Average Error: 0.2 → 0.0
Time: 9.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)
double f(double x, double y, double z) {
        double r212231 = 1.0;
        double r212232 = 4.0;
        double r212233 = x;
        double r212234 = y;
        double r212235 = 0.75;
        double r212236 = r212234 * r212235;
        double r212237 = r212233 + r212236;
        double r212238 = z;
        double r212239 = r212237 - r212238;
        double r212240 = r212232 * r212239;
        double r212241 = r212240 / r212234;
        double r212242 = r212231 + r212241;
        return r212242;
}
↓
double f(double x, double y, double z) {
        double r212243 = 1.0;
        double r212244 = 4.0;
        double r212245 = 0.75;
        double r212246 = x;
        double r212247 = y;
        double r212248 = r212246 / r212247;
        double r212249 = z;
        double r212250 = r212249 / r212247;
        double r212251 = r212248 - r212250;
        double r212252 = r212245 + r212251;
        double r212253 = r212244 * r212252;
        double r212254 = r212243 + r212253;
        return r212254;
}

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 0.2

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

  2. Simplified0.0

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))