Average Error: 0.2 → 0.2
Time: 27.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(y + x\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r504101 = x;
        double r504102 = y;
        double r504103 = r504101 + r504102;
        double r504104 = log(r504103);
        double r504105 = z;
        double r504106 = log(r504105);
        double r504107 = r504104 + r504106;
        double r504108 = t;
        double r504109 = r504107 - r504108;
        double r504110 = a;
        double r504111 = 0.5;
        double r504112 = r504110 - r504111;
        double r504113 = log(r504108);
        double r504114 = r504112 * r504113;
        double r504115 = r504109 + r504114;
        return r504115;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r504116 = y;
        double r504117 = x;
        double r504118 = r504116 + r504117;
        double r504119 = log(r504118);
        double r504120 = z;
        double r504121 = log(r504120);
        double r504122 = t;
        double r504123 = r504121 - r504122;
        double r504124 = a;
        double r504125 = 0.5;
        double r504126 = r504124 - r504125;
        double r504127 = log(r504122);
        double r504128 = r504126 * r504127;
        double r504129 = r504123 + r504128;
        double r504130 = r504119 + r504129;
        return r504130;
}

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

Original0.2
Target0.2
Herbie0.2
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied associate--l+0.2

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

  4. Applied associate-+l+0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 
(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))))