Average Error: 10.5 → 0.3
Time: 19.5s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.054187047083081878059375889087757747407 \cdot 10^{54}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;x \le 1.882285472393660327366431504849834457088 \cdot 10^{-165}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -5.054187047083081878059375889087757747407 \cdot 10^{54}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{elif}\;x \le 1.882285472393660327366431504849834457088 \cdot 10^{-165}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\

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

\end{array}
double f(double x, double y, double z) {
        double r128219999 = x;
        double r128220000 = y;
        double r128220001 = z;
        double r128220002 = r128220000 - r128220001;
        double r128220003 = 1.0;
        double r128220004 = r128220002 + r128220003;
        double r128220005 = r128219999 * r128220004;
        double r128220006 = r128220005 / r128220001;
        return r128220006;
}
↓
double f(double x, double y, double z) {
        double r128220007 = x;
        double r128220008 = -5.054187047083082e+54;
        bool r128220009 = r128220007 <= r128220008;
        double r128220010 = z;
        double r128220011 = y;
        double r128220012 = r128220011 - r128220010;
        double r128220013 = 1.0;
        double r128220014 = r128220012 + r128220013;
        double r128220015 = r128220010 / r128220014;
        double r128220016 = r128220007 / r128220015;
        double r128220017 = 1.8822854723936603e-165;
        bool r128220018 = r128220007 <= r128220017;
        double r128220019 = r128220007 * r128220011;
        double r128220020 = r128220019 / r128220010;
        double r128220021 = r128220007 / r128220010;
        double r128220022 = r128220013 * r128220021;
        double r128220023 = r128220020 + r128220022;
        double r128220024 = r128220023 - r128220007;
        double r128220025 = r128220013 + r128220011;
        double r128220026 = r128220021 * r128220025;
        double r128220027 = r128220026 - r128220007;
        double r128220028 = r128220018 ? r128220024 : r128220027;
        double r128220029 = r128220009 ? r128220016 : r128220028;
        return r128220029;
}

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
Target0.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -5.054187047083082e+54

    1. Initial program 33.6

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

    3. Applied associate-/l*0.1

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

    if -5.054187047083082e+54 < x < 1.8822854723936603e-165

    1. Initial program 0.6

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

    2. Taylor expanded around 0 0.3

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

    if 1.8822854723936603e-165 < x

    1. Initial program 14.5

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

    3. Applied associate-/l*1.5

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

    5. Applied div-inv1.7

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

    6. Simplified1.7

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

    7. Taylor expanded around 0 5.1

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

    8. Simplified0.4

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.054187047083081878059375889087757747407 \cdot 10^{54}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;x \le 1.882285472393660327366431504849834457088 \cdot 10^{-165}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

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

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