Average Error: 6.0 → 0.5
Time: 8.9s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.871003352164139 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -9.609520285206618 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.7178429536978092 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 3.3882771524409995 \cdot 10^{+143}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -1.871003352164139 \cdot 10^{+282}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le -9.609520285206618 \cdot 10^{-248}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 1.7178429536978092 \cdot 10^{-196}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;x \cdot y \le 3.3882771524409995 \cdot 10^{+143}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r32855861 = x;
        double r32855862 = y;
        double r32855863 = r32855861 * r32855862;
        double r32855864 = z;
        double r32855865 = r32855863 / r32855864;
        return r32855865;
}
↓
double f(double x, double y, double z) {
        double r32855866 = x;
        double r32855867 = y;
        double r32855868 = r32855866 * r32855867;
        double r32855869 = -1.871003352164139e+282;
        bool r32855870 = r32855868 <= r32855869;
        double r32855871 = z;
        double r32855872 = r32855871 / r32855867;
        double r32855873 = r32855866 / r32855872;
        double r32855874 = -9.609520285206618e-248;
        bool r32855875 = r32855868 <= r32855874;
        double r32855876 = r32855868 / r32855871;
        double r32855877 = 1.7178429536978092e-196;
        bool r32855878 = r32855868 <= r32855877;
        double r32855879 = r32855867 / r32855871;
        double r32855880 = r32855879 * r32855866;
        double r32855881 = 3.3882771524409995e+143;
        bool r32855882 = r32855868 <= r32855881;
        double r32855883 = r32855882 ? r32855876 : r32855880;
        double r32855884 = r32855878 ? r32855880 : r32855883;
        double r32855885 = r32855875 ? r32855876 : r32855884;
        double r32855886 = r32855870 ? r32855873 : r32855885;
        return r32855886;
}

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

Original6.0
Target6.1
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -1.871003352164139e+282

    1. Initial program 51.5

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

    3. Applied associate-/l*0.3

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

    if -1.871003352164139e+282 < (* x y) < -9.609520285206618e-248 or 1.7178429536978092e-196 < (* x y) < 3.3882771524409995e+143

    1. Initial program 0.2

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

    if -9.609520285206618e-248 < (* x y) < 1.7178429536978092e-196 or 3.3882771524409995e+143 < (* x y)

    1. Initial program 13.0

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

    3. Applied *-un-lft-identity13.0

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

    4. Applied times-frac1.0

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

    5. Simplified1.0

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -1.871003352164139 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -9.609520285206618 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.7178429536978092 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 3.3882771524409995 \cdot 10^{+143}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(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))