Average Error: 1.9 → 1.0
Time: 53.8s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{{e}^{\left(\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b\right)}}}} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b}} \cdot \sqrt[3]{e^{\left(\left(y \cdot \log z - b\right) + t \cdot \log a\right) - \log a \cdot 1.0}}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{{e}^{\left(\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b\right)}}}} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b}} \cdot \sqrt[3]{e^{\left(\left(y \cdot \log z - b\right) + t \cdot \log a\right) - \log a \cdot 1.0}}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r3473158 = x;
        double r3473159 = y;
        double r3473160 = z;
        double r3473161 = log(r3473160);
        double r3473162 = r3473159 * r3473161;
        double r3473163 = t;
        double r3473164 = 1.0;
        double r3473165 = r3473163 - r3473164;
        double r3473166 = a;
        double r3473167 = log(r3473166);
        double r3473168 = r3473165 * r3473167;
        double r3473169 = r3473162 + r3473168;
        double r3473170 = b;
        double r3473171 = r3473169 - r3473170;
        double r3473172 = exp(r3473171);
        double r3473173 = r3473158 * r3473172;
        double r3473174 = r3473173 / r3473159;
        return r3473174;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3473175 = x;
        double r3473176 = cbrt(r3473175);
        double r3473177 = y;
        double r3473178 = cbrt(r3473177);
        double r3473179 = exp(1.0);
        double r3473180 = z;
        double r3473181 = log(r3473180);
        double r3473182 = r3473177 * r3473181;
        double r3473183 = a;
        double r3473184 = log(r3473183);
        double r3473185 = t;
        double r3473186 = 1.0;
        double r3473187 = r3473185 - r3473186;
        double r3473188 = r3473184 * r3473187;
        double r3473189 = r3473182 + r3473188;
        double r3473190 = b;
        double r3473191 = r3473189 - r3473190;
        double r3473192 = pow(r3473179, r3473191);
        double r3473193 = cbrt(r3473192);
        double r3473194 = r3473178 / r3473193;
        double r3473195 = r3473176 / r3473194;
        double r3473196 = r3473176 * r3473176;
        double r3473197 = r3473178 * r3473178;
        double r3473198 = exp(r3473191);
        double r3473199 = cbrt(r3473198);
        double r3473200 = r3473182 - r3473190;
        double r3473201 = r3473185 * r3473184;
        double r3473202 = r3473200 + r3473201;
        double r3473203 = r3473184 * r3473186;
        double r3473204 = r3473202 - r3473203;
        double r3473205 = exp(r3473204);
        double r3473206 = cbrt(r3473205);
        double r3473207 = r3473199 * r3473206;
        double r3473208 = r3473197 / r3473207;
        double r3473209 = r3473196 / r3473208;
        double r3473210 = r3473195 * r3473209;
        return r3473210;
}

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 associate-/l*1.9

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

  5. Applied add-cube-cbrt1.9

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

  6. Applied add-cube-cbrt1.9

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

  7. Applied times-frac1.9

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

  8. Applied add-cube-cbrt1.9

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

  9. Applied times-frac1.0

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

  11. Applied *-un-lft-identity1.0

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{e^{\color{blue}{1 \cdot \left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}}}\]

  12. Applied exp-prod1.0

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{\color{blue}{{\left(e^{1}\right)}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}}}\]

  13. Simplified1.0

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

  14. Taylor expanded around inf 1.0

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\color{blue}{e^{1.0 \cdot \log \left(\frac{1}{a}\right) - \left(\log \left(\frac{1}{z}\right) \cdot y + \left(b + t \cdot \log \left(\frac{1}{a}\right)\right)\right)}}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}}\]

  15. Simplified1.0

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

  16. Final simplification1.0

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

Reproduce

herbie shell --seed 2019142 
(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))