Average Error: 6.0 → 0.8
Time: 2.9s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -5.2328744243323012 \cdot 10^{278}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -1.5805766248223962 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 5.43472 \cdot 10^{-323}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 3.6477517440137462 \cdot 10^{127}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -5.2328744243323012 \cdot 10^{278}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le -1.5805766248223962 \cdot 10^{-144}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 5.43472 \cdot 10^{-323}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le 3.6477517440137462 \cdot 10^{127}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r703631 = x;
        double r703632 = y;
        double r703633 = r703631 * r703632;
        double r703634 = z;
        double r703635 = r703633 / r703634;
        return r703635;
}
↓
double f(double x, double y, double z) {
        double r703636 = x;
        double r703637 = y;
        double r703638 = r703636 * r703637;
        double r703639 = -5.232874424332301e+278;
        bool r703640 = r703638 <= r703639;
        double r703641 = z;
        double r703642 = r703637 / r703641;
        double r703643 = r703636 * r703642;
        double r703644 = -1.5805766248223962e-144;
        bool r703645 = r703638 <= r703644;
        double r703646 = r703638 / r703641;
        double r703647 = 5.4347221042537e-323;
        bool r703648 = r703638 <= r703647;
        double r703649 = r703641 / r703637;
        double r703650 = r703636 / r703649;
        double r703651 = 3.647751744013746e+127;
        bool r703652 = r703638 <= r703651;
        double r703653 = r703652 ? r703646 : r703643;
        double r703654 = r703648 ? r703650 : r703653;
        double r703655 = r703645 ? r703646 : r703654;
        double r703656 = r703640 ? r703643 : r703655;
        return r703656;
}

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
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -5.232874424332301e+278 or 3.647751744013746e+127 < (* x y)

    1. Initial program 22.0

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

    3. Applied *-un-lft-identity22.0

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

    4. Applied times-frac2.9

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

    5. Simplified2.9

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

    if -5.232874424332301e+278 < (* x y) < -1.5805766248223962e-144 or 5.4347221042537e-323 < (* x y) < 3.647751744013746e+127

    1. Initial program 0.3

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

    if -1.5805766248223962e-144 < (* x y) < 5.4347221042537e-323

    1. Initial program 11.1

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

    3. Applied associate-/l*1.0

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -5.2328744243323012 \cdot 10^{278}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -1.5805766248223962 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 5.43472 \cdot 10^{-323}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 3.6477517440137462 \cdot 10^{127}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))