Average Error: 0.2 → 0.0
Time: 2.2s
Precision: binary64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\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) (4.0 * ((double) (((double) (((double) (x / z)) - ((double) (y / z)))) - 0.5))));
}

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

Original0.2
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.2

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

  2. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(\frac{x - y}{z} - 0.5\right)}\]
  3. Using strategy rm

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020184 
(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))