Date:Thursday, March 5th, 2020
Commit:a3b4d238 on findroot
Hostname:warfa with Racket 7.5
Seed:2020065
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

series1.6m (34.1%)

Calls

434 calls:

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 (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* (* 2.0 n) (* (* U (* (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (cbrt (- (- 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*))))

sample1.4m (29.8%)

Algorithm
61×intervals
Results
15.8s30918×body1280valid
15.5s248549×body80valid
10.8s167870×body80nan
8.8s8863×body2560valid
7.2s21374×body640valid
5.3s3314×body5120valid
2.4s10068×body320valid
1.4s9143×body160valid
858.0ms2611×body1280nan
586.0ms2395×body640nan
351.0ms671×body10240exit
207.0ms1153×body320nan
106.0ms8256×pre80true
68.0ms634×body160nan

prune1.1m (24.1%)

simplify13.3s (4.7%)

Algorithm
174×egg-herbie

regimes9.4s (3.4%)

Accuracy

Total 43.8b remaining (21.5%)

Threshold costs 4.2b (2.1%)

9.7b28.2%Toniolo and Linder, Equation (13)
6.4b15.6%Toniolo and Linder, Equation (10+)
5.2b0%Henrywood and Agarwal, Equation (12)
5.0b78.4%Toniolo and Linder, Equation (7)
4.3b37.9%Toniolo and Linder, Equation (10-)

rewrite6.8s (2.4%)

Algorithm
114×rewrite-expression-head
Calls

434 calls:

158.0ms
(* (/ (/ 1 (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
151.0ms
(/ (/ (/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (sqrt (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))) (sqrt (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
94.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
93.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
72.0ms
(sqrt (* (* 2.0 n) (* (* U (* (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))
Rules
28378×add-exp-log
20057×prod-exp
19203×times-frac
15555×sqrt-prod
12519×*-un-lft-identity
10870×add-sqr-sqrt
9733×add-cube-cbrt
9460×pow-exp
7791×div-exp
4673×pow-to-exp
2656×add-cbrt-cube
2447×associate-*l*
1747×associate-*r/
1203×distribute-lft-out
1166×cbrt-unprod
1164×pow1
1094×1-exp rec-exp
952×cbrt-div
905×associate-*r*
873×sqrt-div
870×flip-- flip3--
826×associate-/l*
820×unpow-prod-down
724×frac-times
641×frac-sub
548×add-log-exp
480×cbrt-undiv div-inv
427×associate-/r/
415×associate-/r*
407×cbrt-prod
383×pow-prod-down
352×associate-*l/
347×unswap-sqr
325×flip-+ flip3-+
295×pow-unpow
249×distribute-lft-out--
247×sqr-pow
155×difference-of-squares
146×*-commutative
143×distribute-rgt-neg-in
125×distribute-lft-neg-in
101×frac-2neg clear-num
93×sqrt-pow1
92×distribute-rgt-in distribute-lft-in
78×tan-quot
68×rem-sqrt-square
65×pow1/2 unpow2
62×sub-neg
60×pow1/3
50×pow-pow
45×div-sub
40×associate-/l/ sum-log
36×pow-sub cube-prod
34×swap-sqr
29×+-commutative
26×exp-prod associate--l+
25×frac-add
20×diff-log
17×neg-mul-1
15×associate-+r+
14×log-pow
12×neg-sub0
11×pow-flip pow-prod-up distribute-neg-frac
inv-pow pow-sqr log-prod
neg-log
cos-sum unpow3 rem-exp-log cube-mult
pow-plus pow-neg un-div-inv pow2 distribute-frac-neg associate--r+
cos-diff distribute-rgt-out-- acos-asin exp-sum associate-+l-
rem-cube-cbrt asin-acos associate--r- rem-cbrt-cube
exp-diff sqrt-undiv associate-+l+ quot-tan associate--l- sqrt-unprod associate-+r- sub-div unsub-neg rem-square-sqrt mul0 rem-log-exp

localize2.2s (0.8%)

bsearch2.1s (0.8%)

end1.0ms (0.0%)