Average Error: 17.2 → 0.0
Time: 10.1s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r506063 = x;
        double r506064 = y;
        double r506065 = r506063 * r506064;
        double r506066 = r506064 * r506064;
        double r506067 = r506065 + r506066;
        double r506068 = z;
        double r506069 = r506064 * r506068;
        double r506070 = r506067 - r506069;
        double r506071 = r506070 - r506066;
        return r506071;
}
↓
double f(double x, double y, double z) {
        double r506072 = y;
        double r506073 = x;
        double r506074 = z;
        double r506075 = r506073 - r506074;
        double r506076 = r506072 * r506075;
        return r506076;
}

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

Original17.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.2

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

  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 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (- (+ (* x y) (* y y)) (* y z)) (* y y)))