Average Error: 0.1 → 0.1
Time: 3.8s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[y \cdot \left(\left(1 - z\right) + \log z\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
y \cdot \left(\left(1 - z\right) + \log z\right) + x \cdot 0.5
double f(double x, double y, double z) {
        double r290594 = x;
        double r290595 = 0.5;
        double r290596 = r290594 * r290595;
        double r290597 = y;
        double r290598 = 1.0;
        double r290599 = z;
        double r290600 = r290598 - r290599;
        double r290601 = log(r290599);
        double r290602 = r290600 + r290601;
        double r290603 = r290597 * r290602;
        double r290604 = r290596 + r290603;
        return r290604;
}
↓
double f(double x, double y, double z) {
        double r290605 = y;
        double r290606 = 1.0;
        double r290607 = z;
        double r290608 = r290606 - r290607;
        double r290609 = log(r290607);
        double r290610 = r290608 + r290609;
        double r290611 = r290605 * r290610;
        double r290612 = x;
        double r290613 = 0.5;
        double r290614 = r290612 * r290613;
        double r290615 = r290611 + r290614;
        return r290615;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.1

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

  4. Taylor expanded around 0 0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 
(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)))))