Average Error: 0.1 → 0.1
Time: 23.2s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[y \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{z}}\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) + \left(\left(1 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right)\right)\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
y \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{z}}\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) + \left(\left(1 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right)\right)\right) + x \cdot 0.5
double f(double x, double y, double z) {
        double r14360142 = x;
        double r14360143 = 0.5;
        double r14360144 = r14360142 * r14360143;
        double r14360145 = y;
        double r14360146 = 1.0;
        double r14360147 = z;
        double r14360148 = r14360146 - r14360147;
        double r14360149 = log(r14360147);
        double r14360150 = r14360148 + r14360149;
        double r14360151 = r14360145 * r14360150;
        double r14360152 = r14360144 + r14360151;
        return r14360152;
}
↓
double f(double x, double y, double z) {
        double r14360153 = y;
        double r14360154 = z;
        double r14360155 = cbrt(r14360154);
        double r14360156 = cbrt(r14360155);
        double r14360157 = log(r14360156);
        double r14360158 = r14360155 * r14360155;
        double r14360159 = cbrt(r14360158);
        double r14360160 = log(r14360159);
        double r14360161 = 1.0;
        double r14360162 = r14360161 - r14360154;
        double r14360163 = log(r14360155);
        double r14360164 = r14360163 + r14360163;
        double r14360165 = r14360162 + r14360164;
        double r14360166 = r14360160 + r14360165;
        double r14360167 = r14360157 + r14360166;
        double r14360168 = r14360153 * r14360167;
        double r14360169 = x;
        double r14360170 = 0.5;
        double r14360171 = r14360169 * r14360170;
        double r14360172 = r14360168 + r14360171;
        return r14360172;
}

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

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied associate-+r+0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))