Average Error: 8.7 → 0.2
Time: 7.2s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.632921685862537 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\ \mathbf{elif}\;x \le 2472351452.7513905:\\ \;\;\;\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.632921685862537 \cdot 10^{-81}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\

\mathbf{elif}\;x \le 2472351452.7513905:\\
\;\;\;\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\

\end{array}
double f(double x, double y, double z) {
        double r11757560 = x;
        double r11757561 = y;
        double r11757562 = z;
        double r11757563 = r11757561 - r11757562;
        double r11757564 = 1.0;
        double r11757565 = r11757563 + r11757564;
        double r11757566 = r11757560 * r11757565;
        double r11757567 = r11757566 / r11757562;
        return r11757567;
}
↓
double f(double x, double y, double z) {
        double r11757568 = x;
        double r11757569 = -3.632921685862537e-81;
        bool r11757570 = r11757568 <= r11757569;
        double r11757571 = z;
        double r11757572 = y;
        double r11757573 = r11757572 - r11757571;
        double r11757574 = 1.0;
        double r11757575 = r11757573 + r11757574;
        double r11757576 = r11757571 / r11757575;
        double r11757577 = r11757568 / r11757576;
        double r11757578 = 2472351452.7513905;
        bool r11757579 = r11757568 <= r11757578;
        double r11757580 = r11757575 * r11757568;
        double r11757581 = r11757580 / r11757571;
        double r11757582 = r11757579 ? r11757581 : r11757577;
        double r11757583 = r11757570 ? r11757577 : r11757582;
        return r11757583;
}

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

Original8.7
Target0.5
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1.0\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -3.632921685862537e-81 or 2472351452.7513905 < x

    1. Initial program 19.4

      \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.3

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}}\]

    if -3.632921685862537e-81 < x < 2472351452.7513905

    1. Initial program 0.2

      \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.632921685862537 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\ \mathbf{elif}\;x \le 2472351452.7513905:\\ \;\;\;\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))