Average Error: 12.4 → 2.2
Time: 2.7s
Precision: 64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.78224101529568762 \cdot 10^{-306} \lor \neg \left(x \le 9.58952198226363064 \cdot 10^{-74}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z} + x\\ \end{array}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.78224101529568762 \cdot 10^{-306} \lor \neg \left(x \le 9.58952198226363064 \cdot 10^{-74}\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 r958956 = x;
        double r958957 = y;
        double r958958 = z;
        double r958959 = r958957 + r958958;
        double r958960 = r958956 * r958959;
        double r958961 = r958960 / r958958;
        return r958961;
}
↓
double f(double x, double y, double z) {
        double r958962 = x;
        double r958963 = -1.7822410152956876e-306;
        bool r958964 = r958962 <= r958963;
        double r958965 = 9.58952198226363e-74;
        bool r958966 = r958962 <= r958965;
        double r958967 = !r958966;
        bool r958968 = r958964 || r958967;
        double r958969 = z;
        double r958970 = y;
        double r958971 = r958970 + r958969;
        double r958972 = r958969 / r958971;
        double r958973 = r958962 / r958972;
        double r958974 = r958962 * r958970;
        double r958975 = r958974 / r958969;
        double r958976 = r958975 + r958962;
        double r958977 = r958968 ? r958973 : r958976;
        return r958977;
}

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

Original12.4
Target2.9
Herbie2.2
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.7822410152956876e-306 or 9.58952198226363e-74 < x

    1. Initial program 14.3

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

    3. Applied associate-/l*1.9

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

    if -1.7822410152956876e-306 < x < 9.58952198226363e-74

    1. Initial program 6.3

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

    2. Taylor expanded around 0 3.4

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.78224101529568762 \cdot 10^{-306} \lor \neg \left(x \le 9.58952198226363064 \cdot 10^{-74}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(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))