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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le -6.297922194041028 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, \frac{x}{z} \cdot y\right) - x\\ \mathbf{elif}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le 6.547801510599289 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1.0}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, \frac{x}{z} \cdot y\right) - x\\ \end{array}\]

\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}

↓

\begin{array}{l}
\mathbf{if}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le -6.297922194041028 \cdot 10^{+43}:\\
\;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, \frac{x}{z} \cdot y\right) - x\\

\mathbf{elif}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le 6.547801510599289 \cdot 10^{-77}:\\
\;\;\;\;x \cdot \frac{\left(y - z\right) + 1.0}{z}\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, \frac{x}{z} \cdot y\right) - x\\

\end{array}

double f(double x, double y, double z) {
        double r27297917 = x;
        double r27297918 = y;
        double r27297919 = z;
        double r27297920 = r27297918 - r27297919;
        double r27297921 = 1.0;
        double r27297922 = r27297920 + r27297921;
        double r27297923 = r27297917 * r27297922;
        double r27297924 = r27297923 / r27297919;
        return r27297924;
}

↓

double f(double x, double y, double z) {
        double r27297925 = y;
        double r27297926 = z;
        double r27297927 = r27297925 - r27297926;
        double r27297928 = 1.0;
        double r27297929 = r27297927 + r27297928;
        double r27297930 = x;
        double r27297931 = r27297929 * r27297930;
        double r27297932 = r27297931 / r27297926;
        double r27297933 = -6.297922194041028e+43;
        bool r27297934 = r27297932 <= r27297933;
        double r27297935 = r27297930 / r27297926;
        double r27297936 = r27297935 * r27297925;
        double r27297937 = fma(r27297935, r27297928, r27297936);
        double r27297938 = r27297937 - r27297930;
        double r27297939 = 6.547801510599289e-77;
        bool r27297940 = r27297932 <= r27297939;
        double r27297941 = r27297929 / r27297926;
        double r27297942 = r27297930 * r27297941;
        double r27297943 = r27297940 ? r27297942 : r27297938;
        double r27297944 = r27297934 ? r27297938 : r27297943;
        return r27297944;
}

Original	9.4
Target	0.4
Herbie	0.2

Derivation

Split input into 2 regimes
if (/ (* x (+ (- y z) 1.0)) z) < -6.297922194041028e+43 or 6.547801510599289e-77 < (/ (* x (+ (- y z) 1.0)) z)
1. Initial program 14.7
  \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
2. Taylor expanded around 0 5.0
  \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + 1.0 \cdot \frac{x}{z}\right) - x}\]
3. Simplified0.2
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{z}, 1.0, y \cdot \frac{x}{z}\right) - x}\]
if -6.297922194041028e+43 < (/ (* x (+ (- y z) 1.0)) z) < 6.547801510599289e-77
1. Initial program 0.1
  \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
2. Using strategy rm
3. Applied *-un-lft-identity0.1
  \[\leadsto \frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{\color{blue}{1 \cdot z}}\]
4. Applied times-frac0.3
  \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{\left(y - z\right) + 1.0}{z}}\]
5. Simplified0.3
  \[\leadsto \color{blue}{x} \cdot \frac{\left(y - z\right) + 1.0}{z}\]
Recombined 2 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le -6.297922194041028 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, \frac{x}{z} \cdot y\right) - x\\ \mathbf{elif}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le 6.547801510599289 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1.0}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, \frac{x}{z} \cdot y\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(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))

Error

Target

Derivation

`if (/ (* x (+ (- y z) 1.0)) z) < -6.297922194041028e+43 or 6.547801510599289e-77 < (/ (* x (+ (- y z) 1.0)) z)`

`if -6.297922194041028e+43 < (/ (* x (+ (- y z) 1.0)) z) < 6.547801510599289e-77`

Reproduce