Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt{z}\right)\right) + y \cdot \log \left(\sqrt{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt{z}\right)\right) + y \cdot \log \left(\sqrt{z}\right)\right)
double f(double x, double y, double z) {
        double r301987 = x;
        double r301988 = 0.5;
        double r301989 = r301987 * r301988;
        double r301990 = y;
        double r301991 = 1.0;
        double r301992 = z;
        double r301993 = r301991 - r301992;
        double r301994 = log(r301992);
        double r301995 = r301993 + r301994;
        double r301996 = r301990 * r301995;
        double r301997 = r301989 + r301996;
        return r301997;
}
↓
double f(double x, double y, double z) {
        double r301998 = x;
        double r301999 = 0.5;
        double r302000 = r301998 * r301999;
        double r302001 = y;
        double r302002 = 1.0;
        double r302003 = z;
        double r302004 = r302002 - r302003;
        double r302005 = sqrt(r302003);
        double r302006 = log(r302005);
        double r302007 = r302004 + r302006;
        double r302008 = r302001 * r302007;
        double r302009 = r302001 * r302006;
        double r302010 = r302008 + r302009;
        double r302011 = r302000 + r302010;
        return r302011;
}

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. Using strategy rm

  5. Applied add-sqr-sqrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Applied associate-+r+0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

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

  (+ (* x 0.5) (* y (+ (- 1 z) (log z)))))