Average Error: 0.2 → 0.0
Time: 1.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)
double f(double x, double y, double z) {
        double r332037 = 1.0;
        double r332038 = 4.0;
        double r332039 = x;
        double r332040 = y;
        double r332041 = 0.75;
        double r332042 = r332040 * r332041;
        double r332043 = r332039 + r332042;
        double r332044 = z;
        double r332045 = r332043 - r332044;
        double r332046 = r332038 * r332045;
        double r332047 = r332046 / r332040;
        double r332048 = r332037 + r332047;
        return r332048;
}
↓
double f(double x, double y, double z) {
        double r332049 = 1.0;
        double r332050 = 4.0;
        double r332051 = 0.75;
        double r332052 = x;
        double r332053 = y;
        double r332054 = r332052 / r332053;
        double r332055 = z;
        double r332056 = r332055 / r332053;
        double r332057 = r332054 - r332056;
        double r332058 = r332051 + r332057;
        double r332059 = r332050 * r332058;
        double r332060 = r332049 + r332059;
        return r332060;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 
(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)))