Average Error: 10.2 → 0.1
Time: 7.8s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -32557379355462839325163520 \lor \neg \left(x \le 7.170043320155678175136459501169904402577 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -32557379355462839325163520 \lor \neg \left(x \le 7.170043320155678175136459501169904402577 \cdot 10^{-21}\right):\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r1694243 = x;
        double r1694244 = y;
        double r1694245 = z;
        double r1694246 = r1694244 - r1694245;
        double r1694247 = 1.0;
        double r1694248 = r1694246 + r1694247;
        double r1694249 = r1694243 * r1694248;
        double r1694250 = r1694249 / r1694245;
        return r1694250;
}
↓
double f(double x, double y, double z) {
        double r1694251 = x;
        double r1694252 = -3.255737935546284e+25;
        bool r1694253 = r1694251 <= r1694252;
        double r1694254 = 7.170043320155678e-21;
        bool r1694255 = r1694251 <= r1694254;
        double r1694256 = !r1694255;
        bool r1694257 = r1694253 || r1694256;
        double r1694258 = z;
        double r1694259 = y;
        double r1694260 = r1694259 - r1694258;
        double r1694261 = 1.0;
        double r1694262 = r1694260 + r1694261;
        double r1694263 = r1694258 / r1694262;
        double r1694264 = r1694251 / r1694263;
        double r1694265 = r1694251 * r1694259;
        double r1694266 = r1694265 / r1694258;
        double r1694267 = r1694251 / r1694258;
        double r1694268 = r1694261 * r1694267;
        double r1694269 = r1694266 + r1694268;
        double r1694270 = r1694269 - r1694251;
        double r1694271 = r1694257 ? r1694264 : r1694270;
        return r1694271;
}

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

Original10.2
Target0.4
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -3.255737935546284e+25 or 7.170043320155678e-21 < x

    1. Initial program 25.9

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

    3. Applied associate-/l*0.1

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

    if -3.255737935546284e+25 < x < 7.170043320155678e-21

    1. Initial program 0.3

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

    2. Taylor expanded around 0 0.2

      \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -32557379355462839325163520 \lor \neg \left(x \le 7.170043320155678175136459501169904402577 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(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))