Average Error: 0.1 → 0.0
Time: 9.5s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2
double f(double x, double y, double z) {
        double r565442 = 4.0;
        double r565443 = x;
        double r565444 = y;
        double r565445 = r565443 - r565444;
        double r565446 = z;
        double r565447 = 0.5;
        double r565448 = r565446 * r565447;
        double r565449 = r565445 - r565448;
        double r565450 = r565442 * r565449;
        double r565451 = r565450 / r565446;
        return r565451;
}
↓
double f(double x, double y, double z) {
        double r565452 = 4.0;
        double r565453 = x;
        double r565454 = z;
        double r565455 = r565453 / r565454;
        double r565456 = y;
        double r565457 = r565456 / r565454;
        double r565458 = r565455 - r565457;
        double r565459 = r565452 * r565458;
        double r565460 = 2.0;
        double r565461 = r565459 - r565460;
        return r565461;
}

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

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

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2}\]

  5. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]

Reproduce

herbie shell --seed 2019305 +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))