Average Error: 17.1 → 0.0
Time: 2.0s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r704227 = x;
        double r704228 = y;
        double r704229 = r704227 * r704228;
        double r704230 = z;
        double r704231 = r704228 * r704230;
        double r704232 = r704229 - r704231;
        double r704233 = r704228 * r704228;
        double r704234 = r704232 - r704233;
        double r704235 = r704234 + r704233;
        return r704235;
}
↓
double f(double x, double y, double z) {
        double r704236 = y;
        double r704237 = x;
        double r704238 = z;
        double r704239 = r704237 - r704238;
        double r704240 = r704236 * r704239;
        return r704240;
}

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

Original17.1
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.1

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

  2. Simplified0.0

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

  4. Applied add-sqr-sqrt31.4

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

  5. Applied associate-*r*31.4

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

  7. Applied associate-*l*31.4

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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