Average Error: 0.1 → 0.0
Time: 1.4s
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 code(double x, double y, double z) {
	return (1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y));
}
↓
double code(double x, double y, double z) {
	return (((4.0 * (x / y)) + 2.0) - (4.0 * (z / y)));
}

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 2020091 
(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)))