Average Error: 0.2 → 0.0
Time: 14.2s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4.0 + \frac{x - z}{y} \cdot 4.0\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4.0 + \frac{x - z}{y} \cdot 4.0
double f(double x, double y, double z) {
        double r11732377 = 1.0;
        double r11732378 = 4.0;
        double r11732379 = x;
        double r11732380 = y;
        double r11732381 = 0.75;
        double r11732382 = r11732380 * r11732381;
        double r11732383 = r11732379 + r11732382;
        double r11732384 = z;
        double r11732385 = r11732383 - r11732384;
        double r11732386 = r11732378 * r11732385;
        double r11732387 = r11732386 / r11732380;
        double r11732388 = r11732377 + r11732387;
        return r11732388;
}
↓
double f(double x, double y, double z) {
        double r11732389 = 4.0;
        double r11732390 = x;
        double r11732391 = z;
        double r11732392 = r11732390 - r11732391;
        double r11732393 = y;
        double r11732394 = r11732392 / r11732393;
        double r11732395 = r11732394 * r11732389;
        double r11732396 = r11732389 + r11732395;
        return r11732396;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4.0, 1.0\right)}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 4.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{4.0 + \frac{x - z}{y} \cdot 4.0}\]

  5. Final simplification0.0

    \[\leadsto 4.0 + \frac{x - z}{y} \cdot 4.0\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))