Average Error: 0.1 → 0.1
Time: 17.1s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[0.5 \cdot x + y \cdot \left(\log z + \left(1 - z\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
0.5 \cdot x + y \cdot \left(\log z + \left(1 - z\right)\right)
double f(double x, double y, double z) {
        double r259508 = x;
        double r259509 = 0.5;
        double r259510 = r259508 * r259509;
        double r259511 = y;
        double r259512 = 1.0;
        double r259513 = z;
        double r259514 = r259512 - r259513;
        double r259515 = log(r259513);
        double r259516 = r259514 + r259515;
        double r259517 = r259511 * r259516;
        double r259518 = r259510 + r259517;
        return r259518;
}
↓
double f(double x, double y, double z) {
        double r259519 = 0.5;
        double r259520 = x;
        double r259521 = r259519 * r259520;
        double r259522 = y;
        double r259523 = z;
        double r259524 = log(r259523);
        double r259525 = 1.0;
        double r259526 = r259525 - r259523;
        double r259527 = r259524 + r259526;
        double r259528 = r259522 * r259527;
        double r259529 = r259521 + r259528;
        return r259529;
}

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

Original0.1
Target0.1
Herbie0.1
\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

  1. Initial program 0.1

    \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(1 - z\right) + y \cdot \log z\right)}\]

  4. Simplified0.1

    \[\leadsto x \cdot 0.5 + \left(\color{blue}{\left(1 - z\right) \cdot y} + y \cdot \log z\right)\]

  5. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(\log z \cdot y + \left(1 \cdot y + 0.5 \cdot x\right)\right) - z \cdot y}\]

  6. Simplified0.1

    \[\leadsto \color{blue}{0.5 \cdot x + y \cdot \left(\log z + \left(1 - z\right)\right)}\]

  7. Final simplification0.1

    \[\leadsto 0.5 \cdot x + y \cdot \left(\log z + \left(1 - z\right)\right)\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))