Average Error: 0.0 → 0.0
Time: 14.9s
Precision: 64
\[x \cdot y + \left(x - 1.0\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)\]
x \cdot y + \left(x - 1.0\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)
double f(double x, double y, double z) {
        double r6177225 = x;
        double r6177226 = y;
        double r6177227 = r6177225 * r6177226;
        double r6177228 = 1.0;
        double r6177229 = r6177225 - r6177228;
        double r6177230 = z;
        double r6177231 = r6177229 * r6177230;
        double r6177232 = r6177227 + r6177231;
        return r6177232;
}
↓
double f(double x, double y, double z) {
        double r6177233 = x;
        double r6177234 = y;
        double r6177235 = 1.0;
        double r6177236 = r6177233 - r6177235;
        double r6177237 = z;
        double r6177238 = r6177236 * r6177237;
        double r6177239 = fma(r6177233, r6177234, r6177238);
        return r6177239;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(x - 1.0\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))