Average Error: 0.2 → 0.0
Time: 3.2s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) + \left(-2\right)
double f(double x, double y, double z) {
        double r900215 = 4.0;
        double r900216 = x;
        double r900217 = y;
        double r900218 = r900216 - r900217;
        double r900219 = z;
        double r900220 = 0.5;
        double r900221 = r900219 * r900220;
        double r900222 = r900218 - r900221;
        double r900223 = r900215 * r900222;
        double r900224 = r900223 / r900219;
        return r900224;
}
↓
double f(double x, double y, double z) {
        double r900225 = 4.0;
        double r900226 = x;
        double r900227 = z;
        double r900228 = r900226 / r900227;
        double r900229 = y;
        double r900230 = r900229 / r900227;
        double r900231 = r900228 - r900230;
        double r900232 = r900225 * r900231;
        double r900233 = 2.0;
        double r900234 = -r900233;
        double r900235 = r900232 + r900234;
        return r900235;
}

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  5. Applied div-sub0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(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))