Average Error: 0.1 → 0.1
Time: 26.8s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt{t}\right)\right) + \log \left(\sqrt{t}\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt{t}\right)\right) + \log \left(\sqrt{t}\right)
double f(double x, double y, double z, double t) {
        double r3766963 = x;
        double r3766964 = y;
        double r3766965 = log(r3766964);
        double r3766966 = r3766963 * r3766965;
        double r3766967 = r3766966 - r3766964;
        double r3766968 = z;
        double r3766969 = r3766967 - r3766968;
        double r3766970 = t;
        double r3766971 = log(r3766970);
        double r3766972 = r3766969 + r3766971;
        return r3766972;
}
↓
double f(double x, double y, double z, double t) {
        double r3766973 = x;
        double r3766974 = y;
        double r3766975 = log(r3766974);
        double r3766976 = r3766973 * r3766975;
        double r3766977 = r3766976 - r3766974;
        double r3766978 = z;
        double r3766979 = r3766977 - r3766978;
        double r3766980 = t;
        double r3766981 = sqrt(r3766980);
        double r3766982 = log(r3766981);
        double r3766983 = r3766979 + r3766982;
        double r3766984 = r3766983 + r3766982;
        return r3766984;
}

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

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))