Average Error: 1.2 → 1.4
Time: 5.8s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \left(y \cdot \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{\frac{z - a}{z - t}} \cdot \sqrt[3]{\frac{z - a}{z - t}}}\right) \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{\frac{z - a}{z - t}}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \left(y \cdot \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{\frac{z - a}{z - t}} \cdot \sqrt[3]{\frac{z - a}{z - t}}}\right) \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{\frac{z - a}{z - t}}}
double f(double x, double y, double z, double t, double a) {
        double r732836 = x;
        double r732837 = y;
        double r732838 = z;
        double r732839 = t;
        double r732840 = r732838 - r732839;
        double r732841 = a;
        double r732842 = r732838 - r732841;
        double r732843 = r732840 / r732842;
        double r732844 = r732837 * r732843;
        double r732845 = r732836 + r732844;
        return r732845;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r732846 = x;
        double r732847 = y;
        double r732848 = 1.0;
        double r732849 = cbrt(r732848);
        double r732850 = r732849 * r732849;
        double r732851 = z;
        double r732852 = a;
        double r732853 = r732851 - r732852;
        double r732854 = t;
        double r732855 = r732851 - r732854;
        double r732856 = r732853 / r732855;
        double r732857 = cbrt(r732856);
        double r732858 = r732857 * r732857;
        double r732859 = r732850 / r732858;
        double r732860 = r732847 * r732859;
        double r732861 = r732849 / r732857;
        double r732862 = r732860 * r732861;
        double r732863 = r732846 + r732862;
        return r732863;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.2
Target1.1
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.2

    \[x + y \cdot \frac{z - t}{z - a}\]
  2. Using strategy rm

  3. Applied clear-num1.2

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt1.5

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

  6. Applied add-cube-cbrt1.5

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

  7. Applied times-frac1.5

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

  8. Applied associate-*r*1.4

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

  9. Final simplification1.4

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

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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