Average Error: 0.1 → 0.1
Time: 4.2s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \left(y \cdot \frac{1}{3}\right) \cdot \log z\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \left(y \cdot \frac{1}{3}\right) \cdot \log z\right)
double f(double x, double y, double z) {
        double r294182 = x;
        double r294183 = 0.5;
        double r294184 = r294182 * r294183;
        double r294185 = y;
        double r294186 = 1.0;
        double r294187 = z;
        double r294188 = r294186 - r294187;
        double r294189 = log(r294187);
        double r294190 = r294188 + r294189;
        double r294191 = r294185 * r294190;
        double r294192 = r294184 + r294191;
        return r294192;
}
↓
double f(double x, double y, double z) {
        double r294193 = x;
        double r294194 = 0.5;
        double r294195 = r294193 * r294194;
        double r294196 = 1.0;
        double r294197 = z;
        double r294198 = 2.0;
        double r294199 = cbrt(r294197);
        double r294200 = log(r294199);
        double r294201 = r294198 * r294200;
        double r294202 = r294197 - r294201;
        double r294203 = r294196 - r294202;
        double r294204 = y;
        double r294205 = r294203 * r294204;
        double r294206 = 0.3333333333333333;
        double r294207 = r294204 * r294206;
        double r294208 = log(r294197);
        double r294209 = r294207 * r294208;
        double r294210 = r294205 + r294209;
        double r294211 = r294195 + r294210;
        return r294211;
}

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-cube-cbrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Applied associate-+r+0.1

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

  9. Simplified0.1

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

  11. Applied pow1/30.1

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

  12. Applied log-pow0.1

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

  13. Applied associate-*r*0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(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)))))