Average Error: 0.3 → 0.3
Time: 43.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r1612109 = x;
        double r1612110 = y;
        double r1612111 = r1612109 + r1612110;
        double r1612112 = log(r1612111);
        double r1612113 = z;
        double r1612114 = log(r1612113);
        double r1612115 = r1612112 + r1612114;
        double r1612116 = t;
        double r1612117 = r1612115 - r1612116;
        double r1612118 = a;
        double r1612119 = 0.5;
        double r1612120 = r1612118 - r1612119;
        double r1612121 = log(r1612116);
        double r1612122 = r1612120 * r1612121;
        double r1612123 = r1612117 + r1612122;
        return r1612123;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1612124 = a;
        double r1612125 = 0.5;
        double r1612126 = r1612124 - r1612125;
        double r1612127 = t;
        double r1612128 = sqrt(r1612127);
        double r1612129 = log(r1612128);
        double r1612130 = r1612126 * r1612129;
        double r1612131 = y;
        double r1612132 = x;
        double r1612133 = r1612131 + r1612132;
        double r1612134 = log(r1612133);
        double r1612135 = z;
        double r1612136 = log(r1612135);
        double r1612137 = r1612134 + r1612136;
        double r1612138 = r1612137 - r1612127;
        double r1612139 = r1612138 + r1612130;
        double r1612140 = r1612130 + r1612139;
        return r1612140;
}

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-lft-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019149 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))