Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 2.1s

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 r30206 = 0.954929658551372;
        double r30207 = x;
        double r30208 = r30206 * r30207;
        double r30209 = 0.12900613773279798;
        double r30210 = r30207 * r30207;
        double r30211 = r30210 * r30207;
        double r30212 = r30209 * r30211;
        double r30213 = r30208 - r30212;
        return r30213;
}

↓

double f(double x) {
        double r30214 = 0.954929658551372;
        double r30215 = x;
        double r30216 = 0.12900613773279798;
        double r30217 = -r30216;
        double r30218 = 3.0;
        double r30219 = pow(r30215, r30218);
        double r30220 = r30217 * r30219;
        double r30221 = fma(r30214, r30215, r30220);
        return r30221;
}

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 2020057 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))