Average Error: 0.3 → 0.3
Time: 17.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r230782 = x;
        double r230783 = y;
        double r230784 = r230782 + r230783;
        double r230785 = log(r230784);
        double r230786 = z;
        double r230787 = log(r230786);
        double r230788 = r230785 + r230787;
        double r230789 = t;
        double r230790 = r230788 - r230789;
        double r230791 = a;
        double r230792 = 0.5;
        double r230793 = r230791 - r230792;
        double r230794 = log(r230789);
        double r230795 = r230793 * r230794;
        double r230796 = r230790 + r230795;
        return r230796;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r230797 = x;
        double r230798 = y;
        double r230799 = r230797 + r230798;
        double r230800 = log(r230799);
        double r230801 = z;
        double r230802 = sqrt(r230801);
        double r230803 = log(r230802);
        double r230804 = r230800 + r230803;
        double r230805 = r230804 + r230803;
        double r230806 = t;
        double r230807 = r230805 - r230806;
        double r230808 = a;
        double r230809 = 0.5;
        double r230810 = r230808 - r230809;
        double r230811 = log(r230806);
        double r230812 = r230810 * r230811;
        double r230813 = r230807 + r230812;
        return r230813;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 
(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))))