Average Error: 0.3 → 0.1
Time: 5.1s
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\frac{4 \cdot \left(x - z\right)}{y} + 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\frac{4 \cdot \left(x - z\right)}{y} + 4
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) ((((double) (4.0 * ((double) (x - z)))) / y) + 4.0));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

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

  2. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020182 
(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)))