-diff difference-cubes neg-log distribute-neg-frac
7×inv-pow pow-flip associate-+r+ asin-acos
6×associate-+l- associate--r+ rem-log-exp
5×pow2 pow-plus
4×pow-neg associate-+r- cos-diff unsub-neg
3×sqrt-undiv associate--r-
2×cube-div rem-exp-log associate--l- distribute-frac-neg log-div
1×un-div-inv quot-tan acos-asin exp-sum mul0 rem-cbrt-cube

simplify13.0s (4.5%)

Algorithm
177×egg-herbie

regimes11.5s (4.0%)

Accuracy

Total 39.9b remaining (19.1%)

Threshold costs 4.7b (2.3%)

6.9b20.6%Toniolo and Linder, Equation (13)
6.3b0%Henrywood and Agarwal, Equation (12)
5.7b76.2%Toniolo and Linder, Equation (7)
5.7b15.7%Toniolo and Linder, Equation (10+)
3.9b44.4%Toniolo and Linder, Equation (10-)

localize2.6s (0.9%)

bsearch1.4s (0.5%)

end1.0ms (0.0%)