Average Error: 0.1 → 0.1
Time: 17.6s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log \left(\sqrt{y}\right) \cdot \left(x + x\right) - \left(\left(y + z\right) - \log t\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log \left(\sqrt{y}\right) \cdot \left(x + x\right) - \left(\left(y + z\right) - \log t\right)
double f(double x, double y, double z, double t) {
        double r98924 = x;
        double r98925 = y;
        double r98926 = log(r98925);
        double r98927 = r98924 * r98926;
        double r98928 = r98927 - r98925;
        double r98929 = z;
        double r98930 = r98928 - r98929;
        double r98931 = t;
        double r98932 = log(r98931);
        double r98933 = r98930 + r98932;
        return r98933;
}
↓
double f(double x, double y, double z, double t) {
        double r98934 = y;
        double r98935 = sqrt(r98934);
        double r98936 = log(r98935);
        double r98937 = x;
        double r98938 = r98937 + r98937;
        double r98939 = r98936 * r98938;
        double r98940 = z;
        double r98941 = r98934 + r98940;
        double r98942 = t;
        double r98943 = log(r98942);
        double r98944 = r98941 - r98943;
        double r98945 = r98939 - r98944;
        return r98945;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied add-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  8. Applied associate-+l+0.1

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

  9. Final simplification0.1

    \[\leadsto \log \left(\sqrt{y}\right) \cdot \left(x + x\right) - \left(\left(y + z\right) - \log t\right)\]

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))