Average Error: 17.4 → 0.0
Time: 1.8s
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 r488920 = x;
        double r488921 = y;
        double r488922 = r488920 * r488921;
        double r488923 = r488921 * r488921;
        double r488924 = r488922 + r488923;
        double r488925 = z;
        double r488926 = r488921 * r488925;
        double r488927 = r488924 - r488926;
        double r488928 = r488927 - r488923;
        return r488928;
}
↓
double f(double x, double y, double z) {
        double r488929 = y;
        double r488930 = x;
        double r488931 = z;
        double r488932 = r488930 - r488931;
        double r488933 = r488929 * r488932;
        return r488933;
}

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

Original17.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.4

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

  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 2020081 
(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)))