Average Error: 0.1 → 0.2
Time: 10.9s
Precision: 64
\[\frac{841}{108} \cdot x + \frac{4}{29}\]
↓
\[\frac{\frac{841}{\sqrt{108}}}{\frac{\sqrt{108}}{x}} + \frac{4}{29}\]
\frac{841}{108} \cdot x + \frac{4}{29}
↓
\frac{\frac{841}{\sqrt{108}}}{\frac{\sqrt{108}}{x}} + \frac{4}{29}
double f(double x) {
        double r213525 = 841.0;
        double r213526 = 108.0;
        double r213527 = r213525 / r213526;
        double r213528 = x;
        double r213529 = r213527 * r213528;
        double r213530 = 4.0;
        double r213531 = 29.0;
        double r213532 = r213530 / r213531;
        double r213533 = r213529 + r213532;
        return r213533;
}
↓
double f(double x) {
        double r213534 = 841.0;
        double r213535 = 108.0;
        double r213536 = sqrt(r213535);
        double r213537 = r213534 / r213536;
        double r213538 = x;
        double r213539 = r213536 / r213538;
        double r213540 = r213537 / r213539;
        double r213541 = 4.0;
        double r213542 = 29.0;
        double r213543 = r213541 / r213542;
        double r213544 = r213540 + r213543;
        return r213544;
}

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

    \[\frac{841}{108} \cdot x + \frac{4}{29}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.1

    \[\leadsto \color{blue}{\left(1 \cdot \frac{841}{108}\right)} \cdot x + \frac{4}{29}\]

  4. Applied associate-*l*0.1

    \[\leadsto \color{blue}{1 \cdot \left(\frac{841}{108} \cdot x\right)} + \frac{4}{29}\]

  5. Simplified0.1

    \[\leadsto 1 \cdot \color{blue}{\frac{841}{\frac{108}{x}}} + \frac{4}{29}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity0.1

    \[\leadsto 1 \cdot \frac{841}{\frac{108}{\color{blue}{1 \cdot x}}} + \frac{4}{29}\]

  8. Applied add-sqr-sqrt0.1

    \[\leadsto 1 \cdot \frac{841}{\frac{\color{blue}{\sqrt{108} \cdot \sqrt{108}}}{1 \cdot x}} + \frac{4}{29}\]

  9. Applied times-frac0.2

    \[\leadsto 1 \cdot \frac{841}{\color{blue}{\frac{\sqrt{108}}{1} \cdot \frac{\sqrt{108}}{x}}} + \frac{4}{29}\]

  10. Applied associate-/r*0.2

    \[\leadsto 1 \cdot \color{blue}{\frac{\frac{841}{\frac{\sqrt{108}}{1}}}{\frac{\sqrt{108}}{x}}} + \frac{4}{29}\]

  11. Simplified0.2

    \[\leadsto 1 \cdot \frac{\color{blue}{\frac{841}{\sqrt{108}}}}{\frac{\sqrt{108}}{x}} + \frac{4}{29}\]

  12. Final simplification0.2

    \[\leadsto \frac{\frac{841}{\sqrt{108}}}{\frac{\sqrt{108}}{x}} + \frac{4}{29}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))