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

Average Error: 0.1 → 0.1

Time: 28.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r16345799 = x;
        double r16345800 = y;
        double r16345801 = r16345799 + r16345800;
        double r16345802 = z;
        double r16345803 = r16345801 + r16345802;
        double r16345804 = t;
        double r16345805 = log(r16345804);
        double r16345806 = r16345802 * r16345805;
        double r16345807 = r16345803 - r16345806;
        double r16345808 = a;
        double r16345809 = 0.5;
        double r16345810 = r16345808 - r16345809;
        double r16345811 = b;
        double r16345812 = r16345810 * r16345811;
        double r16345813 = r16345807 + r16345812;
        return r16345813;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r16345814 = z;
        double r16345815 = x;
        double r16345816 = y;
        double r16345817 = r16345815 + r16345816;
        double r16345818 = r16345814 + r16345817;
        double r16345819 = t;
        double r16345820 = cbrt(r16345819);
        double r16345821 = log(r16345820);
        double r16345822 = 0.3333333333333333;
        double r16345823 = pow(r16345819, r16345822);
        double r16345824 = log(r16345823);
        double r16345825 = r16345821 + r16345824;
        double r16345826 = r16345814 * r16345825;
        double r16345827 = r16345818 - r16345826;
        double r16345828 = r16345814 * r16345821;
        double r16345829 = r16345827 - r16345828;
        double r16345830 = a;
        double r16345831 = 0.5;
        double r16345832 = r16345830 - r16345831;
        double r16345833 = b;
        double r16345834 = r16345832 * r16345833;
        double r16345835 = r16345829 + r16345834;
        return r16345835;
}

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 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

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

9. Applied pow1/3 0.1

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

10. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

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