Average Error: 0.1 → 0.1
Time: 19.5s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(x - \left(y + 0.5\right) \cdot \log \left(\sqrt{y}\right)\right) - \left(\left(y + 0.5\right) \cdot \log \left(\sqrt{y}\right) - y\right)\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(x - \left(y + 0.5\right) \cdot \log \left(\sqrt{y}\right)\right) - \left(\left(y + 0.5\right) \cdot \log \left(\sqrt{y}\right) - y\right)\right) - z
double f(double x, double y, double z) {
        double r21031157 = x;
        double r21031158 = y;
        double r21031159 = 0.5;
        double r21031160 = r21031158 + r21031159;
        double r21031161 = log(r21031158);
        double r21031162 = r21031160 * r21031161;
        double r21031163 = r21031157 - r21031162;
        double r21031164 = r21031163 + r21031158;
        double r21031165 = z;
        double r21031166 = r21031164 - r21031165;
        return r21031166;
}
↓
double f(double x, double y, double z) {
        double r21031167 = x;
        double r21031168 = y;
        double r21031169 = 0.5;
        double r21031170 = r21031168 + r21031169;
        double r21031171 = sqrt(r21031168);
        double r21031172 = log(r21031171);
        double r21031173 = r21031170 * r21031172;
        double r21031174 = r21031167 - r21031173;
        double r21031175 = r21031173 - r21031168;
        double r21031176 = r21031174 - r21031175;
        double r21031177 = z;
        double r21031178 = r21031176 - r21031177;
        return r21031178;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

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

  3. Applied add-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--r+0.1

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

  8. Applied associate-+l-0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

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

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