Average Error: 0.2 → 0.0
Time: 11.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\frac{x - z}{y} \cdot 4 + \left(4 \cdot 0.75 + 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\frac{x - z}{y} \cdot 4 + \left(4 \cdot 0.75 + 1\right)
double f(double x, double y, double z) {
        double r181628 = 1.0;
        double r181629 = 4.0;
        double r181630 = x;
        double r181631 = y;
        double r181632 = 0.75;
        double r181633 = r181631 * r181632;
        double r181634 = r181630 + r181633;
        double r181635 = z;
        double r181636 = r181634 - r181635;
        double r181637 = r181629 * r181636;
        double r181638 = r181637 / r181631;
        double r181639 = r181628 + r181638;
        return r181639;
}
↓
double f(double x, double y, double z) {
        double r181640 = x;
        double r181641 = z;
        double r181642 = r181640 - r181641;
        double r181643 = y;
        double r181644 = r181642 / r181643;
        double r181645 = 4.0;
        double r181646 = r181644 * r181645;
        double r181647 = 0.75;
        double r181648 = r181645 * r181647;
        double r181649 = 1.0;
        double r181650 = r181648 + r181649;
        double r181651 = r181646 + r181650;
        return r181651;
}

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 0.2

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

  2. Simplified0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+l+0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019305 
(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)))