Average Error: 0.2 → 0.0
Time: 1.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(1 + \left(0.75 + \frac{x}{y}\right) \cdot 4\right) + 4 \cdot \left(-\frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(1 + \left(0.75 + \frac{x}{y}\right) \cdot 4\right) + 4 \cdot \left(-\frac{z}{y}\right)
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 ((1.0 + ((0.75 + (x / y)) * 4.0)) + (4.0 * -(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. Using strategy rm

  4. Applied div-sub0.0

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

  6. Applied sub-neg0.0

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

  7. Applied associate-+r+0.0

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

  8. Applied distribute-lft-in0.0

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

  9. Applied associate-+r+0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2020078 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))