Average Error: 0.1 → 0.9
Time: 4.6s
Precision: binary64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right) + y \cdot 5
(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))
↓
(FPCore (x y z t)
 :precision binary64
 (+ (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ (* (+ y z) 2.0) t))) (* 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 ((cbrt(x) * cbrt(x)) * (cbrt(x) * (((y + z) * 2.0) + 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. 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 add-cube-cbrt_binary640.9

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \left(\left(y + z\right) \cdot 2 + t\right) + y \cdot 5\]

  5. Applied associate-*l*_binary640.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} + y \cdot 5\]

  6. Simplified0.9

    \[\leadsto \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \color{blue}{\left(\left(\left(y + z\right) \cdot 2 + t\right) \cdot \sqrt[3]{x}\right)} + y \cdot 5\]

  7. Final simplification0.9

    \[\leadsto \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right) + y \cdot 5\]

Reproduce

herbie shell --seed 2020232 
(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)))