Date:Wednesday, April 22nd, 2020
Commit:1c116713 on better-rr
Hostname:warfa with Racket 7.5
Seed:2020113
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:better-rrreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

prune16.5m (36.9%)

Filtered
240220 candidates to 126045 candidates (52.5%)

rewrite15.7m (35.0%)

Algorithm
113×rewrite-expression-head
Calls

434 calls:

54.9s
(* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (* (* (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0)) (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))) (* (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))))
17.2s
(* (/ (/ (- 1.0 (* 5.0 (* v v))) (sqrt (- 1.0 (* 3.0 (* v v))))) (* t 1)) (/ (/ (/ 1 PI) (sqrt 2.0)) (- 1.0 (* v v))))
3.4s
(* (* c0 (* (fabs (/ (cbrt A) (cbrt V))) (sqrt (/ (* (cbrt (cbrt A)) (cbrt (cbrt A))) (cbrt (* (cbrt V) (cbrt V))))))) (sqrt (/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l))))
2.2s
(* (* (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0)) (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))) (* (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))))
1.9s
(sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
Rules
4419762×add-sqr-sqrt
2584997×unswap-sqr
1657990×cbrt-prod
1543003×times-frac
1460919×unpow-prod-down
382290×swap-sqr
200507×*-commutative
184090×*-un-lft-identity
148668×sqrt-prod
143896×sqr-pow
132353×associate-*l*
129031×associate-*r*
114547×add-cube-cbrt
74406×frac-times
71812×associate-/l*
63619×add-exp-log
56074×difference-of-squares
50307×associate-*r/
48531×prod-exp
46387×sqrt-div
33729×associate-/r*
32389×pow-exp
22519×div-exp
20923×associate-*l/
18353×distribute-lft-out--
15484×pow-to-exp
13041×associate-/l/
11620×distribute-lft-out
10602×frac-add
10076×flip-- flip3--
8651×flip-+ flip3-+
8230×frac-sub
5347×clear-num
5134×1-exp
5002×rec-exp
4622×associate-/r/
3960×frac-2neg
3559×tan-quot
3410×add-cbrt-cube
3249×div-inv
2911×un-div-inv
2398×distribute-neg-frac
2064×unpow2
1986×cbrt-unprod
1527×pow1
982×pow-unpow
724×distribute-rgt-neg-in
684×difference-cubes
668×distribute-lft-neg-in
604×pow-prod-down
557×add-log-exp
540×cbrt-undiv
258×exp-prod
189×distribute-rgt-in distribute-lft-in
188×neg-mul-1
181×sqrt-pow1
170×rem-sqrt-square
168×log-prod
108×pow1/2
76×exp-sum
72×+-commutative
71×sub-neg
58×associate-+l+
48×pow-pow associate-+r+
47×pow-flip div-sub
43×pow1/3
42×associate--l+
40×cbrt-div
35×sum-log
31×pow-prod-up pow-sub neg-sub0
27×diff-log
22×pow-neg
20×rem-exp-log
19×exp-diff pow-sqr
17×log-pow
12×associate--l-
10×neg-log
distribute-frac-neg distribute-lft-neg-out
cos-sum remove-double-div associate--r+ rem-log-exp
unpow3 sqrt-unprod inv-pow pow-plus distribute-rgt-out pow2
rem-square-sqrt acos-asin sum-cubes associate-+l-
exp-neg cos-diff asin-acos associate--r-
rem-cube-cbrt associate-+r- unsub-neg rem-cbrt-cube log-div
distribute-lft1-in

simplify7.3m (16.4%)

Algorithm
170×egg-herbie

series2.4m (5.3%)

Calls

434 calls:

21.7s
(sqrt (* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
19.2s
(sqrt (* (cbrt (* (cbrt (cbrt n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
18.9s
(sqrt (* (cbrt (* (cbrt 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*)))))
2.1s
(* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

end1.5m (3.4%)

sample1.2m (2.6%)

Algorithm
59×intervals
Results
15.4s29742×body1280valid
13.3s228682×body80valid
7.9s6936×body2560valid
7.2s20481×body640valid
6.0s115953×body80nan
4.1s1008×body5120valid
2.4s10096×body320valid
1.4s9195×body160valid
896.0ms2670×body1280nan
576.0ms2318×body640nan
216.0ms1232×body320nan
138.0ms354×body10240exit
111.0ms8256×pre80true
66.0ms618×body160nan

regimes8.8s (0.3%)

Accuracy

Total 33.2b remaining (27.9%)

Threshold costs 3.5b (2.9%)

6.4b29.3%Toniolo and Linder, Equation (13)
5.7b76%Toniolo and Linder, Equation (7)
5.0b0%Toniolo and Linder, Equation (10+)
3.8b12.9%Toniolo and Linder, Equation (10-)
3.0b0%Henrywood and Agarwal, Equation (3)

localize2.3s (0.1%)

bsearch1.1s (0.0%)