Average Error: 6.5 → 1.2
Time: 6.4s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -12943396756.221923828125 \lor \neg \left(a \le 4.018884300263023536054951700128720971934 \cdot 10^{-127}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -12943396756.221923828125 \lor \neg \left(a \le 4.018884300263023536054951700128720971934 \cdot 10^{-127}\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 r456953 = x;
        double r456954 = y;
        double r456955 = z;
        double r456956 = t;
        double r456957 = r456955 - r456956;
        double r456958 = r456954 * r456957;
        double r456959 = a;
        double r456960 = r456958 / r456959;
        double r456961 = r456953 - r456960;
        return r456961;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r456962 = a;
        double r456963 = -12943396756.221924;
        bool r456964 = r456962 <= r456963;
        double r456965 = 4.0188843002630235e-127;
        bool r456966 = r456962 <= r456965;
        double r456967 = !r456966;
        bool r456968 = r456964 || r456967;
        double r456969 = x;
        double r456970 = y;
        double r456971 = z;
        double r456972 = t;
        double r456973 = r456971 - r456972;
        double r456974 = r456962 / r456973;
        double r456975 = r456970 / r456974;
        double r456976 = r456969 - r456975;
        double r456977 = r456970 * r456973;
        double r456978 = r456977 / r456962;
        double r456979 = r456969 - r456978;
        double r456980 = r456968 ? r456976 : r456979;
        return r456980;
}

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

Original6.5
Target0.7
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -12943396756.221924 or 4.0188843002630235e-127 < a

    1. Initial program 8.9

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

    3. Applied associate-/l*1.4

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

    if -12943396756.221924 < a < 4.0188843002630235e-127

    1. Initial program 0.8

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -12943396756.221923828125 \lor \neg \left(a \le 4.018884300263023536054951700128720971934 \cdot 10^{-127}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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)))