Date:Tuesday, March 3rd, 2020
Commit:ee6b458f on refactor-and-minor
Hostname:warfa with Racket 7.5
Seed:2020063
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

series1.9m (39.0%)

Calls

444 calls:

6.0s
(sqrt (+ (* (* (* 2.0 n) U) (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* (* l (/ l Om)) 2.0)))) (* (* (* 2.0 n) U) (- (fma (- (* l (/ l Om))) 2.0 (* (* l (/ l Om)) 2.0)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.8s
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
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) (* (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*))))))

sample1.4m (28.7%)

Algorithm
61×intervals
Results
15.8s31083×body1280valid
15.4s249121×body80valid
11.0s167560×body80nan
8.7s8748×body2560valid
7.3s21451×body640valid
5.1s3366×body5120valid
2.4s10344×body320valid
1.3s9157×body160valid
895.0ms2769×body1280nan
591.0ms2343×body640nan
348.0ms687×body10240exit
210.0ms1227×body320nan
126.0ms8256×pre80true
69.0ms624×body160nan

prune1.0m (20.9%)

Filtered
20715 candidates to 10882 candidates (52.5%)

simplify11.7s (4.0%)

Algorithm
177×egg-herbie

regimes9.8s (3.4%)

Accuracy

Total 37.2b remaining (20.6%)

Threshold costs 4.9b (2.7%)

7.7b23.1%Toniolo and Linder, Equation (13)
7.6b-2.1%Henrywood and Agarwal, Equation (12)
5.6b76.7%Toniolo and Linder, Equation (7)
3.7b46.6%Toniolo and Linder, Equation (10-)
2.3b0%Henrywood and Agarwal, Equation (13)

rewrite5.7s (2.0%)

Algorithm
117×rewrite-expression-head
Calls

444 calls:

268.0ms
(* (/ (* 2.0 (* (pow (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ 1 (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
60.0ms
(/ (* 2.0 (* (pow (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ 1 (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))) (tan k))
54.0ms
(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*))))))
49.0ms
(* (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (* PI t)) (/ (cbrt (- 1.0 (* 5.0 (* v v)))) (pow (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) 3)))
45.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
Rules
25199×add-exp-log
15999×prod-exp
9578×pow-exp
9223×div-exp
4954×add-sqr-sqrt
4473×times-frac
4330×*-un-lft-identity
4264×pow-to-exp
3433×add-cube-cbrt
2504×add-cbrt-cube
2257×sqrt-prod
1700×1-exp
1670×associate-*r/
1636×rec-exp
1157×cbrt-div
1118×pow1
1062×flip3-- flip--
1031×unpow-prod-down
1014×associate-*r*
953×cbrt-unprod
906×sqrt-div
858×frac-times
856×associate-*l*
704×cbrt-prod
617×frac-sub
539×cbrt-undiv
538×add-log-exp
447×expm1-log1p-u
444×log1p-expm1-u
438×associate-/l*
434×prod-diff
423×associate-/r*
402×difference-of-squares
354×pow-prod-down
345×sqr-pow
317×distribute-lft-out
310×div-inv
308×unswap-sqr
278×cube-prod
263×associate-*l/
258×pow-unpow
203×associate-/r/
200×distribute-lft-out--
163×distribute-rgt-in distribute-lft-in
155×distribute-rgt-neg-in
144×*-commutative
125×flip-+ flip3-+
107×clear-num frac-2neg
101×fma-def
95×distribute-lft-neg-in
80×sqrt-pow1
65×associate-/l/
63×pow1/2 rem-sqrt-square
52×sub-neg
48×pow1/3
45×unpow3 cube-mult
41×sum-log
36×pow-pow
33×fma-neg
32×fma-udef
30×+-commutative
29×div-sub
27×unpow2
25×cos-sum
24×associate--l+
20×tan-quot
17×hypot-def swap-sqr
16×pow-flip
15×neg-sub0
13×associate-+r+
12×difference-cubes pow-neg frac-add
11×pow-sub neg-mul-1
un-div-inv diff-log
exp-neg exp-prod distribute-rgt-neg-out
inv-pow pow-prod-up associate-+r-
cube-div associate-+l+
pow-sqr unsub-neg exp-sum
sqrt-unprod log-pow log-rec acos-asin log-prod distribute-neg-frac mul-1-neg
log1p-udef log1p-expm1 cos-diff expm1-log1p expm1-udef
rem-cube-cbrt sqrt-undiv pow-plus pow2 distribute-frac-neg asin-acos associate-+l-
exp-diff sqrt-pow2 hypot-udef rem-square-sqrt mul0 rem-cbrt-cube rem-log-exp

bsearch3.5s (1.2%)

localize2.4s (0.8%)

end1.0ms (0.0%)