Average Error: 10.4 → 0.2
Time: 16.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 8.6364206235101057 \cdot 10^{305}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 8.6364206235101057 \cdot 10^{305}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{a - t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r1299883 = x;
        double r1299884 = y;
        double r1299885 = z;
        double r1299886 = t;
        double r1299887 = r1299885 - r1299886;
        double r1299888 = r1299884 * r1299887;
        double r1299889 = a;
        double r1299890 = r1299889 - r1299886;
        double r1299891 = r1299888 / r1299890;
        double r1299892 = r1299883 + r1299891;
        return r1299892;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1299893 = y;
        double r1299894 = z;
        double r1299895 = t;
        double r1299896 = r1299894 - r1299895;
        double r1299897 = r1299893 * r1299896;
        double r1299898 = a;
        double r1299899 = r1299898 - r1299895;
        double r1299900 = r1299897 / r1299899;
        double r1299901 = -inf.0;
        bool r1299902 = r1299900 <= r1299901;
        double r1299903 = 8.636420623510106e+305;
        bool r1299904 = r1299900 <= r1299903;
        double r1299905 = !r1299904;
        bool r1299906 = r1299902 || r1299905;
        double r1299907 = x;
        double r1299908 = r1299896 / r1299899;
        double r1299909 = r1299893 * r1299908;
        double r1299910 = r1299907 + r1299909;
        double r1299911 = r1299907 + r1299900;
        double r1299912 = r1299906 ? r1299910 : r1299911;
        return r1299912;
}

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

Original10.4
Target1.1
Herbie0.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- a t)) < -inf.0 or 8.636420623510106e+305 < (/ (* y (- z t)) (- a t))

    1. Initial program 63.7

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

    3. Applied *-un-lft-identity63.7

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

    4. Applied times-frac0.2

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

    5. Simplified0.2

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

    if -inf.0 < (/ (* y (- z t)) (- a t)) < 8.636420623510106e+305

    1. Initial program 0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 8.6364206235101057 \cdot 10^{305}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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