Average Error: 0.2 → 0.0
Time: 9.7s
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 r933212 = 4.0;
        double r933213 = x;
        double r933214 = y;
        double r933215 = r933213 - r933214;
        double r933216 = z;
        double r933217 = 0.5;
        double r933218 = r933216 * r933217;
        double r933219 = r933215 - r933218;
        double r933220 = r933212 * r933219;
        double r933221 = r933220 / r933216;
        return r933221;
}
↓
double f(double x, double y, double z) {
        double r933222 = 4.0;
        double r933223 = x;
        double r933224 = z;
        double r933225 = r933223 / r933224;
        double r933226 = y;
        double r933227 = r933226 / r933224;
        double r933228 = r933225 - r933227;
        double r933229 = 0.5;
        double r933230 = r933228 - r933229;
        double r933231 = r933222 * r933230;
        return r933231;
}

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 2020042 
(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))