Average Error: 0.1 → 0.1
Time: 1.6s
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(\frac{4}{y} \cdot x + \frac{z}{y} \cdot -4\right) + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(\frac{4}{y} \cdot x + \frac{z}{y} \cdot -4\right) + 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 y) x) (* (/ z y) -4.0)) 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 / y) * x) + ((z / y) * -4.0)) + 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 sub-neg_binary640.2

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

  5. Applied distribute-rgt-in_binary640.2

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

  6. Simplified0.2

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020233 
(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)))