Average Error: 17.8 → 0.0
Time: 14.9s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r318392 = x;
        double r318393 = y;
        double r318394 = r318392 * r318393;
        double r318395 = r318393 * r318393;
        double r318396 = r318394 + r318395;
        double r318397 = z;
        double r318398 = r318393 * r318397;
        double r318399 = r318396 - r318398;
        double r318400 = r318399 - r318395;
        return r318400;
}
↓
double f(double x, double y, double z) {
        double r318401 = x;
        double r318402 = z;
        double r318403 = r318401 - r318402;
        double r318404 = y;
        double r318405 = r318403 * r318404;
        return r318405;
}

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

Original17.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.8

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x - z\right) \cdot y}\]

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019235 +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)))