Average Error: 6.5 → 0.6
Time: 16.5s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.827618842210325856116378407212167275336 \cdot 10^{252}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;x \cdot y \le -1.416922114786241732626195364860208906831 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.654394754607905895780595947422963951718 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 1.866392507649868309583567517907241893789 \cdot 10^{207}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -1.827618842210325856116378407212167275336 \cdot 10^{252}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;x \cdot y \le -1.416922114786241732626195364860208906831 \cdot 10^{-291}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 1.654394754607905895780595947422963951718 \cdot 10^{-114}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le 1.866392507649868309583567517907241893789 \cdot 10^{207}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r195701973 = x;
        double r195701974 = y;
        double r195701975 = r195701973 * r195701974;
        double r195701976 = z;
        double r195701977 = r195701975 / r195701976;
        return r195701977;
}
↓
double f(double x, double y, double z) {
        double r195701978 = x;
        double r195701979 = y;
        double r195701980 = r195701978 * r195701979;
        double r195701981 = -1.8276188422103259e+252;
        bool r195701982 = r195701980 <= r195701981;
        double r195701983 = z;
        double r195701984 = r195701978 / r195701983;
        double r195701985 = r195701984 * r195701979;
        double r195701986 = -1.4169221147862417e-291;
        bool r195701987 = r195701980 <= r195701986;
        double r195701988 = r195701980 / r195701983;
        double r195701989 = 1.654394754607906e-114;
        bool r195701990 = r195701980 <= r195701989;
        double r195701991 = r195701983 / r195701979;
        double r195701992 = r195701978 / r195701991;
        double r195701993 = 1.8663925076498683e+207;
        bool r195701994 = r195701980 <= r195701993;
        double r195701995 = r195701994 ? r195701988 : r195701992;
        double r195701996 = r195701990 ? r195701992 : r195701995;
        double r195701997 = r195701987 ? r195701988 : r195701996;
        double r195701998 = r195701982 ? r195701985 : r195701997;
        return r195701998;
}

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

Original6.5
Target6.3
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -1.8276188422103259e+252

    1. Initial program 40.2

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

    3. Applied associate-/l*0.3

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

    5. Applied associate-/r/0.2

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

    if -1.8276188422103259e+252 < (* x y) < -1.4169221147862417e-291 or 1.654394754607906e-114 < (* x y) < 1.8663925076498683e+207

    1. Initial program 0.2

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

    if -1.4169221147862417e-291 < (* x y) < 1.654394754607906e-114 or 1.8663925076498683e+207 < (* x y)

    1. Initial program 13.9

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

    3. Applied associate-/l*1.2

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -1.827618842210325856116378407212167275336 \cdot 10^{252}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;x \cdot y \le -1.416922114786241732626195364860208906831 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.654394754607905895780595947422963951718 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 1.866392507649868309583567517907241893789 \cdot 10^{207}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(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))