Average Error: 0.3 → 0.2
Time: 2.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\frac{4}{y} \cdot \left(x - z\right) + 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\frac{4}{y} \cdot \left(x - z\right) + 4
double f(double x, double y, double z) {
        double r215948 = 1.0;
        double r215949 = 4.0;
        double r215950 = x;
        double r215951 = y;
        double r215952 = 0.75;
        double r215953 = r215951 * r215952;
        double r215954 = r215950 + r215953;
        double r215955 = z;
        double r215956 = r215954 - r215955;
        double r215957 = r215949 * r215956;
        double r215958 = r215957 / r215951;
        double r215959 = r215948 + r215958;
        return r215959;
}
↓
double f(double x, double y, double z) {
        double r215960 = 4.0;
        double r215961 = y;
        double r215962 = r215960 / r215961;
        double r215963 = x;
        double r215964 = z;
        double r215965 = r215963 - r215964;
        double r215966 = r215962 * r215965;
        double r215967 = r215966 + r215960;
        return r215967;
}

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

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

  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

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019308 
(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)))