Average Error: 27.9 → 2.9
Time: 6.4s
Precision: binary64
\[ \begin{array}{c}[c, s] = \mathsf{sort}([c, s])\\ \end{array} \]
\[\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)} \]
↓
\[\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)} \cdot \frac{\frac{\frac{1}{x}}{s}}{c} \]
(FPCore (x c s)
 :precision binary64
 (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))
↓
(FPCore (x c s)
 :precision binary64
 (* (/ (cos (+ x x)) (* c (* x s))) (/ (/ (/ 1.0 x) s) c)))
double code(double x, double c, double s) {
	return cos((2.0 * x)) / (pow(c, 2.0) * ((x * pow(s, 2.0)) * x));
}
↓
double code(double x, double c, double s) {
	return (cos((x + x)) / (c * (x * s))) * (((1.0 / x) / s) / c);
}

real(8) function code(x, c, s)
    real(8), intent (in) :: x
    real(8), intent (in) :: c
    real(8), intent (in) :: s
    code = cos((2.0d0 * x)) / ((c ** 2.0d0) * ((x * (s ** 2.0d0)) * x))
end function
↓
real(8) function code(x, c, s)
    real(8), intent (in) :: x
    real(8), intent (in) :: c
    real(8), intent (in) :: s
    code = (cos((x + x)) / (c * (x * s))) * (((1.0d0 / x) / s) / c)
end function

public static double code(double x, double c, double s) {
	return Math.cos((2.0 * x)) / (Math.pow(c, 2.0) * ((x * Math.pow(s, 2.0)) * x));
}
↓
public static double code(double x, double c, double s) {
	return (Math.cos((x + x)) / (c * (x * s))) * (((1.0 / x) / s) / c);
}

def code(x, c, s):
	return math.cos((2.0 * x)) / (math.pow(c, 2.0) * ((x * math.pow(s, 2.0)) * x))
↓
def code(x, c, s):
	return (math.cos((x + x)) / (c * (x * s))) * (((1.0 / x) / s) / c)

function code(x, c, s)
	return Float64(cos(Float64(2.0 * x)) / Float64((c ^ 2.0) * Float64(Float64(x * (s ^ 2.0)) * x)))
end
↓
function code(x, c, s)
	return Float64(Float64(cos(Float64(x + x)) / Float64(c * Float64(x * s))) * Float64(Float64(Float64(1.0 / x) / s) / c))
end

function tmp = code(x, c, s)
	tmp = cos((2.0 * x)) / ((c ^ 2.0) * ((x * (s ^ 2.0)) * x));
end
↓
function tmp = code(x, c, s)
	tmp = (cos((x + x)) / (c * (x * s))) * (((1.0 / x) / s) / c);
end

code[x_, c_, s_] := N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / N[(N[Power[c, 2.0], $MachinePrecision] * N[(N[(x * N[Power[s, 2.0], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, c_, s_] := N[(N[(N[Cos[N[(x + x), $MachinePrecision]], $MachinePrecision] / N[(c * N[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(1.0 / x), $MachinePrecision] / s), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]

\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)}
↓
\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)} \cdot \frac{\frac{\frac{1}{x}}{s}}{c}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 27.9

    \[\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)} \]

  2. Simplified2.8

    \[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{\left(x \cdot \left(c \cdot s\right)\right) \cdot \left(x \cdot \left(c \cdot s\right)\right)}} \]

  3. Applied egg-rr2.8

    \[\leadsto \color{blue}{\frac{\cos \left(x + x\right)}{c \cdot \left(s \cdot x\right)} \cdot \frac{1}{c \cdot \left(s \cdot x\right)}} \]

  4. Taylor expanded in s around 0 5.1

    \[\leadsto \frac{\cos \left(x + x\right)}{c \cdot \left(s \cdot x\right)} \cdot \color{blue}{\frac{1}{s \cdot \left(c \cdot x\right)}} \]

  5. Simplified2.9

    \[\leadsto \frac{\cos \left(x + x\right)}{c \cdot \left(s \cdot x\right)} \cdot \color{blue}{\frac{\frac{\frac{1}{x}}{s}}{c}} \]

  6. Final simplification2.9

    \[\leadsto \frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)} \cdot \frac{\frac{\frac{1}{x}}{s}}{c} \]

Reproduce

herbie shell --seed 2022192 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))