Average Error: 0.1 → 0.1
Time: 16.6s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log \left(\sqrt{y}\right) \cdot \left(x + x\right) - \left(y + \left(z - \log t\right)\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log \left(\sqrt{y}\right) \cdot \left(x + x\right) - \left(y + \left(z - \log t\right)\right)
double f(double x, double y, double z, double t) {
        double r98312 = x;
        double r98313 = y;
        double r98314 = log(r98313);
        double r98315 = r98312 * r98314;
        double r98316 = r98315 - r98313;
        double r98317 = z;
        double r98318 = r98316 - r98317;
        double r98319 = t;
        double r98320 = log(r98319);
        double r98321 = r98318 + r98320;
        return r98321;
}
↓
double f(double x, double y, double z, double t) {
        double r98322 = y;
        double r98323 = sqrt(r98322);
        double r98324 = log(r98323);
        double r98325 = x;
        double r98326 = r98325 + r98325;
        double r98327 = r98324 * r98326;
        double r98328 = z;
        double r98329 = t;
        double r98330 = log(r98329);
        double r98331 = r98328 - r98330;
        double r98332 = r98322 + r98331;
        double r98333 = r98327 - r98332;
        return r98333;
}

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-lft-in0.1

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

  6. Applied associate--l+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019294 
(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)))