Average Error: 0.2 → 0.0
Time: 22.0s
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 r550434 = 4.0;
        double r550435 = x;
        double r550436 = y;
        double r550437 = r550435 - r550436;
        double r550438 = z;
        double r550439 = 0.5;
        double r550440 = r550438 * r550439;
        double r550441 = r550437 - r550440;
        double r550442 = r550434 * r550441;
        double r550443 = r550442 / r550438;
        return r550443;
}
↓
double f(double x, double y, double z) {
        double r550444 = 4.0;
        double r550445 = x;
        double r550446 = z;
        double r550447 = r550445 / r550446;
        double r550448 = y;
        double r550449 = r550448 / r550446;
        double r550450 = r550447 - r550449;
        double r550451 = 0.5;
        double r550452 = r550450 - r550451;
        double r550453 = r550444 * r550452;
        return r550453;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 +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))