Average Error: 0.3 → 0.3
Time: 42.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\left(\left(\log z + \log \left(\sqrt[3]{y + x}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\right)\]
\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(\left(\left(\log z + \log \left(\sqrt[3]{y + x}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r30655606 = x;
        double r30655607 = y;
        double r30655608 = r30655606 + r30655607;
        double r30655609 = log(r30655608);
        double r30655610 = z;
        double r30655611 = log(r30655610);
        double r30655612 = r30655609 + r30655611;
        double r30655613 = t;
        double r30655614 = r30655612 - r30655613;
        double r30655615 = a;
        double r30655616 = 0.5;
        double r30655617 = r30655615 - r30655616;
        double r30655618 = log(r30655613);
        double r30655619 = r30655617 * r30655618;
        double r30655620 = r30655614 + r30655619;
        return r30655620;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30655621 = y;
        double r30655622 = x;
        double r30655623 = r30655621 + r30655622;
        double r30655624 = cbrt(r30655623);
        double r30655625 = r30655624 * r30655624;
        double r30655626 = log(r30655625);
        double r30655627 = z;
        double r30655628 = log(r30655627);
        double r30655629 = log(r30655624);
        double r30655630 = r30655628 + r30655629;
        double r30655631 = t;
        double r30655632 = r30655630 - r30655631;
        double r30655633 = log(r30655631);
        double r30655634 = a;
        double r30655635 = 0.5;
        double r30655636 = r30655634 - r30655635;
        double r30655637 = r30655633 * r30655636;
        double r30655638 = r30655632 + r30655637;
        double r30655639 = r30655626 + r30655638;
        return r30655639;
}

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 add-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Applied associate--l+0.3

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

  7. Applied associate-+l+0.3

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

  8. Final simplification0.3

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

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))))