Date:Wednesday, March 4th, 2020
Commit:29625745 on findroot
Hostname:warfa with Racket 7.5
Seed:2020064
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 (36.8%)

Calls

443 calls:

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 (- (- 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*)))))
4.5s
(sqrt (* (* (cbrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (cbrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))) (cbrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))))
1.5s
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

sample1.4m (30.2%)

Algorithm
61×intervals
Results
15.9s31069×body1280valid
15.5s247954×body80valid
10.8s166292×body80nan
8.7s8843×body2560valid
7.1s21086×body640valid
5.3s3387×body5120valid
2.4s10341×body320valid
1.4s9234×body160valid
839.0ms2631×body1280nan
764.0ms2293×body640nan
328.0ms636×body10240exit
225.0ms1264×body320nan
108.0ms8256×pre80true
65.0ms613×body160nan

prune57.5s (20.9%)

simplify12.8s (4.7%)

Algorithm
176×egg-herbie

regimes10.5s (3.8%)

Accuracy

Total 49.2b remaining (23.8%)

Threshold costs 4.8b (2.3%)

12.7b8.5%Toniolo and Linder, Equation (13)
6.2b44.2%Henrywood and Agarwal, Equation (3)
6.1b-9.6%Henrywood and Agarwal, Equation (12)
5.9b75.5%Toniolo and Linder, Equation (7)
3.5b56.1%Toniolo and Linder, Equation (10+)

rewrite6.7s (2.4%)

Algorithm
116×rewrite-expression-head
Calls

443 calls:

85.0ms
(* (* (* (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)) h) l)))
79.0ms
(* (* (* (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)) (/ h l))))
61.0ms
(* (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) a)
58.0ms
(* (* (* (/ (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))
55.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
Rules
37866×add-exp-log
26074×prod-exp
14847×pow-exp
11784×div-exp
8331×times-frac
7055×*-un-lft-identity
6841×pow-to-exp
5952×add-sqr-sqrt
5001×add-cube-cbrt
3702×associate-*r/
3071×sqrt-prod
2691×add-cbrt-cube
1815×associate-*l*
1654×unpow-prod-down
1543×cbrt-prod
1246×pow1
1126×cbrt-unprod
1125×1-exp
1121×rec-exp
1115×flip3-- flip--
1085×distribute-lft-out
1053×frac-times
1050×cbrt-div
832×associate-*r*
718×frac-sub
710×sqrt-div
517×add-log-exp
472×cbrt-undiv
435×associate-*l/
412×pow-prod-down
393×associate-/l*
378×associate-/r*
369×sqr-pow
358×div-inv
323×unswap-sqr
296×associate-/r/
280×flip-+ flip3-+
245×distribute-rgt-neg-in
228×pow-unpow
207×swap-sqr
164×frac-add
156×*-commutative
124×distribute-lft-out--
122×pow1/3
120×distribute-rgt-in distribute-lft-in
119×difference-of-squares
93×sqrt-pow1
90×clear-num frac-2neg
87×cube-div
85×sub-neg
70×exp-prod
62×distribute-lft-neg-in
58×tan-quot
52×pow1/2
43×unpow2
42×rem-sqrt-square pow-pow
39×cube-prod
38×associate--l+
29×associate-/l/
25×pow-prod-up
23×sum-log
19×pow-sqr +-commutative
16×associate--r+
14×pow-plus diff-log
12×pow-flip div-sub
11×associate-+r+
10×pow2 log-prod
rem-cube-cbrt inv-pow sub-div neg-mul-1
log-pow
cos-sum difference-cubes un-div-inv pow-sub neg-sub0
unpow3 cube-mult exp-sum
pow-neg rem-exp-log associate-+l+
cos-diff acos-asin
distribute-rgt-out-- distribute-frac-neg asin-acos distribute-neg-frac rem-log-exp associate-+r-
exp-diff sqrt-undiv unpow1/3 pow3 exp-neg unsub-neg mul0 sum-cubes rem-cbrt-cube

localize2.3s (0.8%)

bsearch1.3s (0.5%)

end1.0ms (0.0%)