Average Error: 0.2 → 0.1
Time: 1.6s
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 r20950 = 0.954929658551372;
        double r20951 = x;
        double r20952 = r20950 * r20951;
        double r20953 = 0.12900613773279798;
        double r20954 = r20951 * r20951;
        double r20955 = r20954 * r20951;
        double r20956 = r20953 * r20955;
        double r20957 = r20952 - r20956;
        return r20957;
}
↓
double f(double x) {
        double r20958 = x;
        double r20959 = 0.954929658551372;
        double r20960 = r20958 * r20959;
        double r20961 = 0.12900613773279798;
        double r20962 = 3.0;
        double r20963 = pow(r20958, r20962);
        double r20964 = r20961 * r20963;
        double r20965 = -r20964;
        double r20966 = r20960 + r20965;
        return r20966;
}

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 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 2020056 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))