Average Error: 2.2 → 1.6
Time: 27.7s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.362884853252186351003430209899103823374 \cdot 10^{-200}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;t \le 8.698046239578131913729902310956849143645 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.362884853252186351003430209899103823374 \cdot 10^{-200}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{elif}\;t \le 8.698046239578131913729902310956849143645 \cdot 10^{-72}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r281916 = x;
        double r281917 = y;
        double r281918 = r281917 - r281916;
        double r281919 = z;
        double r281920 = t;
        double r281921 = r281919 / r281920;
        double r281922 = r281918 * r281921;
        double r281923 = r281916 + r281922;
        return r281923;
}
↓
double f(double x, double y, double z, double t) {
        double r281924 = t;
        double r281925 = -2.3628848532521864e-200;
        bool r281926 = r281924 <= r281925;
        double r281927 = x;
        double r281928 = y;
        double r281929 = r281928 - r281927;
        double r281930 = z;
        double r281931 = r281930 / r281924;
        double r281932 = r281929 * r281931;
        double r281933 = r281927 + r281932;
        double r281934 = 8.698046239578132e-72;
        bool r281935 = r281924 <= r281934;
        double r281936 = r281929 * r281930;
        double r281937 = r281936 / r281924;
        double r281938 = r281927 + r281937;
        double r281939 = r281924 / r281930;
        double r281940 = r281929 / r281939;
        double r281941 = r281927 + r281940;
        double r281942 = r281935 ? r281938 : r281941;
        double r281943 = r281926 ? r281933 : r281942;
        return r281943;
}

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

Original2.2
Target2.5
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -2.3628848532521864e-200

    1. Initial program 1.6

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

    if -2.3628848532521864e-200 < t < 8.698046239578132e-72

    1. Initial program 6.1

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

    3. Applied associate-*r/2.7

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

    if 8.698046239578132e-72 < t

    1. Initial program 1.0

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

    2. Taylor expanded around 0 7.5

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

    3. Simplified1.1

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.362884853252186351003430209899103823374 \cdot 10^{-200}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;t \le 8.698046239578131913729902310956849143645 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(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))))