Average Error: 0.1 → 0.0
Time: 1.8s
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(1 + 4 \cdot 0.25\right) + 4 \cdot \frac{x - z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(1 + 4 \cdot 0.25\right) + 4 \cdot \frac{x - z}{y}
double code(double x, double y, double z) {
	return ((double) (1.0 + (((double) (4.0 * ((double) (((double) (x + ((double) (y * 0.25)))) - z)))) / y)));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (1.0 + ((double) (4.0 * 0.25)))) + ((double) (4.0 * (((double) (x - 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 Error: 0.1 bits

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

  2. SimplifiedError: 0.0 bits

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

  4. Applied distribute-lft-inError: 0.0 bits

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

  5. Applied associate-+r+Error: 0.0 bits

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

  6. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020200 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))