Average Error: 16.8 → 0.0
Time: 16.7s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot \left(-z\right) + x \cdot y\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot \left(-z\right) + x \cdot y
double f(double x, double y, double z) {
        double r23512218 = x;
        double r23512219 = y;
        double r23512220 = r23512218 * r23512219;
        double r23512221 = r23512219 * r23512219;
        double r23512222 = r23512220 + r23512221;
        double r23512223 = z;
        double r23512224 = r23512219 * r23512223;
        double r23512225 = r23512222 - r23512224;
        double r23512226 = r23512225 - r23512221;
        return r23512226;
}
↓
double f(double x, double y, double z) {
        double r23512227 = y;
        double r23512228 = z;
        double r23512229 = -r23512228;
        double r23512230 = r23512227 * r23512229;
        double r23512231 = x;
        double r23512232 = r23512231 * r23512227;
        double r23512233 = r23512230 + r23512232;
        return r23512233;
}

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

Original16.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 16.8

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

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied distribute-rgt-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"

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

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