Average Error: 5.8 → 0.7
Time: 5.7s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} \le -5.553987680801805 \cdot 10^{+297}:\\ \;\;\;\;\frac{1}{\frac{z}{y} \cdot \frac{1}{x}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -1.5715132944212088 \cdot 10^{-279}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -0.0:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 3.281625238257663 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot y}{z} \le -5.553987680801805 \cdot 10^{+297}:\\
\;\;\;\;\frac{1}{\frac{z}{y} \cdot \frac{1}{x}}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le -1.5715132944212088 \cdot 10^{-279}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\mathbf{elif}\;\frac{x \cdot y}{z} \le 3.281625238257663 \cdot 10^{+306}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r13036755 = x;
        double r13036756 = y;
        double r13036757 = r13036755 * r13036756;
        double r13036758 = z;
        double r13036759 = r13036757 / r13036758;
        return r13036759;
}
↓
double f(double x, double y, double z) {
        double r13036760 = x;
        double r13036761 = y;
        double r13036762 = r13036760 * r13036761;
        double r13036763 = z;
        double r13036764 = r13036762 / r13036763;
        double r13036765 = -5.553987680801805e+297;
        bool r13036766 = r13036764 <= r13036765;
        double r13036767 = 1.0;
        double r13036768 = r13036763 / r13036761;
        double r13036769 = r13036767 / r13036760;
        double r13036770 = r13036768 * r13036769;
        double r13036771 = r13036767 / r13036770;
        double r13036772 = -1.5715132944212088e-279;
        bool r13036773 = r13036764 <= r13036772;
        double r13036774 = -0.0;
        bool r13036775 = r13036764 <= r13036774;
        double r13036776 = r13036761 / r13036763;
        double r13036777 = r13036760 * r13036776;
        double r13036778 = 3.281625238257663e+306;
        bool r13036779 = r13036764 <= r13036778;
        double r13036780 = r13036779 ? r13036764 : r13036777;
        double r13036781 = r13036775 ? r13036777 : r13036780;
        double r13036782 = r13036773 ? r13036764 : r13036781;
        double r13036783 = r13036766 ? r13036771 : r13036782;
        return r13036783;
}

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

Original5.8
Target6.0
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 3 regimes

  2. if (/ (* x y) z) < -5.553987680801805e+297

    1. Initial program 52.4

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

    3. Applied clear-num52.4

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity52.4

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

    6. Applied times-frac2.5

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

    if -5.553987680801805e+297 < (/ (* x y) z) < -1.5715132944212088e-279 or -0.0 < (/ (* x y) z) < 3.281625238257663e+306

    1. Initial program 0.5

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

    if -1.5715132944212088e-279 < (/ (* x y) z) < -0.0 or 3.281625238257663e+306 < (/ (* x y) z)

    1. Initial program 14.5

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

    3. Applied *-un-lft-identity14.5

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

    4. Applied times-frac1.2

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

    5. Simplified1.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} \le -5.553987680801805 \cdot 10^{+297}:\\ \;\;\;\;\frac{1}{\frac{z}{y} \cdot \frac{1}{x}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -1.5715132944212088 \cdot 10^{-279}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -0.0:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 3.281625238257663 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 +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))