Average Error: 0.1 → 0.0
Time: 3.0s
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))
↓
(FPCore (x y z) :precision binary64 (+ 2.0 (* 4.0 (- (/ x y) (/ z y)))))
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 2.0 + (4.0 * ((x / y) - (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

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

  2. Simplified0.2

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

  4. Applied sub-neg_binary64_74840.2

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

  5. Applied distribute-rgt-in_binary64_74430.2

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

  6. Simplified0.2

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

  7. Simplified0.2

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

  8. Taylor expanded around 0 0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020292 
(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)))