Average Error: 0.1 → 0.0
Time: 8.7s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)
double f(double x, double y, double z) {
        double r974058 = 4.0;
        double r974059 = x;
        double r974060 = y;
        double r974061 = r974059 - r974060;
        double r974062 = z;
        double r974063 = 0.5;
        double r974064 = r974062 * r974063;
        double r974065 = r974061 - r974064;
        double r974066 = r974058 * r974065;
        double r974067 = r974066 / r974062;
        return r974067;
}
↓
double f(double x, double y, double z) {
        double r974068 = 4.0;
        double r974069 = x;
        double r974070 = z;
        double r974071 = r974069 / r974070;
        double r974072 = y;
        double r974073 = r974072 / r974070;
        double r974074 = r974071 - r974073;
        double r974075 = 0.5;
        double r974076 = r974074 - r974075;
        double r974077 = r974068 * r974076;
        return r974077;
}

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

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(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))