Average Error: 17.8 → 0.0
Time: 1.7s
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 r518530 = x;
        double r518531 = y;
        double r518532 = r518530 * r518531;
        double r518533 = r518531 * r518531;
        double r518534 = r518532 + r518533;
        double r518535 = z;
        double r518536 = r518531 * r518535;
        double r518537 = r518534 - r518536;
        double r518538 = r518537 - r518533;
        return r518538;
}
↓
double f(double x, double y, double z) {
        double r518539 = y;
        double r518540 = x;
        double r518541 = z;
        double r518542 = r518540 - r518541;
        double r518543 = r518539 * r518542;
        return r518543;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020018 
(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)))