Average Error: 6.0 → 0.4
Time: 10.4s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -2.166521247594354925726439343625696917212 \cdot 10^{205}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -1.343713460892298755823259752013121029537 \cdot 10^{-191}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 4.152478566064296352109998791440075706057 \cdot 10^{-204}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 9.404611212472955651642851083785275703569 \cdot 10^{253}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -2.166521247594354925726439343625696917212 \cdot 10^{205}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le -1.343713460892298755823259752013121029537 \cdot 10^{-191}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 4.152478566064296352109998791440075706057 \cdot 10^{-204}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;x \cdot y \le 9.404611212472955651642851083785275703569 \cdot 10^{253}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r37209741 = x;
        double r37209742 = y;
        double r37209743 = r37209741 * r37209742;
        double r37209744 = z;
        double r37209745 = r37209743 / r37209744;
        return r37209745;
}
↓
double f(double x, double y, double z) {
        double r37209746 = x;
        double r37209747 = y;
        double r37209748 = r37209746 * r37209747;
        double r37209749 = -2.166521247594355e+205;
        bool r37209750 = r37209748 <= r37209749;
        double r37209751 = z;
        double r37209752 = r37209751 / r37209747;
        double r37209753 = r37209746 / r37209752;
        double r37209754 = -1.3437134608922988e-191;
        bool r37209755 = r37209748 <= r37209754;
        double r37209756 = r37209748 / r37209751;
        double r37209757 = 4.152478566064296e-204;
        bool r37209758 = r37209748 <= r37209757;
        double r37209759 = r37209747 / r37209751;
        double r37209760 = r37209759 * r37209746;
        double r37209761 = 9.404611212472956e+253;
        bool r37209762 = r37209748 <= r37209761;
        double r37209763 = r37209762 ? r37209756 : r37209760;
        double r37209764 = r37209758 ? r37209760 : r37209763;
        double r37209765 = r37209755 ? r37209756 : r37209764;
        double r37209766 = r37209750 ? r37209753 : r37209765;
        return r37209766;
}

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
Target6.2
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -2.166521247594355e+205

    1. Initial program 27.2

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

    3. Applied associate-/l*1.5

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

    if -2.166521247594355e+205 < (* x y) < -1.3437134608922988e-191 or 4.152478566064296e-204 < (* x y) < 9.404611212472956e+253

    1. Initial program 0.2

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

    if -1.3437134608922988e-191 < (* x y) < 4.152478566064296e-204 or 9.404611212472956e+253 < (* x y)

    1. Initial program 13.8

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

    3. Applied *-un-lft-identity13.8

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

    4. Applied times-frac0.5

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

    5. Simplified0.5

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -2.166521247594354925726439343625696917212 \cdot 10^{205}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -1.343713460892298755823259752013121029537 \cdot 10^{-191}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 4.152478566064296352109998791440075706057 \cdot 10^{-204}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 9.404611212472955651642851083785275703569 \cdot 10^{253}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(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))