Average Error: 17.7 → 0.0
Time: 1.8s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[\mathsf{fma}\left(y, x - z, 0\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
\mathsf{fma}\left(y, x - z, 0\right)
double f(double x, double y, double z) {
        double r553303 = x;
        double r553304 = y;
        double r553305 = r553303 * r553304;
        double r553306 = r553304 * r553304;
        double r553307 = r553305 + r553306;
        double r553308 = z;
        double r553309 = r553304 * r553308;
        double r553310 = r553307 - r553309;
        double r553311 = r553310 - r553306;
        return r553311;
}
↓
double f(double x, double y, double z) {
        double r553312 = y;
        double r553313 = x;
        double r553314 = z;
        double r553315 = r553313 - r553314;
        double r553316 = 0.0;
        double r553317 = fma(r553312, r553315, r553316);
        return r553317;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.7
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.7

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - z, 0\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x - z, 0\right)\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

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

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