Average Error: 2.0 → 2.2
Time: 4.3s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.882056312419036733603591616844183762295 \cdot 10^{-43} \lor \neg \left(x \le 1.194458459626071743850541049104159798314 \cdot 10^{-263}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot z}{t}\right)\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.882056312419036733603591616844183762295 \cdot 10^{-43} \lor \neg \left(x \le 1.194458459626071743850541049104159798314 \cdot 10^{-263}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r526880 = x;
        double r526881 = y;
        double r526882 = r526881 - r526880;
        double r526883 = z;
        double r526884 = t;
        double r526885 = r526883 / r526884;
        double r526886 = r526882 * r526885;
        double r526887 = r526880 + r526886;
        return r526887;
}
↓
double f(double x, double y, double z, double t) {
        double r526888 = x;
        double r526889 = -1.8820563124190367e-43;
        bool r526890 = r526888 <= r526889;
        double r526891 = 1.1944584596260717e-263;
        bool r526892 = r526888 <= r526891;
        double r526893 = !r526892;
        bool r526894 = r526890 || r526893;
        double r526895 = y;
        double r526896 = r526895 - r526888;
        double r526897 = z;
        double r526898 = t;
        double r526899 = r526897 / r526898;
        double r526900 = r526896 * r526899;
        double r526901 = r526888 + r526900;
        double r526902 = r526897 * r526895;
        double r526903 = r526902 / r526898;
        double r526904 = r526888 * r526897;
        double r526905 = r526904 / r526898;
        double r526906 = r526903 - r526905;
        double r526907 = r526888 + r526906;
        double r526908 = r526894 ? r526901 : r526907;
        return r526908;
}

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
Target2.2
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.8820563124190367e-43 or 1.1944584596260717e-263 < x

    1. Initial program 1.2

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

    if -1.8820563124190367e-43 < x < 1.1944584596260717e-263

    1. Initial program 4.2

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

    3. Applied add-cube-cbrt4.9

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

    4. Applied associate-*l*4.9

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

    5. Taylor expanded around 0 4.7

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.882056312419036733603591616844183762295 \cdot 10^{-43} \lor \neg \left(x \le 1.194458459626071743850541049104159798314 \cdot 10^{-263}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot z}{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019356 
(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))))