Average Error: 0.1 → 0.1
Time: 16.9s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(\left(y - \left(z - x\right)\right) - 0.5 \cdot \log y\right) - \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) \cdot y\right) - \log \left(\sqrt[3]{y}\right) \cdot y\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(\left(y - \left(z - x\right)\right) - 0.5 \cdot \log y\right) - \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) \cdot y\right) - \log \left(\sqrt[3]{y}\right) \cdot y
double f(double x, double y, double z) {
        double r302350 = x;
        double r302351 = y;
        double r302352 = 0.5;
        double r302353 = r302351 + r302352;
        double r302354 = log(r302351);
        double r302355 = r302353 * r302354;
        double r302356 = r302350 - r302355;
        double r302357 = r302356 + r302351;
        double r302358 = z;
        double r302359 = r302357 - r302358;
        return r302359;
}
↓
double f(double x, double y, double z) {
        double r302360 = y;
        double r302361 = z;
        double r302362 = x;
        double r302363 = r302361 - r302362;
        double r302364 = r302360 - r302363;
        double r302365 = 0.5;
        double r302366 = log(r302360);
        double r302367 = r302365 * r302366;
        double r302368 = r302364 - r302367;
        double r302369 = cbrt(r302360);
        double r302370 = log(r302369);
        double r302371 = 2.0;
        double r302372 = r302370 * r302371;
        double r302373 = r302372 * r302360;
        double r302374 = r302368 - r302373;
        double r302375 = r302370 * r302360;
        double r302376 = r302374 - r302375;
        return r302376;
}

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
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]

  2. Simplified0.1

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

  4. Applied distribute-rgt-in0.1

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

  5. Applied associate--r+0.1

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

  6. Simplified0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied log-prod0.1

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

  10. Applied distribute-lft-in0.1

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

  11. Applied associate--r+0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

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

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