Average Error: 6.1 → 0.7
Time: 1.4m
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -6.939593118092855 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -1.454055052210347 \cdot 10^{-302}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \le 1.8266963535821708 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.1730839583412028 \cdot 10^{+147}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -6.939593118092855 \cdot 10^{+188}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le -1.454055052210347 \cdot 10^{-302}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;x \cdot y \le 1.8266963535821708 \cdot 10^{-240}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le 1.1730839583412028 \cdot 10^{+147}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r26776886 = x;
        double r26776887 = y;
        double r26776888 = r26776886 * r26776887;
        double r26776889 = z;
        double r26776890 = r26776888 / r26776889;
        return r26776890;
}
↓
double f(double x, double y, double z) {
        double r26776891 = x;
        double r26776892 = y;
        double r26776893 = r26776891 * r26776892;
        double r26776894 = -6.939593118092855e+188;
        bool r26776895 = r26776893 <= r26776894;
        double r26776896 = z;
        double r26776897 = r26776892 / r26776896;
        double r26776898 = r26776891 * r26776897;
        double r26776899 = -1.454055052210347e-302;
        bool r26776900 = r26776893 <= r26776899;
        double r26776901 = 1.0;
        double r26776902 = r26776896 / r26776893;
        double r26776903 = r26776901 / r26776902;
        double r26776904 = 1.8266963535821708e-240;
        bool r26776905 = r26776893 <= r26776904;
        double r26776906 = 1.1730839583412028e+147;
        bool r26776907 = r26776893 <= r26776906;
        double r26776908 = r26776907 ? r26776903 : r26776898;
        double r26776909 = r26776905 ? r26776898 : r26776908;
        double r26776910 = r26776900 ? r26776903 : r26776909;
        double r26776911 = r26776895 ? r26776898 : r26776910;
        return r26776911;
}

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

Original6.1
Target5.4
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -6.939593118092855e+188 or -1.454055052210347e-302 < (* x y) < 1.8266963535821708e-240 or 1.1730839583412028e+147 < (* x y)

    1. Initial program 17.1

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity17.1

      \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot z}}\]

    4. Applied times-frac0.9

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{z}}\]

    5. Simplified0.9

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

    if -6.939593118092855e+188 < (* x y) < -1.454055052210347e-302 or 1.8266963535821708e-240 < (* x y) < 1.1730839583412028e+147

    1. Initial program 0.2

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied clear-num0.6

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -6.939593118092855 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -1.454055052210347 \cdot 10^{-302}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \le 1.8266963535821708 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.1730839583412028 \cdot 10^{+147}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))