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:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
+o rules:numerics

Details

series1.9m (38.1%)

Calls

447 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*)))))
4.9s
(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) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (pow (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)) 1))))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.3m (27.2%)

Algorithm
61×intervals
Results
15.8s29517×body1280valid
15.5s253719×body80valid
9.7s159891×body80nan
9.0s8828×body2560valid
7.1s20160×body640valid
5.3s3336×body5120valid
2.3s9513×body320valid
1.3s8943×body160valid
463.0ms741×body10240exit
158.0ms676×body1280nan
110.0ms586×body640nan
103.0ms8256×pre80true
49.0ms342×body320nan
19.0ms197×body160nan

prune1.0m (21.1%)

simplify13.1s (4.4%)

Algorithm
178×egg-herbie

rewrite12.6s (4.2%)

Algorithm
118×rewrite-expression-head
Calls

447 calls:

458.0ms
(/ 1 (/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) NdChar))
449.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
314.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
303.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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)) (/ h l))))
276.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
Rules
33019×add-exp-log
23797×prod-exp
12940×pow-exp
9330×div-exp
7427×times-frac
6363×add-sqr-sqrt
5491×*-un-lft-identity
5352×pow-to-exp
4731×add-cube-cbrt
3331×sqrt-prod
2719×add-cbrt-cube
2062×1-exp rec-exp
1374×unpow-prod-down
1194×pow1
1124×associate-*r*
1073×cbrt-unprod
919×prod-diff
884×associate-*l*
611×cbrt-prod
590×cbrt-undiv
564×associate-/r*
507×add-log-exp
477×sqr-pow
459×difference-of-squares
448×log1p-expm1-u
447×expm1-log1p-u
441×associate-*r/
421×pow-unpow
416×div-inv
365×associate-/l*
347×pow-prod-down
331×sqrt-div
330×unswap-sqr
302×flip3-- flip--
286×associate-/r/
225×distribute-lft-out--
220×distribute-lft-out
196×frac-times
191×distribute-rgt-in distribute-lft-in
150×distribute-rgt-neg-in
147×*-commutative
111×associate-*l/
108×distribute-lft-neg-in
97×frac-2neg clear-num
93×fma-def
91×unpow2
73×fma-neg
70×flip-+ exp-prod flip3-+
60×pow1/3
57×sqrt-pow1
54×sub-neg
51×pow-pow
42×associate--l+
41×pow-prod-up
39×pow1/2 rem-sqrt-square
36×associate-/l/
35×div-sub
31×fma-udef
30×log-prod
27×pow-sqr
26×frac-sub
25×cos-sum
23×swap-sqr
22×cube-prod associate-+r+ tan-quot
21×sum-log
20×pow-plus
19×+-commutative
17×pow2
16×cbrt-div frac-add
15×pow-sub
13×log-pow
12×pow-flip hypot-def neg-mul-1
10×neg-sub0
diff-log
inv-pow
exp-diff associate-+r-
expm1-log1p expm1-udef
unpow3 pow-neg unsub-neg cube-mult asin-acos distribute-neg-frac rem-log-exp
rem-exp-log rem-cube-cbrt unpow-prod-up hypot-udef acos-asin exp-sum
un-div-inv log1p-udef sin-sum log1p-expm1 distribute-frac-neg
sqrt-undiv associate-+l+ e-exp-1 cos-diff mul0 rem-cbrt-cube

regimes10.7s (3.6%)

Accuracy

Total 36.5b remaining (19.2%)

Threshold costs 4.2b (2.2%)

8.9b3.1%Toniolo and Linder, Equation (13)
6.3b0%Henrywood and Agarwal, Equation (12)
5.6b76.6%Toniolo and Linder, Equation (7)
3.9b44.3%Toniolo and Linder, Equation (10-)
2.7b0%Toniolo and Linder, Equation (10+)

localize2.7s (0.9%)

bsearch1.2s (0.4%)

end0.0ms (0.0%)