Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 2.2s

Precision: 64

Math

\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

↓

\[\mathsf{fma}\left(0.95492965855137202, x, \left(-0.129006137732797982\right) \cdot {x}^{3}\right)\]

C

double f(double x) {
        double r24262 = 0.954929658551372;
        double r24263 = x;
        double r24264 = r24262 * r24263;
        double r24265 = 0.12900613773279798;
        double r24266 = r24263 * r24263;
        double r24267 = r24266 * r24263;
        double r24268 = r24265 * r24267;
        double r24269 = r24264 - r24268;
        return r24269;
}

↓

double f(double x) {
        double r24270 = 0.954929658551372;
        double r24271 = x;
        double r24272 = 0.12900613773279798;
        double r24273 = -r24272;
        double r24274 = 3.0;
        double r24275 = pow(r24271, r24274);
        double r24276 = r24273 * r24275;
        double r24277 = fma(r24270, r24271, r24276);
        return r24277;
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
2. Using strategy rm

3. Applied fma-neg 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.95492965855137202, x, -0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)}\]

4. Simplified 0.1

   \[\leadsto \mathsf{fma}\left(0.95492965855137202, x, \color{blue}{\left(-0.129006137732797982\right) \cdot {x}^{3}}\right)\]

5. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(0.95492965855137202, x, \left(-0.129006137732797982\right) \cdot {x}^{3}\right)\]

Reproduce

herbie shell --seed 2020003 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))