Average Error: 0.1 → 0.0
Time: 11.6s
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 r231163 = 1.0;
        double r231164 = 4.0;
        double r231165 = x;
        double r231166 = y;
        double r231167 = 0.25;
        double r231168 = r231166 * r231167;
        double r231169 = r231165 + r231168;
        double r231170 = z;
        double r231171 = r231169 - r231170;
        double r231172 = r231164 * r231171;
        double r231173 = r231172 / r231166;
        double r231174 = r231163 + r231173;
        return r231174;
}
↓
double f(double x, double y, double z) {
        double r231175 = 1.0;
        double r231176 = 4.0;
        double r231177 = 0.25;
        double r231178 = x;
        double r231179 = y;
        double r231180 = r231178 / r231179;
        double r231181 = z;
        double r231182 = r231181 / r231179;
        double r231183 = r231180 - r231182;
        double r231184 = r231177 + r231183;
        double r231185 = r231176 * r231184;
        double r231186 = r231175 + r231185;
        return r231186;
}

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 2019294 
(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)))