Average Error: 0.1 → 0.1
Time: 2.6s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\mathsf{fma}\left(y + z, x + x, \mathsf{fma}\left(5, y, t \cdot x\right)\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\mathsf{fma}\left(y + z, x + x, \mathsf{fma}\left(5, y, t \cdot x\right)\right)
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) fma(((double) (y + z)), ((double) (x + x)), ((double) fma(5.0, y, ((double) (t * x))))));
}

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. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020113 +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)))