Average Error: 0.1 → 0.0
Time: 1.6s
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + \frac{4 \cdot \left(x - z\right)}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + \frac{4 \cdot \left(x - z\right)}{y}
(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
↓
(FPCore (x y z) :precision binary64 (+ 4.0 (/ (* 4.0 (- x z)) y)))
double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}
↓
double code(double x, double y, double z) {
	return 4.0 + ((4.0 * (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 0.1

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

  2. Simplified0.2

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

  4. Applied associate-*l/_binary64_102510.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020356 
(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)))