Average Error: 0.1 → 0.1
Time: 15.1s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(x \cdot 0.5 + y \cdot \left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right)\right) + y \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) + \log \left(\sqrt[3]{\sqrt[3]{z}}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(x \cdot 0.5 + y \cdot \left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right)\right) + y \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) + \log \left(\sqrt[3]{\sqrt[3]{z}}\right)\right)
double f(double x, double y, double z) {
        double r297218 = x;
        double r297219 = 0.5;
        double r297220 = r297218 * r297219;
        double r297221 = y;
        double r297222 = 1.0;
        double r297223 = z;
        double r297224 = r297222 - r297223;
        double r297225 = log(r297223);
        double r297226 = r297224 + r297225;
        double r297227 = r297221 * r297226;
        double r297228 = r297220 + r297227;
        return r297228;
}
↓
double f(double x, double y, double z) {
        double r297229 = x;
        double r297230 = 0.5;
        double r297231 = r297229 * r297230;
        double r297232 = y;
        double r297233 = 2.0;
        double r297234 = z;
        double r297235 = cbrt(r297234);
        double r297236 = log(r297235);
        double r297237 = r297233 * r297236;
        double r297238 = 1.0;
        double r297239 = r297237 + r297238;
        double r297240 = r297239 - r297234;
        double r297241 = r297232 * r297240;
        double r297242 = r297231 + r297241;
        double r297243 = r297235 * r297235;
        double r297244 = cbrt(r297243);
        double r297245 = log(r297244);
        double r297246 = cbrt(r297235);
        double r297247 = log(r297246);
        double r297248 = r297245 + r297247;
        double r297249 = r297232 * r297248;
        double r297250 = r297242 + r297249;
        return r297250;
}

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. Using strategy rm

  8. Applied distribute-lft-in0.1

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

  10. Applied add-cube-cbrt0.1

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

  11. Applied cbrt-prod0.1

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

  12. Applied log-prod0.1

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

  13. Applied distribute-lft-in0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019298 
(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)))))