Date:Sunday, March 15th, 2020
Commit:1a959946 on master
Hostname:warfa with Racket 7.5
Seed:2020075
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

series2.0m (40.9%)

Calls

436 calls:

5.7s
(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*)))))
5.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.4s
(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*))))))
1.5s
(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

sample1.4m (28.4%)

Algorithm
61×intervals
Results
16.0s250029×body80valid
15.6s30740×body1280valid
11.0s168017×body80nan
9.0s8908×body2560valid
7.1s20910×body640valid
5.3s3269×body5120valid
2.5s10686×body320valid
1.4s9084×body160valid
889.0ms2672×body1280nan
575.0ms2320×body640nan
356.0ms683×body10240exit
229.0ms1282×body320nan
108.0ms8256×pre80true
68.0ms620×body160nan

prune57.0s (19.1%)

Filtered
24042 candidates to 10184 candidates (42.4%)

simplify12.9s (4.3%)

Algorithm
174×egg-herbie

regimes10.6s (3.6%)

Accuracy

Total 33.9b remaining (18.2%)

Threshold costs 3.7b (2%)

7.3b17.9%Toniolo and Linder, Equation (13)
5.9b75.4%Toniolo and Linder, Equation (7)
5.1b0%Henrywood and Agarwal, Equation (12)
4.3b28.3%Toniolo and Linder, Equation (10-)
2.6b8.3%Toniolo and Linder, Equation (10+)

rewrite6.5s (2.2%)

Algorithm
114×rewrite-expression-head
Calls

436 calls:

103.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
87.0ms
(/ (- (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)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
86.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
62.0ms
(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
54.0ms
(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)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
Rules
47134×add-exp-log
34342×prod-exp
24723×pow-exp
17623×div-exp
11689×pow-to-exp
4245×add-sqr-sqrt
3976×1-exp
3970×rec-exp
3337×*-un-lft-identity
3134×times-frac
2846×add-cube-cbrt
2431×add-cbrt-cube
1504×sqrt-prod
1232×unpow-prod-down
1075×pow1
959×cbrt-unprod
790×associate-*r*
746×associate-*l*
709×cbrt-prod
510×add-log-exp
498×cbrt-undiv
476×prod-diff
436×log1p-expm1-u expm1-log1p-u
425×sqr-pow
418×difference-of-squares
409×associate-/l*
344×associate-*r/
316×associate-/r*
296×pow-prod-down
280×cube-prod
277×div-inv
275×unswap-sqr
260×sqrt-div
254×pow-unpow
176×distribute-rgt-in distribute-lft-in
172×distribute-lft-out--
167×flip3-- flip--
136×sqrt-pow1
131×*-commutative frac-times
120×associate-/r/
106×distribute-lft-out
104×flip-+ flip3-+
103×fma-def
102×pow1/3
101×distribute-rgt-neg-in
95×associate-*l/
90×clear-num frac-2neg
89×distribute-lft-neg-in
88×pow1/2
80×swap-sqr
71×exp-prod
69×rem-sqrt-square
58×sub-neg
44×associate--l+
39×fma-neg
38×unpow2
35×hypot-def
33×frac-sub associate-+r+
32×pow-pow
30×associate-/l/
29×pow-flip
27×div-sub
26×fma-udef pow-prod-up cbrt-div
25×sum-log
24×tan-quot
23×cos-sum
20×pow-sqr
19×pow-sub
18×+-commutative
14×diff-log
13×frac-add log-prod
12×inv-pow
11×neg-mul-1
exp-sum
difference-cubes pow-plus pow2
log-pow neg-sub0
associate-+r-
exp-diff unpow3 asin-acos cube-mult log-div
associate-+l+ pow-neg hypot-udef expm1-udef distribute-rgt-out-- distribute-neg-frac
rem-exp-log sqrt-unprod expm1-log1p rem-square-sqrt distribute-frac-neg acos-asin rem-cbrt-cube rem-log-exp
rem-cube-cbrt sqrt-undiv un-div-inv exp-neg neg-log cos-diff associate-+l- unsub-neg sub-div mul0

localize2.6s (0.9%)

bsearch1.8s (0.6%)

end1.0ms (0.0%)