Average Error: 12.5 → 2.9
Time: 12.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.36488771348506872 \cdot 10^{-121} \lor \neg \left(y \le 8.4571023597022895 \cdot 10^{-205}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + x \cdot \left(-z\right)}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.36488771348506872 \cdot 10^{-121} \lor \neg \left(y \le 8.4571023597022895 \cdot 10^{-205}\right):\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r525668 = x;
        double r525669 = y;
        double r525670 = z;
        double r525671 = r525669 - r525670;
        double r525672 = r525668 * r525671;
        double r525673 = r525672 / r525669;
        return r525673;
}
↓
double f(double x, double y, double z) {
        double r525674 = y;
        double r525675 = -1.3648877134850687e-121;
        bool r525676 = r525674 <= r525675;
        double r525677 = 8.45710235970229e-205;
        bool r525678 = r525674 <= r525677;
        double r525679 = !r525678;
        bool r525680 = r525676 || r525679;
        double r525681 = x;
        double r525682 = z;
        double r525683 = r525674 - r525682;
        double r525684 = r525683 / r525674;
        double r525685 = r525681 * r525684;
        double r525686 = r525681 * r525674;
        double r525687 = -r525682;
        double r525688 = r525681 * r525687;
        double r525689 = r525686 + r525688;
        double r525690 = r525689 / r525674;
        double r525691 = r525680 ? r525685 : r525690;
        return r525691;
}

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

Original12.5
Target3.1
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.3648877134850687e-121 or 8.45710235970229e-205 < y

    1. Initial program 13.0

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

    3. Applied *-un-lft-identity13.0

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

    4. Applied times-frac1.3

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

    5. Simplified1.3

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

    if -1.3648877134850687e-121 < y < 8.45710235970229e-205

    1. Initial program 10.4

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

    3. Applied sub-neg10.4

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

    4. Applied distribute-lft-in10.4

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

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.36488771348506872 \cdot 10^{-121} \lor \neg \left(y \le 8.4571023597022895 \cdot 10^{-205}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + x \cdot \left(-z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :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))