Average Error: 0.1 → 0.1
Time: 17.8s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(x + \left(y - z\right)\right) - \left(y + 0.5\right) \cdot \log y\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(x + \left(y - z\right)\right) - \left(y + 0.5\right) \cdot \log y
double f(double x, double y, double z) {
        double r275112 = x;
        double r275113 = y;
        double r275114 = 0.5;
        double r275115 = r275113 + r275114;
        double r275116 = log(r275113);
        double r275117 = r275115 * r275116;
        double r275118 = r275112 - r275117;
        double r275119 = r275118 + r275113;
        double r275120 = z;
        double r275121 = r275119 - r275120;
        return r275121;
}
↓
double f(double x, double y, double z) {
        double r275122 = x;
        double r275123 = y;
        double r275124 = z;
        double r275125 = r275123 - r275124;
        double r275126 = r275122 + r275125;
        double r275127 = 0.5;
        double r275128 = r275123 + r275127;
        double r275129 = log(r275123);
        double r275130 = r275128 * r275129;
        double r275131 = r275126 - r275130;
        return r275131;
}

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. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 
(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))