Average Error: 0.1 → 0.0
Time: 8.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) \cdot 4 + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) \cdot 4 + 1
double f(double x, double y, double z) {
        double r316391 = 1.0;
        double r316392 = 4.0;
        double r316393 = x;
        double r316394 = y;
        double r316395 = 0.25;
        double r316396 = r316394 * r316395;
        double r316397 = r316393 + r316396;
        double r316398 = z;
        double r316399 = r316397 - r316398;
        double r316400 = r316392 * r316399;
        double r316401 = r316400 / r316394;
        double r316402 = r316391 + r316401;
        return r316402;
}
↓
double f(double x, double y, double z) {
        double r316403 = 0.25;
        double r316404 = x;
        double r316405 = y;
        double r316406 = r316404 / r316405;
        double r316407 = z;
        double r316408 = r316407 / r316405;
        double r316409 = r316406 - r316408;
        double r316410 = r316403 + r316409;
        double r316411 = 4.0;
        double r316412 = r316410 * r316411;
        double r316413 = 1.0;
        double r316414 = r316412 + r316413;
        return r316414;
}

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 0.1

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

  2. Simplified0.0

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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)))