Average Error: 0.1 → 0.0
Time: 1.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}
double f(double x, double y, double z) {
        double r376210 = 1.0;
        double r376211 = 4.0;
        double r376212 = x;
        double r376213 = y;
        double r376214 = 0.25;
        double r376215 = r376213 * r376214;
        double r376216 = r376212 + r376215;
        double r376217 = z;
        double r376218 = r376216 - r376217;
        double r376219 = r376211 * r376218;
        double r376220 = r376219 / r376213;
        double r376221 = r376210 + r376220;
        return r376221;
}
↓
double f(double x, double y, double z) {
        double r376222 = 4.0;
        double r376223 = x;
        double r376224 = y;
        double r376225 = r376223 / r376224;
        double r376226 = r376222 * r376225;
        double r376227 = 2.0;
        double r376228 = r376226 + r376227;
        double r376229 = z;
        double r376230 = r376229 / r376224;
        double r376231 = r376222 * r376230;
        double r376232 = r376228 - r376231;
        return r376232;
}

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. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 
(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)))