Average Error: 6.2 → 0.5
Time: 25.2s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.871003352164138983509669622339238961491 \cdot 10^{282}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -9.609520285206617620294914143781194869795 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.717842953697809163237341802420612798171 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 3.388277152440999464105996490605589103728 \cdot 10^{143}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -1.871003352164138983509669622339238961491 \cdot 10^{282}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le -9.609520285206617620294914143781194869795 \cdot 10^{-248}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 1.717842953697809163237341802420612798171 \cdot 10^{-196}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;x \cdot y \le 3.388277152440999464105996490605589103728 \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 r34048652 = x;
        double r34048653 = y;
        double r34048654 = r34048652 * r34048653;
        double r34048655 = z;
        double r34048656 = r34048654 / r34048655;
        return r34048656;
}
↓
double f(double x, double y, double z) {
        double r34048657 = x;
        double r34048658 = y;
        double r34048659 = r34048657 * r34048658;
        double r34048660 = -1.871003352164139e+282;
        bool r34048661 = r34048659 <= r34048660;
        double r34048662 = z;
        double r34048663 = r34048662 / r34048658;
        double r34048664 = r34048657 / r34048663;
        double r34048665 = -9.609520285206618e-248;
        bool r34048666 = r34048659 <= r34048665;
        double r34048667 = r34048659 / r34048662;
        double r34048668 = 1.7178429536978092e-196;
        bool r34048669 = r34048659 <= r34048668;
        double r34048670 = r34048658 / r34048662;
        double r34048671 = r34048670 * r34048657;
        double r34048672 = 3.3882771524409995e+143;
        bool r34048673 = r34048659 <= r34048672;
        double r34048674 = r34048673 ? r34048667 : r34048671;
        double r34048675 = r34048669 ? r34048671 : r34048674;
        double r34048676 = r34048666 ? r34048667 : r34048675;
        double r34048677 = r34048661 ? r34048664 : r34048676;
        return r34048677;
}

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

Original6.2
Target6.4
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

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

    1. Initial program 54.8

      \[\frac{x \cdot y}{z}\]
    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 13.3

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

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

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

    4. Applied times-frac1.1

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

    5. Simplified1.1

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -1.871003352164138983509669622339238961491 \cdot 10^{282}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -9.609520285206617620294914143781194869795 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.717842953697809163237341802420612798171 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 3.388277152440999464105996490605589103728 \cdot 10^{143}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 +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))