Average Error: 0.1 → 0.0
Time: 17.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r170159 = 1.0;
        double r170160 = 4.0;
        double r170161 = x;
        double r170162 = y;
        double r170163 = 0.25;
        double r170164 = r170162 * r170163;
        double r170165 = r170161 + r170164;
        double r170166 = z;
        double r170167 = r170165 - r170166;
        double r170168 = r170160 * r170167;
        double r170169 = r170168 / r170162;
        double r170170 = r170159 + r170169;
        return r170170;
}
↓
double f(double x, double y, double z) {
        double r170171 = 2.0;
        double r170172 = 4.0;
        double r170173 = x;
        double r170174 = y;
        double r170175 = r170173 / r170174;
        double r170176 = z;
        double r170177 = r170176 / r170174;
        double r170178 = r170175 - r170177;
        double r170179 = r170172 * r170178;
        double r170180 = r170171 + r170179;
        return r170180;
}

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

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

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{2 + 4 \cdot \frac{x - z}{y}}\]
  5. Using strategy rm

  6. Applied div-sub0.0

    \[\leadsto 2 + 4 \cdot \color{blue}{\left(\frac{x}{y} - \frac{z}{y}\right)}\]

  7. Final simplification0.0

    \[\leadsto 2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))