Average Error: 0.3 → 0.3
Time: 38.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log \left(\sqrt[3]{y + x}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log \left(\sqrt[3]{y + x}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r19539650 = x;
        double r19539651 = y;
        double r19539652 = r19539650 + r19539651;
        double r19539653 = log(r19539652);
        double r19539654 = z;
        double r19539655 = log(r19539654);
        double r19539656 = r19539653 + r19539655;
        double r19539657 = t;
        double r19539658 = r19539656 - r19539657;
        double r19539659 = a;
        double r19539660 = 0.5;
        double r19539661 = r19539659 - r19539660;
        double r19539662 = log(r19539657);
        double r19539663 = r19539661 * r19539662;
        double r19539664 = r19539658 + r19539663;
        return r19539664;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r19539665 = y;
        double r19539666 = x;
        double r19539667 = r19539665 + r19539666;
        double r19539668 = cbrt(r19539667);
        double r19539669 = r19539668 * r19539668;
        double r19539670 = log(r19539669);
        double r19539671 = log(r19539668);
        double r19539672 = t;
        double r19539673 = log(r19539672);
        double r19539674 = a;
        double r19539675 = 0.5;
        double r19539676 = r19539674 - r19539675;
        double r19539677 = r19539673 * r19539676;
        double r19539678 = z;
        double r19539679 = log(r19539678);
        double r19539680 = r19539679 - r19539672;
        double r19539681 = r19539677 + r19539680;
        double r19539682 = r19539671 + r19539681;
        double r19539683 = r19539670 + r19539682;
        return r19539683;
}

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. Using strategy rm

  3. Applied associate--l+0.3

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

  4. Applied associate-+l+0.3

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

  6. Applied add-cube-cbrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied associate-+l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

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

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