Average Error: 2.0 → 0.9
Time: 57.9s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[x + \left(\left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right) \cdot \left(y - x\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
x + \left(\left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right) \cdot \left(y - x\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}
double f(double x, double y, double z, double t) {
        double r31006783 = x;
        double r31006784 = y;
        double r31006785 = r31006784 - r31006783;
        double r31006786 = z;
        double r31006787 = t;
        double r31006788 = r31006786 / r31006787;
        double r31006789 = r31006785 * r31006788;
        double r31006790 = r31006783 + r31006789;
        return r31006790;
}
↓
double f(double x, double y, double z, double t) {
        double r31006791 = x;
        double r31006792 = z;
        double r31006793 = cbrt(r31006792);
        double r31006794 = t;
        double r31006795 = cbrt(r31006794);
        double r31006796 = r31006793 / r31006795;
        double r31006797 = r31006796 * r31006796;
        double r31006798 = y;
        double r31006799 = r31006798 - r31006791;
        double r31006800 = r31006797 * r31006799;
        double r31006801 = r31006800 * r31006796;
        double r31006802 = r31006791 + r31006801;
        return r31006802;
}

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

Original2.0
Target2.1
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 2.0

    \[x + \left(y - x\right) \cdot \frac{z}{t}\]
  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 add-cube-cbrt2.7

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

  5. Applied times-frac2.7

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

  6. Applied associate-*r*0.9

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

  7. Simplified0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ 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))))