Average Error: 0.1 → 0.0
Time: 9.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \frac{x - z}{y} + \left(4 \cdot 0.25 + 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \frac{x - z}{y} + \left(4 \cdot 0.25 + 1\right)
double f(double x, double y, double z) {
        double r228619 = 1.0;
        double r228620 = 4.0;
        double r228621 = x;
        double r228622 = y;
        double r228623 = 0.25;
        double r228624 = r228622 * r228623;
        double r228625 = r228621 + r228624;
        double r228626 = z;
        double r228627 = r228625 - r228626;
        double r228628 = r228620 * r228627;
        double r228629 = r228628 / r228622;
        double r228630 = r228619 + r228629;
        return r228630;
}
↓
double f(double x, double y, double z) {
        double r228631 = 4.0;
        double r228632 = x;
        double r228633 = z;
        double r228634 = r228632 - r228633;
        double r228635 = y;
        double r228636 = r228634 / r228635;
        double r228637 = r228631 * r228636;
        double r228638 = 0.25;
        double r228639 = r228631 * r228638;
        double r228640 = 1.0;
        double r228641 = r228639 + r228640;
        double r228642 = r228637 + r228641;
        return r228642;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(\frac{x - z}{y} + 0.25\right) + 1}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x - z}{y} + 4 \cdot 0.25\right)} + 1\]

  5. Applied associate-+l+0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + \left(4 \cdot 0.25 + 1\right)}\]

  6. Final simplification0.0

    \[\leadsto 4 \cdot \frac{x - z}{y} + \left(4 \cdot 0.25 + 1\right)\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))