Average Error: 0.1 → 0.1
Time: 7.0s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + y\right) + z\right) - \left(\left(\left(z \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right) \cdot 4 + z \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2\right)\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b\]
\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(\left(z \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right) \cdot 4 + z \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2\right)\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r444750 = x;
        double r444751 = y;
        double r444752 = r444750 + r444751;
        double r444753 = z;
        double r444754 = r444752 + r444753;
        double r444755 = t;
        double r444756 = log(r444755);
        double r444757 = r444753 * r444756;
        double r444758 = r444754 - r444757;
        double r444759 = a;
        double r444760 = 0.5;
        double r444761 = r444759 - r444760;
        double r444762 = b;
        double r444763 = r444761 * r444762;
        double r444764 = r444758 + r444763;
        return r444764;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r444765 = x;
        double r444766 = y;
        double r444767 = r444765 + r444766;
        double r444768 = z;
        double r444769 = r444767 + r444768;
        double r444770 = t;
        double r444771 = cbrt(r444770);
        double r444772 = cbrt(r444771);
        double r444773 = log(r444772);
        double r444774 = r444768 * r444773;
        double r444775 = 4.0;
        double r444776 = r444774 * r444775;
        double r444777 = 2.0;
        double r444778 = r444773 * r444777;
        double r444779 = r444768 * r444778;
        double r444780 = r444776 + r444779;
        double r444781 = log(r444771);
        double r444782 = r444768 * r444781;
        double r444783 = r444780 + r444782;
        double r444784 = r444769 - r444783;
        double r444785 = a;
        double r444786 = 0.5;
        double r444787 = r444785 - r444786;
        double r444788 = b;
        double r444789 = r444787 * r444788;
        double r444790 = r444784 + r444789;
        return r444790;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.3
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

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-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied log-prod0.1

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

  10. Applied distribute-lft-in0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Simplified0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\left(\color{blue}{\left(z \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right) \cdot 4} + z \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right)\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b\]

  13. Simplified0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\left(\left(z \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right) \cdot 4 + \color{blue}{z \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2\right)}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b\]

  14. Final simplification0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\left(\left(z \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right) \cdot 4 + z \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2\right)\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b\]

Reproduce

herbie shell --seed 2020056 
(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)))