Average Error: 0.3 → 0.3
Time: 1.1m
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r18728787 = x;
        double r18728788 = y;
        double r18728789 = r18728787 + r18728788;
        double r18728790 = log(r18728789);
        double r18728791 = z;
        double r18728792 = log(r18728791);
        double r18728793 = r18728790 + r18728792;
        double r18728794 = t;
        double r18728795 = r18728793 - r18728794;
        double r18728796 = a;
        double r18728797 = 0.5;
        double r18728798 = r18728796 - r18728797;
        double r18728799 = log(r18728794);
        double r18728800 = r18728798 * r18728799;
        double r18728801 = r18728795 + r18728800;
        return r18728801;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r18728802 = a;
        double r18728803 = 0.5;
        double r18728804 = r18728802 - r18728803;
        double r18728805 = t;
        double r18728806 = sqrt(r18728805);
        double r18728807 = log(r18728806);
        double r18728808 = r18728804 * r18728807;
        double r18728809 = y;
        double r18728810 = x;
        double r18728811 = r18728809 + r18728810;
        double r18728812 = log(r18728811);
        double r18728813 = z;
        double r18728814 = log(r18728813);
        double r18728815 = r18728812 + r18728814;
        double r18728816 = r18728815 - r18728805;
        double r18728817 = r18728816 + r18728808;
        double r18728818 = r18728808 + r18728817;
        return r18728818;
}

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-lft-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Final simplification0.3

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

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))))