Average Error: 6.7 → 2.3
Time: 7.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.57808943454970652 \cdot 10^{-307}:\\ \;\;\;\;x + \left(\frac{y}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{\frac{z - x}{\sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}}{{\left(\sqrt[3]{\sqrt[3]{t}}\right)}^{3}}\right) \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}\\ \mathbf{elif}\;t \le 4.22353994051715781 \cdot 10^{104}:\\ \;\;\;\;x + \frac{y \cdot z + y \cdot \left(-x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.57808943454970652 \cdot 10^{-307}:\\
\;\;\;\;x + \left(\frac{y}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{\frac{z - x}{\sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}}{{\left(\sqrt[3]{\sqrt[3]{t}}\right)}^{3}}\right) \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}\\

\mathbf{elif}\;t \le 4.22353994051715781 \cdot 10^{104}:\\
\;\;\;\;x + \frac{y \cdot z + y \cdot \left(-x\right)}{t}\\

\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 r312684 = x;
        double r312685 = y;
        double r312686 = z;
        double r312687 = r312686 - r312684;
        double r312688 = r312685 * r312687;
        double r312689 = t;
        double r312690 = r312688 / r312689;
        double r312691 = r312684 + r312690;
        return r312691;
}
↓
double f(double x, double y, double z, double t) {
        double r312692 = t;
        double r312693 = -1.5780894345497065e-307;
        bool r312694 = r312692 <= r312693;
        double r312695 = x;
        double r312696 = y;
        double r312697 = cbrt(r312692);
        double r312698 = r312696 / r312697;
        double r312699 = z;
        double r312700 = r312699 - r312695;
        double r312701 = r312700 / r312697;
        double r312702 = cbrt(r312701);
        double r312703 = r312702 * r312702;
        double r312704 = cbrt(r312697);
        double r312705 = 3.0;
        double r312706 = pow(r312704, r312705);
        double r312707 = r312703 / r312706;
        double r312708 = r312698 * r312707;
        double r312709 = r312708 * r312702;
        double r312710 = r312695 + r312709;
        double r312711 = 4.223539940517158e+104;
        bool r312712 = r312692 <= r312711;
        double r312713 = r312696 * r312699;
        double r312714 = -r312695;
        double r312715 = r312696 * r312714;
        double r312716 = r312713 + r312715;
        double r312717 = r312716 / r312692;
        double r312718 = r312695 + r312717;
        double r312719 = r312697 * r312697;
        double r312720 = r312696 / r312719;
        double r312721 = r312720 * r312701;
        double r312722 = r312695 + r312721;
        double r312723 = r312712 ? r312718 : r312722;
        double r312724 = r312694 ? r312710 : r312723;
        return r312724;
}

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

Original6.7
Target2.0
Herbie2.3
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.5780894345497065e-307

    1. Initial program 6.8

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

    3. Applied add-cube-cbrt7.3

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

    4. Applied times-frac3.1

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt3.3

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

    8. Applied add-cube-cbrt3.3

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

    9. Applied associate-*r*3.3

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

    10. Simplified2.7

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

    if -1.5780894345497065e-307 < t < 4.223539940517158e+104

    1. Initial program 2.7

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

    3. Applied sub-neg2.7

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

    4. Applied distribute-lft-in2.7

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

    if 4.223539940517158e+104 < t

    1. Initial program 12.3

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

    3. Applied add-cube-cbrt12.5

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

    4. Applied times-frac0.8

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.57808943454970652 \cdot 10^{-307}:\\ \;\;\;\;x + \left(\frac{y}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{\frac{z - x}{\sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}}{{\left(\sqrt[3]{\sqrt[3]{t}}\right)}^{3}}\right) \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}\\ \mathbf{elif}\;t \le 4.22353994051715781 \cdot 10^{104}:\\ \;\;\;\;x + \frac{y \cdot z + y \cdot \left(-x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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)))