Average Error: 17.6 → 0.0
Time: 1.8s
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 r509036 = x;
        double r509037 = y;
        double r509038 = r509036 * r509037;
        double r509039 = z;
        double r509040 = r509037 * r509039;
        double r509041 = r509038 - r509040;
        double r509042 = r509037 * r509037;
        double r509043 = r509041 - r509042;
        double r509044 = r509043 + r509042;
        return r509044;
}
↓
double f(double x, double y, double z) {
        double r509045 = y;
        double r509046 = x;
        double r509047 = z;
        double r509048 = r509046 - r509047;
        double r509049 = r509045 * r509048;
        return r509049;
}

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 2020089 +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)))