Average Error: 0.3 → 0.3
Time: 21.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log t + 3 \cdot \log \left(\sqrt[3]{x + y}\right)\right) + \left(\log z - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(a - 0.5\right) \cdot \log t + 3 \cdot \log \left(\sqrt[3]{x + y}\right)\right) + \left(\log z - t\right)
double f(double x, double y, double z, double t, double a) {
        double r258651 = x;
        double r258652 = y;
        double r258653 = r258651 + r258652;
        double r258654 = log(r258653);
        double r258655 = z;
        double r258656 = log(r258655);
        double r258657 = r258654 + r258656;
        double r258658 = t;
        double r258659 = r258657 - r258658;
        double r258660 = a;
        double r258661 = 0.5;
        double r258662 = r258660 - r258661;
        double r258663 = log(r258658);
        double r258664 = r258662 * r258663;
        double r258665 = r258659 + r258664;
        return r258665;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r258666 = a;
        double r258667 = 0.5;
        double r258668 = r258666 - r258667;
        double r258669 = t;
        double r258670 = log(r258669);
        double r258671 = r258668 * r258670;
        double r258672 = 3.0;
        double r258673 = x;
        double r258674 = y;
        double r258675 = r258673 + r258674;
        double r258676 = cbrt(r258675);
        double r258677 = log(r258676);
        double r258678 = r258672 * r258677;
        double r258679 = r258671 + r258678;
        double r258680 = z;
        double r258681 = log(r258680);
        double r258682 = r258681 - r258669;
        double r258683 = r258679 + r258682;
        return r258683;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019308 
(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))))