Average Error: 6.4 → 1.6
Time: 3.2s
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 r468822 = x;
        double r468823 = y;
        double r468824 = r468823 - r468822;
        double r468825 = z;
        double r468826 = r468824 * r468825;
        double r468827 = t;
        double r468828 = r468826 / r468827;
        double r468829 = r468822 + r468828;
        return r468829;
}
↓
double f(double x, double y, double z, double t) {
        double r468830 = t;
        double r468831 = -2.3628848532521864e-200;
        bool r468832 = r468830 <= r468831;
        double r468833 = x;
        double r468834 = y;
        double r468835 = r468834 - r468833;
        double r468836 = z;
        double r468837 = r468836 / r468830;
        double r468838 = r468835 * r468837;
        double r468839 = r468833 + r468838;
        double r468840 = 8.698046239578132e-72;
        bool r468841 = r468830 <= r468840;
        double r468842 = r468835 * r468836;
        double r468843 = r468842 / r468830;
        double r468844 = r468833 + r468843;
        double r468845 = r468830 / r468836;
        double r468846 = r468835 / r468845;
        double r468847 = r468833 + r468846;
        double r468848 = r468841 ? r468844 : r468847;
        double r468849 = r468832 ? r468839 : r468848;
        return r468849;
}

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 -9.0255111955330046e-135) (- x (* (/ z t) (- x y))) (if (< x 4.2750321637007147e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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