Average Error: 6.4 → 1.6
Time: 20.0s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.362884853252186351003430209899103823374 \cdot 10^{-200}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;t \le 8.698046239578131913729902310956849143645 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot 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 r361919 = x;
        double r361920 = y;
        double r361921 = r361920 - r361919;
        double r361922 = z;
        double r361923 = r361921 * r361922;
        double r361924 = t;
        double r361925 = r361923 / r361924;
        double r361926 = r361919 + r361925;
        return r361926;
}
↓
double f(double x, double y, double z, double t) {
        double r361927 = t;
        double r361928 = -2.3628848532521864e-200;
        bool r361929 = r361927 <= r361928;
        double r361930 = x;
        double r361931 = y;
        double r361932 = r361931 - r361930;
        double r361933 = z;
        double r361934 = r361933 / r361927;
        double r361935 = r361932 * r361934;
        double r361936 = r361930 + r361935;
        double r361937 = 8.698046239578132e-72;
        bool r361938 = r361927 <= r361937;
        double r361939 = r361932 * r361933;
        double r361940 = r361939 / r361927;
        double r361941 = r361930 + r361940;
        double r361942 = r361927 / r361933;
        double r361943 = r361932 / r361942;
        double r361944 = r361930 + r361943;
        double r361945 = r361938 ? r361941 : r361944;
        double r361946 = r361929 ? r361936 : r361945;
        return r361946;
}

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

Original6.4
Target2.1
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -2.3628848532521864e-200

    1. Initial program 7.1

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

    3. Applied *-un-lft-identity7.1

      \[\leadsto x + \frac{\left(y - x\right) \cdot z}{\color{blue}{1 \cdot t}}\]

    4. Applied times-frac1.6

      \[\leadsto x + \color{blue}{\frac{y - x}{1} \cdot \frac{z}{t}}\]

    5. Simplified1.6

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

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

    1. Initial program 2.7

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

    if 8.698046239578132e-72 < t

    1. Initial program 7.5

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

    3. Applied associate-/l*1.1

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
  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 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

  (+ x (/ (* (- y x) z) t)))