Average Error: 0.0 → 0.0
Time: 624.0ms
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 r100091 = x;
        double r100092 = y;
        double r100093 = z;
        double r100094 = r100093 + r100091;
        double r100095 = r100092 * r100094;
        double r100096 = r100091 + r100095;
        return r100096;
}
↓
double f(double x, double y, double z) {
        double r100097 = y;
        double r100098 = z;
        double r100099 = x;
        double r100100 = r100098 + r100099;
        double r100101 = fma(r100097, r100100, r100099);
        return r100101;
}

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 2020060 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))