Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 15.6s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r17536 = 0.954929658551372;
        double r17537 = x;
        double r17538 = r17536 * r17537;
        double r17539 = 0.12900613773279798;
        double r17540 = r17537 * r17537;
        double r17541 = r17540 * r17537;
        double r17542 = r17539 * r17541;
        double r17543 = r17538 - r17542;
        return r17543;
}

↓

double f(double x) {
        double r17544 = 0.954929658551372;
        double r17545 = x;
        double r17546 = 3.0;
        double r17547 = pow(r17545, r17546);
        double r17548 = -r17547;
        double r17549 = 0.12900613773279798;
        double r17550 = r17548 * r17549;
        double r17551 = fma(r17544, r17545, r17550);
        return r17551;
}

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

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))