Average Error: 62.0 → 0
Time: 3.2s
Precision: binary64
Cost: 1600
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right) \]
↓
\[\begin{array}{l} t_0 := \left(x \cdot x\right) \cdot 3\\ \left(t_0 + y \cdot y\right) \cdot \left(t_0 - y \cdot y\right) - \left(y \cdot y\right) \cdot -2 \end{array} \]
(FPCore (x y)
 :precision binary64
 (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))
↓
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* x x) 3.0)))
   (- (* (+ t_0 (* y y)) (- t_0 (* y y))) (* (* y y) -2.0))))
double code(double x, double y) {
	return (9.0 * pow(x, 4.0)) - ((y * y) * ((y * y) - 2.0));
}
↓
double code(double x, double y) {
	double t_0 = (x * x) * 3.0;
	return ((t_0 + (y * y)) * (t_0 - (y * y))) - ((y * y) * -2.0);
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (9.0d0 * (x ** 4.0d0)) - ((y * y) * ((y * y) - 2.0d0))
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = (x * x) * 3.0d0
    code = ((t_0 + (y * y)) * (t_0 - (y * y))) - ((y * y) * (-2.0d0))
end function

public static double code(double x, double y) {
	return (9.0 * Math.pow(x, 4.0)) - ((y * y) * ((y * y) - 2.0));
}
↓
public static double code(double x, double y) {
	double t_0 = (x * x) * 3.0;
	return ((t_0 + (y * y)) * (t_0 - (y * y))) - ((y * y) * -2.0);
}

def code(x, y):
	return (9.0 * math.pow(x, 4.0)) - ((y * y) * ((y * y) - 2.0))
↓
def code(x, y):
	t_0 = (x * x) * 3.0
	return ((t_0 + (y * y)) * (t_0 - (y * y))) - ((y * y) * -2.0)

function code(x, y)
	return Float64(Float64(9.0 * (x ^ 4.0)) - Float64(Float64(y * y) * Float64(Float64(y * y) - 2.0)))
end
↓
function code(x, y)
	t_0 = Float64(Float64(x * x) * 3.0)
	return Float64(Float64(Float64(t_0 + Float64(y * y)) * Float64(t_0 - Float64(y * y))) - Float64(Float64(y * y) * -2.0))
end

function tmp = code(x, y)
	tmp = (9.0 * (x ^ 4.0)) - ((y * y) * ((y * y) - 2.0));
end
↓
function tmp = code(x, y)
	t_0 = (x * x) * 3.0;
	tmp = ((t_0 + (y * y)) * (t_0 - (y * y))) - ((y * y) * -2.0);
end

code[x_, y_] := N[(N[(9.0 * N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision] - N[(N[(y * y), $MachinePrecision] * N[(N[(y * y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := Block[{t$95$0 = N[(N[(x * x), $MachinePrecision] * 3.0), $MachinePrecision]}, N[(N[(N[(t$95$0 + N[(y * y), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * y), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]]

9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\begin{array}{l}
t_0 := \left(x \cdot x\right) \cdot 3\\
\left(t_0 + y \cdot y\right) \cdot \left(t_0 - y \cdot y\right) - \left(y \cdot y\right) \cdot -2
\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 62.0

    \[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right) \]

  2. Applied egg-rr52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} - {\left(y \cdot y\right)}^{2}\right) - \left(y \cdot y\right) \cdot -2} \]

  3. Applied egg-rr0

    \[\leadsto \color{blue}{\left(\left(x \cdot x\right) \cdot 3 + y \cdot y\right) \cdot \left(\left(x \cdot x\right) \cdot 3 - y \cdot y\right)} - \left(y \cdot y\right) \cdot -2 \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :precision binary64
  :pre (and (== x 10864.0) (== y 18817.0))
  (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))