Average Error: 0.1 → 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 r600131 = 4.0;
        double r600132 = x;
        double r600133 = y;
        double r600134 = r600132 - r600133;
        double r600135 = z;
        double r600136 = 0.5;
        double r600137 = r600135 * r600136;
        double r600138 = r600134 - r600137;
        double r600139 = r600131 * r600138;
        double r600140 = r600139 / r600135;
        return r600140;
}
↓
double f(double x, double y, double z) {
        double r600141 = 4.0;
        double r600142 = x;
        double r600143 = y;
        double r600144 = r600142 - r600143;
        double r600145 = z;
        double r600146 = r600144 / r600145;
        double r600147 = r600141 * r600146;
        double r600148 = 2.0;
        double r600149 = r600147 - r600148;
        return r600149;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 
(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))