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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -4.6266794377330075 \cdot 10^{-145}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, y \cdot \frac{x}{z}\right) - x\\ \mathbf{elif}\;x \le 1.3597213738421031 \cdot 10^{-288}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x + 1.0 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, y \cdot \frac{x}{z}\right) - x\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -4.6266794377330075 \cdot 10^{-145}:\\
\;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, y \cdot \frac{x}{z}\right) - x\\

\mathbf{elif}\;x \le 1.3597213738421031 \cdot 10^{-288}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x + 1.0 \cdot x}{z}\\

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

\end{array}

double f(double x, double y, double z) {
        double r20379253 = x;
        double r20379254 = y;
        double r20379255 = z;
        double r20379256 = r20379254 - r20379255;
        double r20379257 = 1.0;
        double r20379258 = r20379256 + r20379257;
        double r20379259 = r20379253 * r20379258;
        double r20379260 = r20379259 / r20379255;
        return r20379260;
}

↓

double f(double x, double y, double z) {
        double r20379261 = x;
        double r20379262 = -4.6266794377330075e-145;
        bool r20379263 = r20379261 <= r20379262;
        double r20379264 = z;
        double r20379265 = r20379261 / r20379264;
        double r20379266 = 1.0;
        double r20379267 = y;
        double r20379268 = r20379267 * r20379265;
        double r20379269 = fma(r20379265, r20379266, r20379268);
        double r20379270 = r20379269 - r20379261;
        double r20379271 = 1.3597213738421031e-288;
        bool r20379272 = r20379261 <= r20379271;
        double r20379273 = r20379267 - r20379264;
        double r20379274 = r20379273 * r20379261;
        double r20379275 = r20379266 * r20379261;
        double r20379276 = r20379274 + r20379275;
        double r20379277 = r20379276 / r20379264;
        double r20379278 = r20379272 ? r20379277 : r20379270;
        double r20379279 = r20379263 ? r20379270 : r20379278;
        return r20379279;
}

Original	9.8
Target	0.5
Herbie	0.8

Derivation

Split input into 2 regimes
if x < -4.6266794377330075e-145 or 1.3597213738421031e-288 < x
1. Initial program 11.9
  \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
2. Taylor expanded around 0 4.1
  \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + 1.0 \cdot \frac{x}{z}\right) - x}\]
3. Simplified0.9
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{z}, 1.0, y \cdot \frac{x}{z}\right) - x}\]
if -4.6266794377330075e-145 < x < 1.3597213738421031e-288
1. Initial program 0.2
  \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
2. Using strategy rm
3. Applied distribute-rgt-in0.2
  \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x + 1.0 \cdot x}}{z}\]
Recombined 2 regimes into one program.
Final simplification0.8
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.6266794377330075 \cdot 10^{-145}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, y \cdot \frac{x}{z}\right) - x\\ \mathbf{elif}\;x \le 1.3597213738421031 \cdot 10^{-288}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x + 1.0 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1.0, y \cdot \frac{x}{z}\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +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 < -4.6266794377330075e-145 or 1.3597213738421031e-288 < x`

`if -4.6266794377330075e-145 < x < 1.3597213738421031e-288`

Reproduce