Average Error: 0.3 → 0.3
Time: 33.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log z + \log t \cdot a\right) - \left(t + 0.5 \cdot \log t\right)\right) + \log \left(y + x\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log z + \log t \cdot a\right) - \left(t + 0.5 \cdot \log t\right)\right) + \log \left(y + x\right)
double f(double x, double y, double z, double t, double a) {
        double r18928129 = x;
        double r18928130 = y;
        double r18928131 = r18928129 + r18928130;
        double r18928132 = log(r18928131);
        double r18928133 = z;
        double r18928134 = log(r18928133);
        double r18928135 = r18928132 + r18928134;
        double r18928136 = t;
        double r18928137 = r18928135 - r18928136;
        double r18928138 = a;
        double r18928139 = 0.5;
        double r18928140 = r18928138 - r18928139;
        double r18928141 = log(r18928136);
        double r18928142 = r18928140 * r18928141;
        double r18928143 = r18928137 + r18928142;
        return r18928143;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r18928144 = z;
        double r18928145 = log(r18928144);
        double r18928146 = t;
        double r18928147 = log(r18928146);
        double r18928148 = a;
        double r18928149 = r18928147 * r18928148;
        double r18928150 = r18928145 + r18928149;
        double r18928151 = 0.5;
        double r18928152 = r18928151 * r18928147;
        double r18928153 = r18928146 + r18928152;
        double r18928154 = r18928150 - r18928153;
        double r18928155 = y;
        double r18928156 = x;
        double r18928157 = r18928155 + r18928156;
        double r18928158 = log(r18928157);
        double r18928159 = r18928154 + r18928158;
        return r18928159;
}

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 associate--l+0.3

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

  4. Applied associate-+l+0.3

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

  5. Taylor expanded around 0 0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019162 
(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))))