Average Error: 0.1 → 0.1
Time: 12.9s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[2 \cdot \log \left(\sqrt{t}\right) + \left(\left(x \cdot \log y - y\right) - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
2 \cdot \log \left(\sqrt{t}\right) + \left(\left(x \cdot \log y - y\right) - z\right)
double f(double x, double y, double z, double t) {
        double r81253 = x;
        double r81254 = y;
        double r81255 = log(r81254);
        double r81256 = r81253 * r81255;
        double r81257 = r81256 - r81254;
        double r81258 = z;
        double r81259 = r81257 - r81258;
        double r81260 = t;
        double r81261 = log(r81260);
        double r81262 = r81259 + r81261;
        return r81262;
}
↓
double f(double x, double y, double z, double t) {
        double r81263 = 2.0;
        double r81264 = t;
        double r81265 = sqrt(r81264);
        double r81266 = log(r81265);
        double r81267 = r81263 * r81266;
        double r81268 = x;
        double r81269 = y;
        double r81270 = log(r81269);
        double r81271 = r81268 * r81270;
        double r81272 = r81271 - r81269;
        double r81273 = z;
        double r81274 = r81272 - r81273;
        double r81275 = r81267 + r81274;
        return r81275;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied associate-+r+0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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)))