Average Error: 0.1 → 0.1
Time: 5.1s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[x \cdot \left(\left(\mathsf{fma}\left(2, z, y\right) + y\right) + t\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
x \cdot \left(\left(\mathsf{fma}\left(2, z, y\right) + y\right) + t\right) + y \cdot 5
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x * ((double) (((double) (((double) (((double) (y + z)) + z)) + y)) + t)))) + ((double) (y * 5.0))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x * ((double) (((double) (((double) fma(2.0, z, y)) + y)) + t)))) + ((double) (y * 5.0))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]

  2. Taylor expanded around 0 0.1

    \[\leadsto x \cdot \left(\left(\color{blue}{\left(2 \cdot z + y\right)} + y\right) + t\right) + y \cdot 5\]

  3. Simplified0.1

    \[\leadsto x \cdot \left(\left(\color{blue}{\mathsf{fma}\left(2, z, y\right)} + y\right) + t\right) + y \cdot 5\]

  4. Final simplification0.1

    \[\leadsto x \cdot \left(\left(\mathsf{fma}\left(2, z, y\right) + y\right) + t\right) + y \cdot 5\]

Reproduce

herbie shell --seed 2020123 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5)))