Average Error: 0.1 → 0.1
Time: 20.4s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(\left(y + x\right) - \left(\left(y + 0.5\right) \cdot \log \left(\left|\sqrt[3]{y}\right|\right) + \left(y + 0.5\right) \cdot \log \left(\sqrt{\sqrt[3]{y}}\right)\right)\right) - \log \left(\sqrt{y}\right) \cdot \left(y + 0.5\right)\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(\left(y + x\right) - \left(\left(y + 0.5\right) \cdot \log \left(\left|\sqrt[3]{y}\right|\right) + \left(y + 0.5\right) \cdot \log \left(\sqrt{\sqrt[3]{y}}\right)\right)\right) - \log \left(\sqrt{y}\right) \cdot \left(y + 0.5\right)\right) - z
double f(double x, double y, double z) {
        double r20479347 = x;
        double r20479348 = y;
        double r20479349 = 0.5;
        double r20479350 = r20479348 + r20479349;
        double r20479351 = log(r20479348);
        double r20479352 = r20479350 * r20479351;
        double r20479353 = r20479347 - r20479352;
        double r20479354 = r20479353 + r20479348;
        double r20479355 = z;
        double r20479356 = r20479354 - r20479355;
        return r20479356;
}
↓
double f(double x, double y, double z) {
        double r20479357 = y;
        double r20479358 = x;
        double r20479359 = r20479357 + r20479358;
        double r20479360 = 0.5;
        double r20479361 = r20479357 + r20479360;
        double r20479362 = cbrt(r20479357);
        double r20479363 = fabs(r20479362);
        double r20479364 = log(r20479363);
        double r20479365 = r20479361 * r20479364;
        double r20479366 = sqrt(r20479362);
        double r20479367 = log(r20479366);
        double r20479368 = r20479361 * r20479367;
        double r20479369 = r20479365 + r20479368;
        double r20479370 = r20479359 - r20479369;
        double r20479371 = sqrt(r20479357);
        double r20479372 = log(r20479371);
        double r20479373 = r20479372 * r20479361;
        double r20479374 = r20479370 - r20479373;
        double r20479375 = z;
        double r20479376 = r20479374 - r20479375;
        return r20479376;
}

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. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  5. Applied add-sqr-sqrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Applied associate--r+0.1

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

  10. Applied add-cube-cbrt0.1

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

  11. Applied sqrt-prod0.1

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

  12. Applied log-prod0.1

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

  13. Applied distribute-rgt-in0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(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))