Average Error: 0.2 → 0.0
Time: 12.9s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r15886169 = 1.0;
        double r15886170 = 4.0;
        double r15886171 = x;
        double r15886172 = y;
        double r15886173 = 0.75;
        double r15886174 = r15886172 * r15886173;
        double r15886175 = r15886171 + r15886174;
        double r15886176 = z;
        double r15886177 = r15886175 - r15886176;
        double r15886178 = r15886170 * r15886177;
        double r15886179 = r15886178 / r15886172;
        double r15886180 = r15886169 + r15886179;
        return r15886180;
}
↓
double f(double x, double y, double z) {
        double r15886181 = 4.0;
        double r15886182 = x;
        double r15886183 = y;
        double r15886184 = r15886182 / r15886183;
        double r15886185 = z;
        double r15886186 = r15886185 / r15886183;
        double r15886187 = r15886184 - r15886186;
        double r15886188 = r15886181 * r15886187;
        double r15886189 = r15886181 + r15886188;
        return r15886189;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(0.75 - \frac{z - x}{y}\right) + 1.0}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 4.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{4.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)}\]

  5. Final simplification0.0

    \[\leadsto 4.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019162 
(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)))