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 r557012 = x;
        double r557013 = y;
        double r557014 = r557012 * r557013;
        double r557015 = z;
        double r557016 = r557013 * r557015;
        double r557017 = r557014 - r557016;
        double r557018 = r557013 * r557013;
        double r557019 = r557017 - r557018;
        double r557020 = r557019 + r557018;
        return r557020;
}
↓
double f(double x, double y, double z) {
        double r557021 = y;
        double r557022 = x;
        double r557023 = z;
        double r557024 = r557022 - r557023;
        double r557025 = r557021 * r557024;
        return r557025;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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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)))