Average Error: 6.6 → 1.0
Time: 17.8s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x - \frac{\sqrt[3]{x - z} \cdot \left(\sqrt[3]{x - z} \cdot \frac{1}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{y}}}\right)}{\frac{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}{\sqrt[3]{x - z}}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x - \frac{\sqrt[3]{x - z} \cdot \left(\sqrt[3]{x - z} \cdot \frac{1}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{y}}}\right)}{\frac{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}{\sqrt[3]{x - z}}}
double f(double x, double y, double z, double t) {
        double r304826 = x;
        double r304827 = y;
        double r304828 = z;
        double r304829 = r304828 - r304826;
        double r304830 = r304827 * r304829;
        double r304831 = t;
        double r304832 = r304830 / r304831;
        double r304833 = r304826 + r304832;
        return r304833;
}
↓
double f(double x, double y, double z, double t) {
        double r304834 = x;
        double r304835 = z;
        double r304836 = r304834 - r304835;
        double r304837 = cbrt(r304836);
        double r304838 = 1.0;
        double r304839 = t;
        double r304840 = cbrt(r304839);
        double r304841 = y;
        double r304842 = cbrt(r304841);
        double r304843 = r304840 / r304842;
        double r304844 = r304843 * r304843;
        double r304845 = r304838 / r304844;
        double r304846 = r304837 * r304845;
        double r304847 = r304837 * r304846;
        double r304848 = r304843 / r304837;
        double r304849 = r304847 / r304848;
        double r304850 = r304834 - r304849;
        return r304850;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.6
Target2.0
Herbie1.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.6

    \[x + \frac{y \cdot \left(z - x\right)}{t}\]

  2. Simplified6.6

    \[\leadsto \color{blue}{x - \frac{y \cdot \left(x - z\right)}{t}}\]
  3. Using strategy rm

  4. Applied clear-num6.6

    \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{y \cdot \left(x - z\right)}}}\]

  5. Simplified2.0

    \[\leadsto x - \frac{1}{\color{blue}{\frac{\frac{t}{y}}{x - z}}}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt2.5

    \[\leadsto x - \frac{1}{\frac{\frac{t}{y}}{\color{blue}{\left(\sqrt[3]{x - z} \cdot \sqrt[3]{x - z}\right) \cdot \sqrt[3]{x - z}}}}\]

  8. Applied add-cube-cbrt2.6

    \[\leadsto x - \frac{1}{\frac{\frac{t}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}}{\left(\sqrt[3]{x - z} \cdot \sqrt[3]{x - z}\right) \cdot \sqrt[3]{x - z}}}\]

  9. Applied add-cube-cbrt2.7

    \[\leadsto x - \frac{1}{\frac{\frac{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\left(\sqrt[3]{x - z} \cdot \sqrt[3]{x - z}\right) \cdot \sqrt[3]{x - z}}}\]

  10. Applied times-frac2.7

    \[\leadsto x - \frac{1}{\frac{\color{blue}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{y}}}}{\left(\sqrt[3]{x - z} \cdot \sqrt[3]{x - z}\right) \cdot \sqrt[3]{x - z}}}\]

  11. Applied times-frac1.0

    \[\leadsto x - \frac{1}{\color{blue}{\frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{x - z} \cdot \sqrt[3]{x - z}} \cdot \frac{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}{\sqrt[3]{x - z}}}}\]

  12. Applied associate-/r*1.0

    \[\leadsto x - \color{blue}{\frac{\frac{1}{\frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{x - z} \cdot \sqrt[3]{x - z}}}}{\frac{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}{\sqrt[3]{x - z}}}}\]

  13. Simplified1.0

    \[\leadsto x - \frac{\color{blue}{\left(\frac{1}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{y}}} \cdot \sqrt[3]{x - z}\right) \cdot \sqrt[3]{x - z}}}{\frac{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}{\sqrt[3]{x - z}}}\]

  14. Final simplification1.0

    \[\leadsto x - \frac{\sqrt[3]{x - z} \cdot \left(\sqrt[3]{x - z} \cdot \frac{1}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{y}}}\right)}{\frac{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}{\sqrt[3]{x - z}}}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

  (+ x (/ (* y (- z x)) t)))