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

Average Error: 0.1 → 0.1

Time: 7.5s

Precision: 64

Math

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

↓

\[\left(\left(\left(x + y\right) + z\right) - \left(\left(2 \cdot z\right) \cdot \left(\log \left({t}^{\frac{1}{3}}\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r361731 = x;
        double r361732 = y;
        double r361733 = r361731 + r361732;
        double r361734 = z;
        double r361735 = r361733 + r361734;
        double r361736 = t;
        double r361737 = log(r361736);
        double r361738 = r361734 * r361737;
        double r361739 = r361735 - r361738;
        double r361740 = a;
        double r361741 = 0.5;
        double r361742 = r361740 - r361741;
        double r361743 = b;
        double r361744 = r361742 * r361743;
        double r361745 = r361739 + r361744;
        return r361745;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r361746 = x;
        double r361747 = y;
        double r361748 = r361746 + r361747;
        double r361749 = z;
        double r361750 = r361748 + r361749;
        double r361751 = 2.0;
        double r361752 = r361751 * r361749;
        double r361753 = t;
        double r361754 = 0.3333333333333333;
        double r361755 = pow(r361753, r361754);
        double r361756 = log(r361755);
        double r361757 = cbrt(r361753);
        double r361758 = cbrt(r361757);
        double r361759 = log(r361758);
        double r361760 = r361756 + r361759;
        double r361761 = r361752 * r361760;
        double r361762 = r361759 * r361749;
        double r361763 = r361761 + r361762;
        double r361764 = r361750 - r361763;
        double r361765 = a;
        double r361766 = 0.5;
        double r361767 = r361765 - r361766;
        double r361768 = b;
        double r361769 = r361767 * r361768;
        double r361770 = r361764 + r361769;
        return r361770;
}

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-lft-in 0.1

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

6. Simplified 0.1

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\color{blue}{z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right)} + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b\]
7. Using strategy rm

8. Applied add-cube-cbrt 0.1

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + z \cdot \log \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \sqrt[3]{\sqrt[3]{t}}\right)}\right)\right) + \left(a - 0.5\right) \cdot b\]

9. Applied log-prod 0.1

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + z \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right)}\right)\right) + \left(a - 0.5\right) \cdot b\]

10. Applied distribute-rgt-in 0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot z + \log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot z\right)}\right)\right) + \left(a - 0.5\right) \cdot b\]

11. Applied associate-+r+ 0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot z\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot z\right)}\right) + \left(a - 0.5\right) \cdot b\]

12. Simplified 0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\color{blue}{\left(2 \cdot z\right) \cdot \left(\log \left({t}^{\frac{1}{3}}\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right)} + \log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]

13. Final simplification 0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\left(2 \cdot z\right) \cdot \left(\log \left({t}^{\frac{1}{3}}\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]

Reproduce

herbie shell --seed 2020081 
(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)))