Average Error: 5.8 → 0.4
Time: 4.3s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 8.372301841351568798694844482890536564686 \cdot 10^{181}:\\ \;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) = -\infty:\\
\;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 8.372301841351568798694844482890536564686 \cdot 10^{181}:\\
\;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r325836 = x;
        double r325837 = y;
        double r325838 = z;
        double r325839 = t;
        double r325840 = r325838 - r325839;
        double r325841 = r325837 * r325840;
        double r325842 = a;
        double r325843 = r325841 / r325842;
        double r325844 = r325836 - r325843;
        return r325844;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r325845 = y;
        double r325846 = z;
        double r325847 = t;
        double r325848 = r325846 - r325847;
        double r325849 = r325845 * r325848;
        double r325850 = -inf.0;
        bool r325851 = r325849 <= r325850;
        double r325852 = x;
        double r325853 = a;
        double r325854 = r325845 / r325853;
        double r325855 = r325854 * r325848;
        double r325856 = r325852 - r325855;
        double r325857 = 8.372301841351569e+181;
        bool r325858 = r325849 <= r325857;
        double r325859 = 1.0;
        double r325860 = r325859 / r325853;
        double r325861 = r325849 * r325860;
        double r325862 = r325852 - r325861;
        double r325863 = r325853 / r325848;
        double r325864 = r325845 / r325863;
        double r325865 = r325852 - r325864;
        double r325866 = r325858 ? r325862 : r325865;
        double r325867 = r325851 ? r325856 : r325866;
        return r325867;
}

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

Original5.8
Target0.7
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.2

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.2

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

    if -inf.0 < (* y (- z t)) < 8.372301841351569e+181

    1. Initial program 0.3

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

    3. Applied div-inv0.4

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

    if 8.372301841351569e+181 < (* y (- z t))

    1. Initial program 23.4

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

    3. Applied associate-/l*0.9

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 8.372301841351568798694844482890536564686 \cdot 10^{181}:\\ \;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 
(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)))