Rosa's Benchmark

Average Error: 0.2 → 0.1

Time: 14.8s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x) {
        double r31897 = 0.954929658551372;
        double r31898 = x;
        double r31899 = r31897 * r31898;
        double r31900 = 0.12900613773279798;
        double r31901 = r31898 * r31898;
        double r31902 = r31901 * r31898;
        double r31903 = r31900 * r31902;
        double r31904 = r31899 - r31903;
        return r31904;
}

↓

double f(double x) {
        double r31905 = 0.954929658551372;
        double r31906 = x;
        double r31907 = 0.12900613773279798;
        double r31908 = r31906 * r31907;
        double r31909 = r31906 * r31908;
        double r31910 = r31906 * r31909;
        double r31911 = -r31910;
        double r31912 = fma(r31905, r31906, r31911);
        return r31912;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

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

2. Simplified 0.2

   \[\leadsto \color{blue}{0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {x}^{3}}\]
3. Using strategy rm

4. Applied fma-neg 0.1

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

5. Simplified 0.1

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

7. Applied unpow3 0.2

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

8. Applied associate-*l* 0.1

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

10. Applied associate-*l* 0.1

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

11. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))