Average Error: 1.2 → 0.4
Time: 4.3s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.4286636126829549 \cdot 10^{-64} \lor \neg \left(y \le 0.043009032465073517\right):\\ \;\;\;\;x + 1 \cdot \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.4286636126829549 \cdot 10^{-64} \lor \neg \left(y \le 0.043009032465073517\right):\\
\;\;\;\;x + 1 \cdot \frac{y}{\frac{z - a}{z - t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r645785 = x;
        double r645786 = y;
        double r645787 = z;
        double r645788 = t;
        double r645789 = r645787 - r645788;
        double r645790 = a;
        double r645791 = r645787 - r645790;
        double r645792 = r645789 / r645791;
        double r645793 = r645786 * r645792;
        double r645794 = r645785 + r645793;
        return r645794;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r645795 = y;
        double r645796 = -4.428663612682955e-64;
        bool r645797 = r645795 <= r645796;
        double r645798 = 0.04300903246507352;
        bool r645799 = r645795 <= r645798;
        double r645800 = !r645799;
        bool r645801 = r645797 || r645800;
        double r645802 = x;
        double r645803 = 1.0;
        double r645804 = z;
        double r645805 = a;
        double r645806 = r645804 - r645805;
        double r645807 = t;
        double r645808 = r645804 - r645807;
        double r645809 = r645806 / r645808;
        double r645810 = r645795 / r645809;
        double r645811 = r645803 * r645810;
        double r645812 = r645802 + r645811;
        double r645813 = r645795 * r645808;
        double r645814 = r645813 / r645806;
        double r645815 = r645802 + r645814;
        double r645816 = r645801 ? r645812 : r645815;
        return r645816;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.2
Target1.1
Herbie0.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.428663612682955e-64 or 0.04300903246507352 < y

    1. Initial program 0.5

      \[x + y \cdot \frac{z - t}{z - a}\]
    2. Using strategy rm

    3. Applied clear-num0.6

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity0.6

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

    6. Applied associate-*l*0.6

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

    7. Simplified0.5

      \[\leadsto x + 1 \cdot \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]

    if -4.428663612682955e-64 < y < 0.04300903246507352

    1. Initial program 2.0

      \[x + y \cdot \frac{z - t}{z - a}\]
    2. Using strategy rm

    3. Applied associate-*r/0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.4286636126829549 \cdot 10^{-64} \lor \neg \left(y \le 0.043009032465073517\right):\\ \;\;\;\;x + 1 \cdot \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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