Average Error: 0.1 → 0.1
Time: 13.4s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(y \cdot \left(\left(1 - z\right) + \log \left({z}^{\frac{2}{3}}\right)\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(y \cdot \left(\left(1 - z\right) + \log \left({z}^{\frac{2}{3}}\right)\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r218231 = x;
        double r218232 = 0.5;
        double r218233 = r218231 * r218232;
        double r218234 = y;
        double r218235 = 1.0;
        double r218236 = z;
        double r218237 = r218235 - r218236;
        double r218238 = log(r218236);
        double r218239 = r218237 + r218238;
        double r218240 = r218234 * r218239;
        double r218241 = r218233 + r218240;
        return r218241;
}
↓
double f(double x, double y, double z) {
        double r218242 = x;
        double r218243 = 0.5;
        double r218244 = r218242 * r218243;
        double r218245 = y;
        double r218246 = 1.0;
        double r218247 = z;
        double r218248 = r218246 - r218247;
        double r218249 = 0.6666666666666666;
        double r218250 = pow(r218247, r218249);
        double r218251 = log(r218250);
        double r218252 = r218248 + r218251;
        double r218253 = r218245 * r218252;
        double r218254 = cbrt(r218247);
        double r218255 = log(r218254);
        double r218256 = r218245 * r218255;
        double r218257 = r218253 + r218256;
        double r218258 = r218244 + r218257;
        return r218258;
}

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

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

  8. Applied distribute-lft-in0.1

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

  9. Simplified0.1

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

  11. Applied add-log-exp0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019208 
(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)))))