Date:Thursday, March 5th, 2020
Commit:7606e899 on refactor-and-minor
Hostname:warfa with Racket 7.5
Seed:2020065
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

prune1.9m (32.9%)

Filtered
38705 candidates to 18033 candidates (46.6%)

series1.8m (30.9%)

Calls

438 calls:

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*)))))
4.6s
(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*)))))))
4.5s
(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*))))

sample1.4m (24.2%)

Algorithm
61×intervals
Results
16.2s30918×body1280valid
15.9s248549×body80valid
11.0s167870×body80nan
9.0s8863×body2560valid
7.4s21374×body640valid
5.4s3314×body5120valid
2.4s10068×body320valid
1.4s9143×body160valid
876.0ms2611×body1280nan
595.0ms2395×body640nan
346.0ms671×body10240exit
204.0ms1153×body320nan
113.0ms8256×pre80true
70.0ms634×body160nan

simplify18.3s (5.2%)

Algorithm
175×egg-herbie

rewrite9.8s (2.8%)

Algorithm
115×rewrite-expression-head
Calls

438 calls:

358.0ms
(/ (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (sqrt (sqrt 2.0)) (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt (sqrt 2.0))))))
152.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
149.0ms
(/ (/ (/ 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))))))
82.0ms
(* (* (* (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))))
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
68360×times-frac
64808×sqrt-prod
32862×*-un-lft-identity
30974×add-sqr-sqrt
30202×add-cube-cbrt
29705×add-exp-log
20921×prod-exp
9737×pow-exp
8163×div-exp
4700×pow-to-exp
2649×add-cbrt-cube
1656×associate-*r/
1183×div-inv
1154×cbrt-unprod distribute-lft-out
1151×1-exp rec-exp
1119×pow1
920×cbrt-div
857×flip-- flip3--
810×associate-*r*
788×associate-/r* sqrt-div
759×associate-/l*
750×unpow-prod-down
730×associate-*l*
699×frac-times
628×frac-sub
525×cbrt-prod
502×add-log-exp
495×cbrt-undiv
449×associate-/r/
439×expm1-log1p-u
438×log1p-expm1-u
357×pow-prod-down
340×prod-diff
303×associate-*l/
294×pow-unpow
251×unswap-sqr
241×flip-+ flip3-+
239×distribute-lft-out--
223×sqr-pow
166×distribute-rgt-in distribute-lft-in
149×distribute-rgt-neg-in
135×distribute-lft-neg-in
130×*-commutative
112×difference-of-squares
107×clear-num frac-2neg
90×pow1/3
77×tan-quot
76×sqrt-pow1
66×fma-def
54×exp-prod
53×pow-pow
52×rem-sqrt-square associate--l+
51×pow1/2
50×sub-neg
49×swap-sqr
47×cos-sum
45×div-sub
43×log-pow
36×pow-sub
31×associate-/l/
27×neg-mul-1
26×sum-log
25×fma-udef unpow2
23×log-prod
18×distribute-neg-frac
17×fma-neg
16×+-commutative
15×pow-prod-up
13×associate-+r+ pow-sqr
12×hypot-def
11×neg-sub0
pow-flip
inv-pow frac-add diff-log
pow-plus un-div-inv pow2 rem-log-exp
hypot-udef
rem-exp-log pow-neg distribute-frac-neg
asin-acos associate-+r- acos-asin neg-log exp-sum associate-+l-
associate-+l+ cos-diff
exp-diff sqrt-undiv sqrt-pow2 log1p-udef quot-tan sqrt-unprod sin-sum log1p-expm1 expm1-log1p unsub-neg rem-square-sqrt mul0 expm1-udef

regimes9.4s (2.7%)

Accuracy

Total 40.5b remaining (23.1%)

Threshold costs 4.3b (2.5%)

9.7b28.2%Toniolo and Linder, Equation (13)
6.2b16.1%Toniolo and Linder, Equation (10+)
5.9b0%Henrywood and Agarwal, Equation (12)
5.2b77.9%Toniolo and Linder, Equation (7)
4.3b37.9%Toniolo and Linder, Equation (10-)

localize2.3s (0.7%)

bsearch2.2s (0.6%)

end1.0ms (0.0%)