Average Error: 17.4 → 0.0
Time: 13.5s
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 r40232 = x;
        double r40233 = y;
        double r40234 = r40232 * r40233;
        double r40235 = r40233 * r40233;
        double r40236 = r40234 + r40235;
        double r40237 = z;
        double r40238 = r40233 * r40237;
        double r40239 = r40236 - r40238;
        double r40240 = r40239 - r40235;
        return r40240;
}
↓
double f(double x, double y, double z) {
        double r40241 = y;
        double r40242 = x;
        double r40243 = z;
        double r40244 = r40242 - r40243;
        double r40245 = r40241 * r40244;
        return r40245;
}

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 2019315 +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)))