Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Average Error: 0.1 → 0.1

Time: 26.5s

Precision: 64

Math

\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]

↓

\[\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a - 0.5\right) \cdot b\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r340846 = x;
        double r340847 = y;
        double r340848 = r340846 + r340847;
        double r340849 = z;
        double r340850 = r340848 + r340849;
        double r340851 = t;
        double r340852 = log(r340851);
        double r340853 = r340849 * r340852;
        double r340854 = r340850 - r340853;
        double r340855 = a;
        double r340856 = 0.5;
        double r340857 = r340855 - r340856;
        double r340858 = b;
        double r340859 = r340857 * r340858;
        double r340860 = r340854 + r340859;
        return r340860;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r340861 = x;
        double r340862 = y;
        double r340863 = r340861 + r340862;
        double r340864 = z;
        double r340865 = t;
        double r340866 = log(r340865);
        double r340867 = r340864 * r340866;
        double r340868 = r340864 - r340867;
        double r340869 = r340863 + r340868;
        double r340870 = a;
        double r340871 = 0.5;
        double r340872 = r340870 - r340871;
        double r340873 = b;
        double r340874 = r340872 * r340873;
        double r340875 = r340869 + r340874;
        return r340875;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Target

Original	0.1
Target	0.4
Herbie	0.1

\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

1. Initial program 0.1

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
2. Using strategy rm

3. Applied associate--l+ 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))