Average Error: 6.1 → 1.9
Time: 19.3s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.465265749393871 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \mathbf{elif}\;t \le 1.9712458760545623 \cdot 10^{+50}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5.465265749393871 \cdot 10^{-262}:\\
\;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\

\mathbf{elif}\;t \le 1.9712458760545623 \cdot 10^{+50}:\\
\;\;\;\;\frac{y \cdot \left(z - x\right)}{t} + x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r15219826 = x;
        double r15219827 = y;
        double r15219828 = z;
        double r15219829 = r15219828 - r15219826;
        double r15219830 = r15219827 * r15219829;
        double r15219831 = t;
        double r15219832 = r15219830 / r15219831;
        double r15219833 = r15219826 + r15219832;
        return r15219833;
}
↓
double f(double x, double y, double z, double t) {
        double r15219834 = t;
        double r15219835 = -5.465265749393871e-262;
        bool r15219836 = r15219834 <= r15219835;
        double r15219837 = x;
        double r15219838 = y;
        double r15219839 = cbrt(r15219834);
        double r15219840 = r15219839 * r15219839;
        double r15219841 = r15219838 / r15219840;
        double r15219842 = z;
        double r15219843 = r15219842 - r15219837;
        double r15219844 = r15219843 / r15219839;
        double r15219845 = r15219841 * r15219844;
        double r15219846 = r15219837 + r15219845;
        double r15219847 = 1.9712458760545623e+50;
        bool r15219848 = r15219834 <= r15219847;
        double r15219849 = r15219838 * r15219843;
        double r15219850 = r15219849 / r15219834;
        double r15219851 = r15219850 + r15219837;
        double r15219852 = r15219848 ? r15219851 : r15219846;
        double r15219853 = r15219836 ? r15219846 : r15219852;
        return r15219853;
}

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

Original6.1
Target2.0
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if t < -5.465265749393871e-262 or 1.9712458760545623e+50 < t

    1. Initial program 7.4

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

    3. Applied add-cube-cbrt7.8

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

    4. Applied times-frac1.8

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

    if -5.465265749393871e-262 < t < 1.9712458760545623e+50

    1. Initial program 2.1

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

    2. Taylor expanded around 0 2.0

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

    3. Simplified3.4

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

    5. Applied associate-*l/2.1

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.465265749393871 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \mathbf{elif}\;t \le 1.9712458760545623 \cdot 10^{+50}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

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

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