Average Error: 0.1 → 0.2
Time: 1.5s
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(x - z\right) \cdot \frac{4}{y} + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(x - z\right) \cdot \frac{4}{y} + 2
(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))
↓
(FPCore (x y z) :precision binary64 (+ (* (- x z) (/ 4.0 y)) 2.0))
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 ((x - z) * (4.0 / y)) + 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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020220 
(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)))