Average Error: 0.3 → 0.0
Time: 1.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(1 + 0.75 \cdot 4\right) + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(1 + 0.75 \cdot 4\right) + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r269844 = 1.0;
        double r269845 = 4.0;
        double r269846 = x;
        double r269847 = y;
        double r269848 = 0.75;
        double r269849 = r269847 * r269848;
        double r269850 = r269846 + r269849;
        double r269851 = z;
        double r269852 = r269850 - r269851;
        double r269853 = r269845 * r269852;
        double r269854 = r269853 / r269847;
        double r269855 = r269844 + r269854;
        return r269855;
}
↓
double f(double x, double y, double z) {
        double r269856 = 1.0;
        double r269857 = 0.75;
        double r269858 = 4.0;
        double r269859 = r269857 * r269858;
        double r269860 = r269856 + r269859;
        double r269861 = x;
        double r269862 = z;
        double r269863 = r269861 - r269862;
        double r269864 = y;
        double r269865 = r269863 / r269864;
        double r269866 = r269865 * r269858;
        double r269867 = r269860 + r269866;
        return r269867;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

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

  2. Simplified0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 
(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)))