Average Error: 0.1 → 0.0
Time: 5.6s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(2.0 + \frac{x}{y} \cdot 4.0\right) - 4.0 \cdot \frac{z}{y}\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(2.0 + \frac{x}{y} \cdot 4.0\right) - 4.0 \cdot \frac{z}{y}
double f(double x, double y, double z) {
        double r6968252 = 1.0;
        double r6968253 = 4.0;
        double r6968254 = x;
        double r6968255 = y;
        double r6968256 = 0.25;
        double r6968257 = r6968255 * r6968256;
        double r6968258 = r6968254 + r6968257;
        double r6968259 = z;
        double r6968260 = r6968258 - r6968259;
        double r6968261 = r6968253 * r6968260;
        double r6968262 = r6968261 / r6968255;
        double r6968263 = r6968252 + r6968262;
        return r6968263;
}
↓
double f(double x, double y, double z) {
        double r6968264 = 2.0;
        double r6968265 = x;
        double r6968266 = y;
        double r6968267 = r6968265 / r6968266;
        double r6968268 = 4.0;
        double r6968269 = r6968267 * r6968268;
        double r6968270 = r6968264 + r6968269;
        double r6968271 = z;
        double r6968272 = r6968271 / r6968266;
        double r6968273 = r6968268 * r6968272;
        double r6968274 = r6968270 - r6968273;
        return r6968274;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1.0 - 4.0 \cdot \left(\frac{z - x}{y} - 0.25\right)}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 2.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Final simplification0.0

    \[\leadsto \left(2.0 + \frac{x}{y} \cdot 4.0\right) - 4.0 \cdot \frac{z}{y}\]

Reproduce

herbie shell --seed 2019156 
(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)))