Average Error: 0.2 → 0.0
Time: 12.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 4
double f(double x, double y, double z) {
        double r20579576 = 1.0;
        double r20579577 = 4.0;
        double r20579578 = x;
        double r20579579 = y;
        double r20579580 = 0.75;
        double r20579581 = r20579579 * r20579580;
        double r20579582 = r20579578 + r20579581;
        double r20579583 = z;
        double r20579584 = r20579582 - r20579583;
        double r20579585 = r20579577 * r20579584;
        double r20579586 = r20579585 / r20579579;
        double r20579587 = r20579576 + r20579586;
        return r20579587;
}
↓
double f(double x, double y, double z) {
        double r20579588 = 4.0;
        double r20579589 = x;
        double r20579590 = y;
        double r20579591 = r20579589 / r20579590;
        double r20579592 = z;
        double r20579593 = r20579592 / r20579590;
        double r20579594 = r20579591 - r20579593;
        double r20579595 = r20579588 * r20579594;
        double r20579596 = r20579595 + r20579588;
        return r20579596;
}

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

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

  2. Simplified0.0

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

  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

    \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 4}\]
  5. Using strategy rm

  6. Applied div-sub0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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)))