Average Error: 0.1 → 0.0
Time: 8.9s
Precision: binary64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)
double code(double x, double y, double z) {
	return ((double) (((double) (4.0 * ((double) (((double) (x - y)) - ((double) (z * 0.5)))))) / z));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (4.0 * ((double) (x / z)))) - ((double) (((double) (4.0 * ((double) (y / z)))) + 2.0))));
}

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. Using strategy rm

  3. Applied clear-num0.3

    \[\leadsto \color{blue}{\frac{1}{\frac{z}{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}}}\]

  4. Taylor expanded around 0 0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020163 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))