Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)
double f(double x, double y, double z) {
        double r9886453 = x;
        double r9886454 = y;
        double r9886455 = r9886453 * r9886454;
        double r9886456 = 1.0;
        double r9886457 = r9886453 - r9886456;
        double r9886458 = z;
        double r9886459 = r9886457 * r9886458;
        double r9886460 = r9886455 + r9886459;
        return r9886460;
}
↓
double f(double x, double y, double z) {
        double r9886461 = x;
        double r9886462 = y;
        double r9886463 = 1.0;
        double r9886464 = r9886461 - r9886463;
        double r9886465 = z;
        double r9886466 = r9886464 * r9886465;
        double r9886467 = fma(r9886461, r9886462, r9886466);
        return r9886467;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(x - 1\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))