Average Error: 0.1 → 0.0
Time: 11.3s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\frac{x - y}{z} - 0.5\right) \cdot 4\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\frac{x - y}{z} - 0.5\right) \cdot 4
double f(double x, double y, double z) {
        double r969946 = 4.0;
        double r969947 = x;
        double r969948 = y;
        double r969949 = r969947 - r969948;
        double r969950 = z;
        double r969951 = 0.5;
        double r969952 = r969950 * r969951;
        double r969953 = r969949 - r969952;
        double r969954 = r969946 * r969953;
        double r969955 = r969954 / r969950;
        return r969955;
}
↓
double f(double x, double y, double z) {
        double r969956 = x;
        double r969957 = y;
        double r969958 = r969956 - r969957;
        double r969959 = z;
        double r969960 = r969958 / r969959;
        double r969961 = 0.5;
        double r969962 = r969960 - r969961;
        double r969963 = 4.0;
        double r969964 = r969962 * r969963;
        return r969964;
}

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

Target

Original0.1
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

    \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{x - y}{z} - 0.5\right) \cdot 4}\]

  3. Final simplification0.0

    \[\leadsto \left(\frac{x - y}{z} - 0.5\right) \cdot 4\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4 (/ x z)) (+ 2 (* 4 (/ y z))))

  (/ (* 4 (- (- x y) (* z 0.5))) z))