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: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

prune1.8m (32.2%)

series1.7m (31.0%)

Calls

430 calls:

5.1s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.9s
(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 (* (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*)))))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

sample1.4m (25.2%)

Algorithm
61×intervals
Results
15.8s30918×body1280valid
15.6s248549×body80valid
11.0s167870×body80nan
8.9s8863×body2560valid
7.3s21374×body640valid
5.4s3314×body5120valid
2.6s10068×body320valid
1.4s9143×body160valid
867.0ms2611×body1280nan
607.0ms2395×body640nan
371.0ms671×body10240exit
203.0ms1153×body320nan
110.0ms8256×pre80true
74.0ms634×body160nan

simplify16.7s (5.0%)

Algorithm
174×egg-herbie

regimes9.0s (2.7%)

Accuracy

Total 41.2b remaining (24%)

Threshold costs 4.1b (2.4%)

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-)

rewrite8.7s (2.6%)

Algorithm
114×rewrite-expression-head
Calls

430 calls:

401.0ms
(/ (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (sqrt (sqrt 2.0)) (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt (sqrt 2.0))))))
83.0ms
(* (* (* (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))))
76.0ms
(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*)))))))
65.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
45.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
61186×times-frac
56729×sqrt-prod
29809×add-exp-log
28387×add-sqr-sqrt
28203×*-un-lft-identity
27518×add-cube-cbrt
21045×prod-exp
9729×pow-exp
8142×div-exp
4694×pow-to-exp
2684×add-cbrt-cube
1681×associate-*r/
1205×cbrt-unprod
1167×div-inv
1158×1-exp rec-exp
1126×pow1
1009×prod-diff
923×cbrt-div
861×flip-- flip3--
846×associate-*r*
767×unpow-prod-down
757×associate-*l*
738×associate-/r*
702×frac-times
630×frac-sub
581×cbrt-prod
506×sqrt-div
483×add-log-exp
481×cbrt-undiv
449×associate-/l*
430×log1p-expm1-u expm1-log1p-u
369×pow-prod-down
304×associate-*l/
268×pow-unpow
261×unswap-sqr
232×distribute-lft-out--
230×sqr-pow
173×associate-/r/
170×distribute-rgt-in distribute-lft-in
168×distribute-lft-out
140×log-prod
138×distribute-rgt-neg-in
137×difference-of-squares
134×*-commutative
126×distribute-lft-neg-in
101×clear-num frac-2neg
100×flip-+ flip3-+
89×pow1/3
75×exp-sum sqrt-pow1
71×tan-quot
57×exp-prod
56×swap-sqr
54×sub-neg
52×pow1/2 associate--l+
48×rem-sqrt-square fma-def
47×log-pow cos-sum
44×div-sub
43×fma-neg
42×pow-pow
36×pow-sub
26×fma-udef
25×associate-/l/ unpow2
18×sum-log neg-mul-1
15×pow-prod-up rem-log-exp
13×associate-+r+ pow-sqr
12×+-commutative hypot-def
10×pow-flip
neg-sub0 diff-log distribute-neg-frac
inv-pow
un-div-inv
rem-exp-log pow-plus pow2
frac-add hypot-udef
pow-neg distribute-frac-neg
distribute-rgt-out-- associate-+r- acos-asin
sqrt-undiv asin-acos cos-diff
exp-diff sqrt-pow2 associate-+l+ quot-tan sqrt-unprod sin-sum unsub-neg rem-square-sqrt sub-div neg-log mul0 associate-+l-

localize2.3s (0.7%)

bsearch2.2s (0.7%)

end1.0ms (0.0%)