Average Error: 0.3 → 0.3
Time: 23.9s
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 r5416027 = x;
        double r5416028 = y;
        double r5416029 = r5416027 + r5416028;
        double r5416030 = log(r5416029);
        double r5416031 = z;
        double r5416032 = log(r5416031);
        double r5416033 = r5416030 + r5416032;
        double r5416034 = t;
        double r5416035 = r5416033 - r5416034;
        double r5416036 = a;
        double r5416037 = 0.5;
        double r5416038 = r5416036 - r5416037;
        double r5416039 = log(r5416034);
        double r5416040 = r5416038 * r5416039;
        double r5416041 = r5416035 + r5416040;
        return r5416041;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r5416042 = y;
        double r5416043 = x;
        double r5416044 = r5416042 + r5416043;
        double r5416045 = log(r5416044);
        double r5416046 = z;
        double r5416047 = cbrt(r5416046);
        double r5416048 = r5416047 * r5416047;
        double r5416049 = log(r5416048);
        double r5416050 = r5416045 + r5416049;
        double r5416051 = log(r5416047);
        double r5416052 = r5416050 + r5416051;
        double r5416053 = t;
        double r5416054 = r5416052 - r5416053;
        double r5416055 = a;
        double r5416056 = 0.5;
        double r5416057 = r5416055 - r5416056;
        double r5416058 = log(r5416053);
        double r5416059 = r5416057 * r5416058;
        double r5416060 = r5416054 + r5416059;
        return r5416060;
}

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
Target0.2
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 2019156 +o rules:numerics
(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))))