Average Error: 10.2 → 0.4
Time: 15.1s
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 r502218 = x;
        double r502219 = y;
        double r502220 = z;
        double r502221 = r502219 - r502220;
        double r502222 = 1.0;
        double r502223 = r502221 + r502222;
        double r502224 = r502218 * r502223;
        double r502225 = r502224 / r502220;
        return r502225;
}
↓
double f(double x, double y, double z) {
        double r502226 = z;
        double r502227 = -395330988786.38336;
        bool r502228 = r502226 <= r502227;
        double r502229 = 6.815802930557607e-126;
        bool r502230 = r502226 <= r502229;
        double r502231 = !r502230;
        bool r502232 = r502228 || r502231;
        double r502233 = x;
        double r502234 = y;
        double r502235 = r502234 - r502226;
        double r502236 = 1.0;
        double r502237 = r502235 + r502236;
        double r502238 = r502226 / r502237;
        double r502239 = r502233 / r502238;
        double r502240 = r502233 * r502237;
        double r502241 = r502240 / r502226;
        double r502242 = r502232 ? r502239 : r502241;
        return r502242;
}

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 
(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))