Average Error: 0.1 → 0.0
Time: 3.2s
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \frac{x - z}{y} + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \frac{x - z}{y} + 2
(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))
↓
(FPCore (x y z) :precision binary64 (+ (* 4.0 (/ (- x z) 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 (4.0 * ((x - z) / 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

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

  4. Applied div-inv_binary64_118690.2

    \[\leadsto \color{blue}{\left(4 \cdot \frac{1}{y}\right)} \cdot \left(x - z\right) + 2\]

  5. Applied associate-*l*_binary64_118150.2

    \[\leadsto \color{blue}{4 \cdot \left(\frac{1}{y} \cdot \left(x - z\right)\right)} + 2\]

  6. Simplified0.0

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

  7. Final simplification0.0

    \[\leadsto 4 \cdot \frac{x - z}{y} + 2\]

Reproduce

herbie shell --seed 2020280 
(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)))