Average Error: 0.1 → 0.1
Time: 18.9s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r289310 = x;
        double r289311 = 0.5;
        double r289312 = r289310 * r289311;
        double r289313 = y;
        double r289314 = 1.0;
        double r289315 = z;
        double r289316 = r289314 - r289315;
        double r289317 = log(r289315);
        double r289318 = r289316 + r289317;
        double r289319 = r289313 * r289318;
        double r289320 = r289312 + r289319;
        return r289320;
}
↓
double f(double x, double y, double z) {
        double r289321 = x;
        double r289322 = 0.5;
        double r289323 = r289321 * r289322;
        double r289324 = y;
        double r289325 = 2.0;
        double r289326 = z;
        double r289327 = cbrt(r289326);
        double r289328 = log(r289327);
        double r289329 = r289325 * r289328;
        double r289330 = 1.0;
        double r289331 = r289329 + r289330;
        double r289332 = r289331 - r289326;
        double r289333 = r289332 + r289328;
        double r289334 = r289324 * r289333;
        double r289335 = r289323 + r289334;
        return r289335;
}

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-cube-cbrt0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right)\]

  4. Applied log-prod0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\right)\]

  5. Applied associate-+r+0.1

    \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)}\]

  6. Simplified0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\color{blue}{\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right)} + \log \left(\sqrt[3]{z}\right)\right)\]

  7. Final simplification0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{z}\right)\right)\]

Reproduce

herbie shell --seed 2019303 
(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)))))