Average Error: 13.1 → 0.0
Time: 1.4s
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 r397452 = x;
        double r397453 = y;
        double r397454 = r397452 * r397453;
        double r397455 = r397453 * r397453;
        double r397456 = r397454 - r397455;
        double r397457 = r397456 + r397455;
        double r397458 = z;
        double r397459 = r397453 * r397458;
        double r397460 = r397457 - r397459;
        return r397460;
}
↓
double f(double x, double y, double z) {
        double r397461 = y;
        double r397462 = x;
        double r397463 = z;
        double r397464 = r397462 - r397463;
        double r397465 = r397461 * r397464;
        return r397465;
}

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

Original13.1
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.1

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

  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 2020062 +o rules:numerics
(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)))