Average Error: 17.6 → 0.0
Time: 3.5s
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 r453512 = x;
        double r453513 = y;
        double r453514 = r453512 * r453513;
        double r453515 = z;
        double r453516 = r453513 * r453515;
        double r453517 = r453514 - r453516;
        double r453518 = r453513 * r453513;
        double r453519 = r453517 - r453518;
        double r453520 = r453519 + r453518;
        return r453520;
}
↓
double f(double x, double y, double z) {
        double r453521 = y;
        double r453522 = x;
        double r453523 = z;
        double r453524 = r453522 - r453523;
        double r453525 = r453521 * r453524;
        return r453525;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(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)))