Average Error: 0.3 → 0.3
Time: 32.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r22834175 = x;
        double r22834176 = y;
        double r22834177 = r22834175 + r22834176;
        double r22834178 = log(r22834177);
        double r22834179 = z;
        double r22834180 = log(r22834179);
        double r22834181 = r22834178 + r22834180;
        double r22834182 = t;
        double r22834183 = r22834181 - r22834182;
        double r22834184 = a;
        double r22834185 = 0.5;
        double r22834186 = r22834184 - r22834185;
        double r22834187 = log(r22834182);
        double r22834188 = r22834186 * r22834187;
        double r22834189 = r22834183 + r22834188;
        return r22834189;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r22834190 = y;
        double r22834191 = x;
        double r22834192 = r22834190 + r22834191;
        double r22834193 = log(r22834192);
        double r22834194 = z;
        double r22834195 = cbrt(r22834194);
        double r22834196 = r22834195 * r22834195;
        double r22834197 = log(r22834196);
        double r22834198 = r22834193 + r22834197;
        double r22834199 = log(r22834195);
        double r22834200 = r22834198 + r22834199;
        double r22834201 = t;
        double r22834202 = r22834200 - r22834201;
        double r22834203 = a;
        double r22834204 = 0.5;
        double r22834205 = r22834203 - r22834204;
        double r22834206 = log(r22834201);
        double r22834207 = r22834205 * r22834206;
        double r22834208 = r22834202 + r22834207;
        return r22834208;
}

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

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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 add-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))