Average Error: 12.3 → 2.6
Time: 13.7s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 1.3817440569525898 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;x \le 4.0099369996684946 \cdot 10^{-103}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le 1.3817440569525898 \cdot 10^{-289}:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;x \le 4.0099369996684946 \cdot 10^{-103}:\\
\;\;\;\;x - \frac{z \cdot x}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r35586672 = x;
        double r35586673 = y;
        double r35586674 = z;
        double r35586675 = r35586673 - r35586674;
        double r35586676 = r35586672 * r35586675;
        double r35586677 = r35586676 / r35586673;
        return r35586677;
}
↓
double f(double x, double y, double z) {
        double r35586678 = x;
        double r35586679 = 1.3817440569525898e-289;
        bool r35586680 = r35586678 <= r35586679;
        double r35586681 = y;
        double r35586682 = z;
        double r35586683 = r35586681 - r35586682;
        double r35586684 = r35586683 / r35586681;
        double r35586685 = r35586678 * r35586684;
        double r35586686 = 4.0099369996684946e-103;
        bool r35586687 = r35586678 <= r35586686;
        double r35586688 = r35586682 * r35586678;
        double r35586689 = r35586688 / r35586681;
        double r35586690 = r35586678 - r35586689;
        double r35586691 = r35586687 ? r35586690 : r35586685;
        double r35586692 = r35586680 ? r35586685 : r35586691;
        return r35586692;
}

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

Original12.3
Target2.8
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 1.3817440569525898e-289 or 4.0099369996684946e-103 < x

    1. Initial program 13.5

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

    3. Applied *-un-lft-identity13.5

      \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{1 \cdot y}}\]

    4. Applied times-frac2.4

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

    5. Simplified2.4

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

    if 1.3817440569525898e-289 < x < 4.0099369996684946e-103

    1. Initial program 6.2

      \[\frac{x \cdot \left(y - z\right)}{y}\]

    2. Taylor expanded around 0 3.4

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 1.3817440569525898 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;x \le 4.0099369996684946 \cdot 10^{-103}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(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))