Average Error: 0.3 → 0.3
Time: 17.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r206 = x;
        double r207 = y;
        double r208 = r206 + r207;
        double r209 = log(r208);
        double r210 = z;
        double r211 = log(r210);
        double r212 = r209 + r211;
        double r213 = t;
        double r214 = r212 - r213;
        double r215 = a;
        double r216 = 0.5;
        double r217 = r215 - r216;
        double r218 = log(r213);
        double r219 = r217 * r218;
        double r220 = r214 + r219;
        return r220;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r221 = x;
        double r222 = y;
        double r223 = r221 + r222;
        double r224 = log(r223);
        double r225 = 3.0;
        double r226 = pow(r224, r225);
        double r227 = z;
        double r228 = log(r227);
        double r229 = pow(r228, r225);
        double r230 = r226 + r229;
        double r231 = r228 - r224;
        double r232 = r228 * r231;
        double r233 = r224 * r224;
        double r234 = r232 + r233;
        double r235 = r230 / r234;
        double r236 = t;
        double r237 = r235 - r236;
        double r238 = a;
        double r239 = 0.5;
        double r240 = r238 - r239;
        double r241 = log(r236);
        double r242 = r240 * r241;
        double r243 = r237 + r242;
        return r243;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied flip3-+0.3

    \[\leadsto \left(\color{blue}{\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log \left(x + y\right) \cdot \log \left(x + y\right) + \left(\log z \cdot \log z - \log \left(x + y\right) \cdot \log z\right)}} - t\right) + \left(a - 0.5\right) \cdot \log t\]

  4. Simplified0.3

    \[\leadsto \left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\color{blue}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)}} - t\right) + \left(a - 0.5\right) \cdot \log t\]

  5. Final simplification0.3

    \[\leadsto \left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]

Reproduce

herbie shell --seed 2020025 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))