Average Error: 0.2 → 0.0
Time: 4.2s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x - y}{z} - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x - y}{z} - 0.5\right)
double f(double x, double y, double z) {
        double r665043 = 4.0;
        double r665044 = x;
        double r665045 = y;
        double r665046 = r665044 - r665045;
        double r665047 = z;
        double r665048 = 0.5;
        double r665049 = r665047 * r665048;
        double r665050 = r665046 - r665049;
        double r665051 = r665043 * r665050;
        double r665052 = r665051 / r665047;
        return r665052;
}
↓
double f(double x, double y, double z) {
        double r665053 = 4.0;
        double r665054 = x;
        double r665055 = y;
        double r665056 = r665054 - r665055;
        double r665057 = z;
        double r665058 = r665056 / r665057;
        double r665059 = 0.5;
        double r665060 = r665058 - r665059;
        double r665061 = r665053 * r665060;
        return r665061;
}

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

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

Derivation

  1. Initial program 0.2

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 1978988140 
(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))