Average Error: 0.2 → 0.0
Time: 8.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\frac{x - z}{y} + 0.75\right) + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(\frac{x - z}{y} + 0.75\right) + 1
double f(double x, double y, double z) {
        double r218461 = 1.0;
        double r218462 = 4.0;
        double r218463 = x;
        double r218464 = y;
        double r218465 = 0.75;
        double r218466 = r218464 * r218465;
        double r218467 = r218463 + r218466;
        double r218468 = z;
        double r218469 = r218467 - r218468;
        double r218470 = r218462 * r218469;
        double r218471 = r218470 / r218464;
        double r218472 = r218461 + r218471;
        return r218472;
}
↓
double f(double x, double y, double z) {
        double r218473 = 4.0;
        double r218474 = x;
        double r218475 = z;
        double r218476 = r218474 - r218475;
        double r218477 = y;
        double r218478 = r218476 / r218477;
        double r218479 = 0.75;
        double r218480 = r218478 + r218479;
        double r218481 = r218473 * r218480;
        double r218482 = 1.0;
        double r218483 = r218481 + r218482;
        return r218483;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 
(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)))