Average Error: 6.5 → 1.6
Time: 20.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.584406202812830128924411129162326193187 \cdot 10^{-168} \lor \neg \left(t \le 150412601825096175811127520041088581632\right):\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -4.584406202812830128924411129162326193187 \cdot 10^{-168} \lor \neg \left(t \le 150412601825096175811127520041088581632\right):\\
\;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r321766 = x;
        double r321767 = y;
        double r321768 = z;
        double r321769 = r321768 - r321766;
        double r321770 = r321767 * r321769;
        double r321771 = t;
        double r321772 = r321770 / r321771;
        double r321773 = r321766 + r321772;
        return r321773;
}
↓
double f(double x, double y, double z, double t) {
        double r321774 = t;
        double r321775 = -4.58440620281283e-168;
        bool r321776 = r321774 <= r321775;
        double r321777 = 1.5041260182509618e+38;
        bool r321778 = r321774 <= r321777;
        double r321779 = !r321778;
        bool r321780 = r321776 || r321779;
        double r321781 = y;
        double r321782 = r321781 / r321774;
        double r321783 = z;
        double r321784 = x;
        double r321785 = r321783 - r321784;
        double r321786 = r321782 * r321785;
        double r321787 = r321786 + r321784;
        double r321788 = r321781 * r321785;
        double r321789 = r321788 / r321774;
        double r321790 = r321784 + r321789;
        double r321791 = r321780 ? r321787 : r321790;
        return r321791;
}

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
Target2.0
Herbie1.6
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if t < -4.58440620281283e-168 or 1.5041260182509618e+38 < t

    1. Initial program 8.4

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

    3. Applied add-cube-cbrt8.7

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

    4. Applied times-frac1.8

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

    6. Applied add-cube-cbrt1.9

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

    8. Applied pow11.9

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

    9. Applied pow11.9

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

    10. Applied pow-prod-down1.9

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

    11. Simplified2.4

      \[\leadsto x + {\color{blue}{\left(\frac{y}{\frac{t}{z - x}}\right)}}^{1}\]
    12. Using strategy rm

    13. Applied associate-/r/1.4

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

    if -4.58440620281283e-168 < t < 1.5041260182509618e+38

    1. Initial program 2.0

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.584406202812830128924411129162326193187 \cdot 10^{-168} \lor \neg \left(t \le 150412601825096175811127520041088581632\right):\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 
(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)))