Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 15.4s

Precision: 64

Math

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

↓

\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}\]

C

double f(double x) {
        double r572892 = 0.954929658551372;
        double r572893 = x;
        double r572894 = r572892 * r572893;
        double r572895 = 0.12900613773279798;
        double r572896 = r572893 * r572893;
        double r572897 = r572896 * r572893;
        double r572898 = r572895 * r572897;
        double r572899 = r572894 - r572898;
        return r572899;
}

↓

double f(double x) {
        double r572900 = 0.954929658551372;
        double r572901 = x;
        double r572902 = r572900 * r572901;
        double r572903 = 0.12900613773279798;
        double r572904 = 3.0;
        double r572905 = pow(r572901, r572904);
        double r572906 = r572903 * r572905;
        double r572907 = r572902 - r572906;
        return r572907;
}

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 pow1 0.1

   \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot \color{blue}{{x}^{1}}\right)\]

4. Applied pow2 0.1

   \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\color{blue}{{x}^{2}} \cdot {x}^{1}\right)\]

5. Applied pow-prod-up 0.1

   \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \color{blue}{{x}^{\left(2 + 1\right)}}\]

6. Simplified 0.1

   \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{\color{blue}{3}}\]

7. Final simplification 0.1

   \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}\]

Reproduce

herbie shell --seed 2019133 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))