Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 2.0s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r23216 = 0.954929658551372;
        double r23217 = x;
        double r23218 = r23216 * r23217;
        double r23219 = 0.12900613773279798;
        double r23220 = r23217 * r23217;
        double r23221 = r23220 * r23217;
        double r23222 = r23219 * r23221;
        double r23223 = r23218 - r23222;
        return r23223;
}

↓

double f(double x) {
        double r23224 = x;
        double r23225 = 0.954929658551372;
        double r23226 = 0.12900613773279798;
        double r23227 = 3.0;
        double r23228 = pow(r23224, r23227);
        double r23229 = r23226 * r23228;
        double r23230 = -r23229;
        double r23231 = fma(r23224, r23225, r23230);
        return r23231;
}

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. Simplified 0.1

   \[\leadsto \color{blue}{x \cdot \left(0.95492965855137202 - 0.129006137732797982 \cdot \left(x \cdot x\right)\right)}\]
3. Using strategy rm

4. Applied sub-neg 0.1

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

5. Applied distribute-lft-in 0.1

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

6. Simplified 0.1

   \[\leadsto x \cdot 0.95492965855137202 + \color{blue}{\left(-0.129006137732797982 \cdot {x}^{3}\right)}\]
7. Using strategy rm

8. Applied fma-def 0.1

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

9. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))