Average Error: 0.1 → 0.1
Time: 19.8s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x - \left(\left(\left(\left(y + 0.5\right) \cdot \log \left(\sqrt{y}\right) - y\right) + \left(y + 0.5\right) \cdot \log \left(\sqrt{y}\right)\right) + z\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x - \left(\left(\left(\left(y + 0.5\right) \cdot \log \left(\sqrt{y}\right) - y\right) + \left(y + 0.5\right) \cdot \log \left(\sqrt{y}\right)\right) + z\right)
double f(double x, double y, double z) {
        double r19573651 = x;
        double r19573652 = y;
        double r19573653 = 0.5;
        double r19573654 = r19573652 + r19573653;
        double r19573655 = log(r19573652);
        double r19573656 = r19573654 * r19573655;
        double r19573657 = r19573651 - r19573656;
        double r19573658 = r19573657 + r19573652;
        double r19573659 = z;
        double r19573660 = r19573658 - r19573659;
        return r19573660;
}
↓
double f(double x, double y, double z) {
        double r19573661 = x;
        double r19573662 = y;
        double r19573663 = 0.5;
        double r19573664 = r19573662 + r19573663;
        double r19573665 = sqrt(r19573662);
        double r19573666 = log(r19573665);
        double r19573667 = r19573664 * r19573666;
        double r19573668 = r19573667 - r19573662;
        double r19573669 = r19573668 + r19573667;
        double r19573670 = z;
        double r19573671 = r19573669 + r19573670;
        double r19573672 = r19573661 - r19573671;
        return r19573672;
}

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. Using strategy rm

  3. Applied associate-+l-0.1

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

  4. Applied associate--l-0.1

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

  6. Applied add-sqr-sqrt0.1

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

  7. Applied log-prod0.1

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

  8. Applied distribute-lft-in0.1

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

  9. Applied associate--l+0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(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))