Average Error: 0.2 → 0.0
Time: 4.5min
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(0.75 - \left(\frac{z}{y} - \frac{x}{y}\right)\right) \cdot 4 + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(0.75 - \left(\frac{z}{y} - \frac{x}{y}\right)\right) \cdot 4 + 1
double code(double x, double y, double z) {
	return ((double) (1.0 + (((double) (4.0 * ((double) (((double) (x + ((double) (y * 0.75)))) - z)))) / y)));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (0.75 - ((double) ((z / y) - (x / y))))) * 4.0)) + 1.0));
}

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 0.2

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(0.75 - \frac{z - x}{y}\right) \cdot 4 + 1}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto \left(0.75 - \color{blue}{\left(\frac{z}{y} - \frac{x}{y}\right)}\right) \cdot 4 + 1\]

  5. Final simplification0.0

    \[\leadsto \left(0.75 - \left(\frac{z}{y} - \frac{x}{y}\right)\right) \cdot 4 + 1\]

Reproduce

herbie shell --seed 2020181 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))