Average Error: 10.5 → 0.3
Time: 2.8s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.61943798913748523 \cdot 10^{55}:\\ \;\;\;\;\frac{x}{\frac{1}{\frac{\left(y - z\right) + 1}{z}}}\\ \mathbf{elif}\;z \le 2.2731223542198846 \cdot 10^{49}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.61943798913748523 \cdot 10^{55}:\\
\;\;\;\;\frac{x}{\frac{1}{\frac{\left(y - z\right) + 1}{z}}}\\

\mathbf{elif}\;z \le 2.2731223542198846 \cdot 10^{49}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\

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

\end{array}
double f(double x, double y, double z) {
        double r673707 = x;
        double r673708 = y;
        double r673709 = z;
        double r673710 = r673708 - r673709;
        double r673711 = 1.0;
        double r673712 = r673710 + r673711;
        double r673713 = r673707 * r673712;
        double r673714 = r673713 / r673709;
        return r673714;
}
↓
double f(double x, double y, double z) {
        double r673715 = z;
        double r673716 = -2.619437989137485e+55;
        bool r673717 = r673715 <= r673716;
        double r673718 = x;
        double r673719 = 1.0;
        double r673720 = y;
        double r673721 = r673720 - r673715;
        double r673722 = 1.0;
        double r673723 = r673721 + r673722;
        double r673724 = r673723 / r673715;
        double r673725 = r673719 / r673724;
        double r673726 = r673718 / r673725;
        double r673727 = 2.2731223542198846e+49;
        bool r673728 = r673715 <= r673727;
        double r673729 = r673718 * r673720;
        double r673730 = r673729 / r673715;
        double r673731 = r673718 / r673715;
        double r673732 = r673722 * r673731;
        double r673733 = r673730 + r673732;
        double r673734 = r673733 - r673718;
        double r673735 = r673715 / r673723;
        double r673736 = r673718 / r673735;
        double r673737 = r673728 ? r673734 : r673736;
        double r673738 = r673717 ? r673726 : r673737;
        return r673738;
}

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

Original10.5
Target0.5
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -2.619437989137485e+55

    1. Initial program 20.9

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    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 clear-num0.1

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

    if -2.619437989137485e+55 < z < 2.2731223542198846e+49

    1. Initial program 0.8

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

    2. Taylor expanded around 0 0.5

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

    if 2.2731223542198846e+49 < z

    1. Initial program 18.2

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

    3. Applied associate-/l*0.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.61943798913748523 \cdot 10^{55}:\\ \;\;\;\;\frac{x}{\frac{1}{\frac{\left(y - z\right) + 1}{z}}}\\ \mathbf{elif}\;z \le 2.2731223542198846 \cdot 10^{49}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 
(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))