Average Error: 0.0 → 0.0
Time: 11.9s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\left(\frac{1 \cdot z}{1 - \frac{x \cdot y}{1 \cdot z}} - \frac{y \cdot x}{\frac{1 \cdot z}{x \cdot y} - 1}\right) + \left(-y\right) \cdot z\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\left(\frac{1 \cdot z}{1 - \frac{x \cdot y}{1 \cdot z}} - \frac{y \cdot x}{\frac{1 \cdot z}{x \cdot y} - 1}\right) + \left(-y\right) \cdot z
double f(double x, double y, double z) {
        double r433241 = x;
        double r433242 = y;
        double r433243 = r433241 * r433242;
        double r433244 = z;
        double r433245 = 1.0;
        double r433246 = r433245 - r433242;
        double r433247 = r433244 * r433246;
        double r433248 = r433243 + r433247;
        return r433248;
}
↓
double f(double x, double y, double z) {
        double r433249 = 1.0;
        double r433250 = z;
        double r433251 = r433249 * r433250;
        double r433252 = 1.0;
        double r433253 = x;
        double r433254 = y;
        double r433255 = r433253 * r433254;
        double r433256 = r433255 / r433251;
        double r433257 = r433252 - r433256;
        double r433258 = r433251 / r433257;
        double r433259 = r433254 * r433253;
        double r433260 = r433251 / r433255;
        double r433261 = r433260 - r433252;
        double r433262 = r433259 / r433261;
        double r433263 = r433258 - r433262;
        double r433264 = -r433254;
        double r433265 = r433264 * r433250;
        double r433266 = r433263 + r433265;
        return r433266;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original0.0
Target0.0
Herbie0.0
\[z - \left(z - x\right) \cdot y\]

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot \left(1 - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Simplified0.0

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

  8. Applied flip-+26.0

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

  10. Applied div-sub26.0

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

  11. Simplified11.0

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

  12. Simplified0.0

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

  13. Final simplification0.0

    \[\leadsto \left(\frac{1 \cdot z}{1 - \frac{x \cdot y}{1 \cdot z}} - \frac{y \cdot x}{\frac{1 \cdot z}{x \cdot y} - 1}\right) + \left(-y\right) \cdot z\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (- z (* (- z x) y))

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