Average Error: 0.3 → 0.3
Time: 26.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log t + 3 \cdot \log \left(\sqrt[3]{x + y}\right)\right) + \left(\log z - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(a - 0.5\right) \cdot \log t + 3 \cdot \log \left(\sqrt[3]{x + y}\right)\right) + \left(\log z - t\right)
double f(double x, double y, double z, double t, double a) {
        double r236124 = x;
        double r236125 = y;
        double r236126 = r236124 + r236125;
        double r236127 = log(r236126);
        double r236128 = z;
        double r236129 = log(r236128);
        double r236130 = r236127 + r236129;
        double r236131 = t;
        double r236132 = r236130 - r236131;
        double r236133 = a;
        double r236134 = 0.5;
        double r236135 = r236133 - r236134;
        double r236136 = log(r236131);
        double r236137 = r236135 * r236136;
        double r236138 = r236132 + r236137;
        return r236138;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r236139 = a;
        double r236140 = 0.5;
        double r236141 = r236139 - r236140;
        double r236142 = t;
        double r236143 = log(r236142);
        double r236144 = r236141 * r236143;
        double r236145 = 3.0;
        double r236146 = x;
        double r236147 = y;
        double r236148 = r236146 + r236147;
        double r236149 = cbrt(r236148);
        double r236150 = log(r236149);
        double r236151 = r236145 * r236150;
        double r236152 = r236144 + r236151;
        double r236153 = z;
        double r236154 = log(r236153);
        double r236155 = r236154 - r236142;
        double r236156 = r236152 + r236155;
        return r236156;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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