Average Error: 0.1 → 0.1
Time: 28.8s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log t + \left(\left(\left(\log \left(\sqrt{y}\right) \cdot x + \log \left(\sqrt{y}\right) \cdot x\right) - y\right) - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log t + \left(\left(\left(\log \left(\sqrt{y}\right) \cdot x + \log \left(\sqrt{y}\right) \cdot x\right) - y\right) - z\right)
double f(double x, double y, double z, double t) {
        double r4329122 = x;
        double r4329123 = y;
        double r4329124 = log(r4329123);
        double r4329125 = r4329122 * r4329124;
        double r4329126 = r4329125 - r4329123;
        double r4329127 = z;
        double r4329128 = r4329126 - r4329127;
        double r4329129 = t;
        double r4329130 = log(r4329129);
        double r4329131 = r4329128 + r4329130;
        return r4329131;
}
↓
double f(double x, double y, double z, double t) {
        double r4329132 = t;
        double r4329133 = log(r4329132);
        double r4329134 = y;
        double r4329135 = sqrt(r4329134);
        double r4329136 = log(r4329135);
        double r4329137 = x;
        double r4329138 = r4329136 * r4329137;
        double r4329139 = r4329138 + r4329138;
        double r4329140 = r4329139 - r4329134;
        double r4329141 = z;
        double r4329142 = r4329140 - r4329141;
        double r4329143 = r4329133 + r4329142;
        return r4329143;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))