Average Error: 0.1 → 0.0
Time: 15.2s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4.0 + 2.0\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4.0 + 2.0
double f(double x, double y, double z) {
        double r13053106 = 1.0;
        double r13053107 = 4.0;
        double r13053108 = x;
        double r13053109 = y;
        double r13053110 = 0.25;
        double r13053111 = r13053109 * r13053110;
        double r13053112 = r13053108 + r13053111;
        double r13053113 = z;
        double r13053114 = r13053112 - r13053113;
        double r13053115 = r13053107 * r13053114;
        double r13053116 = r13053115 / r13053109;
        double r13053117 = r13053106 + r13053116;
        return r13053117;
}
↓
double f(double x, double y, double z) {
        double r13053118 = x;
        double r13053119 = y;
        double r13053120 = r13053118 / r13053119;
        double r13053121 = z;
        double r13053122 = r13053121 / r13053119;
        double r13053123 = r13053120 - r13053122;
        double r13053124 = 4.0;
        double r13053125 = r13053123 * r13053124;
        double r13053126 = 2.0;
        double r13053127 = r13053125 + r13053126;
        return r13053127;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(0.25 + \frac{x - z}{y}, 4.0, 1.0\right)}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 2.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\frac{x - z}{y} \cdot 4.0 + 2.0}\]
  5. Using strategy rm

  6. Applied div-sub0.0

    \[\leadsto \color{blue}{\left(\frac{x}{y} - \frac{z}{y}\right)} \cdot 4.0 + 2.0\]

  7. Final simplification0.0

    \[\leadsto \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4.0 + 2.0\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))