Average Error: 12.6 → 1.8
Time: 1.9s
Precision: 64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9.8456142423116168 \cdot 10^{75} \lor \neg \left(z \le 1.8397994472727401 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z} + x\\ \end{array}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -9.8456142423116168 \cdot 10^{75} \lor \neg \left(z \le 1.8397994472727401 \cdot 10^{-10}\right):\\
\;\;\;\;\frac{x}{\frac{z}{y + z}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot y}{z} + x\\

\end{array}
double f(double x, double y, double z) {
        double r468804 = x;
        double r468805 = y;
        double r468806 = z;
        double r468807 = r468805 + r468806;
        double r468808 = r468804 * r468807;
        double r468809 = r468808 / r468806;
        return r468809;
}
↓
double f(double x, double y, double z) {
        double r468810 = z;
        double r468811 = -9.845614242311617e+75;
        bool r468812 = r468810 <= r468811;
        double r468813 = 1.83979944727274e-10;
        bool r468814 = r468810 <= r468813;
        double r468815 = !r468814;
        bool r468816 = r468812 || r468815;
        double r468817 = x;
        double r468818 = y;
        double r468819 = r468818 + r468810;
        double r468820 = r468810 / r468819;
        double r468821 = r468817 / r468820;
        double r468822 = r468817 * r468818;
        double r468823 = r468822 / r468810;
        double r468824 = r468823 + r468817;
        double r468825 = r468816 ? r468821 : r468824;
        return r468825;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original12.6
Target3.3
Herbie1.8
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -9.845614242311617e+75 or 1.83979944727274e-10 < z

    1. Initial program 18.2

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

    3. Applied associate-/l*0.1

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + z}}}\]

    if -9.845614242311617e+75 < z < 1.83979944727274e-10

    1. Initial program 6.6

      \[\frac{x \cdot \left(y + z\right)}{z}\]

    2. Taylor expanded around 0 3.6

      \[\leadsto \color{blue}{\frac{x \cdot y}{z} + x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.8456142423116168 \cdot 10^{75} \lor \neg \left(z \le 1.8397994472727401 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))