Average Error: 0.1 → 0.1
Time: 17.0s
Precision: binary64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[2 \cdot \left(x \cdot y\right) + \left(x \cdot t + \left(2 \cdot \left(x \cdot z\right) + y \cdot 5\right)\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
2 \cdot \left(x \cdot y\right) + \left(x \cdot t + \left(2 \cdot \left(x \cdot z\right) + y \cdot 5\right)\right)
(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))
↓
(FPCore (x y z t)
 :precision binary64
 (+ (* 2.0 (* x y)) (+ (* x t) (+ (* 2.0 (* x z)) (* y 5.0)))))
double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}
↓
double code(double x, double y, double z, double t) {
	return (2.0 * (x * y)) + ((x * t) + ((2.0 * (x * z)) + (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. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2021096 
(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 5.0)))