Average Error: 1.9 → 1.0
Time: 1.3m
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\left(\left(y - x\right) \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}} + x\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\left(\left(y - x\right) \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}} + x
double f(double x, double y, double z, double t) {
        double r27154722 = x;
        double r27154723 = y;
        double r27154724 = r27154723 - r27154722;
        double r27154725 = z;
        double r27154726 = t;
        double r27154727 = r27154725 / r27154726;
        double r27154728 = r27154724 * r27154727;
        double r27154729 = r27154722 + r27154728;
        return r27154729;
}
↓
double f(double x, double y, double z, double t) {
        double r27154730 = y;
        double r27154731 = x;
        double r27154732 = r27154730 - r27154731;
        double r27154733 = z;
        double r27154734 = cbrt(r27154733);
        double r27154735 = t;
        double r27154736 = cbrt(r27154735);
        double r27154737 = r27154734 / r27154736;
        double r27154738 = r27154737 * r27154737;
        double r27154739 = r27154732 * r27154738;
        double r27154740 = r27154739 * r27154737;
        double r27154741 = r27154740 + r27154731;
        return r27154741;
}

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

Original1.9
Target2.0
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  3. Applied add-cube-cbrt2.4

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

  4. Applied add-cube-cbrt2.5

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

  5. Applied times-frac2.5

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

  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. Simplified1.0

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

  8. Final simplification1.0

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

Reproduce

herbie shell --seed 2019200 
(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))))