Average Error: 13.3 → 0.0
Time: 2.5s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r588469 = x;
        double r588470 = y;
        double r588471 = r588469 * r588470;
        double r588472 = r588470 * r588470;
        double r588473 = r588471 - r588472;
        double r588474 = r588473 + r588472;
        double r588475 = z;
        double r588476 = r588470 * r588475;
        double r588477 = r588474 - r588476;
        return r588477;
}
↓
double f(double x, double y, double z) {
        double r588478 = y;
        double r588479 = x;
        double r588480 = z;
        double r588481 = r588479 - r588480;
        double r588482 = r588478 * r588481;
        return r588482;
}

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

Original13.3
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.3

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

  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 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

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