Average Error: 1.3 → 0.3
Time: 11.9s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.637379201468953986949485320636358182223 \cdot 10^{-36} \lor \neg \left(y \le 3.205739178188263417782161531329637455788 \cdot 10^{-56}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.637379201468953986949485320636358182223 \cdot 10^{-36} \lor \neg \left(y \le 3.205739178188263417782161531329637455788 \cdot 10^{-56}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{a - t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r378038 = x;
        double r378039 = y;
        double r378040 = z;
        double r378041 = t;
        double r378042 = r378040 - r378041;
        double r378043 = a;
        double r378044 = r378043 - r378041;
        double r378045 = r378042 / r378044;
        double r378046 = r378039 * r378045;
        double r378047 = r378038 + r378046;
        return r378047;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r378048 = y;
        double r378049 = -4.637379201468954e-36;
        bool r378050 = r378048 <= r378049;
        double r378051 = 3.2057391781882634e-56;
        bool r378052 = r378048 <= r378051;
        double r378053 = !r378052;
        bool r378054 = r378050 || r378053;
        double r378055 = x;
        double r378056 = z;
        double r378057 = t;
        double r378058 = r378056 - r378057;
        double r378059 = a;
        double r378060 = r378059 - r378057;
        double r378061 = r378058 / r378060;
        double r378062 = r378048 * r378061;
        double r378063 = r378055 + r378062;
        double r378064 = r378048 * r378058;
        double r378065 = 1.0;
        double r378066 = r378065 / r378060;
        double r378067 = r378064 * r378066;
        double r378068 = r378055 + r378067;
        double r378069 = r378054 ? r378063 : r378068;
        return r378069;
}

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
Target0.3
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.637379201468954e-36 or 3.2057391781882634e-56 < y

    1. Initial program 0.4

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

    if -4.637379201468954e-36 < y < 3.2057391781882634e-56

    1. Initial program 2.3

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

    3. Applied div-inv2.3

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

    4. Applied associate-*r*0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.637379201468953986949485320636358182223 \cdot 10^{-36} \lor \neg \left(y \le 3.205739178188263417782161531329637455788 \cdot 10^{-56}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :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)))))