Average Error: 0.2 → 0.0
Time: 16.2s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)
double f(double x, double y, double z) {
        double r568958 = 4.0;
        double r568959 = x;
        double r568960 = y;
        double r568961 = r568959 - r568960;
        double r568962 = z;
        double r568963 = 0.5;
        double r568964 = r568962 * r568963;
        double r568965 = r568961 - r568964;
        double r568966 = r568958 * r568965;
        double r568967 = r568966 / r568962;
        return r568967;
}
↓
double f(double x, double y, double z) {
        double r568968 = 4.0;
        double r568969 = x;
        double r568970 = z;
        double r568971 = r568969 / r568970;
        double r568972 = y;
        double r568973 = r568972 / r568970;
        double r568974 = 0.5;
        double r568975 = r568973 + r568974;
        double r568976 = r568971 - r568975;
        double r568977 = r568968 * r568976;
        return r568977;
}

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. 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. Applied associate--l-0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(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))