Average Error: 6.1 → 1.9
Time: 18.0s
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 r19355825 = x;
        double r19355826 = y;
        double r19355827 = z;
        double r19355828 = r19355827 - r19355825;
        double r19355829 = r19355826 * r19355828;
        double r19355830 = t;
        double r19355831 = r19355829 / r19355830;
        double r19355832 = r19355825 + r19355831;
        return r19355832;
}
↓
double f(double x, double y, double z, double t) {
        double r19355833 = t;
        double r19355834 = -5.465265749393871e-262;
        bool r19355835 = r19355833 <= r19355834;
        double r19355836 = x;
        double r19355837 = y;
        double r19355838 = cbrt(r19355833);
        double r19355839 = r19355838 * r19355838;
        double r19355840 = r19355837 / r19355839;
        double r19355841 = z;
        double r19355842 = r19355841 - r19355836;
        double r19355843 = r19355842 / r19355838;
        double r19355844 = r19355840 * r19355843;
        double r19355845 = r19355836 + r19355844;
        double r19355846 = 1.9712458760545623e+50;
        bool r19355847 = r19355833 <= r19355846;
        double r19355848 = r19355837 * r19355842;
        double r19355849 = r19355848 / r19355833;
        double r19355850 = r19355849 + r19355836;
        double r19355851 = r19355847 ? r19355850 : r19355845;
        double r19355852 = r19355835 ? r19355845 : r19355851;
        return r19355852;
}

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)))