Average Error: 10.1 → 0.4
Time: 7.5s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.659244719723380893322790679238792235926 \cdot 10^{73}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;x \le 2.380298721942920237570399274099843251842 \cdot 10^{69}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1 + y}{z} - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.659244719723380893322790679238792235926 \cdot 10^{73}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{elif}\;x \le 2.380298721942920237570399274099843251842 \cdot 10^{69}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{1 + y}{z} - x\\

\end{array}
double f(double x, double y, double z) {
        double r428023 = x;
        double r428024 = y;
        double r428025 = z;
        double r428026 = r428024 - r428025;
        double r428027 = 1.0;
        double r428028 = r428026 + r428027;
        double r428029 = r428023 * r428028;
        double r428030 = r428029 / r428025;
        return r428030;
}
↓
double f(double x, double y, double z) {
        double r428031 = x;
        double r428032 = -1.659244719723381e+73;
        bool r428033 = r428031 <= r428032;
        double r428034 = z;
        double r428035 = y;
        double r428036 = r428035 - r428034;
        double r428037 = 1.0;
        double r428038 = r428036 + r428037;
        double r428039 = r428034 / r428038;
        double r428040 = r428031 / r428039;
        double r428041 = 2.3802987219429202e+69;
        bool r428042 = r428031 <= r428041;
        double r428043 = r428031 * r428035;
        double r428044 = r428043 / r428034;
        double r428045 = r428031 / r428034;
        double r428046 = r428037 * r428045;
        double r428047 = r428044 + r428046;
        double r428048 = r428047 - r428031;
        double r428049 = r428037 + r428035;
        double r428050 = r428049 / r428034;
        double r428051 = r428031 * r428050;
        double r428052 = r428051 - r428031;
        double r428053 = r428042 ? r428048 : r428052;
        double r428054 = r428033 ? r428040 : r428053;
        return r428054;
}

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

Original10.1
Target0.5
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.659244719723381e+73

    1. Initial program 33.3

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

    3. Applied associate-/l*0.1

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

    if -1.659244719723381e+73 < x < 2.3802987219429202e+69

    1. Initial program 1.2

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

    2. Taylor expanded around 0 0.5

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

    if 2.3802987219429202e+69 < x

    1. Initial program 34.1

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

    2. Taylor expanded around 0 10.8

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

    3. Taylor expanded around 0 10.8

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

    4. Simplified0.1

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

    6. Applied div-inv0.1

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

    7. Applied associate-*l*0.1

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

    8. Simplified0.1

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.659244719723380893322790679238792235926 \cdot 10^{73}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;x \le 2.380298721942920237570399274099843251842 \cdot 10^{69}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1 + y}{z} - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.7148310671343599e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.87410881643954616e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

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