Average Error: 0.2 → 0.2
Time: 2.8s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[\mathsf{fma}\left(x, 0.95492965855137202, -0.129006137732797982 \cdot {x}^{3}\right)\]
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)
double f(double x) {
        double r31021 = 0.954929658551372;
        double r31022 = x;
        double r31023 = r31021 * r31022;
        double r31024 = 0.12900613773279798;
        double r31025 = r31022 * r31022;
        double r31026 = r31025 * r31022;
        double r31027 = r31024 * r31026;
        double r31028 = r31023 - r31027;
        return r31028;
}
↓
double f(double x) {
        double r31029 = x;
        double r31030 = 0.954929658551372;
        double r31031 = 0.12900613773279798;
        double r31032 = 3.0;
        double r31033 = pow(r31029, r31032);
        double r31034 = r31031 * r31033;
        double r31035 = -r31034;
        double r31036 = fma(r31029, r31030, r31035);
        return r31036;
}

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. Simplified0.1

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

  4. Applied sub-neg0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.2

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

  8. Applied fma-def0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))