Average Error: 0.1 → 0.0
Time: 2.4s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(1 + 0.25 \cdot 4\right) + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(1 + 0.25 \cdot 4\right) + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r328507 = 1.0;
        double r328508 = 4.0;
        double r328509 = x;
        double r328510 = y;
        double r328511 = 0.25;
        double r328512 = r328510 * r328511;
        double r328513 = r328509 + r328512;
        double r328514 = z;
        double r328515 = r328513 - r328514;
        double r328516 = r328508 * r328515;
        double r328517 = r328516 / r328510;
        double r328518 = r328507 + r328517;
        return r328518;
}
↓
double f(double x, double y, double z) {
        double r328519 = 1.0;
        double r328520 = 0.25;
        double r328521 = 4.0;
        double r328522 = r328520 * r328521;
        double r328523 = r328519 + r328522;
        double r328524 = x;
        double r328525 = z;
        double r328526 = r328524 - r328525;
        double r328527 = y;
        double r328528 = r328526 / r328527;
        double r328529 = r328528 * r328521;
        double r328530 = r328523 + r328529;
        return r328530;
}

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 0.1

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

  2. Simplified0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(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)))