Average Error: 0.1 → 0.1
Time: 23.6s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\log t + \left(\left(\log \left(\sqrt{y}\right) \cdot x - y\right) - z\right)\right) + \log \left(\sqrt{y}\right) \cdot x\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\log t + \left(\left(\log \left(\sqrt{y}\right) \cdot x - y\right) - z\right)\right) + \log \left(\sqrt{y}\right) \cdot x
double f(double x, double y, double z, double t) {
        double r5499055 = x;
        double r5499056 = y;
        double r5499057 = log(r5499056);
        double r5499058 = r5499055 * r5499057;
        double r5499059 = r5499058 - r5499056;
        double r5499060 = z;
        double r5499061 = r5499059 - r5499060;
        double r5499062 = t;
        double r5499063 = log(r5499062);
        double r5499064 = r5499061 + r5499063;
        return r5499064;
}
↓
double f(double x, double y, double z, double t) {
        double r5499065 = t;
        double r5499066 = log(r5499065);
        double r5499067 = y;
        double r5499068 = sqrt(r5499067);
        double r5499069 = log(r5499068);
        double r5499070 = x;
        double r5499071 = r5499069 * r5499070;
        double r5499072 = r5499071 - r5499067;
        double r5499073 = z;
        double r5499074 = r5499072 - r5499073;
        double r5499075 = r5499066 + r5499074;
        double r5499076 = r5499075 + r5499071;
        return r5499076;
}

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. Applied associate--l+0.1

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

  8. Applied associate-+l+0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))