Average Error: 0.1 → 0.0
Time: 5.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + \left(\frac{x}{\frac{y}{4}} - \frac{z}{\frac{y}{4}}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + \left(\frac{x}{\frac{y}{4}} - \frac{z}{\frac{y}{4}}\right)
double f(double x, double y, double z) {
        double r301477 = 1.0;
        double r301478 = 4.0;
        double r301479 = x;
        double r301480 = y;
        double r301481 = 0.75;
        double r301482 = r301480 * r301481;
        double r301483 = r301479 + r301482;
        double r301484 = z;
        double r301485 = r301483 - r301484;
        double r301486 = r301478 * r301485;
        double r301487 = r301486 / r301480;
        double r301488 = r301477 + r301487;
        return r301488;
}
↓
double f(double x, double y, double z) {
        double r301489 = 4.0;
        double r301490 = x;
        double r301491 = y;
        double r301492 = r301491 / r301489;
        double r301493 = r301490 / r301492;
        double r301494 = z;
        double r301495 = r301494 / r301492;
        double r301496 = r301493 - r301495;
        double r301497 = r301489 + r301496;
        return r301497;
}

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

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

  2. Simplified0.0

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

  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

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

  6. Applied div-sub0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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)))