Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 10.8s

Precision: 64

Math

\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

↓

\[\mathsf{fma}\left(0.954929658551372, x, \left(\left(-0.12900613773279798\right) \cdot x\right) \cdot \left(x \cdot x\right)\right)\]

C

double f(double x) {
        double r400966 = 0.954929658551372;
        double r400967 = x;
        double r400968 = r400966 * r400967;
        double r400969 = 0.12900613773279798;
        double r400970 = r400967 * r400967;
        double r400971 = r400970 * r400967;
        double r400972 = r400969 * r400971;
        double r400973 = r400968 - r400972;
        return r400973;
}

↓

double f(double x) {
        double r400974 = 0.954929658551372;
        double r400975 = x;
        double r400976 = 0.12900613773279798;
        double r400977 = -r400976;
        double r400978 = r400977 * r400975;
        double r400979 = r400975 * r400975;
        double r400980 = r400978 * r400979;
        double r400981 = fma(r400974, r400975, r400980);
        return r400981;
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
2. Using strategy rm

3. Applied pow3 0.1

   \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \color{blue}{{x}^{3}}\]
4. Using strategy rm

5. Applied fma-neg 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.954929658551372, x, -0.12900613773279798 \cdot {x}^{3}\right)}\]

6. Simplified 0.1

   \[\leadsto \mathsf{fma}\left(0.954929658551372, x, \color{blue}{\left(\left(-0.12900613773279798\right) \cdot x\right) \cdot \left(x \cdot x\right)}\right)\]

7. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(0.954929658551372, x, \left(\left(-0.12900613773279798\right) \cdot x\right) \cdot \left(x \cdot x\right)\right)\]

Reproduce

herbie shell --seed 2019144 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))