Average Error: 2.0 → 6.6
Time: 15.2s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\frac{y \cdot z}{t} + \left(x - \frac{x \cdot z}{t}\right)\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\frac{y \cdot z}{t} + \left(x - \frac{x \cdot z}{t}\right)
double f(double x, double y, double z, double t) {
        double r459185 = x;
        double r459186 = y;
        double r459187 = r459186 - r459185;
        double r459188 = z;
        double r459189 = t;
        double r459190 = r459188 / r459189;
        double r459191 = r459187 * r459190;
        double r459192 = r459185 + r459191;
        return r459192;
}
↓
double f(double x, double y, double z, double t) {
        double r459193 = y;
        double r459194 = z;
        double r459195 = r459193 * r459194;
        double r459196 = t;
        double r459197 = r459195 / r459196;
        double r459198 = x;
        double r459199 = r459198 * r459194;
        double r459200 = r459199 / r459196;
        double r459201 = r459198 - r459200;
        double r459202 = r459197 + r459201;
        return r459202;
}

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
Herbie6.6
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  3. Applied add-cube-cbrt2.6

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

  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. Final simplification6.6

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

Reproduce

herbie shell --seed 2019294 
(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))))