Average Error: 6.5 → 1.5
Time: 12.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.61770217190675352 \cdot 10^{36} \lor \neg \left(t \le 2.9560956140306957 \cdot 10^{26}\right):\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot y}{t}\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.61770217190675352 \cdot 10^{36} \lor \neg \left(t \le 2.9560956140306957 \cdot 10^{26}\right):\\
\;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r573749 = x;
        double r573750 = y;
        double r573751 = z;
        double r573752 = r573751 - r573749;
        double r573753 = r573750 * r573752;
        double r573754 = t;
        double r573755 = r573753 / r573754;
        double r573756 = r573749 + r573755;
        return r573756;
}
↓
double f(double x, double y, double z, double t) {
        double r573757 = t;
        double r573758 = -1.6177021719067535e+36;
        bool r573759 = r573757 <= r573758;
        double r573760 = 2.9560956140306957e+26;
        bool r573761 = r573757 <= r573760;
        double r573762 = !r573761;
        bool r573763 = r573759 || r573762;
        double r573764 = x;
        double r573765 = z;
        double r573766 = r573765 - r573764;
        double r573767 = y;
        double r573768 = r573757 / r573767;
        double r573769 = r573766 / r573768;
        double r573770 = r573764 + r573769;
        double r573771 = r573765 * r573767;
        double r573772 = r573771 / r573757;
        double r573773 = r573764 * r573767;
        double r573774 = r573773 / r573757;
        double r573775 = r573772 - r573774;
        double r573776 = r573764 + r573775;
        double r573777 = r573763 ? r573770 : r573776;
        return r573777;
}

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

Original6.5
Target2.2
Herbie1.5
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.6177021719067535e+36 or 2.9560956140306957e+26 < t

    1. Initial program 10.2

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

    2. Taylor expanded around 0 10.2

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

    3. Simplified1.3

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

    if -1.6177021719067535e+36 < t < 2.9560956140306957e+26

    1. Initial program 1.8

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

    2. Taylor expanded around 0 1.8

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

    3. Simplified3.2

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

    5. Applied div-sub3.2

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

    6. Simplified4.1

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

    7. Simplified1.8

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.61770217190675352 \cdot 10^{36} \lor \neg \left(t \le 2.9560956140306957 \cdot 10^{26}\right):\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot y}{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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