Average Error: 1.7 → 1.7
Time: 49.4s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}}\right)\right) \cdot \sqrt[3]{\left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}}\right)\right) \cdot \sqrt[3]{\left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r4948089 = x;
        double r4948090 = y;
        double r4948091 = z;
        double r4948092 = log(r4948091);
        double r4948093 = r4948090 * r4948092;
        double r4948094 = t;
        double r4948095 = 1.0;
        double r4948096 = r4948094 - r4948095;
        double r4948097 = a;
        double r4948098 = log(r4948097);
        double r4948099 = r4948096 * r4948098;
        double r4948100 = r4948093 + r4948099;
        double r4948101 = b;
        double r4948102 = r4948100 - r4948101;
        double r4948103 = exp(r4948102);
        double r4948104 = r4948089 * r4948103;
        double r4948105 = r4948104 / r4948090;
        return r4948105;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r4948106 = x;
        double r4948107 = exp(1.0);
        double r4948108 = a;
        double r4948109 = log(r4948108);
        double r4948110 = t;
        double r4948111 = 1.0;
        double r4948112 = r4948110 - r4948111;
        double r4948113 = r4948109 * r4948112;
        double r4948114 = z;
        double r4948115 = log(r4948114);
        double r4948116 = y;
        double r4948117 = r4948115 * r4948116;
        double r4948118 = r4948113 + r4948117;
        double r4948119 = b;
        double r4948120 = r4948118 - r4948119;
        double r4948121 = pow(r4948107, r4948120);
        double r4948122 = r4948106 * r4948121;
        double r4948123 = r4948122 / r4948116;
        double r4948124 = cbrt(r4948123);
        double r4948125 = exp(r4948120);
        double r4948126 = r4948106 * r4948125;
        double r4948127 = r4948126 / r4948116;
        double r4948128 = cbrt(r4948127);
        double r4948129 = cbrt(r4948128);
        double r4948130 = r4948129 * r4948129;
        double r4948131 = r4948129 * r4948130;
        double r4948132 = r4948128 * r4948128;
        double r4948133 = r4948132 * r4948128;
        double r4948134 = cbrt(r4948133);
        double r4948135 = r4948131 * r4948134;
        double r4948136 = r4948124 * r4948135;
        return r4948136;
}

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 1.7

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

  3. Applied add-cube-cbrt1.7

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

  5. Applied *-un-lft-identity1.7

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

  6. Applied exp-prod1.7

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

  7. Simplified1.7

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

  9. Applied add-cube-cbrt1.7

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

  11. Applied add-cbrt-cube1.7

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

  12. Final simplification1.7

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

Reproduce

herbie shell --seed 2019172 
(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))