Average Error: 0.1 → 0.1
Time: 2.5s
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 r20182 = 0.954929658551372;
        double r20183 = x;
        double r20184 = r20182 * r20183;
        double r20185 = 0.12900613773279798;
        double r20186 = r20183 * r20183;
        double r20187 = r20186 * r20183;
        double r20188 = r20185 * r20187;
        double r20189 = r20184 - r20188;
        return r20189;
}
↓
double f(double x) {
        double r20190 = x;
        double r20191 = 0.954929658551372;
        double r20192 = r20190 * r20191;
        double r20193 = 0.12900613773279798;
        double r20194 = 3.0;
        double r20195 = pow(r20190, r20194);
        double r20196 = r20193 * r20195;
        double r20197 = -r20196;
        double r20198 = r20192 + r20197;
        return r20198;
}

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 2020081 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))