Average Error: 0.2 → 0.0
Time: 15.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4
double f(double x, double y, double z) {
        double r36193 = 1.0;
        double r36194 = 4.0;
        double r36195 = x;
        double r36196 = y;
        double r36197 = 0.25;
        double r36198 = r36196 * r36197;
        double r36199 = r36195 + r36198;
        double r36200 = z;
        double r36201 = r36199 - r36200;
        double r36202 = r36194 * r36201;
        double r36203 = r36202 / r36196;
        double r36204 = r36193 + r36203;
        return r36204;
}
↓
double f(double x, double y, double z) {
        double r36205 = 2.0;
        double r36206 = x;
        double r36207 = y;
        double r36208 = r36206 / r36207;
        double r36209 = z;
        double r36210 = r36209 / r36207;
        double r36211 = r36208 - r36210;
        double r36212 = 4.0;
        double r36213 = r36211 * r36212;
        double r36214 = r36205 + r36213;
        return r36214;
}

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

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + \left(\frac{x - z}{y} + 0.25\right) \cdot 4}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{2 + \frac{x - z}{y} \cdot 4}\]
  5. Using strategy rm

  6. Applied div-sub0.0

    \[\leadsto 2 + \color{blue}{\left(\frac{x}{y} - \frac{z}{y}\right)} \cdot 4\]

  7. Final simplification0.0

    \[\leadsto 2 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]

Reproduce

herbie shell --seed 2019310 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))