Average Error: 10.2 → 0.4
Time: 14.6s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -395330988786.383362 \lor \neg \left(z \le 6.8158029305576074 \cdot 10^{-126}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -395330988786.383362 \lor \neg \left(z \le 6.8158029305576074 \cdot 10^{-126}\right):\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r442322 = x;
        double r442323 = y;
        double r442324 = z;
        double r442325 = r442323 - r442324;
        double r442326 = 1.0;
        double r442327 = r442325 + r442326;
        double r442328 = r442322 * r442327;
        double r442329 = r442328 / r442324;
        return r442329;
}
↓
double f(double x, double y, double z) {
        double r442330 = z;
        double r442331 = -395330988786.38336;
        bool r442332 = r442330 <= r442331;
        double r442333 = 6.815802930557607e-126;
        bool r442334 = r442330 <= r442333;
        double r442335 = !r442334;
        bool r442336 = r442332 || r442335;
        double r442337 = x;
        double r442338 = y;
        double r442339 = r442338 - r442330;
        double r442340 = 1.0;
        double r442341 = r442339 + r442340;
        double r442342 = r442330 / r442341;
        double r442343 = r442337 / r442342;
        double r442344 = r442337 * r442341;
        double r442345 = r442344 / r442330;
        double r442346 = r442336 ? r442343 : r442345;
        return r442346;
}

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
Target0.5
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -395330988786.38336 or 6.815802930557607e-126 < z

    1. Initial program 14.7

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

    3. Applied associate-/l*0.5

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

    if -395330988786.38336 < z < 6.815802930557607e-126

    1. Initial program 0.1

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -395330988786.383362 \lor \neg \left(z \le 6.8158029305576074 \cdot 10^{-126}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 +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) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))