Average Error: 1.9 → 1.2
Time: 46.7s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\log z \cdot y + \left(\left(t - 1.0\right) \cdot \log a - b\right)}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\log z \cdot y + \left(\left(t - 1.0\right) \cdot \log a - b\right)}}}}}{\sqrt[3]{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\log z \cdot y + \left(\left(t - 1.0\right) \cdot \log a - b\right)}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\log z \cdot y + \left(\left(t - 1.0\right) \cdot \log a - b\right)}}}}}{\sqrt[3]{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r3870166 = x;
        double r3870167 = y;
        double r3870168 = z;
        double r3870169 = log(r3870168);
        double r3870170 = r3870167 * r3870169;
        double r3870171 = t;
        double r3870172 = 1.0;
        double r3870173 = r3870171 - r3870172;
        double r3870174 = a;
        double r3870175 = log(r3870174);
        double r3870176 = r3870173 * r3870175;
        double r3870177 = r3870170 + r3870176;
        double r3870178 = b;
        double r3870179 = r3870177 - r3870178;
        double r3870180 = exp(r3870179);
        double r3870181 = r3870166 * r3870180;
        double r3870182 = r3870181 / r3870167;
        return r3870182;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3870183 = x;
        double r3870184 = cbrt(r3870183);
        double r3870185 = r3870184 * r3870184;
        double r3870186 = y;
        double r3870187 = cbrt(r3870186);
        double r3870188 = z;
        double r3870189 = log(r3870188);
        double r3870190 = r3870189 * r3870186;
        double r3870191 = t;
        double r3870192 = 1.0;
        double r3870193 = r3870191 - r3870192;
        double r3870194 = a;
        double r3870195 = log(r3870194);
        double r3870196 = r3870193 * r3870195;
        double r3870197 = b;
        double r3870198 = r3870196 - r3870197;
        double r3870199 = r3870190 + r3870198;
        double r3870200 = exp(r3870199);
        double r3870201 = sqrt(r3870200);
        double r3870202 = r3870187 / r3870201;
        double r3870203 = r3870185 / r3870202;
        double r3870204 = r3870184 / r3870202;
        double r3870205 = r3870203 * r3870204;
        double r3870206 = r3870205 / r3870187;
        return r3870206;
}

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 1.9

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

  3. Applied add-sqr-sqrt2.0

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

  4. Taylor expanded around inf 2.0

    \[\leadsto \frac{x \cdot \left(\sqrt{\color{blue}{e^{1.0 \cdot \log \left(\frac{1}{a}\right) - \left(\log \left(\frac{1}{z}\right) \cdot y + \left(b + t \cdot \log \left(\frac{1}{a}\right)\right)\right)}}} \cdot \sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{y}\]

  5. Simplified1.9

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

  7. Applied add-cube-cbrt2.0

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

  8. Applied associate-/r*2.0

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

  9. Simplified1.8

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

  11. Applied add-cube-cbrt1.8

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

  12. Applied times-frac1.2

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

  13. Final simplification1.2

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

Reproduce

herbie shell --seed 2019162 
(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))