Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 933.0ms

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r121179 = x;
        double r121180 = y;
        double r121181 = z;
        double r121182 = r121181 + r121179;
        double r121183 = r121180 * r121182;
        double r121184 = r121179 + r121183;
        return r121184;
}

↓

double f(double x, double y, double z) {
        double r121185 = x;
        double r121186 = y;
        double r121187 = z;
        double r121188 = r121186 * r121185;
        double r121189 = fma(r121186, r121187, r121188);
        double r121190 = r121185 + r121189;
        return r121190;
}

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. Using strategy rm

3. Applied distribute-lft-in 0.0

   \[\leadsto x + \color{blue}{\left(y \cdot z + y \cdot x\right)}\]
4. Using strategy rm

5. Applied fma-def 0.0

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

6. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))