Average Error: 0.1 → 0.1
Time: 1.8s
Precision: 64
\[\frac{841}{108} \cdot x + \frac{4}{29}\]
↓
\[841 \cdot \frac{x}{108} + \frac{4}{29}\]
\frac{841}{108} \cdot x + \frac{4}{29}
↓
841 \cdot \frac{x}{108} + \frac{4}{29}
double f(double x) {
        double r282576 = 841.0;
        double r282577 = 108.0;
        double r282578 = r282576 / r282577;
        double r282579 = x;
        double r282580 = r282578 * r282579;
        double r282581 = 4.0;
        double r282582 = 29.0;
        double r282583 = r282581 / r282582;
        double r282584 = r282580 + r282583;
        return r282584;
}
↓
double f(double x) {
        double r282585 = 841.0;
        double r282586 = x;
        double r282587 = 108.0;
        double r282588 = r282586 / r282587;
        double r282589 = r282585 * r282588;
        double r282590 = 4.0;
        double r282591 = 29.0;
        double r282592 = r282590 / r282591;
        double r282593 = r282589 + r282592;
        return r282593;
}

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

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

  3. Applied div-inv0.3

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

  4. Applied associate-*l*0.2

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019354 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))