Average Error: 0.1 → 0.1
Time: 45.0s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(y \cdot 1 + \left(\log z - z\right) \cdot y\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(y \cdot 1 + \left(\log z - z\right) \cdot y\right) + x \cdot 0.5
double f(double x, double y, double z) {
        double r14905255 = x;
        double r14905256 = 0.5;
        double r14905257 = r14905255 * r14905256;
        double r14905258 = y;
        double r14905259 = 1.0;
        double r14905260 = z;
        double r14905261 = r14905259 - r14905260;
        double r14905262 = log(r14905260);
        double r14905263 = r14905261 + r14905262;
        double r14905264 = r14905258 * r14905263;
        double r14905265 = r14905257 + r14905264;
        return r14905265;
}
↓
double f(double x, double y, double z) {
        double r14905266 = y;
        double r14905267 = 1.0;
        double r14905268 = r14905266 * r14905267;
        double r14905269 = z;
        double r14905270 = log(r14905269);
        double r14905271 = r14905270 - r14905269;
        double r14905272 = r14905271 * r14905266;
        double r14905273 = r14905268 + r14905272;
        double r14905274 = x;
        double r14905275 = 0.5;
        double r14905276 = r14905274 * r14905275;
        double r14905277 = r14905273 + r14905276;
        return r14905277;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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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

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"

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

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))