Average Error: 0.2 → 0.0
Time: 13.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
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)
double f(double x, double y, double z) {
        double r16341336 = 1.0;
        double r16341337 = 4.0;
        double r16341338 = x;
        double r16341339 = y;
        double r16341340 = 0.75;
        double r16341341 = r16341339 * r16341340;
        double r16341342 = r16341338 + r16341341;
        double r16341343 = z;
        double r16341344 = r16341342 - r16341343;
        double r16341345 = r16341337 * r16341344;
        double r16341346 = r16341345 / r16341339;
        double r16341347 = r16341336 + r16341346;
        return r16341347;
}
↓
double f(double x, double y, double z) {
        double r16341348 = 4.0;
        double r16341349 = x;
        double r16341350 = y;
        double r16341351 = r16341349 / r16341350;
        double r16341352 = z;
        double r16341353 = r16341352 / r16341350;
        double r16341354 = r16341351 - r16341353;
        double r16341355 = r16341348 * r16341354;
        double r16341356 = r16341348 + r16341355;
        return r16341356;
}

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 0.2

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

  2. Simplified0.0

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))