Average Error: 0.1 → 0.0
Time: 10.6s
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 r697192 = 4.0;
        double r697193 = x;
        double r697194 = y;
        double r697195 = r697193 - r697194;
        double r697196 = z;
        double r697197 = 0.5;
        double r697198 = r697196 * r697197;
        double r697199 = r697195 - r697198;
        double r697200 = r697192 * r697199;
        double r697201 = r697200 / r697196;
        return r697201;
}
↓
double f(double x, double y, double z) {
        double r697202 = 4.0;
        double r697203 = x;
        double r697204 = y;
        double r697205 = r697203 - r697204;
        double r697206 = z;
        double r697207 = r697205 / r697206;
        double r697208 = r697202 * r697207;
        double r697209 = 2.0;
        double r697210 = r697208 - r697209;
        return r697210;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x - y\right) - z \cdot \frac{1}{2}\right)}{z}}\]

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(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))