Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 23.2s

Precision: 64

Math

\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

↓

\[\mathsf{fma}\left(0.9549296585513720181381813745247200131416, x, -0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)\]

C

double f(double x) {
        double r17888 = 0.954929658551372;
        double r17889 = x;
        double r17890 = r17888 * r17889;
        double r17891 = 0.12900613773279798;
        double r17892 = r17889 * r17889;
        double r17893 = r17892 * r17889;
        double r17894 = r17891 * r17893;
        double r17895 = r17890 - r17894;
        return r17895;
}

↓

double f(double x) {
        double r17896 = 0.954929658551372;
        double r17897 = x;
        double r17898 = 0.12900613773279798;
        double r17899 = 3.0;
        double r17900 = pow(r17897, r17899);
        double r17901 = r17898 * r17900;
        double r17902 = -r17901;
        double r17903 = fma(r17896, r17897, r17902);
        return r17903;
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
2. Using strategy rm

3. Applied fma-neg 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.9549296585513720181381813745247200131416, x, -0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)}\]

4. Simplified 0.1

   \[\leadsto \mathsf{fma}\left(0.9549296585513720181381813745247200131416, x, \color{blue}{-0.1290061377327979819096270830414141528308 \cdot {x}^{3}}\right)\]

5. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(0.9549296585513720181381813745247200131416, x, -0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))