Date:Wednesday, February 26th, 2020
Commit:2c6cda94 on refactor-and-minor
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

series2.0m (38.0%)

Calls

440 calls:

4.9s
(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*)))))
4.8s
(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) (- (- 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*))))))
4.6s
(expm1 (expm1 (log1p (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))

sample1.4m (26.7%)

Algorithm
61×intervals
Results
16.6s29503×body1280valid
16.4s253269×body80valid
10.1s159481×body80nan
9.0s8832×body2560valid
7.4s20043×body640valid
5.6s3367×body5120valid
2.4s9831×body320valid
1.4s9106×body160valid
607.0ms674×body10240exit
151.0ms624×body1280nan
127.0ms619×body640nan
114.0ms8256×pre80true
50.0ms338×body320nan
19.0ms191×body160nan

prune1.0m (19.6%)

Filtered
21797 candidates to 11037 candidates (50.6%)

rewrite20.4s (6.5%)

Algorithm
116×rewrite-expression-head
Calls

440 calls:

3.6s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
792.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
681.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
526.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* (* t (* (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))) (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))) (- 1.0 (* v v))))
472.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
Rules
33444×add-exp-log
23425×prod-exp
11694×pow-exp
9459×div-exp
5289×add-sqr-sqrt
5203×pow-to-exp
4790×times-frac
4472×*-un-lft-identity
3634×add-cube-cbrt
2585×add-cbrt-cube
2246×sqrt-prod
1727×unpow-prod-down
1397×associate-*l*
1327×rec-exp 1-exp
1265×pow1
1136×cbrt-unprod
1050×associate-*r/
932×associate-*r*
654×prod-diff
636×cbrt-prod
621×difference-of-squares
517×sqrt-div
512×add-log-exp
511×sqr-pow
483×associate-/l*
475×cbrt-undiv
472×frac-times
442×expm1-log1p-u
441×log1p-expm1-u
437×pow-prod-down
372×cube-prod
361×flip3-- flip--
357×associate-*l/ cbrt-div
342×associate-/r*
316×pow-unpow
284×div-inv
264×distribute-lft-out--
259×distribute-rgt-neg-in
247×associate-/r/
244×unswap-sqr
220×distribute-lft-out
214×distribute-lft-neg-in
185×flip-+ flip3-+
170×distribute-rgt-in distribute-lft-in
146×*-commutative
131×exp-sum
96×fma-def
95×clear-num frac-2neg
92×cos-sum
91×exp-prod
74×tan-quot
73×div-sub
64×sqrt-pow1
60×pow1/3
57×sub-neg log-div
49×frac-sub
48×fma-neg
47×exp-diff
46×associate-/l/ associate--l+
45×pow1/2
44×rem-sqrt-square
43×pow-sub
42×swap-sqr
36×pow-pow
28×log-pow
26×log-prod
25×fma-udef sum-log
24×neg-mul-1 unpow2
19×+-commutative
18×neg-sub0
17×pow-prod-up pow-sqr
15×associate--r+
13×hypot-def
12×diff-log
11×difference-cubes
10×pow-neg
rem-log-exp
rem-cube-cbrt pow-plus
frac-add pow2 unpow3 cube-mult distribute-neg-frac
rem-exp-log inv-pow pow-flip sub-div
sqrt-undiv associate-+l+ un-div-inv associate-+r- associate-+r+ neg-log cos-diff expm1-log1p hypot-udef unsub-neg acos-asin asin-acos distribute-rgt-out-- expm1-udef
rem-cbrt-cube
cube-div log1p-udef log1p-expm1 distribute-frac-neg associate--r- associate-+l-
pow3 associate--l- mul0

simplify12.5s (4.0%)

Algorithm
176×egg-herbie

regimes11.3s (3.6%)

Accuracy

Total 42.9b remaining (22.8%)

Threshold costs 4.9b (2.6%)

9.2b5.8%Toniolo and Linder, Equation (13)
6.0b53.5%Henrywood and Agarwal, Equation (3)
6.0b0%Henrywood and Agarwal, Equation (12)
5.6b76.2%Toniolo and Linder, Equation (7)
3.4b51%Toniolo and Linder, Equation (10-)

localize2.5s (0.8%)

bsearch2.5s (0.8%)

end1.0ms (0.0%)