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 r829329 = 4.0;
        double r829330 = x;
        double r829331 = y;
        double r829332 = r829330 - r829331;
        double r829333 = z;
        double r829334 = 0.5;
        double r829335 = r829333 * r829334;
        double r829336 = r829332 - r829335;
        double r829337 = r829329 * r829336;
        double r829338 = r829337 / r829333;
        return r829338;
}
↓
double f(double x, double y, double z) {
        double r829339 = 4.0;
        double r829340 = x;
        double r829341 = y;
        double r829342 = r829340 - r829341;
        double r829343 = z;
        double r829344 = r829342 / r829343;
        double r829345 = r829339 * r829344;
        double r829346 = 2.0;
        double r829347 = -r829346;
        double r829348 = r829345 + r829347;
        return r829348;
}

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 2020083 
(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))