Average Error: 0.0 → 0.0
Time: 610.0ms
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, z + x, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, z + x, x\right)
double f(double x, double y, double z) {
        double r117842 = x;
        double r117843 = y;
        double r117844 = z;
        double r117845 = r117844 + r117842;
        double r117846 = r117843 * r117845;
        double r117847 = r117842 + r117846;
        return r117847;
}
↓
double f(double x, double y, double z) {
        double r117848 = y;
        double r117849 = z;
        double r117850 = x;
        double r117851 = r117849 + r117850;
        double r117852 = fma(r117848, r117851, r117850);
        return r117852;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))