Average Error: 2.1 → 1.2
Time: 18.5s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[x + \frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{y - x}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\right)\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
x + \frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{y - x}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\right)
double f(double x, double y, double z, double t) {
        double r502866 = x;
        double r502867 = y;
        double r502868 = r502867 - r502866;
        double r502869 = z;
        double r502870 = t;
        double r502871 = r502869 / r502870;
        double r502872 = r502868 * r502871;
        double r502873 = r502866 + r502872;
        return r502873;
}
↓
double f(double x, double y, double z, double t) {
        double r502874 = x;
        double r502875 = y;
        double r502876 = r502875 - r502874;
        double r502877 = cbrt(r502876);
        double r502878 = r502877 * r502877;
        double r502879 = t;
        double r502880 = cbrt(r502879);
        double r502881 = r502878 / r502880;
        double r502882 = r502877 / r502880;
        double r502883 = z;
        double r502884 = r502883 / r502880;
        double r502885 = r502882 * r502884;
        double r502886 = r502881 * r502885;
        double r502887 = r502874 + r502886;
        return r502887;
}

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

Original2.1
Target2.3
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 2.1

    \[x + \left(y - x\right) \cdot \frac{z}{t}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt2.6

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

  4. Applied *-un-lft-identity2.6

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

  5. Applied times-frac2.6

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

  6. Applied associate-*r*4.5

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

  7. Simplified4.5

    \[\leadsto x + \color{blue}{\frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \frac{z}{\sqrt[3]{t}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt4.6

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

  10. Applied times-frac4.6

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

  11. Applied associate-*l*1.2

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

  12. Final simplification1.2

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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