Average Error: 0.1 → 0.2
Time: 50.1s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(x - \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right)\right) - \log \left(\sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) + \left(y - z\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(x - \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right)\right) - \log \left(\sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) + \left(y - z\right)
double f(double x, double y, double z) {
        double r250978 = x;
        double r250979 = y;
        double r250980 = 0.5;
        double r250981 = r250979 + r250980;
        double r250982 = log(r250979);
        double r250983 = r250981 * r250982;
        double r250984 = r250978 - r250983;
        double r250985 = r250984 + r250979;
        double r250986 = z;
        double r250987 = r250985 - r250986;
        return r250987;
}
↓
double f(double x, double y, double z) {
        double r250988 = x;
        double r250989 = 2.0;
        double r250990 = y;
        double r250991 = cbrt(r250990);
        double r250992 = log(r250991);
        double r250993 = r250989 * r250992;
        double r250994 = 0.5;
        double r250995 = r250990 + r250994;
        double r250996 = r250993 * r250995;
        double r250997 = r250988 - r250996;
        double r250998 = r250992 * r250995;
        double r250999 = r250997 - r250998;
        double r251000 = z;
        double r251001 = r250990 - r251000;
        double r251002 = r250999 + r251001;
        return r251002;
}

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

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 associate--l+0.1

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

  5. Applied add-cube-cbrt0.1

    \[\leadsto \left(x - \left(y + 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)}\right) + \left(y - z\right)\]

  6. Applied log-prod0.2

    \[\leadsto \left(x - \left(y + 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)}\right) + \left(y - z\right)\]

  7. Applied distribute-rgt-in0.2

    \[\leadsto \left(x - \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right) + \log \left(\sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right)}\right) + \left(y - z\right)\]

  8. Applied associate--r+0.2

    \[\leadsto \color{blue}{\left(\left(x - \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) - \log \left(\sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right)} + \left(y - z\right)\]

  9. Simplified0.2

    \[\leadsto \left(\color{blue}{\left(x - \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right)\right)} - \log \left(\sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) + \left(y - z\right)\]

  10. Final simplification0.2

    \[\leadsto \left(\left(x - \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot \left(y + 0.5\right)\right) - \log \left(\sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right) + \left(y - z\right)\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

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

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