Average Error: 0.2 → 0.0
Time: 13.5s
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 r16650949 = 1.0;
        double r16650950 = 4.0;
        double r16650951 = x;
        double r16650952 = y;
        double r16650953 = 0.75;
        double r16650954 = r16650952 * r16650953;
        double r16650955 = r16650951 + r16650954;
        double r16650956 = z;
        double r16650957 = r16650955 - r16650956;
        double r16650958 = r16650950 * r16650957;
        double r16650959 = r16650958 / r16650952;
        double r16650960 = r16650949 + r16650959;
        return r16650960;
}
↓
double f(double x, double y, double z) {
        double r16650961 = 4.0;
        double r16650962 = x;
        double r16650963 = y;
        double r16650964 = r16650962 / r16650963;
        double r16650965 = z;
        double r16650966 = r16650965 / r16650963;
        double r16650967 = r16650964 - r16650966;
        double r16650968 = r16650961 * r16650967;
        double r16650969 = r16650961 + r16650968;
        return r16650969;
}

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

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

  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 2019179 
(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)))