Average Error: 0.2 → 0.0
Time: 10.9s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r12140212 = 1.0;
        double r12140213 = 4.0;
        double r12140214 = x;
        double r12140215 = y;
        double r12140216 = 0.75;
        double r12140217 = r12140215 * r12140216;
        double r12140218 = r12140214 + r12140217;
        double r12140219 = z;
        double r12140220 = r12140218 - r12140219;
        double r12140221 = r12140213 * r12140220;
        double r12140222 = r12140221 / r12140215;
        double r12140223 = r12140212 + r12140222;
        return r12140223;
}
↓
double f(double x, double y, double z) {
        double r12140224 = 4.0;
        double r12140225 = x;
        double r12140226 = y;
        double r12140227 = r12140225 / r12140226;
        double r12140228 = z;
        double r12140229 = r12140228 / r12140226;
        double r12140230 = r12140227 - r12140229;
        double r12140231 = r12140224 * r12140230;
        double r12140232 = r12140224 + r12140231;
        return r12140232;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.2

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

  2. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(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)))