Average Error: 6.6 → 2.0
Time: 2.9s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.51178833086014192 \cdot 10^{-107} \lor \neg \left(x \le 1.44337867331050735 \cdot 10^{-230}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{t} \cdot \left(z \cdot \sqrt[3]{y - x}\right)\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.51178833086014192 \cdot 10^{-107} \lor \neg \left(x \le 1.44337867331050735 \cdot 10^{-230}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{t} \cdot \left(z \cdot \sqrt[3]{y - x}\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r504880 = x;
        double r504881 = y;
        double r504882 = r504881 - r504880;
        double r504883 = z;
        double r504884 = r504882 * r504883;
        double r504885 = t;
        double r504886 = r504884 / r504885;
        double r504887 = r504880 + r504886;
        return r504887;
}
↓
double f(double x, double y, double z, double t) {
        double r504888 = x;
        double r504889 = -3.511788330860142e-107;
        bool r504890 = r504888 <= r504889;
        double r504891 = 1.4433786733105074e-230;
        bool r504892 = r504888 <= r504891;
        double r504893 = !r504892;
        bool r504894 = r504890 || r504893;
        double r504895 = y;
        double r504896 = r504895 - r504888;
        double r504897 = z;
        double r504898 = t;
        double r504899 = r504897 / r504898;
        double r504900 = r504896 * r504899;
        double r504901 = r504888 + r504900;
        double r504902 = cbrt(r504896);
        double r504903 = r504902 * r504902;
        double r504904 = r504903 / r504898;
        double r504905 = r504897 * r504902;
        double r504906 = r504904 * r504905;
        double r504907 = r504888 + r504906;
        double r504908 = r504894 ? r504901 : r504907;
        return r504908;
}

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

Original6.6
Target2.0
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -3.511788330860142e-107 or 1.4433786733105074e-230 < x

    1. Initial program 7.0

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

    3. Applied *-un-lft-identity7.0

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

    4. Applied times-frac1.1

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

    5. Simplified1.1

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

    if -3.511788330860142e-107 < x < 1.4433786733105074e-230

    1. Initial program 5.5

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

    3. Applied associate-/l*4.3

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
    4. Using strategy rm

    5. Applied div-inv4.4

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

    6. Applied add-cube-cbrt5.0

      \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}{t \cdot \frac{1}{z}}\]

    7. Applied times-frac4.7

      \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{t} \cdot \frac{\sqrt[3]{y - x}}{\frac{1}{z}}}\]

    8. Simplified4.7

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.51178833086014192 \cdot 10^{-107} \lor \neg \left(x \le 1.44337867331050735 \cdot 10^{-230}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{t} \cdot \left(z \cdot \sqrt[3]{y - x}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(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)))