Average Error: 0.2 → 0.0
Time: 14.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + \left(\left(\frac{x}{y} - \frac{z}{y}\right) + 0.75\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + \left(\left(\frac{x}{y} - \frac{z}{y}\right) + 0.75\right) \cdot 4
double f(double x, double y, double z) {
        double r204076 = 1.0;
        double r204077 = 4.0;
        double r204078 = x;
        double r204079 = y;
        double r204080 = 0.75;
        double r204081 = r204079 * r204080;
        double r204082 = r204078 + r204081;
        double r204083 = z;
        double r204084 = r204082 - r204083;
        double r204085 = r204077 * r204084;
        double r204086 = r204085 / r204079;
        double r204087 = r204076 + r204086;
        return r204087;
}
↓
double f(double x, double y, double z) {
        double r204088 = 1.0;
        double r204089 = x;
        double r204090 = y;
        double r204091 = r204089 / r204090;
        double r204092 = z;
        double r204093 = r204092 / r204090;
        double r204094 = r204091 - r204093;
        double r204095 = 0.75;
        double r204096 = r204094 + r204095;
        double r204097 = 4.0;
        double r204098 = r204096 * r204097;
        double r204099 = r204088 + r204098;
        return r204099;
}

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

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(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)))