Average Error: 0.3 → 0.3
Time: 29.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log \left(x + y\right) - t\right) - \left(\left(-\log z\right) - \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log \left(x + y\right) - t\right) - \left(\left(-\log z\right) - \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r298027 = x;
        double r298028 = y;
        double r298029 = r298027 + r298028;
        double r298030 = log(r298029);
        double r298031 = z;
        double r298032 = log(r298031);
        double r298033 = r298030 + r298032;
        double r298034 = t;
        double r298035 = r298033 - r298034;
        double r298036 = a;
        double r298037 = 0.5;
        double r298038 = r298036 - r298037;
        double r298039 = log(r298034);
        double r298040 = r298038 * r298039;
        double r298041 = r298035 + r298040;
        return r298041;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r298042 = x;
        double r298043 = y;
        double r298044 = r298042 + r298043;
        double r298045 = log(r298044);
        double r298046 = t;
        double r298047 = r298045 - r298046;
        double r298048 = z;
        double r298049 = log(r298048);
        double r298050 = -r298049;
        double r298051 = a;
        double r298052 = 0.5;
        double r298053 = r298051 - r298052;
        double r298054 = log(r298046);
        double r298055 = r298053 * r298054;
        double r298056 = r298050 - r298055;
        double r298057 = r298047 - r298056;
        return r298057;
}

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. Simplified0.3

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

  4. Applied sub-neg0.3

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

  5. Applied associate--l+0.3

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

  6. Applied associate--r+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019179 
(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))))