Average Error: 0.1 → 0.1
Time: 4.3s
Precision: binary64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(\left(y + z\right) \cdot 2\right) \cdot x + \left(y \cdot 5 + x \cdot t\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(\left(y + z\right) \cdot 2\right) \cdot x + \left(y \cdot 5 + x \cdot t\right)
(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))
↓
(FPCore (x y z t)
 :precision binary64
 (+ (* (* (+ y z) 2.0) x) (+ (* y 5.0) (* x t))))
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 (((y + z) * 2.0) * x) + ((y * 5.0) + (x * t));
}

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. Using strategy rm

  4. Applied distribute-rgt-in_binary64_41200.1

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

  5. Applied associate-+l+_binary64_41030.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020355 
(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)))