Average Error: 6.3 → 0.8
Time: 1.9s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -2.666618308604909 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.291536027190061 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 2.0802670635728964 \cdot 10^{198}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y = -\infty:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le -2.666618308604909 \cdot 10^{-248}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 1.291536027190061 \cdot 10^{-88}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le 2.0802670635728964 \cdot 10^{198}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r850982 = x;
        double r850983 = y;
        double r850984 = r850982 * r850983;
        double r850985 = z;
        double r850986 = r850984 / r850985;
        return r850986;
}
↓
double f(double x, double y, double z) {
        double r850987 = x;
        double r850988 = y;
        double r850989 = r850987 * r850988;
        double r850990 = -inf.0;
        bool r850991 = r850989 <= r850990;
        double r850992 = z;
        double r850993 = r850992 / r850988;
        double r850994 = r850987 / r850993;
        double r850995 = -2.666618308604909e-248;
        bool r850996 = r850989 <= r850995;
        double r850997 = r850989 / r850992;
        double r850998 = 1.291536027190061e-88;
        bool r850999 = r850989 <= r850998;
        double r851000 = r850988 / r850992;
        double r851001 = r850987 * r851000;
        double r851002 = 2.0802670635728964e+198;
        bool r851003 = r850989 <= r851002;
        double r851004 = r850987 / r850992;
        double r851005 = r851004 * r850988;
        double r851006 = r851003 ? r850997 : r851005;
        double r851007 = r850999 ? r851001 : r851006;
        double r851008 = r850996 ? r850997 : r851007;
        double r851009 = r850991 ? r850994 : r851008;
        return r851009;
}

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

Original6.3
Target6.0
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (* x y) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.3

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

    if -inf.0 < (* x y) < -2.666618308604909e-248 or 1.291536027190061e-88 < (* x y) < 2.0802670635728964e+198

    1. Initial program 0.2

      \[\frac{x \cdot y}{z}\]

    if -2.666618308604909e-248 < (* x y) < 1.291536027190061e-88

    1. Initial program 8.6

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

    3. Applied *-un-lft-identity8.6

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

    4. Applied times-frac1.6

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

    5. Simplified1.6

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

    if 2.0802670635728964e+198 < (* x y)

    1. Initial program 28.2

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

    3. Applied associate-/l*1.3

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

    5. Applied associate-/r/1.2

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -2.666618308604909 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.291536027190061 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 2.0802670635728964 \cdot 10^{198}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

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

  (/ (* x y) z))