Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2

Average Error: 1.9 → 1.9

Time: 1.1m

Precision: 64

Math

\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r4714273 = x;
        double r4714274 = y;
        double r4714275 = z;
        double r4714276 = log(r4714275);
        double r4714277 = r4714274 * r4714276;
        double r4714278 = t;
        double r4714279 = 1.0;
        double r4714280 = r4714278 - r4714279;
        double r4714281 = a;
        double r4714282 = log(r4714281);
        double r4714283 = r4714280 * r4714282;
        double r4714284 = r4714277 + r4714283;
        double r4714285 = b;
        double r4714286 = r4714284 - r4714285;
        double r4714287 = exp(r4714286);
        double r4714288 = r4714273 * r4714287;
        double r4714289 = r4714288 / r4714274;
        return r4714289;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r4714290 = t;
        double r4714291 = 1.0;
        double r4714292 = r4714290 - r4714291;
        double r4714293 = a;
        double r4714294 = log(r4714293);
        double r4714295 = r4714292 * r4714294;
        double r4714296 = z;
        double r4714297 = log(r4714296);
        double r4714298 = y;
        double r4714299 = r4714297 * r4714298;
        double r4714300 = r4714295 + r4714299;
        double r4714301 = b;
        double r4714302 = r4714300 - r4714301;
        double r4714303 = exp(r4714302);
        double r4714304 = x;
        double r4714305 = r4714303 * r4714304;
        double r4714306 = r4714305 / r4714298;
        double r4714307 = cbrt(r4714306);
        double r4714308 = r4714307 * r4714307;
        double r4714309 = r4714307 * r4714308;
        double r4714310 = cbrt(r4714309);
        double r4714311 = r4714307 * r4714310;
        double r4714312 = r4714310 * r4714311;
        return r4714312;
}

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 1.9

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
2. Using strategy rm

3. Applied add-cube-cbrt 1.9

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

5. Applied add-cube-cbrt 1.9

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

7. Applied add-cube-cbrt 1.9

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

8. Final simplification 1.9

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))