Average Error: 0.1 → 0.2
Time: 1.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\mathsf{fma}\left(\frac{4}{y}, x - z, 2\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\mathsf{fma}\left(\frac{4}{y}, x - z, 2\right)
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 fma((4.0 / y), (x - z), 2.0);
}

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. Simplified0.2

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x - z, 2\right)}\]

  5. Final simplification0.2

    \[\leadsto \mathsf{fma}\left(\frac{4}{y}, x - z, 2\right)\]

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(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)))