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

Average Error: 0.1 → 0.1

Time: 27.1s

Precision: 64

Math

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

↓

\[\left(\left(\left(z + \left(x + y\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot \left(z + z\right)\right) - z \cdot \log \left({t}^{\frac{1}{3}}\right)\right) + \left(a - 0.5\right) \cdot b\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r15802874 = x;
        double r15802875 = y;
        double r15802876 = r15802874 + r15802875;
        double r15802877 = z;
        double r15802878 = r15802876 + r15802877;
        double r15802879 = t;
        double r15802880 = log(r15802879);
        double r15802881 = r15802877 * r15802880;
        double r15802882 = r15802878 - r15802881;
        double r15802883 = a;
        double r15802884 = 0.5;
        double r15802885 = r15802883 - r15802884;
        double r15802886 = b;
        double r15802887 = r15802885 * r15802886;
        double r15802888 = r15802882 + r15802887;
        return r15802888;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r15802889 = z;
        double r15802890 = x;
        double r15802891 = y;
        double r15802892 = r15802890 + r15802891;
        double r15802893 = r15802889 + r15802892;
        double r15802894 = t;
        double r15802895 = cbrt(r15802894);
        double r15802896 = log(r15802895);
        double r15802897 = r15802889 + r15802889;
        double r15802898 = r15802896 * r15802897;
        double r15802899 = r15802893 - r15802898;
        double r15802900 = 0.3333333333333333;
        double r15802901 = pow(r15802894, r15802900);
        double r15802902 = log(r15802901);
        double r15802903 = r15802889 * r15802902;
        double r15802904 = r15802899 - r15802903;
        double r15802905 = a;
        double r15802906 = 0.5;
        double r15802907 = r15802905 - r15802906;
        double r15802908 = b;
        double r15802909 = r15802907 * r15802908;
        double r15802910 = r15802904 + r15802909;
        return r15802910;
}

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	0.3
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 add-cube-cbrt 0.1

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

4. Applied log-prod 0.1

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

5. Applied distribute-rgt-in 0.1

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

6. Applied associate--r+ 0.1

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

7. Simplified 0.1

   \[\leadsto \left(\color{blue}{\left(\left(\left(y + x\right) + z\right) - \log \left(\sqrt[3]{t}\right) \cdot \left(z + z\right)\right)} - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]
8. Using strategy rm

9. Applied pow1/3 0.1

   \[\leadsto \left(\left(\left(\left(y + x\right) + z\right) - \log \left(\sqrt[3]{t}\right) \cdot \left(z + z\right)\right) - \log \color{blue}{\left({t}^{\frac{1}{3}}\right)} \cdot z\right) + \left(a - 0.5\right) \cdot b\]

10. Final simplification 0.1

    \[\leadsto \left(\left(\left(z + \left(x + y\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot \left(z + z\right)\right) - z \cdot \log \left({t}^{\frac{1}{3}}\right)\right) + \left(a - 0.5\right) \cdot b\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :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)))