Average Error: 0.1 → 0.2
Time: 5.9s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \left(y + 0.5\right) \cdot \log \left({y}^{\frac{1}{3}}\right)\right) + y\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \left(y + 0.5\right) \cdot \log \left({y}^{\frac{1}{3}}\right)\right) + y\right) - z
double f(double x, double y, double z) {
        double r383432 = x;
        double r383433 = y;
        double r383434 = 0.5;
        double r383435 = r383433 + r383434;
        double r383436 = log(r383433);
        double r383437 = r383435 * r383436;
        double r383438 = r383432 - r383437;
        double r383439 = r383438 + r383433;
        double r383440 = z;
        double r383441 = r383439 - r383440;
        return r383441;
}
↓
double f(double x, double y, double z) {
        double r383442 = x;
        double r383443 = y;
        double r383444 = cbrt(r383443);
        double r383445 = r383444 * r383444;
        double r383446 = log(r383445);
        double r383447 = 0.5;
        double r383448 = r383443 + r383447;
        double r383449 = r383446 * r383448;
        double r383450 = r383442 - r383449;
        double r383451 = 0.3333333333333333;
        double r383452 = pow(r383443, r383451);
        double r383453 = log(r383452);
        double r383454 = r383448 * r383453;
        double r383455 = r383450 - r383454;
        double r383456 = r383455 + r383443;
        double r383457 = z;
        double r383458 = r383456 - r383457;
        return r383458;
}

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
Herbie0.2
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.2

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

  5. Applied distribute-lft-in0.2

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

  6. Applied associate--r+0.2

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

  7. Simplified0.2

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

  9. Applied pow1/30.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

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

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