Average Error: 0.1 → 0.1
Time: 21.0s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]
↓
\[\left(1.0 \cdot y + y \cdot \left(\log z - z\right)\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)
↓
\left(1.0 \cdot y + y \cdot \left(\log z - z\right)\right) + x \cdot 0.5
double f(double x, double y, double z) {
        double r16842290 = x;
        double r16842291 = 0.5;
        double r16842292 = r16842290 * r16842291;
        double r16842293 = y;
        double r16842294 = 1.0;
        double r16842295 = z;
        double r16842296 = r16842294 - r16842295;
        double r16842297 = log(r16842295);
        double r16842298 = r16842296 + r16842297;
        double r16842299 = r16842293 * r16842298;
        double r16842300 = r16842292 + r16842299;
        return r16842300;
}
↓
double f(double x, double y, double z) {
        double r16842301 = 1.0;
        double r16842302 = y;
        double r16842303 = r16842301 * r16842302;
        double r16842304 = z;
        double r16842305 = log(r16842304);
        double r16842306 = r16842305 - r16842304;
        double r16842307 = r16842302 * r16842306;
        double r16842308 = r16842303 + r16842307;
        double r16842309 = x;
        double r16842310 = 0.5;
        double r16842311 = r16842309 * r16842310;
        double r16842312 = r16842308 + r16842311;
        return r16842312;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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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

    \[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]

  2. Taylor expanded around 0 0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(1.0 \cdot y + y \cdot \log z\right) - z \cdot y\right)}\]

  3. Simplified0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(\log z - z\right) + y \cdot 1.0\right)}\]

  4. Final simplification0.1

    \[\leadsto \left(1.0 \cdot y + y \cdot \left(\log z - z\right)\right) + x \cdot 0.5\]

Reproduce

herbie shell --seed 2019158 
(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)))))