Average Error: 0.1 → 0.1
Time: 24.3s
Precision: 64
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[\left(0.954929658551372 - \left(x \cdot 0.12900613773279798\right) \cdot x\right) \cdot x\]
0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
\left(0.954929658551372 - \left(x \cdot 0.12900613773279798\right) \cdot x\right) \cdot x
double f(double x) {
        double r879628 = 0.954929658551372;
        double r879629 = x;
        double r879630 = r879628 * r879629;
        double r879631 = 0.12900613773279798;
        double r879632 = r879629 * r879629;
        double r879633 = r879632 * r879629;
        double r879634 = r879631 * r879633;
        double r879635 = r879630 - r879634;
        return r879635;
}
↓
double f(double x) {
        double r879636 = 0.954929658551372;
        double r879637 = x;
        double r879638 = 0.12900613773279798;
        double r879639 = r879637 * r879638;
        double r879640 = r879639 * r879637;
        double r879641 = r879636 - r879640;
        double r879642 = r879641 * r879637;
        return r879642;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)}\]
  3. Using strategy rm

  4. Applied associate-*r*0.1

    \[\leadsto x \cdot \left(0.954929658551372 - \color{blue}{\left(0.12900613773279798 \cdot x\right) \cdot x}\right)\]

  5. Final simplification0.1

    \[\leadsto \left(0.954929658551372 - \left(x \cdot 0.12900613773279798\right) \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))