Average Error: 0.1 → 0.0
Time: 2.4s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x - y}{z} + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x - y}{z} + \left(-2\right)
double f(double x, double y, double z) {
        double r942208 = 4.0;
        double r942209 = x;
        double r942210 = y;
        double r942211 = r942209 - r942210;
        double r942212 = z;
        double r942213 = 0.5;
        double r942214 = r942212 * r942213;
        double r942215 = r942211 - r942214;
        double r942216 = r942208 * r942215;
        double r942217 = r942216 / r942212;
        return r942217;
}
↓
double f(double x, double y, double z) {
        double r942218 = 4.0;
        double r942219 = x;
        double r942220 = y;
        double r942221 = r942219 - r942220;
        double r942222 = z;
        double r942223 = r942221 / r942222;
        double r942224 = r942218 * r942223;
        double r942225 = 2.0;
        double r942226 = -r942225;
        double r942227 = r942224 + r942226;
        return r942227;
}

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. 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

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

Reproduce

herbie shell --seed 2020065 
(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))