Average Error: 0.1 → 0.4
Time: 5.4s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[x \cdot \left(\left(\left(\sqrt[3]{\left(y + z\right) + z} \cdot \sqrt[3]{\left(y + z\right) + z}\right) \cdot \sqrt[3]{\left(y + z\right) + z} + y\right) + t\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
x \cdot \left(\left(\left(\sqrt[3]{\left(y + z\right) + z} \cdot \sqrt[3]{\left(y + z\right) + z}\right) \cdot \sqrt[3]{\left(y + z\right) + z} + y\right) + t\right) + y \cdot 5
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 ((x * ((((cbrt(((y + z) + z)) * cbrt(((y + z) + z))) * cbrt(((y + z) + z))) + y) + t)) + (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. Using strategy rm

  3. Applied add-cube-cbrt0.4

    \[\leadsto x \cdot \left(\left(\color{blue}{\left(\sqrt[3]{\left(y + z\right) + z} \cdot \sqrt[3]{\left(y + z\right) + z}\right) \cdot \sqrt[3]{\left(y + z\right) + z}} + y\right) + t\right) + y \cdot 5\]

  4. Final simplification0.4

    \[\leadsto x \cdot \left(\left(\left(\sqrt[3]{\left(y + z\right) + z} \cdot \sqrt[3]{\left(y + z\right) + z}\right) \cdot \sqrt[3]{\left(y + z\right) + z} + y\right) + t\right) + y \cdot 5\]

Reproduce

herbie shell --seed 2020079 
(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)))