Average Error: 12.9 → 0.0
Time: 10.7s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r311510 = x;
        double r311511 = y;
        double r311512 = r311510 * r311511;
        double r311513 = r311511 * r311511;
        double r311514 = r311512 - r311513;
        double r311515 = r311514 + r311513;
        double r311516 = z;
        double r311517 = r311511 * r311516;
        double r311518 = r311515 - r311517;
        return r311518;
}
↓
double f(double x, double y, double z) {
        double r311519 = y;
        double r311520 = x;
        double r311521 = z;
        double r311522 = r311520 - r311521;
        double r311523 = r311519 * r311522;
        return r311523;
}

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

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.9

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

  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 2019294 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

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