Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Average Error: 0.0 → 0.4

Time: 6.1s

Precision: 64

Math

\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

↓

\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)\right)\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r38236 = x;
        double r38237 = y;
        double r38238 = 1.0;
        double r38239 = r38237 - r38238;
        double r38240 = z;
        double r38241 = r38239 * r38240;
        double r38242 = r38236 - r38241;
        double r38243 = t;
        double r38244 = r38243 - r38238;
        double r38245 = a;
        double r38246 = r38244 * r38245;
        double r38247 = r38242 - r38246;
        double r38248 = r38237 + r38243;
        double r38249 = 2.0;
        double r38250 = r38248 - r38249;
        double r38251 = b;
        double r38252 = r38250 * r38251;
        double r38253 = r38247 + r38252;
        return r38253;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r38254 = x;
        double r38255 = y;
        double r38256 = 1.0;
        double r38257 = r38255 - r38256;
        double r38258 = z;
        double r38259 = r38257 * r38258;
        double r38260 = r38254 - r38259;
        double r38261 = t;
        double r38262 = r38261 - r38256;
        double r38263 = a;
        double r38264 = cbrt(r38263);
        double r38265 = r38264 * r38264;
        double r38266 = cbrt(r38265);
        double r38267 = r38266 * r38266;
        double r38268 = cbrt(r38264);
        double r38269 = r38268 * r38268;
        double r38270 = r38267 * r38269;
        double r38271 = r38262 * r38270;
        double r38272 = r38271 * r38264;
        double r38273 = r38260 - r38272;
        double r38274 = r38255 + r38261;
        double r38275 = 2.0;
        double r38276 = r38274 - r38275;
        double r38277 = b;
        double r38278 = r38276 * r38277;
        double r38279 = r38273 + r38278;
        return r38279;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Derivation

1. Initial program 0.0

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
2. Using strategy rm

3. Applied add-cube-cbrt 0.4

   \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)}\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

4. Applied associate-*r* 0.4

   \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(\left(t - 1\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}}\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
5. Using strategy rm

6. Applied add-cube-cbrt 0.4

   \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}\right)\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

7. Applied cbrt-prod 0.4

   \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)}\right)\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

8. Applied add-cube-cbrt 0.4

   \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} \cdot \left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)\right)\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

9. Applied cbrt-prod 0.4

   \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \left(\color{blue}{\left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)} \cdot \left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)\right)\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

10. Applied swap-sqr 0.4

    \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)\right)}\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

11. Final simplification 0.4

    \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)\right)\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) b)))