Average Error: 0.1 → 0.0
Time: 14.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \frac{x - z}{y} + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \frac{x - z}{y} + 2
double f(double x, double y, double z) {
        double r217291 = 1.0;
        double r217292 = 4.0;
        double r217293 = x;
        double r217294 = y;
        double r217295 = 0.25;
        double r217296 = r217294 * r217295;
        double r217297 = r217293 + r217296;
        double r217298 = z;
        double r217299 = r217297 - r217298;
        double r217300 = r217292 * r217299;
        double r217301 = r217300 / r217294;
        double r217302 = r217291 + r217301;
        return r217302;
}
↓
double f(double x, double y, double z) {
        double r217303 = 4.0;
        double r217304 = x;
        double r217305 = z;
        double r217306 = r217304 - r217305;
        double r217307 = y;
        double r217308 = r217306 / r217307;
        double r217309 = r217303 * r217308;
        double r217310 = 2.0;
        double r217311 = r217309 + r217310;
        return r217311;
}

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 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + \left(\frac{x - z}{y} + 0.25\right) \cdot 4}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 2}\]

  5. Final simplification0.0

    \[\leadsto 4 \cdot \frac{x - z}{y} + 2\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))