Average Error: 0.2 → 0.0
Time: 2.2s
Precision: binary64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
↓
\[4 + 4 \cdot \frac{x - z}{y} \]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + 4 \cdot \frac{x - z}{y}

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
↓
(FPCore (x y z) :precision binary64 (+ 4.0 (* 4.0 (/ (- x z) y))))
double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}
↓
double code(double x, double y, double z) {
	return 4.0 + (4.0 * ((x - z) / y));
}

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

Derivation

  1. Initial program 0.2

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

  2. Simplified0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x - z, 4\right)} \]

  3. Applied fma-udef_binary640.2

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

  4. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y}} + 4 \]

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022160 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))