Average Error: 0.3 → 0.3
Time: 20.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[3 \cdot \log \left(\sqrt[3]{z}\right) + \left(\log \left(x + y\right) - \left(t - \left(a - \frac{1}{2}\right) \cdot \log t\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
3 \cdot \log \left(\sqrt[3]{z}\right) + \left(\log \left(x + y\right) - \left(t - \left(a - \frac{1}{2}\right) \cdot \log t\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r234603 = x;
        double r234604 = y;
        double r234605 = r234603 + r234604;
        double r234606 = log(r234605);
        double r234607 = z;
        double r234608 = log(r234607);
        double r234609 = r234606 + r234608;
        double r234610 = t;
        double r234611 = r234609 - r234610;
        double r234612 = a;
        double r234613 = 0.5;
        double r234614 = r234612 - r234613;
        double r234615 = log(r234610);
        double r234616 = r234614 * r234615;
        double r234617 = r234611 + r234616;
        return r234617;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r234618 = 3.0;
        double r234619 = z;
        double r234620 = cbrt(r234619);
        double r234621 = log(r234620);
        double r234622 = r234618 * r234621;
        double r234623 = x;
        double r234624 = y;
        double r234625 = r234623 + r234624;
        double r234626 = log(r234625);
        double r234627 = t;
        double r234628 = a;
        double r234629 = 1.0;
        double r234630 = 2.0;
        double r234631 = r234629 / r234630;
        double r234632 = r234628 - r234631;
        double r234633 = log(r234627);
        double r234634 = r234632 * r234633;
        double r234635 = r234627 - r234634;
        double r234636 = r234626 - r234635;
        double r234637 = r234622 + r234636;
        return r234637;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

Derivation

  1. Initial program 0.3

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

  2. Simplified0.3

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

  4. Applied add-cube-cbrt0.3

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

  5. Applied log-prod0.3

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

  6. Applied associate-+r+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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