Average Error: 0.1 → 0.1
Time: 4.7s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + x \cdot 0.5\right) + y \cdot \log \left(\sqrt[3]{z}\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + x \cdot 0.5\right) + y \cdot \log \left(\sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r291160 = x;
        double r291161 = 0.5;
        double r291162 = r291160 * r291161;
        double r291163 = y;
        double r291164 = 1.0;
        double r291165 = z;
        double r291166 = r291164 - r291165;
        double r291167 = log(r291165);
        double r291168 = r291166 + r291167;
        double r291169 = r291163 * r291168;
        double r291170 = r291162 + r291169;
        return r291170;
}
↓
double f(double x, double y, double z) {
        double r291171 = y;
        double r291172 = 1.0;
        double r291173 = z;
        double r291174 = r291172 - r291173;
        double r291175 = cbrt(r291173);
        double r291176 = r291175 * r291175;
        double r291177 = log(r291176);
        double r291178 = r291174 + r291177;
        double r291179 = r291171 * r291178;
        double r291180 = x;
        double r291181 = 0.5;
        double r291182 = r291180 * r291181;
        double r291183 = r291179 + r291182;
        double r291184 = log(r291175);
        double r291185 = r291171 * r291184;
        double r291186 = r291183 + r291185;
        return r291186;
}

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. Applied associate-+r+0.1

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

  6. Applied add-cube-cbrt0.1

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

  7. Applied log-prod0.1

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

  8. Applied distribute-lft-in0.1

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

  9. Applied associate-+r+0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(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)))))