Average Error: 0.1 → 0.1
Time: 25.9s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r85199 = x;
        double r85200 = y;
        double r85201 = log(r85200);
        double r85202 = r85199 * r85201;
        double r85203 = r85202 - r85200;
        double r85204 = z;
        double r85205 = r85203 - r85204;
        double r85206 = t;
        double r85207 = log(r85206);
        double r85208 = r85205 + r85207;
        return r85208;
}
↓
double f(double x, double y, double z, double t) {
        double r85209 = y;
        double r85210 = cbrt(r85209);
        double r85211 = r85210 * r85210;
        double r85212 = log(r85211);
        double r85213 = x;
        double r85214 = r85212 * r85213;
        double r85215 = log(r85210);
        double r85216 = r85215 * r85213;
        double r85217 = r85216 - r85209;
        double r85218 = r85214 + r85217;
        double r85219 = z;
        double r85220 = r85218 - r85219;
        double r85221 = t;
        double r85222 = log(r85221);
        double r85223 = r85220 + r85222;
        return r85223;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Applied associate--l+0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(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)))