Average Error: 5.7 → 0.6
Time: 12.7s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -6.4435085564630181 \cdot 10^{176}:\\ \;\;\;\;\frac{t - z}{a} \cdot y + x\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.59757199093709241 \cdot 10^{153}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}} + x\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -6.4435085564630181 \cdot 10^{176}:\\
\;\;\;\;\frac{t - z}{a} \cdot y + x\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 1.59757199093709241 \cdot 10^{153}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r240811 = x;
        double r240812 = y;
        double r240813 = z;
        double r240814 = t;
        double r240815 = r240813 - r240814;
        double r240816 = r240812 * r240815;
        double r240817 = a;
        double r240818 = r240816 / r240817;
        double r240819 = r240811 - r240818;
        return r240819;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r240820 = y;
        double r240821 = z;
        double r240822 = t;
        double r240823 = r240821 - r240822;
        double r240824 = r240820 * r240823;
        double r240825 = -6.443508556463018e+176;
        bool r240826 = r240824 <= r240825;
        double r240827 = r240822 - r240821;
        double r240828 = a;
        double r240829 = r240827 / r240828;
        double r240830 = r240829 * r240820;
        double r240831 = x;
        double r240832 = r240830 + r240831;
        double r240833 = 1.5975719909370924e+153;
        bool r240834 = r240824 <= r240833;
        double r240835 = r240824 / r240828;
        double r240836 = r240831 - r240835;
        double r240837 = r240828 / r240820;
        double r240838 = r240827 / r240837;
        double r240839 = r240838 + r240831;
        double r240840 = r240834 ? r240836 : r240839;
        double r240841 = r240826 ? r240832 : r240840;
        return r240841;
}

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

Original5.7
Target0.6
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -6.443508556463018e+176

    1. Initial program 22.7

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

    2. Simplified0.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t - z, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef0.9

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

    5. Simplified1.0

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

    7. Applied associate-/r/1.5

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

    if -6.443508556463018e+176 < (* y (- z t)) < 1.5975719909370924e+153

    1. Initial program 0.4

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

    if 1.5975719909370924e+153 < (* y (- z t))

    1. Initial program 21.2

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

    2. Simplified0.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t - z, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef0.8

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

    5. Simplified0.8

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -6.4435085564630181 \cdot 10^{176}:\\ \;\;\;\;\frac{t - z}{a} \cdot y + x\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.59757199093709241 \cdot 10^{153}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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