Average Error: 17.7 → 0.0
Time: 2.3s
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 r590138 = x;
        double r590139 = y;
        double r590140 = r590138 * r590139;
        double r590141 = z;
        double r590142 = r590139 * r590141;
        double r590143 = r590140 - r590142;
        double r590144 = r590139 * r590139;
        double r590145 = r590143 - r590144;
        double r590146 = r590145 + r590144;
        return r590146;
}
↓
double f(double x, double y, double z) {
        double r590147 = y;
        double r590148 = x;
        double r590149 = z;
        double r590150 = r590148 - r590149;
        double r590151 = r590147 * r590150;
        return r590151;
}

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

Original17.7
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.7

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

  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 2020021 
(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)))