Average Error: 12.9 → 3.0
Time: 23.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 2.671134861887030249556007998877586662964 \cdot 10^{144}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le 2.671134861887030249556007998877586662964 \cdot 10^{144}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\

\end{array}
double f(double x, double y, double z) {
        double r95609633 = x;
        double r95609634 = y;
        double r95609635 = z;
        double r95609636 = r95609634 - r95609635;
        double r95609637 = r95609633 * r95609636;
        double r95609638 = r95609637 / r95609634;
        return r95609638;
}
↓
double f(double x, double y, double z) {
        double r95609639 = z;
        double r95609640 = 2.6711348618870302e+144;
        bool r95609641 = r95609639 <= r95609640;
        double r95609642 = x;
        double r95609643 = y;
        double r95609644 = r95609643 - r95609639;
        double r95609645 = r95609643 / r95609644;
        double r95609646 = r95609642 / r95609645;
        double r95609647 = r95609642 / r95609643;
        double r95609648 = r95609647 * r95609644;
        double r95609649 = r95609641 ? r95609646 : r95609648;
        return r95609649;
}

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

Original12.9
Target3.3
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < 2.6711348618870302e+144

    1. Initial program 13.0

      \[\frac{x \cdot \left(y - z\right)}{y}\]
    2. Using strategy rm

    3. Applied associate-/l*2.1

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

    if 2.6711348618870302e+144 < z

    1. Initial program 12.3

      \[\frac{x \cdot \left(y - z\right)}{y}\]
    2. Using strategy rm

    3. Applied associate-/l*12.1

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

    5. Applied associate-/r/11.9

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 2.671134861887030249556007998877586662964 \cdot 10^{144}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))