Average Error: 0.2 → 0.0
Time: 1.1s
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 r345382 = 1.0;
        double r345383 = 4.0;
        double r345384 = x;
        double r345385 = y;
        double r345386 = 0.75;
        double r345387 = r345385 * r345386;
        double r345388 = r345384 + r345387;
        double r345389 = z;
        double r345390 = r345388 - r345389;
        double r345391 = r345383 * r345390;
        double r345392 = r345391 / r345385;
        double r345393 = r345382 + r345392;
        return r345393;
}
↓
double f(double x, double y, double z) {
        double r345394 = 1.0;
        double r345395 = 4.0;
        double r345396 = 0.75;
        double r345397 = x;
        double r345398 = y;
        double r345399 = r345397 / r345398;
        double r345400 = z;
        double r345401 = r345400 / r345398;
        double r345402 = r345399 - r345401;
        double r345403 = r345396 + r345402;
        double r345404 = r345395 * r345403;
        double r345405 = r345394 + r345404;
        return r345405;
}

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 2020062 
(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)))