Date:Wednesday, February 26th, 2020
Commit:a943e6d1 on master
Hostname:warfa with Racket 7.5
Seed:2020057
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 (38.4%)

Calls

432 calls:

5.1s
(expm1 (expm1 (log1p (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.9s
(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 (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

sample1.5m (30.0%)

Algorithm
61×intervals
Results
17.8s31047×body1280valid
16.7s249062×body80valid
11.0s165921×body80nan
8.9s8832×body2560valid
8.1s20951×body640valid
5.5s3367×body5120valid
2.6s10175×body320valid
1.5s9256×body160valid
906.0ms2642×body1280nan
609.0ms2339×body640nan
603.0ms674×body10240exit
222.0ms1189×body320nan
121.0ms8256×pre80true
71.0ms591×body160nan

prune59.6s (20.1%)

simplify12.2s (4.1%)

Algorithm
175×egg-herbie

regimes10.9s (3.7%)

Accuracy

Total 41.9b remaining (23.5%)

Threshold costs 3.8b (2.2%)

9.2b5.8%Toniolo and Linder, Equation (13)
6.0b53.5%Henrywood and Agarwal, Equation (3)
6.0b0%Henrywood and Agarwal, Equation (12)
5.6b76.3%Toniolo and Linder, Equation (7)
3.4b51.1%Toniolo and Linder, Equation (10-)

rewrite6.2s (2.1%)

Algorithm
115×rewrite-expression-head
Calls

432 calls:

231.0ms
(/ (- (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)))))
84.0ms
(* (* (* (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)))))
84.0ms
(/ (- (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)))))
82.0ms
(* (* (* (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)) (/ h l))))
61.0ms
(/ (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))))))
Rules
33022×add-exp-log
23142×prod-exp
11614×pow-exp
9366×div-exp
5150×pow-to-exp
5064×add-sqr-sqrt
4530×times-frac
4245×*-un-lft-identity
3429×add-cube-cbrt
2560×add-cbrt-cube
1999×sqrt-prod
1748×unpow-prod-down
1354×associate-*l*
1322×rec-exp 1-exp
1305×pow1
1132×cbrt-unprod
972×associate-*r*
957×associate-*r/
653×prod-diff
606×difference-of-squares
528×sqr-pow
509×cbrt-prod
505×sqrt-div
504×add-log-exp
476×pow-prod-down
471×associate-/l*
460×cbrt-undiv
440×frac-times
434×log1p-expm1-u expm1-log1p-u
366×cube-prod
361×flip3-- flip--
346×cbrt-div
337×associate-*l/
309×associate-/r*
271×div-inv
270×pow-unpow
259×distribute-rgt-neg-in
249×distribute-lft-out--
245×associate-/r/
242×unswap-sqr
224×distribute-lft-out
214×distribute-lft-neg-in
160×distribute-rgt-in distribute-lft-in
154×*-commutative
153×flip-+ flip3-+
131×exp-sum
92×cos-sum
91×clear-num exp-prod frac-2neg
90×fma-def
74×tan-quot
60×sqrt-pow1
57×log-div
56×sub-neg
48×pow1/3
47×exp-diff fma-neg
44×associate-/l/
42×associate--l+
41×pow1/2 pow-pow
40×rem-sqrt-square
33×frac-sub
31×hypot-def
28×log-pow
26×div-sub sum-log log-prod
25×swap-sqr
24×neg-mul-1
23×fma-udef unpow2
20×+-commutative
18×neg-sub0
14×pow-prod-up pow-sqr
12×pow-sub
11×difference-cubes diff-log associate--r+
10×pow-neg
8×rem-log-exp
6×rem-cube-cbrt frac-add distribute-neg-frac
5×rem-exp-log pow-plus expm1-log1p expm1-udef
4×associate-+l+ un-div-inv associate-+r- associate-+r+ inv-pow neg-log cos-diff pow2 unsub-neg pow-flip unpow3 cube-mult acos-asin asin-acos
3×log1p-udef log1p-expm1 hypot-udef distribute-rgt-out--
2×cube-div distribute-frac-neg associate--r- rem-cbrt-cube associate-+l-
1×sqrt-undiv pow3 associate--l- sub-div mul0

bsearch2.5s (0.9%)

localize2.2s (0.7%)

end1.0ms (0.0%)