Average Error: 2.0 → 0.8
Time: 23.4s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[x + \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \left(y - x\right)\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
x + \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \left(y - x\right)\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}
double f(double x, double y, double z, double t) {
        double r26782797 = x;
        double r26782798 = y;
        double r26782799 = r26782798 - r26782797;
        double r26782800 = z;
        double r26782801 = t;
        double r26782802 = r26782800 / r26782801;
        double r26782803 = r26782799 * r26782802;
        double r26782804 = r26782797 + r26782803;
        return r26782804;
}
↓
double f(double x, double y, double z, double t) {
        double r26782805 = x;
        double r26782806 = z;
        double r26782807 = cbrt(r26782806);
        double r26782808 = t;
        double r26782809 = cbrt(r26782808);
        double r26782810 = r26782807 / r26782809;
        double r26782811 = y;
        double r26782812 = r26782811 - r26782805;
        double r26782813 = r26782810 * r26782812;
        double r26782814 = r26782810 * r26782813;
        double r26782815 = r26782814 * r26782810;
        double r26782816 = r26782805 + r26782815;
        return r26782816;
}

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
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  3. Applied add-cube-cbrt2.5

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

  4. Applied add-cube-cbrt2.6

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

  5. Applied times-frac2.6

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

  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. Simplified0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2019169 
(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))))