Average Error: 1.4 → 0.6
Time: 12.6s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.832820342516793827730684172945515970478 \cdot 10^{-90} \lor \neg \left(y \le 1.214722434795299731395141250101727642281 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{z - t}{z - a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.832820342516793827730684172945515970478 \cdot 10^{-90} \lor \neg \left(y \le 1.214722434795299731395141250101727642281 \cdot 10^{-105}\right):\\
\;\;\;\;\frac{z - t}{z - a} \cdot y + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r487781 = x;
        double r487782 = y;
        double r487783 = z;
        double r487784 = t;
        double r487785 = r487783 - r487784;
        double r487786 = a;
        double r487787 = r487783 - r487786;
        double r487788 = r487785 / r487787;
        double r487789 = r487782 * r487788;
        double r487790 = r487781 + r487789;
        return r487790;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r487791 = y;
        double r487792 = -4.832820342516794e-90;
        bool r487793 = r487791 <= r487792;
        double r487794 = 1.2147224347952997e-105;
        bool r487795 = r487791 <= r487794;
        double r487796 = !r487795;
        bool r487797 = r487793 || r487796;
        double r487798 = z;
        double r487799 = t;
        double r487800 = r487798 - r487799;
        double r487801 = a;
        double r487802 = r487798 - r487801;
        double r487803 = r487800 / r487802;
        double r487804 = r487803 * r487791;
        double r487805 = x;
        double r487806 = r487804 + r487805;
        double r487807 = r487791 * r487800;
        double r487808 = r487807 / r487802;
        double r487809 = r487808 + r487805;
        double r487810 = r487797 ? r487806 : r487809;
        return r487810;
}

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

Original1.4
Target1.4
Herbie0.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.832820342516794e-90 or 1.2147224347952997e-105 < y

    1. Initial program 0.7

      \[x + y \cdot \frac{z - t}{z - a}\]

    if -4.832820342516794e-90 < y < 1.2147224347952997e-105

    1. Initial program 2.7

      \[x + y \cdot \frac{z - t}{z - a}\]

    2. Simplified4.0

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

    4. Applied *-un-lft-identity4.0

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

    5. Applied *-un-lft-identity4.0

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

    6. Applied times-frac4.0

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

    7. Applied associate-*l*4.0

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

    8. Simplified0.4

      \[\leadsto \frac{1}{1} \cdot \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} + x\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.832820342516793827730684172945515970478 \cdot 10^{-90} \lor \neg \left(y \le 1.214722434795299731395141250101727642281 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{z - t}{z - a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

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

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