Average Error: 17.8 → 0.0
Time: 2.2s
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 r477540 = x;
        double r477541 = y;
        double r477542 = r477540 * r477541;
        double r477543 = z;
        double r477544 = r477541 * r477543;
        double r477545 = r477542 - r477544;
        double r477546 = r477541 * r477541;
        double r477547 = r477545 - r477546;
        double r477548 = r477547 + r477546;
        return r477548;
}
↓
double f(double x, double y, double z) {
        double r477549 = y;
        double r477550 = x;
        double r477551 = z;
        double r477552 = r477550 - r477551;
        double r477553 = r477549 * r477552;
        return r477553;
}

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

Original17.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.8

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

  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 2020060 +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)))