Average Error: 13.2 → 0.0
Time: 1.4s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot x + y \cdot \left(-z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot x + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r457133 = x;
        double r457134 = y;
        double r457135 = r457133 * r457134;
        double r457136 = r457134 * r457134;
        double r457137 = r457135 - r457136;
        double r457138 = r457137 + r457136;
        double r457139 = z;
        double r457140 = r457134 * r457139;
        double r457141 = r457138 - r457140;
        return r457141;
}
↓
double f(double x, double y, double z) {
        double r457142 = y;
        double r457143 = x;
        double r457144 = r457142 * r457143;
        double r457145 = z;
        double r457146 = -r457145;
        double r457147 = r457142 * r457146;
        double r457148 = r457144 + r457147;
        return r457148;
}

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

Original13.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.2

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

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

    \[\leadsto y \cdot \color{blue}{\left(x + \left(-z\right)\right)}\]

  5. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{y \cdot x + y \cdot \left(-z\right)}\]

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019354 +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)))