Average Error: 0.2 → 0.1
Time: 1.8s
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + \left(\frac{4}{y} \cdot x + \frac{z}{y} \cdot -4\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + \left(\frac{4}{y} \cdot x + \frac{z}{y} \cdot -4\right)
(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 y) x) (* (/ z y) -4.0))))
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 / y) * x) + ((z / y) * -4.0));
}

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 0.2

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

  2. Simplified0.2

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

  4. Applied sub-neg_binary640.2

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

  5. Applied distribute-rgt-in_binary640.2

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

  6. Simplified0.2

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020233 
(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)))