Average Error: 0.1 → 0.1
Time: 2.1s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot 0.95492965855137202 + \left(-0.129006137732797982 \cdot {x}^{3}\right)\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot 0.95492965855137202 + \left(-0.129006137732797982 \cdot {x}^{3}\right)
double f(double x) {
        double r27236 = 0.954929658551372;
        double r27237 = x;
        double r27238 = r27236 * r27237;
        double r27239 = 0.12900613773279798;
        double r27240 = r27237 * r27237;
        double r27241 = r27240 * r27237;
        double r27242 = r27239 * r27241;
        double r27243 = r27238 - r27242;
        return r27243;
}
↓
double f(double x) {
        double r27244 = x;
        double r27245 = 0.954929658551372;
        double r27246 = r27244 * r27245;
        double r27247 = 0.12900613773279798;
        double r27248 = 3.0;
        double r27249 = pow(r27244, r27248);
        double r27250 = r27247 * r27249;
        double r27251 = -r27250;
        double r27252 = r27246 + r27251;
        return r27252;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  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. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))