Average Error: 17.6 → 0.0
Time: 1.3s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r570192 = x;
        double r570193 = y;
        double r570194 = r570192 * r570193;
        double r570195 = r570193 * r570193;
        double r570196 = r570194 + r570195;
        double r570197 = z;
        double r570198 = r570193 * r570197;
        double r570199 = r570196 - r570198;
        double r570200 = r570199 - r570195;
        return r570200;
}
↓
double f(double x, double y, double z) {
        double r570201 = y;
        double r570202 = x;
        double r570203 = z;
        double r570204 = r570202 - r570203;
        double r570205 = r570201 * r570204;
        return r570205;
}

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

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

  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 2020065 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

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

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