Average Error: 10.9 → 0.6
Time: 16.2s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.832820342516793827730684172945515970478 \cdot 10^{-90}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \le 1.214722434795299731395141250101727642281 \cdot 10^{-105}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}} + x\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.832820342516793827730684172945515970478 \cdot 10^{-90}:\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

\mathbf{elif}\;y \le 1.214722434795299731395141250101727642281 \cdot 10^{-105}:\\
\;\;\;\;\frac{\left(z - t\right) \cdot y}{z - a} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r473747 = x;
        double r473748 = y;
        double r473749 = z;
        double r473750 = t;
        double r473751 = r473749 - r473750;
        double r473752 = r473748 * r473751;
        double r473753 = a;
        double r473754 = r473749 - r473753;
        double r473755 = r473752 / r473754;
        double r473756 = r473747 + r473755;
        return r473756;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r473757 = y;
        double r473758 = -4.832820342516794e-90;
        bool r473759 = r473757 <= r473758;
        double r473760 = x;
        double r473761 = z;
        double r473762 = t;
        double r473763 = r473761 - r473762;
        double r473764 = a;
        double r473765 = r473761 - r473764;
        double r473766 = r473763 / r473765;
        double r473767 = r473757 * r473766;
        double r473768 = r473760 + r473767;
        double r473769 = 1.2147224347952997e-105;
        bool r473770 = r473757 <= r473769;
        double r473771 = r473763 * r473757;
        double r473772 = r473771 / r473765;
        double r473773 = r473772 + r473760;
        double r473774 = r473765 / r473763;
        double r473775 = r473757 / r473774;
        double r473776 = r473775 + r473760;
        double r473777 = r473770 ? r473773 : r473776;
        double r473778 = r473759 ? r473768 : r473777;
        return r473778;
}

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

Original10.9
Target1.4
Herbie0.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -4.832820342516794e-90

    1. Initial program 18.1

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

    2. Simplified18.1

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

    4. Applied *-un-lft-identity18.1

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

    5. Applied times-frac0.6

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

    6. Simplified0.6

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

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

    1. Initial program 0.4

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

    2. Simplified0.4

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

    if 1.2147224347952997e-105 < y

    1. Initial program 16.4

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

    2. Simplified16.4

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

    4. Applied associate-/l*0.7

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

  4. Final simplification0.6

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

Reproduce

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

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

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