Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, x + z, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, x + z, x\right)
double f(double x, double y, double z) {
        double r6401933 = x;
        double r6401934 = y;
        double r6401935 = z;
        double r6401936 = r6401935 + r6401933;
        double r6401937 = r6401934 * r6401936;
        double r6401938 = r6401933 + r6401937;
        return r6401938;
}
↓
double f(double x, double y, double z) {
        double r6401939 = y;
        double r6401940 = x;
        double r6401941 = z;
        double r6401942 = r6401940 + r6401941;
        double r6401943 = fma(r6401939, r6401942, r6401940);
        return r6401943;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))