Average Error: 5.1 → 0.1
Time: 1.7s
Precision: binary64
\[x \cdot \left(1 + y \cdot y\right) \]
↓
\[x + y \cdot \left(y \cdot x\right) \]
(FPCore (x y) :precision binary64 (* x (+ 1.0 (* y y))))
↓
(FPCore (x y) :precision binary64 (+ x (* y (* y x))))
double code(double x, double y) {
	return x * (1.0 + (y * y));
}
↓
double code(double x, double y) {
	return x + (y * (y * x));
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (1.0d0 + (y * y))
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y * (y * x))
end function

public static double code(double x, double y) {
	return x * (1.0 + (y * y));
}
↓
public static double code(double x, double y) {
	return x + (y * (y * x));
}

def code(x, y):
	return x * (1.0 + (y * y))
↓
def code(x, y):
	return x + (y * (y * x))

function code(x, y)
	return Float64(x * Float64(1.0 + Float64(y * y)))
end
↓
function code(x, y)
	return Float64(x + Float64(y * Float64(y * x)))
end

function tmp = code(x, y)
	tmp = x * (1.0 + (y * y));
end
↓
function tmp = code(x, y)
	tmp = x + (y * (y * x));
end

code[x_, y_] := N[(x * N[(1.0 + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x + N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x \cdot \left(1 + y \cdot y\right)
↓
x + y \cdot \left(y \cdot x\right)

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.1
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y \]

Derivation

  1. Initial program 5.1

    \[x \cdot \left(1 + y \cdot y\right) \]

  2. Simplified5.1

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

  3. Applied egg-rr5.1

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

  4. Taylor expanded in x around 0 5.1

    \[\leadsto \color{blue}{{y}^{2} \cdot x} + x \]

  5. Simplified0.1

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

  6. Final simplification0.1

    \[\leadsto x + y \cdot \left(y \cdot x\right) \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"
  :precision binary64

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1.0 (* y y))))