Average Error: 0.3 → 0.3
Time: 29.9s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r19291669 = x;
        double r19291670 = y;
        double r19291671 = r19291669 + r19291670;
        double r19291672 = log(r19291671);
        double r19291673 = z;
        double r19291674 = log(r19291673);
        double r19291675 = r19291672 + r19291674;
        double r19291676 = t;
        double r19291677 = r19291675 - r19291676;
        double r19291678 = a;
        double r19291679 = 0.5;
        double r19291680 = r19291678 - r19291679;
        double r19291681 = log(r19291676);
        double r19291682 = r19291680 * r19291681;
        double r19291683 = r19291677 + r19291682;
        return r19291683;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r19291684 = t;
        double r19291685 = sqrt(r19291684);
        double r19291686 = log(r19291685);
        double r19291687 = a;
        double r19291688 = 0.5;
        double r19291689 = r19291687 - r19291688;
        double r19291690 = r19291686 * r19291689;
        double r19291691 = y;
        double r19291692 = x;
        double r19291693 = r19291691 + r19291692;
        double r19291694 = log(r19291693);
        double r19291695 = z;
        double r19291696 = log(r19291695);
        double r19291697 = r19291694 + r19291696;
        double r19291698 = r19291697 - r19291684;
        double r19291699 = r19291698 + r19291690;
        double r19291700 = r19291690 + r19291699;
        return r19291700;
}

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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-rgt-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(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))))