Average Error: 2.0 → 2.0
Time: 45.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}}\right)}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}}\right)}
double f(double x, double y, double z, double t, double a, double b) {
        double r2551331 = x;
        double r2551332 = y;
        double r2551333 = z;
        double r2551334 = log(r2551333);
        double r2551335 = r2551332 * r2551334;
        double r2551336 = t;
        double r2551337 = 1.0;
        double r2551338 = r2551336 - r2551337;
        double r2551339 = a;
        double r2551340 = log(r2551339);
        double r2551341 = r2551338 * r2551340;
        double r2551342 = r2551335 + r2551341;
        double r2551343 = b;
        double r2551344 = r2551342 - r2551343;
        double r2551345 = exp(r2551344);
        double r2551346 = r2551331 * r2551345;
        double r2551347 = r2551346 / r2551332;
        return r2551347;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r2551348 = x;
        double r2551349 = a;
        double r2551350 = log(r2551349);
        double r2551351 = t;
        double r2551352 = 1.0;
        double r2551353 = r2551351 - r2551352;
        double r2551354 = r2551350 * r2551353;
        double r2551355 = z;
        double r2551356 = log(r2551355);
        double r2551357 = y;
        double r2551358 = r2551356 * r2551357;
        double r2551359 = r2551354 + r2551358;
        double r2551360 = b;
        double r2551361 = r2551359 - r2551360;
        double r2551362 = exp(r2551361);
        double r2551363 = r2551348 * r2551362;
        double r2551364 = cbrt(r2551357);
        double r2551365 = r2551364 * r2551364;
        double r2551366 = r2551363 / r2551365;
        double r2551367 = cbrt(r2551365);
        double r2551368 = cbrt(r2551364);
        double r2551369 = cbrt(r2551368);
        double r2551370 = cbrt(r2551367);
        double r2551371 = r2551369 * r2551370;
        double r2551372 = r2551367 * r2551371;
        double r2551373 = r2551366 / r2551372;
        return r2551373;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.0

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt2.0

    \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\]

  4. Applied associate-/r*2.0

    \[\leadsto \color{blue}{\frac{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt2.0

    \[\leadsto \frac{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}}\]

  7. Applied cbrt-prod2.0

    \[\leadsto \frac{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\color{blue}{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt2.0

    \[\leadsto \frac{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}}}\]

  10. Applied cbrt-prod2.0

    \[\leadsto \frac{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \sqrt[3]{\color{blue}{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}}}}\]

  11. Applied cbrt-prod2.0

    \[\leadsto \frac{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}}}\right)}}\]

  12. Final simplification2.0

    \[\leadsto \frac{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}}\right)}\]

Reproduce

herbie shell --seed 2019133 
(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))