Average Error: 1.3 → 0.8
Time: 5.0s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -45229.051772816601 \lor \neg \left(y \le 3.4619444818921188 \cdot 10^{70}\right):\\ \;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -45229.051772816601 \lor \neg \left(y \le 3.4619444818921188 \cdot 10^{70}\right):\\
\;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{z - a}\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r650058 = x;
        double r650059 = y;
        double r650060 = z;
        double r650061 = t;
        double r650062 = r650060 - r650061;
        double r650063 = a;
        double r650064 = r650060 - r650063;
        double r650065 = r650062 / r650064;
        double r650066 = r650059 * r650065;
        double r650067 = r650058 + r650066;
        return r650067;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r650068 = y;
        double r650069 = -45229.0517728166;
        bool r650070 = r650068 <= r650069;
        double r650071 = 3.461944481892119e+70;
        bool r650072 = r650068 <= r650071;
        double r650073 = !r650072;
        bool r650074 = r650070 || r650073;
        double r650075 = x;
        double r650076 = z;
        double r650077 = t;
        double r650078 = r650076 - r650077;
        double r650079 = 1.0;
        double r650080 = a;
        double r650081 = r650076 - r650080;
        double r650082 = r650079 / r650081;
        double r650083 = r650078 * r650082;
        double r650084 = r650068 * r650083;
        double r650085 = r650075 + r650084;
        double r650086 = r650068 * r650078;
        double r650087 = r650086 / r650081;
        double r650088 = r650075 + r650087;
        double r650089 = r650074 ? r650085 : r650088;
        return r650089;
}

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
Target1.2
Herbie0.8
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -45229.0517728166 or 3.461944481892119e+70 < y

    1. Initial program 0.7

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

    3. Applied div-inv0.8

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

    if -45229.0517728166 < y < 3.461944481892119e+70

    1. Initial program 1.7

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

    3. Applied associate-*r/0.8

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -45229.051772816601 \lor \neg \left(y \le 3.4619444818921188 \cdot 10^{70}\right):\\ \;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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