Average Error: 0.2 → 0.0
Time: 10.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + \left(\frac{x - z}{y} + 0.75\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + \left(\frac{x - z}{y} + 0.75\right) \cdot 4
double f(double x, double y, double z) {
        double r212508 = 1.0;
        double r212509 = 4.0;
        double r212510 = x;
        double r212511 = y;
        double r212512 = 0.75;
        double r212513 = r212511 * r212512;
        double r212514 = r212510 + r212513;
        double r212515 = z;
        double r212516 = r212514 - r212515;
        double r212517 = r212509 * r212516;
        double r212518 = r212517 / r212511;
        double r212519 = r212508 + r212518;
        return r212519;
}
↓
double f(double x, double y, double z) {
        double r212520 = 1.0;
        double r212521 = x;
        double r212522 = z;
        double r212523 = r212521 - r212522;
        double r212524 = y;
        double r212525 = r212523 / r212524;
        double r212526 = 0.75;
        double r212527 = r212525 + r212526;
        double r212528 = 4.0;
        double r212529 = r212527 * r212528;
        double r212530 = r212520 + r212529;
        return r212530;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(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)))