Average Error: 2.1 → 2.0
Time: 1.2m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{{\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)} \cdot {\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}}\right)}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{{\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)} \cdot {\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}}\right)}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r4209018 = x;
        double r4209019 = y;
        double r4209020 = z;
        double r4209021 = log(r4209020);
        double r4209022 = r4209019 * r4209021;
        double r4209023 = t;
        double r4209024 = 1.0;
        double r4209025 = r4209023 - r4209024;
        double r4209026 = a;
        double r4209027 = log(r4209026);
        double r4209028 = r4209025 * r4209027;
        double r4209029 = r4209022 + r4209028;
        double r4209030 = b;
        double r4209031 = r4209029 - r4209030;
        double r4209032 = exp(r4209031);
        double r4209033 = r4209018 * r4209032;
        double r4209034 = r4209033 / r4209019;
        return r4209034;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r4209035 = x;
        double r4209036 = a;
        double r4209037 = log(r4209036);
        double r4209038 = t;
        double r4209039 = 1.0;
        double r4209040 = r4209038 - r4209039;
        double r4209041 = r4209037 * r4209040;
        double r4209042 = z;
        double r4209043 = log(r4209042);
        double r4209044 = y;
        double r4209045 = r4209043 * r4209044;
        double r4209046 = r4209041 + r4209045;
        double r4209047 = b;
        double r4209048 = r4209046 - r4209047;
        double r4209049 = exp(r4209048);
        double r4209050 = cbrt(r4209049);
        double r4209051 = r4209050 * r4209050;
        double r4209052 = exp(1.0);
        double r4209053 = sqrt(r4209052);
        double r4209054 = pow(r4209053, r4209048);
        double r4209055 = r4209054 * r4209054;
        double r4209056 = cbrt(r4209055);
        double r4209057 = r4209051 * r4209056;
        double r4209058 = cbrt(r4209057);
        double r4209059 = r4209051 * r4209058;
        double r4209060 = r4209035 * r4209059;
        double r4209061 = r4209060 / r4209044;
        return r4209061;
}

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 2.1

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

  3. Applied add-cube-cbrt2.1

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

  5. Applied add-cube-cbrt2.1

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

  7. Applied *-un-lft-identity2.1

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

  8. Applied exp-prod2.1

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

  9. Simplified2.1

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

  11. Applied add-sqr-sqrt2.0

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

  12. Applied unpow-prod-down2.0

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

  13. Final simplification2.0

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

Reproduce

herbie shell --seed 2019168 
(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))