Average Error: 0.3 → 0.3
Time: 16.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\]
\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(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r63117 = x;
        double r63118 = y;
        double r63119 = r63117 + r63118;
        double r63120 = log(r63119);
        double r63121 = z;
        double r63122 = log(r63121);
        double r63123 = r63120 + r63122;
        double r63124 = t;
        double r63125 = r63123 - r63124;
        double r63126 = a;
        double r63127 = 0.5;
        double r63128 = r63126 - r63127;
        double r63129 = log(r63124);
        double r63130 = r63128 * r63129;
        double r63131 = r63125 + r63130;
        return r63131;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r63132 = x;
        double r63133 = y;
        double r63134 = r63132 + r63133;
        double r63135 = log(r63134);
        double r63136 = z;
        double r63137 = log(r63136);
        double r63138 = r63135 + r63137;
        double r63139 = t;
        double r63140 = r63138 - r63139;
        double r63141 = sqrt(r63139);
        double r63142 = log(r63141);
        double r63143 = a;
        double r63144 = 0.5;
        double r63145 = r63143 - r63144;
        double r63146 = r63142 * r63145;
        double r63147 = r63140 + r63146;
        double r63148 = r63147 + r63146;
        return r63148;
}

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 add-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-rgt-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019318 
(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))))