Average Error: 17.8 → 0.0
Time: 2.1s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r645587 = x;
        double r645588 = y;
        double r645589 = r645587 * r645588;
        double r645590 = z;
        double r645591 = r645588 * r645590;
        double r645592 = r645589 - r645591;
        double r645593 = r645588 * r645588;
        double r645594 = r645592 - r645593;
        double r645595 = r645594 + r645593;
        return r645595;
}
↓
double f(double x, double y, double z) {
        double r645596 = y;
        double r645597 = x;
        double r645598 = z;
        double r645599 = r645597 - r645598;
        double r645600 = r645596 * r645599;
        return r645600;
}

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

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

  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 2020060 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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