Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(4 \cdot y, -z, x\right)\]
x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(4 \cdot y, -z, x\right)
double f(double x, double y, double z) {
        double r143138 = x;
        double r143139 = y;
        double r143140 = 4.0;
        double r143141 = r143139 * r143140;
        double r143142 = z;
        double r143143 = r143141 * r143142;
        double r143144 = r143138 - r143143;
        return r143144;
}
↓
double f(double x, double y, double z) {
        double r143145 = 4.0;
        double r143146 = y;
        double r143147 = r143145 * r143146;
        double r143148 = z;
        double r143149 = -r143148;
        double r143150 = x;
        double r143151 = fma(r143147, r143149, r143150);
        return r143151;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x - \left(y \cdot 4\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(4 \cdot y, -z, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(4 \cdot y, -z, x\right)\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  (- x (* (* y 4.0) z)))