Average Error: 17.6 → 0.0
Time: 2.7s
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 r456322 = x;
        double r456323 = y;
        double r456324 = r456322 * r456323;
        double r456325 = z;
        double r456326 = r456323 * r456325;
        double r456327 = r456324 - r456326;
        double r456328 = r456323 * r456323;
        double r456329 = r456327 - r456328;
        double r456330 = r456329 + r456328;
        return r456330;
}
↓
double f(double x, double y, double z) {
        double r456331 = y;
        double r456332 = x;
        double r456333 = z;
        double r456334 = r456332 - r456333;
        double r456335 = r456331 * r456334;
        return r456335;
}

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 2020036 +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)))