Average Error: 17.5 → 0.0
Time: 1.3s
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 r621452 = x;
        double r621453 = y;
        double r621454 = r621452 * r621453;
        double r621455 = z;
        double r621456 = r621453 * r621455;
        double r621457 = r621454 - r621456;
        double r621458 = r621453 * r621453;
        double r621459 = r621457 - r621458;
        double r621460 = r621459 + r621458;
        return r621460;
}
↓
double f(double x, double y, double z) {
        double r621461 = y;
        double r621462 = x;
        double r621463 = z;
        double r621464 = r621462 - r621463;
        double r621465 = r621461 * r621464;
        return r621465;
}

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

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 
(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)))