\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -3.239102902922398389619014729318862756466 \cdot 10^{124}:\\ \;\;\;\;\left|\mathsf{fma}\left(\frac{x}{y}, -z, \frac{4}{y} + \frac{x}{y}\right)\right|\\ \mathbf{elif}\;x \le 1.554015068869189362092407590282578679209 \cdot 10^{-127}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|

↓

\begin{array}{l}
\mathbf{if}\;x \le -3.239102902922398389619014729318862756466 \cdot 10^{124}:\\
\;\;\;\;\left|\mathsf{fma}\left(\frac{x}{y}, -z, \frac{4}{y} + \frac{x}{y}\right)\right|\\

\mathbf{elif}\;x \le 1.554015068869189362092407590282578679209 \cdot 10^{-127}:\\
\;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\

\mathbf{else}:\\
\;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\

\end{array}

double f(double x, double y, double z) {
        double r2956912 = x;
        double r2956913 = 4.0;
        double r2956914 = r2956912 + r2956913;
        double r2956915 = y;
        double r2956916 = r2956914 / r2956915;
        double r2956917 = r2956912 / r2956915;
        double r2956918 = z;
        double r2956919 = r2956917 * r2956918;
        double r2956920 = r2956916 - r2956919;
        double r2956921 = fabs(r2956920);
        return r2956921;
}

↓

double f(double x, double y, double z) {
        double r2956922 = x;
        double r2956923 = -3.2391029029223984e+124;
        bool r2956924 = r2956922 <= r2956923;
        double r2956925 = y;
        double r2956926 = r2956922 / r2956925;
        double r2956927 = z;
        double r2956928 = -r2956927;
        double r2956929 = 4.0;
        double r2956930 = r2956929 / r2956925;
        double r2956931 = r2956930 + r2956926;
        double r2956932 = fma(r2956926, r2956928, r2956931);
        double r2956933 = fabs(r2956932);
        double r2956934 = 1.5540150688691894e-127;
        bool r2956935 = r2956922 <= r2956934;
        double r2956936 = r2956922 + r2956929;
        double r2956937 = r2956922 * r2956927;
        double r2956938 = r2956936 - r2956937;
        double r2956939 = r2956938 / r2956925;
        double r2956940 = fabs(r2956939);
        double r2956941 = r2956936 / r2956925;
        double r2956942 = r2956927 / r2956925;
        double r2956943 = r2956922 * r2956942;
        double r2956944 = r2956941 - r2956943;
        double r2956945 = fabs(r2956944);
        double r2956946 = r2956935 ? r2956940 : r2956945;
        double r2956947 = r2956924 ? r2956933 : r2956946;
        return r2956947;
}

Derivation

Split input into 3 regimes
if x < -3.2391029029223984e+124
1. Initial program 0.1
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied associate-*l/13.4
  \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]
4. Applied sub-div13.4
  \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
5. Taylor expanded around 0 13.4
  \[\leadsto \left|\color{blue}{\left(\frac{x}{y} + 4 \cdot \frac{1}{y}\right) - \frac{x \cdot z}{y}}\right|\]
6. Simplified0.1
  \[\leadsto \left|\color{blue}{\mathsf{fma}\left(\frac{x}{y}, -z, \frac{4}{y} + \frac{x}{y}\right)}\right|\]
if -3.2391029029223984e+124 < x < 1.5540150688691894e-127
1. Initial program 2.3
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied associate-*l/0.7
  \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]
4. Applied sub-div0.7
  \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
if 1.5540150688691894e-127 < x
1. Initial program 1.1
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied div-inv1.1
  \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot z\right|\]
4. Applied associate-*l*1.6
  \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \left(\frac{1}{y} \cdot z\right)}\right|\]
5. Simplified1.6
  \[\leadsto \left|\frac{x + 4}{y} - x \cdot \color{blue}{\frac{z}{y}}\right|\]
Recombined 3 regimes into one program.
Final simplification0.9
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.239102902922398389619014729318862756466 \cdot 10^{124}:\\ \;\;\;\;\left|\mathsf{fma}\left(\frac{x}{y}, -z, \frac{4}{y} + \frac{x}{y}\right)\right|\\ \mathbf{elif}\;x \le 1.554015068869189362092407590282578679209 \cdot 10^{-127}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

Error

Derivation

`if x < -3.2391029029223984e+124`

`if -3.2391029029223984e+124 < x < 1.5540150688691894e-127`

`if 1.5540150688691894e-127 < x`

Reproduce