Average Error: 17.6 → 0.0
Time: 3.7s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r369485 = x;
        double r369486 = y;
        double r369487 = r369485 * r369486;
        double r369488 = z;
        double r369489 = r369486 * r369488;
        double r369490 = r369487 - r369489;
        double r369491 = r369486 * r369486;
        double r369492 = r369490 - r369491;
        double r369493 = r369492 + r369491;
        return r369493;
}
↓
double f(double x, double y, double z) {
        double r369494 = x;
        double r369495 = z;
        double r369496 = r369494 - r369495;
        double r369497 = y;
        double r369498 = r369496 * r369497;
        return r369498;
}

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

Original17.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.6

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

  2. Simplified0.0

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

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019308 
(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)))