Average Error: 0.2 → 0.0
Time: 1.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)
double f(double x, double y, double z) {
        double r247183 = 1.0;
        double r247184 = 4.0;
        double r247185 = x;
        double r247186 = y;
        double r247187 = 0.75;
        double r247188 = r247186 * r247187;
        double r247189 = r247185 + r247188;
        double r247190 = z;
        double r247191 = r247189 - r247190;
        double r247192 = r247184 * r247191;
        double r247193 = r247192 / r247186;
        double r247194 = r247183 + r247193;
        return r247194;
}
↓
double f(double x, double y, double z) {
        double r247195 = 1.0;
        double r247196 = 4.0;
        double r247197 = 0.75;
        double r247198 = x;
        double r247199 = y;
        double r247200 = r247198 / r247199;
        double r247201 = z;
        double r247202 = r247201 / r247199;
        double r247203 = r247200 - r247202;
        double r247204 = r247197 + r247203;
        double r247205 = r247196 * r247204;
        double r247206 = r247195 + r247205;
        return r247206;
}

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

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

  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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019354 
(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)))