Average Error: 0.1 → 0.1
Time: 13.2s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(\log z + 1\right) - z\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\left(\log z + 1\right) - z\right)
double f(double x, double y, double z) {
        double r209941 = x;
        double r209942 = 0.5;
        double r209943 = r209941 * r209942;
        double r209944 = y;
        double r209945 = 1.0;
        double r209946 = z;
        double r209947 = r209945 - r209946;
        double r209948 = log(r209946);
        double r209949 = r209947 + r209948;
        double r209950 = r209944 * r209949;
        double r209951 = r209943 + r209950;
        return r209951;
}
↓
double f(double x, double y, double z) {
        double r209952 = x;
        double r209953 = 0.5;
        double r209954 = r209952 * r209953;
        double r209955 = y;
        double r209956 = z;
        double r209957 = log(r209956);
        double r209958 = 1.0;
        double r209959 = r209957 + r209958;
        double r209960 = r209959 - r209956;
        double r209961 = r209955 * r209960;
        double r209962 = r209954 + r209961;
        return r209962;
}

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

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around 0 0.1

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

  4. Applied pow10.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

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

  (+ (* x 0.5) (* y (+ (- 1 z) (log z)))))