Average Error: 0.1 → 0.0
Time: 9.2s
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 r340938 = 1.0;
        double r340939 = 4.0;
        double r340940 = x;
        double r340941 = y;
        double r340942 = 0.75;
        double r340943 = r340941 * r340942;
        double r340944 = r340940 + r340943;
        double r340945 = z;
        double r340946 = r340944 - r340945;
        double r340947 = r340939 * r340946;
        double r340948 = r340947 / r340941;
        double r340949 = r340938 + r340948;
        return r340949;
}
↓
double f(double x, double y, double z) {
        double r340950 = 4.0;
        double r340951 = x;
        double r340952 = y;
        double r340953 = r340951 / r340952;
        double r340954 = z;
        double r340955 = r340954 / r340952;
        double r340956 = r340953 - r340955;
        double r340957 = r340950 * r340956;
        double r340958 = r340957 + r340950;
        return r340958;
}

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

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

  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 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)))