Average Error: 13.0 → 0.0
Time: 1.3s
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 r496313 = x;
        double r496314 = y;
        double r496315 = r496313 * r496314;
        double r496316 = r496314 * r496314;
        double r496317 = r496315 - r496316;
        double r496318 = r496317 + r496316;
        double r496319 = z;
        double r496320 = r496314 * r496319;
        double r496321 = r496318 - r496320;
        return r496321;
}
↓
double f(double x, double y, double z) {
        double r496322 = y;
        double r496323 = x;
        double r496324 = z;
        double r496325 = r496323 - r496324;
        double r496326 = r496322 * r496325;
        return r496326;
}

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

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

Derivation

  1. Initial program 13.0

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

  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 2020065 +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)))