Average Error: 6.2 → 0.4
Time: 3.2s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.8448302221257819 \cdot 10^{209}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 4.77051970732716704 \cdot 10^{192}:\\ \;\;\;\;\left(x + \frac{t \cdot y}{a}\right) - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -1.8448302221257819 \cdot 10^{209}:\\
\;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 4.77051970732716704 \cdot 10^{192}:\\
\;\;\;\;\left(x + \frac{t \cdot y}{a}\right) - \frac{z \cdot y}{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 r274840 = x;
        double r274841 = y;
        double r274842 = z;
        double r274843 = t;
        double r274844 = r274842 - r274843;
        double r274845 = r274841 * r274844;
        double r274846 = a;
        double r274847 = r274845 / r274846;
        double r274848 = r274840 - r274847;
        return r274848;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r274849 = y;
        double r274850 = z;
        double r274851 = t;
        double r274852 = r274850 - r274851;
        double r274853 = r274849 * r274852;
        double r274854 = -1.844830222125782e+209;
        bool r274855 = r274853 <= r274854;
        double r274856 = x;
        double r274857 = a;
        double r274858 = r274849 / r274857;
        double r274859 = r274858 * r274852;
        double r274860 = r274856 - r274859;
        double r274861 = 4.770519707327167e+192;
        bool r274862 = r274853 <= r274861;
        double r274863 = r274851 * r274849;
        double r274864 = r274863 / r274857;
        double r274865 = r274856 + r274864;
        double r274866 = r274850 * r274849;
        double r274867 = r274866 / r274857;
        double r274868 = r274865 - r274867;
        double r274869 = r274857 / r274852;
        double r274870 = r274849 / r274869;
        double r274871 = r274856 - r274870;
        double r274872 = r274862 ? r274868 : r274871;
        double r274873 = r274855 ? r274860 : r274872;
        return r274873;
}

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

Original6.2
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 3 regimes

  2. if (* y (- z t)) < -1.844830222125782e+209

    1. Initial program 30.2

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

    3. Applied associate-/l*0.7

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

    5. Applied associate-/r/0.5

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

    if -1.844830222125782e+209 < (* y (- z t)) < 4.770519707327167e+192

    1. Initial program 0.3

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

    2. Taylor expanded around 0 0.3

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

    if 4.770519707327167e+192 < (* y (- z t))

    1. Initial program 27.1

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

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.8448302221257819 \cdot 10^{209}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 4.77051970732716704 \cdot 10^{192}:\\ \;\;\;\;\left(x + \frac{t \cdot y}{a}\right) - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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)))