Average Error: 13.2 → 0.0
Time: 3.1s
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 r558820 = x;
        double r558821 = y;
        double r558822 = r558820 * r558821;
        double r558823 = r558821 * r558821;
        double r558824 = r558822 - r558823;
        double r558825 = r558824 + r558823;
        double r558826 = z;
        double r558827 = r558821 * r558826;
        double r558828 = r558825 - r558827;
        return r558828;
}
↓
double f(double x, double y, double z) {
        double r558829 = y;
        double r558830 = x;
        double r558831 = z;
        double r558832 = r558830 - r558831;
        double r558833 = r558829 * r558832;
        return r558833;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020039 +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)))