Average Error: 0.2 → 0.2
Time: 7.6s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\frac{4}{z} \cdot \left(x - y\right) - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\frac{4}{z} \cdot \left(x - y\right) - 2
double f(double x, double y, double z) {
        double r605655 = 4.0;
        double r605656 = x;
        double r605657 = y;
        double r605658 = r605656 - r605657;
        double r605659 = z;
        double r605660 = 0.5;
        double r605661 = r605659 * r605660;
        double r605662 = r605658 - r605661;
        double r605663 = r605655 * r605662;
        double r605664 = r605663 / r605659;
        return r605664;
}
↓
double f(double x, double y, double z) {
        double r605665 = 4.0;
        double r605666 = z;
        double r605667 = r605665 / r605666;
        double r605668 = x;
        double r605669 = y;
        double r605670 = r605668 - r605669;
        double r605671 = r605667 * r605670;
        double r605672 = 2.0;
        double r605673 = r605671 - r605672;
        return r605673;
}

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
Herbie0.2
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

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 simplification0.2

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

Reproduce

herbie shell --seed 2019297 
(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))