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 r528196 = x;
        double r528197 = y;
        double r528198 = r528196 * r528197;
        double r528199 = r528197 * r528197;
        double r528200 = r528198 - r528199;
        double r528201 = r528200 + r528199;
        double r528202 = z;
        double r528203 = r528197 * r528202;
        double r528204 = r528201 - r528203;
        return r528204;
}
↓
double f(double x, double y, double z) {
        double r528205 = y;
        double r528206 = x;
        double r528207 = z;
        double r528208 = r528206 - r528207;
        double r528209 = r528205 * r528208;
        return r528209;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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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 2020036 
(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)))