Average Error: 0.1 → 0.0
Time: 2.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)
double f(double x, double y, double z) {
        double r346175 = 1.0;
        double r346176 = 4.0;
        double r346177 = x;
        double r346178 = y;
        double r346179 = 0.25;
        double r346180 = r346178 * r346179;
        double r346181 = r346177 + r346180;
        double r346182 = z;
        double r346183 = r346181 - r346182;
        double r346184 = r346176 * r346183;
        double r346185 = r346184 / r346178;
        double r346186 = r346175 + r346185;
        return r346186;
}
↓
double f(double x, double y, double z) {
        double r346187 = 1.0;
        double r346188 = 4.0;
        double r346189 = 0.25;
        double r346190 = x;
        double r346191 = y;
        double r346192 = r346190 / r346191;
        double r346193 = z;
        double r346194 = r346193 / r346191;
        double r346195 = r346192 - r346194;
        double r346196 = r346189 + r346195;
        double r346197 = r346188 * r346196;
        double r346198 = r346187 + r346197;
        return r346198;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + 4 \cdot \left(0.25 + \frac{x - z}{y}\right)}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto 1 + 4 \cdot \left(0.25 + \color{blue}{\left(\frac{x}{y} - \frac{z}{y}\right)}\right)\]

  5. Final simplification0.0

    \[\leadsto 1 + 4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))