mixedcos

Average Error: 28.4 → 0.8

Time: 6.8s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := \cos \left(x + x\right)\\ \mathbf{if}\;\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(x \cdot \left(x \cdot {s}^{2}\right)\right)} \leq \infty:\\ \;\;\;\;\frac{t_0}{c \cdot \left(x \cdot s\right)} \cdot \frac{1}{\frac{c}{\frac{1}{x \cdot s}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t_0}{x} \cdot \frac{1}{c \cdot s}}{x \cdot \left(c \cdot s\right)}\\ \end{array} \]

FPCore

(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
 (let* ((t_0 (cos (+ x x))))
   (if (<=
        (/ (cos (* 2.0 x)) (* (pow c 2.0) (* x (* x (pow s 2.0)))))
        INFINITY)
     (* (/ t_0 (* c (* x s))) (/ 1.0 (/ c (/ 1.0 (* x s)))))
     (/ (* (/ t_0 x) (/ 1.0 (* c s))) (* x (* c 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) {
	double t_0 = cos((x + x));
	double tmp;
	if ((cos((2.0 * x)) / (pow(c, 2.0) * (x * (x * pow(s, 2.0))))) <= ((double) INFINITY)) {
		tmp = (t_0 / (c * (x * s))) * (1.0 / (c / (1.0 / (x * s))));
	} else {
		tmp = ((t_0 / x) * (1.0 / (c * s))) / (x * (c * s));
	}
	return tmp;
}

Java

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) {
	double t_0 = Math.cos((x + x));
	double tmp;
	if ((Math.cos((2.0 * x)) / (Math.pow(c, 2.0) * (x * (x * Math.pow(s, 2.0))))) <= Double.POSITIVE_INFINITY) {
		tmp = (t_0 / (c * (x * s))) * (1.0 / (c / (1.0 / (x * s))));
	} else {
		tmp = ((t_0 / x) * (1.0 / (c * s))) / (x * (c * s));
	}
	return tmp;
}

Python

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):
	t_0 = math.cos((x + x))
	tmp = 0
	if (math.cos((2.0 * x)) / (math.pow(c, 2.0) * (x * (x * math.pow(s, 2.0))))) <= math.inf:
		tmp = (t_0 / (c * (x * s))) * (1.0 / (c / (1.0 / (x * s))))
	else:
		tmp = ((t_0 / x) * (1.0 / (c * s))) / (x * (c * s))
	return tmp

Julia

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)
	t_0 = cos(Float64(x + x))
	tmp = 0.0
	if (Float64(cos(Float64(2.0 * x)) / Float64((c ^ 2.0) * Float64(x * Float64(x * (s ^ 2.0))))) <= Inf)
		tmp = Float64(Float64(t_0 / Float64(c * Float64(x * s))) * Float64(1.0 / Float64(c / Float64(1.0 / Float64(x * s)))));
	else
		tmp = Float64(Float64(Float64(t_0 / x) * Float64(1.0 / Float64(c * s))) / Float64(x * Float64(c * s)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, c, s)
	t_0 = cos((x + x));
	tmp = 0.0;
	if ((cos((2.0 * x)) / ((c ^ 2.0) * (x * (x * (s ^ 2.0))))) <= Inf)
		tmp = (t_0 / (c * (x * s))) * (1.0 / (c / (1.0 / (x * s))));
	else
		tmp = ((t_0 / x) * (1.0 / (c * s))) / (x * (c * s));
	end
	tmp_2 = tmp;
end

Wolfram

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_] := Block[{t$95$0 = N[Cos[N[(x + x), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / N[(N[Power[c, 2.0], $MachinePrecision] * N[(x * N[(x * N[Power[s, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(t$95$0 / N[(c * N[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(c / N[(1.0 / N[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$0 / x), $MachinePrecision] * N[(1.0 / N[(c * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(c * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 (pow.f64 c 2) (*.f64 (*.f64 x (pow.f64 s 2)) x))) < +inf.0

   1. Initial program 18.4

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

   2. Simplified 2.7

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

   3. Applied egg-rr 0.4

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

   4. Applied egg-rr 0.3

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

   if +inf.0 < (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 (pow.f64 c 2) (*.f64 (*.f64 x (pow.f64 s 2)) x)))

   1. Initial program 64.0

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

   2. Simplified 2.7

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

   3. Applied egg-rr 10.9

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

   4. Applied egg-rr 2.4

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

   5. Applied egg-rr 2.5

      \[\leadsto \frac{\color{blue}{\frac{\cos \left(x + x\right)}{x} \cdot \frac{1}{c \cdot s}}}{x \cdot \left(c \cdot s\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(x \cdot \left(x \cdot {s}^{2}\right)\right)} \leq \infty:\\ \;\;\;\;\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)} \cdot \frac{1}{\frac{c}{\frac{1}{x \cdot s}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cos \left(x + x\right)}{x} \cdot \frac{1}{c \cdot s}}{x \cdot \left(c \cdot s\right)}\\ \end{array} \]

Reproduce

herbie shell --seed 2022197 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))