Average Error: 6.0 → 0.4
Time: 5.9s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.6927132490810346 \cdot 10^{197} \lor \neg \left(y \cdot \left(z - t\right) \le 1.30684209979948884 \cdot 10^{187}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -5.6927132490810346 \cdot 10^{197} \lor \neg \left(y \cdot \left(z - t\right) \le 1.30684209979948884 \cdot 10^{187}\right):\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r269048 = x;
        double r269049 = y;
        double r269050 = z;
        double r269051 = t;
        double r269052 = r269050 - r269051;
        double r269053 = r269049 * r269052;
        double r269054 = a;
        double r269055 = r269053 / r269054;
        double r269056 = r269048 - r269055;
        return r269056;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r269057 = y;
        double r269058 = z;
        double r269059 = t;
        double r269060 = r269058 - r269059;
        double r269061 = r269057 * r269060;
        double r269062 = -5.6927132490810346e+197;
        bool r269063 = r269061 <= r269062;
        double r269064 = 1.3068420997994888e+187;
        bool r269065 = r269061 <= r269064;
        double r269066 = !r269065;
        bool r269067 = r269063 || r269066;
        double r269068 = x;
        double r269069 = a;
        double r269070 = r269069 / r269060;
        double r269071 = r269057 / r269070;
        double r269072 = r269068 - r269071;
        double r269073 = r269061 / r269069;
        double r269074 = r269068 - r269073;
        double r269075 = r269067 ? r269072 : r269074;
        return r269075;
}

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

Original6.0
Target0.7
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -5.6927132490810346e+197 or 1.3068420997994888e+187 < (* y (- z t))

    1. Initial program 26.5

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

    3. Applied associate-/l*1.0

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

    if -5.6927132490810346e+197 < (* y (- z t)) < 1.3068420997994888e+187

    1. Initial program 0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.6927132490810346 \cdot 10^{197} \lor \neg \left(y \cdot \left(z - t\right) \le 1.30684209979948884 \cdot 10^{187}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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