Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\left(z \cdot 1 + x \cdot y\right) + y \cdot \left(-z\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\left(z \cdot 1 + x \cdot y\right) + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r669372 = x;
        double r669373 = y;
        double r669374 = r669372 * r669373;
        double r669375 = z;
        double r669376 = 1.0;
        double r669377 = r669376 - r669373;
        double r669378 = r669375 * r669377;
        double r669379 = r669374 + r669378;
        return r669379;
}
↓
double f(double x, double y, double z) {
        double r669380 = z;
        double r669381 = 1.0;
        double r669382 = r669380 * r669381;
        double r669383 = x;
        double r669384 = y;
        double r669385 = r669383 * r669384;
        double r669386 = r669382 + r669385;
        double r669387 = -r669380;
        double r669388 = r669384 * r669387;
        double r669389 = r669386 + r669388;
        return r669389;
}

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

Original0.0
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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  5. Applied sub-neg0.0

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

  6. Applied distribute-lft-in0.0

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

  7. Applied associate-+r+0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(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))))