Average Error: 0.1 → 0.1
Time: 14.6s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.95492965855137202 \cdot x - {x}^{3} \cdot 0.129006137732797982\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.95492965855137202 \cdot x - {x}^{3} \cdot 0.129006137732797982
double f(double x) {
        double r18330 = 0.954929658551372;
        double r18331 = x;
        double r18332 = r18330 * r18331;
        double r18333 = 0.12900613773279798;
        double r18334 = r18331 * r18331;
        double r18335 = r18334 * r18331;
        double r18336 = r18333 * r18335;
        double r18337 = r18332 - r18336;
        return r18337;
}
↓
double f(double x) {
        double r18338 = 0.954929658551372;
        double r18339 = x;
        double r18340 = r18338 * r18339;
        double r18341 = 3.0;
        double r18342 = pow(r18339, r18341);
        double r18343 = 0.12900613773279798;
        double r18344 = r18342 * r18343;
        double r18345 = r18340 - r18344;
        return r18345;
}

Error

Bits error versus x

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Results

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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 *-un-lft-identity0.1

    \[\leadsto 0.95492965855137202 \cdot x - \color{blue}{\left(1 \cdot 0.129006137732797982\right)} \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  4. Applied associate-*l*0.1

    \[\leadsto 0.95492965855137202 \cdot x - \color{blue}{1 \cdot \left(0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)}\]

  5. Simplified0.1

    \[\leadsto 0.95492965855137202 \cdot x - 1 \cdot \color{blue}{\left({x}^{3} \cdot 0.129006137732797982\right)}\]

  6. Final simplification0.1

    \[\leadsto 0.95492965855137202 \cdot x - {x}^{3} \cdot 0.129006137732797982\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))