Average Error: 9.8 → 0.1
Time: 3.5s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.255498797056056848092969270439685610774 \cdot 10^{-31} \lor \neg \left(x \le 18356449162475356553216\right):\\ \;\;\;\;\frac{x}{\frac{-z}{-\left(\left(y - z\right) + 1\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.255498797056056848092969270439685610774 \cdot 10^{-31} \lor \neg \left(x \le 18356449162475356553216\right):\\
\;\;\;\;\frac{x}{\frac{-z}{-\left(\left(y - z\right) + 1\right)}}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\

\end{array}
double f(double x, double y, double z) {
        double r716747 = x;
        double r716748 = y;
        double r716749 = z;
        double r716750 = r716748 - r716749;
        double r716751 = 1.0;
        double r716752 = r716750 + r716751;
        double r716753 = r716747 * r716752;
        double r716754 = r716753 / r716749;
        return r716754;
}
↓
double f(double x, double y, double z) {
        double r716755 = x;
        double r716756 = -1.2554987970560568e-31;
        bool r716757 = r716755 <= r716756;
        double r716758 = 1.8356449162475357e+22;
        bool r716759 = r716755 <= r716758;
        double r716760 = !r716759;
        bool r716761 = r716757 || r716760;
        double r716762 = z;
        double r716763 = -r716762;
        double r716764 = y;
        double r716765 = r716764 - r716762;
        double r716766 = 1.0;
        double r716767 = r716765 + r716766;
        double r716768 = -r716767;
        double r716769 = r716763 / r716768;
        double r716770 = r716755 / r716769;
        double r716771 = r716755 * r716764;
        double r716772 = r716771 / r716762;
        double r716773 = r716755 / r716762;
        double r716774 = r716766 * r716773;
        double r716775 = r716772 + r716774;
        double r716776 = r716775 - r716755;
        double r716777 = r716761 ? r716770 : r716776;
        return r716777;
}

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

Original9.8
Target0.5
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.2554987970560568e-31 or 1.8356449162475357e+22 < x

    1. Initial program 24.1

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.1

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
    4. Using strategy rm

    5. Applied frac-2neg0.1

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

    if -1.2554987970560568e-31 < x < 1.8356449162475357e+22

    1. Initial program 0.2

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*5.5

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

    4. Taylor expanded around 0 0.1

      \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.255498797056056848092969270439685610774 \cdot 10^{-31} \lor \neg \left(x \le 18356449162475356553216\right):\\ \;\;\;\;\frac{x}{\frac{-z}{-\left(\left(y - z\right) + 1\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019356 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1)) z))