Average Error: 0.1 → 0.1
Time: 4.5s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(\left(1 - z\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\left(\left(1 - z\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right)
double f(double x, double y, double z) {
        double r304296 = x;
        double r304297 = 0.5;
        double r304298 = r304296 * r304297;
        double r304299 = y;
        double r304300 = 1.0;
        double r304301 = z;
        double r304302 = r304300 - r304301;
        double r304303 = log(r304301);
        double r304304 = r304302 + r304303;
        double r304305 = r304299 * r304304;
        double r304306 = r304298 + r304305;
        return r304306;
}
↓
double f(double x, double y, double z) {
        double r304307 = x;
        double r304308 = 0.5;
        double r304309 = r304307 * r304308;
        double r304310 = y;
        double r304311 = 1.0;
        double r304312 = z;
        double r304313 = r304311 - r304312;
        double r304314 = sqrt(r304312);
        double r304315 = log(r304314);
        double r304316 = r304313 + r304315;
        double r304317 = r304316 + r304315;
        double r304318 = r304310 * r304317;
        double r304319 = r304309 + r304318;
        return r304319;
}

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 add-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied associate-+r+0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 
(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)))))