Average Error: 0.2 → 0.0
Time: 3.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(1 + 0.75 \cdot 4\right) + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(1 + 0.75 \cdot 4\right) + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r329213 = 1.0;
        double r329214 = 4.0;
        double r329215 = x;
        double r329216 = y;
        double r329217 = 0.75;
        double r329218 = r329216 * r329217;
        double r329219 = r329215 + r329218;
        double r329220 = z;
        double r329221 = r329219 - r329220;
        double r329222 = r329214 * r329221;
        double r329223 = r329222 / r329216;
        double r329224 = r329213 + r329223;
        return r329224;
}
↓
double f(double x, double y, double z) {
        double r329225 = 1.0;
        double r329226 = 0.75;
        double r329227 = 4.0;
        double r329228 = r329226 * r329227;
        double r329229 = r329225 + r329228;
        double r329230 = x;
        double r329231 = z;
        double r329232 = r329230 - r329231;
        double r329233 = y;
        double r329234 = r329232 / r329233;
        double r329235 = r329234 * r329227;
        double r329236 = r329229 + r329235;
        return r329236;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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 distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020003 
(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)))