Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B

Average Error: 0.0 → 0.0

Time: 2.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r6949 = x;
        double r6950 = y;
        double r6951 = r6949 + r6950;
        double r6952 = z;
        double r6953 = r6951 * r6952;
        return r6953;
}

↓

double f(double x, double y, double z) {
        double r6954 = x;
        double r6955 = z;
        double r6956 = y;
        double r6957 = r6955 * r6956;
        double r6958 = fma(r6954, r6955, r6957);
        return r6958;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.0

   \[\left(x + y\right) \cdot z\]
2. Using strategy rm

3. Applied pow1 0.0

   \[\leadsto \left(x + y\right) \cdot \color{blue}{{z}^{1}}\]

4. Applied pow1 0.0

   \[\leadsto \color{blue}{{\left(x + y\right)}^{1}} \cdot {z}^{1}\]

5. Applied pow-prod-down 0.0

   \[\leadsto \color{blue}{{\left(\left(x + y\right) \cdot z\right)}^{1}}\]

6. Simplified 0.0

   \[\leadsto {\color{blue}{\left(\mathsf{fma}\left(x, z, z \cdot y\right)\right)}}^{1}\]

7. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))