Average Error: 0.3 → 0.0
Time: 21.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \frac{x - z}{y} + 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \frac{x - z}{y} + 4
double f(double x, double y, double z) {
        double r227039 = 1.0;
        double r227040 = 4.0;
        double r227041 = x;
        double r227042 = y;
        double r227043 = 0.75;
        double r227044 = r227042 * r227043;
        double r227045 = r227041 + r227044;
        double r227046 = z;
        double r227047 = r227045 - r227046;
        double r227048 = r227040 * r227047;
        double r227049 = r227048 / r227042;
        double r227050 = r227039 + r227049;
        return r227050;
}
↓
double f(double x, double y, double z) {
        double r227051 = 4.0;
        double r227052 = x;
        double r227053 = z;
        double r227054 = r227052 - r227053;
        double r227055 = y;
        double r227056 = r227054 / r227055;
        double r227057 = r227051 * r227056;
        double r227058 = r227057 + r227051;
        return r227058;
}

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

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

  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

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

  5. Final simplification0.0

    \[\leadsto 4 \cdot \frac{x - z}{y} + 4\]

Reproduce

herbie shell --seed 2019306 
(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)))