Average Error: 6.3 → 2.0
Time: 7.8s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -3.452448754215592666401325047530086075569 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le -0.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 1.395820271589989163064226214695740260426 \cdot 10^{278}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -3.452448754215592666401325047530086075569 \cdot 10^{-299}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le -0.0:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le 1.395820271589989163064226214695740260426 \cdot 10^{278}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r482790 = x;
        double r482791 = y;
        double r482792 = r482790 * r482791;
        double r482793 = z;
        double r482794 = r482792 / r482793;
        return r482794;
}
↓
double f(double x, double y, double z) {
        double r482795 = x;
        double r482796 = y;
        double r482797 = r482795 * r482796;
        double r482798 = -3.4524487542155927e-299;
        bool r482799 = r482797 <= r482798;
        double r482800 = z;
        double r482801 = r482797 / r482800;
        double r482802 = -0.0;
        bool r482803 = r482797 <= r482802;
        double r482804 = r482800 / r482796;
        double r482805 = r482795 / r482804;
        double r482806 = 1.3958202715899892e+278;
        bool r482807 = r482797 <= r482806;
        double r482808 = r482796 / r482800;
        double r482809 = r482795 * r482808;
        double r482810 = r482807 ? r482801 : r482809;
        double r482811 = r482803 ? r482805 : r482810;
        double r482812 = r482799 ? r482801 : r482811;
        return r482812;
}

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
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -3.4524487542155927e-299 or -0.0 < (* x y) < 1.3958202715899892e+278

    1. Initial program 3.8

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

    if -3.4524487542155927e-299 < (* x y) < -0.0

    1. Initial program 16.8

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

    3. Applied associate-/l*0.1

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

    if 1.3958202715899892e+278 < (* x y)

    1. Initial program 48.8

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

    3. Applied *-un-lft-identity48.8

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -3.452448754215592666401325047530086075569 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le -0.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 1.395820271589989163064226214695740260426 \cdot 10^{278}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(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 1.70421306606504721e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))