Average Error: 0.2 → 0.0
Time: 2.3s
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\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 (- (/ x y) (/ z y)))))
double code(double x, double y, double z) {
	return ((double) (1.0 + (((double) (4.0 * ((double) (((double) (x + ((double) (y * 0.75)))) - z)))) / y)));
}
↓
double code(double x, double y, double z) {
	return ((double) (4.0 + ((double) (4.0 * ((double) ((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 0.2

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

  2. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

    \[\leadsto \color{blue}{4 + \frac{x - z}{y} \cdot 4}\]
  5. Using strategy rm

  6. Applied div-sub_binary640.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020210 
(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)))