Average Error: 2.0 → 2.3
Time: 22.5s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.554823316875534896184772785418734299257 \cdot 10^{-17} \lor \neg \left(x \le 4.078756460901570138913603373694752199382 \cdot 10^{-273}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -5.554823316875534896184772785418734299257 \cdot 10^{-17} \lor \neg \left(x \le 4.078756460901570138913603373694752199382 \cdot 10^{-273}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r404895 = x;
        double r404896 = y;
        double r404897 = r404896 - r404895;
        double r404898 = z;
        double r404899 = t;
        double r404900 = r404898 / r404899;
        double r404901 = r404897 * r404900;
        double r404902 = r404895 + r404901;
        return r404902;
}
↓
double f(double x, double y, double z, double t) {
        double r404903 = x;
        double r404904 = -5.554823316875535e-17;
        bool r404905 = r404903 <= r404904;
        double r404906 = 4.07875646090157e-273;
        bool r404907 = r404903 <= r404906;
        double r404908 = !r404907;
        bool r404909 = r404905 || r404908;
        double r404910 = y;
        double r404911 = r404910 - r404903;
        double r404912 = z;
        double r404913 = t;
        double r404914 = r404912 / r404913;
        double r404915 = r404911 * r404914;
        double r404916 = r404903 + r404915;
        double r404917 = r404911 * r404912;
        double r404918 = r404917 / r404913;
        double r404919 = r404903 + r404918;
        double r404920 = r404909 ? r404916 : r404919;
        return r404920;
}

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
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -5.554823316875535e-17 or 4.07875646090157e-273 < x

    1. Initial program 1.1

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

    if -5.554823316875535e-17 < x < 4.07875646090157e-273

    1. Initial program 4.0

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

    3. Applied associate-*r/5.2

      \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot z}{t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.554823316875534896184772785418734299257 \cdot 10^{-17} \lor \neg \left(x \le 4.078756460901570138913603373694752199382 \cdot 10^{-273}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 
(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))))