Average Error: 0.1 → 0.1
Time: 2.3s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.95492965855137202 \cdot x + \left(-0.129006137732797982\right) \cdot {x}^{3}\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.95492965855137202 \cdot x + \left(-0.129006137732797982\right) \cdot {x}^{3}
double f(double x) {
        double r20300 = 0.954929658551372;
        double r20301 = x;
        double r20302 = r20300 * r20301;
        double r20303 = 0.12900613773279798;
        double r20304 = r20301 * r20301;
        double r20305 = r20304 * r20301;
        double r20306 = r20303 * r20305;
        double r20307 = r20302 - r20306;
        return r20307;
}
↓
double f(double x) {
        double r20308 = 0.954929658551372;
        double r20309 = x;
        double r20310 = r20308 * r20309;
        double r20311 = 0.12900613773279798;
        double r20312 = -r20311;
        double r20313 = 3.0;
        double r20314 = pow(r20309, r20313);
        double r20315 = r20312 * r20314;
        double r20316 = r20310 + r20315;
        return r20316;
}

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. Using strategy rm

  3. Applied sub-neg0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))