Average Error: 17.5 → 0.0
Time: 1.7s
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 r476478 = x;
        double r476479 = y;
        double r476480 = r476478 * r476479;
        double r476481 = z;
        double r476482 = r476479 * r476481;
        double r476483 = r476480 - r476482;
        double r476484 = r476479 * r476479;
        double r476485 = r476483 - r476484;
        double r476486 = r476485 + r476484;
        return r476486;
}
↓
double f(double x, double y, double z) {
        double r476487 = y;
        double r476488 = x;
        double r476489 = z;
        double r476490 = r476488 - r476489;
        double r476491 = r476487 * r476490;
        return r476491;
}

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

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

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

  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 2020083 
(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)))