Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 2.4s

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 r19469 = 0.954929658551372;
        double r19470 = x;
        double r19471 = r19469 * r19470;
        double r19472 = 0.12900613773279798;
        double r19473 = r19470 * r19470;
        double r19474 = r19473 * r19470;
        double r19475 = r19472 * r19474;
        double r19476 = r19471 - r19475;
        return r19476;
}

↓

double f(double x) {
        double r19477 = x;
        double r19478 = 0.954929658551372;
        double r19479 = 0.12900613773279798;
        double r19480 = 3.0;
        double r19481 = pow(r19477, r19480);
        double r19482 = r19479 * r19481;
        double r19483 = -r19482;
        double r19484 = fma(r19477, r19478, r19483);
        return r19484;
}

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 2020081 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))