Average Error: 0.2 → 0.0
Time: 4.4s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x - y}{z} - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x - y}{z} - 2
double f(double x, double y, double z) {
        double r779248 = 4.0;
        double r779249 = x;
        double r779250 = y;
        double r779251 = r779249 - r779250;
        double r779252 = z;
        double r779253 = 0.5;
        double r779254 = r779252 * r779253;
        double r779255 = r779251 - r779254;
        double r779256 = r779248 * r779255;
        double r779257 = r779256 / r779252;
        return r779257;
}
↓
double f(double x, double y, double z) {
        double r779258 = 4.0;
        double r779259 = x;
        double r779260 = y;
        double r779261 = r779259 - r779260;
        double r779262 = z;
        double r779263 = r779261 / r779262;
        double r779264 = r779258 * r779263;
        double r779265 = 2.0;
        double r779266 = r779264 - r779265;
        return r779266;
}

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. Final simplification0.0

    \[\leadsto 4 \cdot \frac{x - y}{z} - 2\]

Reproduce

herbie shell --seed 2019294 
(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))