Average Error: 0.1 → 0.1
Time: 24.7s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(x - \log y \cdot \left(y + 0.5\right)\right) + y\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(x - \log y \cdot \left(y + 0.5\right)\right) + y\right) - z
double f(double x, double y, double z) {
        double r366674 = x;
        double r366675 = y;
        double r366676 = 0.5;
        double r366677 = r366675 + r366676;
        double r366678 = log(r366675);
        double r366679 = r366677 * r366678;
        double r366680 = r366674 - r366679;
        double r366681 = r366680 + r366675;
        double r366682 = z;
        double r366683 = r366681 - r366682;
        return r366683;
}
↓
double f(double x, double y, double z) {
        double r366684 = x;
        double r366685 = y;
        double r366686 = log(r366685);
        double r366687 = 0.5;
        double r366688 = r366685 + r366687;
        double r366689 = r366686 * r366688;
        double r366690 = r366684 - r366689;
        double r366691 = r366690 + r366685;
        double r366692 = z;
        double r366693 = r366691 - r366692;
        return r366693;
}

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 *-un-lft-identity0.1

    \[\leadsto \left(\left(x - \left(y + 0.5\right) \cdot \log \color{blue}{\left(1 \cdot y\right)}\right) + y\right) - z\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(x - \left(y + 0.5\right) \cdot \color{blue}{\left(\log 1 + \log y\right)}\right) + y\right) - z\]

  5. Applied distribute-rgt-in0.1

    \[\leadsto \left(\left(x - \color{blue}{\left(\log 1 \cdot \left(y + 0.5\right) + \log y \cdot \left(y + 0.5\right)\right)}\right) + y\right) - z\]

  6. Applied associate--r+0.1

    \[\leadsto \left(\color{blue}{\left(\left(x - \log 1 \cdot \left(y + 0.5\right)\right) - \log y \cdot \left(y + 0.5\right)\right)} + y\right) - z\]

  7. Simplified0.1

    \[\leadsto \left(\left(\color{blue}{\left(x - 0\right)} - \log y \cdot \left(y + 0.5\right)\right) + y\right) - z\]

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020043 
(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))