Average Error: 0.3 → 0.0
Time: 10.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(1 + \frac{x - z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(1 + \frac{x - z}{y}\right)
double f(double x, double y, double z) {
        double r144959 = 1.0;
        double r144960 = 4.0;
        double r144961 = x;
        double r144962 = y;
        double r144963 = 0.75;
        double r144964 = r144962 * r144963;
        double r144965 = r144961 + r144964;
        double r144966 = z;
        double r144967 = r144965 - r144966;
        double r144968 = r144960 * r144967;
        double r144969 = r144968 / r144962;
        double r144970 = r144959 + r144969;
        return r144970;
}
↓
double f(double x, double y, double z) {
        double r144971 = 4.0;
        double r144972 = 1.0;
        double r144973 = x;
        double r144974 = z;
        double r144975 = r144973 - r144974;
        double r144976 = y;
        double r144977 = r144975 / r144976;
        double r144978 = r144972 + r144977;
        double r144979 = r144971 * r144978;
        return r144979;
}

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 0.3

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

  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. Applied associate-+r-0.0

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

  6. Taylor expanded around 0 0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019294 
(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)))