Average Error: 0.1 → 0.1
Time: 2.3s
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 r24735 = 0.954929658551372;
        double r24736 = x;
        double r24737 = r24735 * r24736;
        double r24738 = 0.12900613773279798;
        double r24739 = r24736 * r24736;
        double r24740 = r24739 * r24736;
        double r24741 = r24738 * r24740;
        double r24742 = r24737 - r24741;
        return r24742;
}
↓
double f(double x) {
        double r24743 = x;
        double r24744 = 0.954929658551372;
        double r24745 = r24743 * r24744;
        double r24746 = 0.12900613773279798;
        double r24747 = 3.0;
        double r24748 = pow(r24743, r24747);
        double r24749 = r24746 * r24748;
        double r24750 = -r24749;
        double r24751 = r24745 + r24750;
        return r24751;
}

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 2020039 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))