Average Error: 0.0 → 0.0
Time: 23.2s
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 r3896191 = x;
        double r3896192 = y;
        double r3896193 = z;
        double r3896194 = r3896193 + r3896191;
        double r3896195 = r3896192 * r3896194;
        double r3896196 = r3896191 + r3896195;
        return r3896196;
}
↓
double f(double x, double y, double z) {
        double r3896197 = y;
        double r3896198 = x;
        double r3896199 = z;
        double r3896200 = r3896198 + r3896199;
        double r3896201 = fma(r3896197, r3896200, r3896198);
        return r3896201;
}

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 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))