Average Error: 17.6 → 0.0
Time: 1.3s
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 r512219 = x;
        double r512220 = y;
        double r512221 = r512219 * r512220;
        double r512222 = z;
        double r512223 = r512220 * r512222;
        double r512224 = r512221 - r512223;
        double r512225 = r512220 * r512220;
        double r512226 = r512224 - r512225;
        double r512227 = r512226 + r512225;
        return r512227;
}
↓
double f(double x, double y, double z) {
        double r512228 = y;
        double r512229 = x;
        double r512230 = z;
        double r512231 = r512229 - r512230;
        double r512232 = r512228 * r512231;
        return r512232;
}

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 2020065 +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)))