Average Error: 10.7 → 0.4
Time: 24.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \le 2.886184098505586518165870377542885099677 \cdot 10^{246}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty:\\
\;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\

\mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \le 2.886184098505586518165870377542885099677 \cdot 10^{246}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r109072075 = x;
        double r109072076 = y;
        double r109072077 = z;
        double r109072078 = t;
        double r109072079 = r109072077 - r109072078;
        double r109072080 = r109072076 * r109072079;
        double r109072081 = a;
        double r109072082 = r109072077 - r109072081;
        double r109072083 = r109072080 / r109072082;
        double r109072084 = r109072075 + r109072083;
        return r109072084;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r109072085 = y;
        double r109072086 = z;
        double r109072087 = t;
        double r109072088 = r109072086 - r109072087;
        double r109072089 = r109072085 * r109072088;
        double r109072090 = a;
        double r109072091 = r109072086 - r109072090;
        double r109072092 = r109072089 / r109072091;
        double r109072093 = -inf.0;
        bool r109072094 = r109072092 <= r109072093;
        double r109072095 = x;
        double r109072096 = r109072091 / r109072088;
        double r109072097 = r109072085 / r109072096;
        double r109072098 = r109072095 + r109072097;
        double r109072099 = 2.8861840985055865e+246;
        bool r109072100 = r109072092 <= r109072099;
        double r109072101 = r109072095 + r109072092;
        double r109072102 = r109072100 ? r109072101 : r109072098;
        double r109072103 = r109072094 ? r109072098 : r109072102;
        return r109072103;
}

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

Original10.7
Target1.4
Herbie0.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- z a)) < -inf.0 or 2.8861840985055865e+246 < (/ (* y (- z t)) (- z a))

    1. Initial program 59.0

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

    3. Applied associate-/l*1.2

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

    if -inf.0 < (/ (* y (- z t)) (- z a)) < 2.8861840985055865e+246

    1. Initial program 0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \le 2.886184098505586518165870377542885099677 \cdot 10^{246}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(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))))