Average Error: 0.1 → 0.0
Time: 14.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r254413 = 1.0;
        double r254414 = 4.0;
        double r254415 = x;
        double r254416 = y;
        double r254417 = 0.75;
        double r254418 = r254416 * r254417;
        double r254419 = r254415 + r254418;
        double r254420 = z;
        double r254421 = r254419 - r254420;
        double r254422 = r254414 * r254421;
        double r254423 = r254422 / r254416;
        double r254424 = r254413 + r254423;
        return r254424;
}
↓
double f(double x, double y, double z) {
        double r254425 = 4.0;
        double r254426 = 1.0;
        double r254427 = x;
        double r254428 = y;
        double r254429 = r254427 / r254428;
        double r254430 = r254426 + r254429;
        double r254431 = z;
        double r254432 = r254431 / r254428;
        double r254433 = r254430 - r254432;
        double r254434 = r254425 * r254433;
        return r254434;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(0.75 - \frac{z - x}{y}\right) \cdot 4 + 1}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 4\right) - 4 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}\]

  5. Final simplification0.0

    \[\leadsto 4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))