Average Error: 0.1 → 0.0
Time: 1.8s
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 r907156 = 4.0;
        double r907157 = x;
        double r907158 = y;
        double r907159 = r907157 - r907158;
        double r907160 = z;
        double r907161 = 0.5;
        double r907162 = r907160 * r907161;
        double r907163 = r907159 - r907162;
        double r907164 = r907156 * r907163;
        double r907165 = r907164 / r907160;
        return r907165;
}
↓
double f(double x, double y, double z) {
        double r907166 = 4.0;
        double r907167 = x;
        double r907168 = y;
        double r907169 = r907167 - r907168;
        double r907170 = z;
        double r907171 = r907169 / r907170;
        double r907172 = r907166 * r907171;
        double r907173 = 2.0;
        double r907174 = -r907173;
        double r907175 = r907172 + r907174;
        return r907175;
}

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 2020027 
(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))