Average Error: 0.1 → 0.1
Time: 16.7s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {x}^{3}\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {x}^{3}
double f(double x) {
        double r21473 = 0.954929658551372;
        double r21474 = x;
        double r21475 = r21473 * r21474;
        double r21476 = 0.12900613773279798;
        double r21477 = r21474 * r21474;
        double r21478 = r21477 * r21474;
        double r21479 = r21476 * r21478;
        double r21480 = r21475 - r21479;
        return r21480;
}
↓
double f(double x) {
        double r21481 = 0.954929658551372;
        double r21482 = x;
        double r21483 = r21481 * r21482;
        double r21484 = 0.12900613773279798;
        double r21485 = 3.0;
        double r21486 = pow(r21482, r21485);
        double r21487 = r21484 * r21486;
        double r21488 = r21483 - r21487;
        return r21488;
}

Error

Bits error versus x

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Your Program's Arguments

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

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020043 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))