Average Error: 0.2 → 0.0
Time: 1.9s
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 r793122 = 4.0;
        double r793123 = x;
        double r793124 = y;
        double r793125 = r793123 - r793124;
        double r793126 = z;
        double r793127 = 0.5;
        double r793128 = r793126 * r793127;
        double r793129 = r793125 - r793128;
        double r793130 = r793122 * r793129;
        double r793131 = r793130 / r793126;
        return r793131;
}
↓
double f(double x, double y, double z) {
        double r793132 = 4.0;
        double r793133 = x;
        double r793134 = y;
        double r793135 = r793133 - r793134;
        double r793136 = z;
        double r793137 = r793135 / r793136;
        double r793138 = r793132 * r793137;
        double r793139 = 2.0;
        double r793140 = -r793139;
        double r793141 = r793138 + r793140;
        return r793141;
}

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

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

Reproduce

herbie shell --seed 2020049 
(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))