Average Error: 0.1 → 0.1
Time: 6.3s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(2 \cdot \log \left(\sqrt[3]{t}\right) + x \cdot \log y\right) - \left(z + y\right)\right) + \log \left(\sqrt[3]{t}\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(2 \cdot \log \left(\sqrt[3]{t}\right) + x \cdot \log y\right) - \left(z + y\right)\right) + \log \left(\sqrt[3]{t}\right)
double f(double x, double y, double z, double t) {
        double r106200 = x;
        double r106201 = y;
        double r106202 = log(r106201);
        double r106203 = r106200 * r106202;
        double r106204 = r106203 - r106201;
        double r106205 = z;
        double r106206 = r106204 - r106205;
        double r106207 = t;
        double r106208 = log(r106207);
        double r106209 = r106206 + r106208;
        return r106209;
}
↓
double f(double x, double y, double z, double t) {
        double r106210 = 2.0;
        double r106211 = t;
        double r106212 = cbrt(r106211);
        double r106213 = log(r106212);
        double r106214 = r106210 * r106213;
        double r106215 = x;
        double r106216 = y;
        double r106217 = log(r106216);
        double r106218 = r106215 * r106217;
        double r106219 = r106214 + r106218;
        double r106220 = z;
        double r106221 = r106220 + r106216;
        double r106222 = r106219 - r106221;
        double r106223 = r106222 + r106213;
        return r106223;
}

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-cube-cbrt0.1

    \[\leadsto \left(\left(x \cdot \log y - y\right) - z\right) + \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(x \cdot \log y - y\right) - z\right) + \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\]

  5. Applied associate-+r+0.1

    \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) + \log \left(\sqrt[3]{t}\right)}\]

  6. Simplified0.1

    \[\leadsto \color{blue}{\left(\left(2 \cdot \log \left(\sqrt[3]{t}\right) + x \cdot \log y\right) - \left(z + y\right)\right)} + \log \left(\sqrt[3]{t}\right)\]

  7. Final simplification0.1

    \[\leadsto \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right) + x \cdot \log y\right) - \left(z + y\right)\right) + \log \left(\sqrt[3]{t}\right)\]

Reproduce

herbie shell --seed 2020047 
(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)))