Average Error: 1.3 → 1.4
Time: 18.3s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.347512852047913:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\\ \mathbf{elif}\;t \le 2.7589848075703794 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + x\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -4.347512852047913:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\\

\mathbf{elif}\;t \le 2.7589848075703794 \cdot 10^{-216}:\\
\;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r24959740 = x;
        double r24959741 = y;
        double r24959742 = z;
        double r24959743 = t;
        double r24959744 = r24959742 - r24959743;
        double r24959745 = a;
        double r24959746 = r24959745 - r24959743;
        double r24959747 = r24959744 / r24959746;
        double r24959748 = r24959741 * r24959747;
        double r24959749 = r24959740 + r24959748;
        return r24959749;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r24959750 = t;
        double r24959751 = -4.347512852047913;
        bool r24959752 = r24959750 <= r24959751;
        double r24959753 = x;
        double r24959754 = y;
        double r24959755 = a;
        double r24959756 = z;
        double r24959757 = r24959756 - r24959750;
        double r24959758 = r24959755 / r24959757;
        double r24959759 = r24959750 / r24959757;
        double r24959760 = r24959758 - r24959759;
        double r24959761 = r24959754 / r24959760;
        double r24959762 = r24959753 + r24959761;
        double r24959763 = 2.7589848075703794e-216;
        bool r24959764 = r24959750 <= r24959763;
        double r24959765 = r24959757 * r24959754;
        double r24959766 = r24959755 - r24959750;
        double r24959767 = r24959765 / r24959766;
        double r24959768 = r24959753 + r24959767;
        double r24959769 = r24959757 / r24959766;
        double r24959770 = r24959754 * r24959769;
        double r24959771 = r24959770 + r24959753;
        double r24959772 = r24959764 ? r24959768 : r24959771;
        double r24959773 = r24959752 ? r24959762 : r24959772;
        return r24959773;
}

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

Original1.3
Target0.4
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -4.347512852047913

    1. Initial program 0.1

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

    3. Applied associate-*r/16.2

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

    5. Applied associate-/l*0.1

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

    7. Applied div-sub0.1

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

    if -4.347512852047913 < t < 2.7589848075703794e-216

    1. Initial program 3.2

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

    3. Applied associate-*r/3.4

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

    if 2.7589848075703794e-216 < t

    1. Initial program 0.7

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.347512852047913:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\\ \mathbf{elif}\;t \le 2.7589848075703794 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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