Average Error: 0.3 → 0.3
Time: 9.3s
Precision: binary64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x} \]
↓
\[\begin{array}{l} t_0 := \frac{\sin x \cdot \tan x}{\cos x}\\ \frac{1 - t_0}{1 + t_0} \end{array} \]
(FPCore (x)
 :precision binary64
 (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
↓
(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ (* (sin x) (tan x)) (cos x)))) (/ (- 1.0 t_0) (+ 1.0 t_0))))
double code(double x) {
	return (1.0 - (tan(x) * tan(x))) / (1.0 + (tan(x) * tan(x)));
}
↓
double code(double x) {
	double t_0 = (sin(x) * tan(x)) / cos(x);
	return (1.0 - t_0) / (1.0 + t_0);
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 - (tan(x) * tan(x))) / (1.0d0 + (tan(x) * tan(x)))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = (sin(x) * tan(x)) / cos(x)
    code = (1.0d0 - t_0) / (1.0d0 + t_0)
end function

public static double code(double x) {
	return (1.0 - (Math.tan(x) * Math.tan(x))) / (1.0 + (Math.tan(x) * Math.tan(x)));
}
↓
public static double code(double x) {
	double t_0 = (Math.sin(x) * Math.tan(x)) / Math.cos(x);
	return (1.0 - t_0) / (1.0 + t_0);
}

def code(x):
	return (1.0 - (math.tan(x) * math.tan(x))) / (1.0 + (math.tan(x) * math.tan(x)))
↓
def code(x):
	t_0 = (math.sin(x) * math.tan(x)) / math.cos(x)
	return (1.0 - t_0) / (1.0 + t_0)

function code(x)
	return Float64(Float64(1.0 - Float64(tan(x) * tan(x))) / Float64(1.0 + Float64(tan(x) * tan(x))))
end
↓
function code(x)
	t_0 = Float64(Float64(sin(x) * tan(x)) / cos(x))
	return Float64(Float64(1.0 - t_0) / Float64(1.0 + t_0))
end

function tmp = code(x)
	tmp = (1.0 - (tan(x) * tan(x))) / (1.0 + (tan(x) * tan(x)));
end
↓
function tmp = code(x)
	t_0 = (sin(x) * tan(x)) / cos(x);
	tmp = (1.0 - t_0) / (1.0 + t_0);
end

code[x_] := N[(N[(1.0 - N[(N[Tan[x], $MachinePrecision] * N[Tan[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[Tan[x], $MachinePrecision] * N[Tan[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := Block[{t$95$0 = N[(N[(N[Sin[x], $MachinePrecision] * N[Tan[x], $MachinePrecision]), $MachinePrecision] / N[Cos[x], $MachinePrecision]), $MachinePrecision]}, N[(N[(1.0 - t$95$0), $MachinePrecision] / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision]]

\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\begin{array}{l}
t_0 := \frac{\sin x \cdot \tan x}{\cos x}\\
\frac{1 - t_0}{1 + t_0}
\end{array}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x} \]

  2. Applied egg-rr0.4

    \[\leadsto \frac{1 - \color{blue}{\frac{\sin x \cdot \tan x}{\cos x}}}{1 + \tan x \cdot \tan x} \]

  3. Applied egg-rr0.3

    \[\leadsto \frac{1 - \frac{\sin x \cdot \tan x}{\cos x}}{1 + \color{blue}{\frac{\tan x \cdot \sin x}{\cos x}}} \]

  4. Final simplification0.3

    \[\leadsto \frac{1 - \frac{\sin x \cdot \tan x}{\cos x}}{1 + \frac{\sin x \cdot \tan x}{\cos x}} \]

Reproduce

herbie shell --seed 2022153 
(FPCore (x)
  :name "Trigonometry B"
  :precision binary64
  (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))