Average Error: 0.2 → 0.0
Time: 15.0s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + \left(\left(\frac{x}{y} - \frac{z}{y}\right) + 0.75\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + \left(\left(\frac{x}{y} - \frac{z}{y}\right) + 0.75\right) \cdot 4
double f(double x, double y, double z) {
        double r216380 = 1.0;
        double r216381 = 4.0;
        double r216382 = x;
        double r216383 = y;
        double r216384 = 0.75;
        double r216385 = r216383 * r216384;
        double r216386 = r216382 + r216385;
        double r216387 = z;
        double r216388 = r216386 - r216387;
        double r216389 = r216381 * r216388;
        double r216390 = r216389 / r216383;
        double r216391 = r216380 + r216390;
        return r216391;
}
↓
double f(double x, double y, double z) {
        double r216392 = 1.0;
        double r216393 = x;
        double r216394 = y;
        double r216395 = r216393 / r216394;
        double r216396 = z;
        double r216397 = r216396 / r216394;
        double r216398 = r216395 - r216397;
        double r216399 = 0.75;
        double r216400 = r216398 + r216399;
        double r216401 = 4.0;
        double r216402 = r216400 * r216401;
        double r216403 = r216392 + r216402;
        return r216403;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(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)))