Average Error: 0.2 → 0.1
Time: 13.6s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \left(0.95492965855137202 - \left(0.129006137732797982 \cdot x\right) \cdot x\right)\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot \left(0.95492965855137202 - \left(0.129006137732797982 \cdot x\right) \cdot x\right)
double f(double x) {
        double r21245 = 0.954929658551372;
        double r21246 = x;
        double r21247 = r21245 * r21246;
        double r21248 = 0.12900613773279798;
        double r21249 = r21246 * r21246;
        double r21250 = r21249 * r21246;
        double r21251 = r21248 * r21250;
        double r21252 = r21247 - r21251;
        return r21252;
}
↓
double f(double x) {
        double r21253 = x;
        double r21254 = 0.954929658551372;
        double r21255 = 0.12900613773279798;
        double r21256 = r21255 * r21253;
        double r21257 = r21256 * r21253;
        double r21258 = r21254 - r21257;
        double r21259 = r21253 * r21258;
        return r21259;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

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