?

Average Error: 0.7 → 0.7
Time: 2.2min
Precision: binary64
Cost: 39360

?

\[\left(10^{-5} \leq x \land x \leq 1\right) \land \left(1 \leq tau \land tau \leq 5\right)\]
\[\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi} \]
↓
\[\begin{array}{l} t_1 := \left(x \cdot \pi\right) \cdot tau\\ \frac{\sin t_1}{t_1} \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi} \end{array} \]
(FPCore (x tau)
 :precision binary64
 (* (/ (sin (* (* x PI) tau)) (* (* x PI) tau)) (/ (sin (* x PI)) (* x PI))))
↓
(FPCore (x tau)
 :precision binary64
 (let* ((t_1 (* (* x PI) tau)))
   (* (/ (sin t_1) t_1) (/ (sin (* x PI)) (* x PI)))))
double code(double x, double tau) {
	return (sin(((x * ((double) M_PI)) * tau)) / ((x * ((double) M_PI)) * tau)) * (sin((x * ((double) M_PI))) / (x * ((double) M_PI)));
}
↓
double code(double x, double tau) {
	double t_1 = (x * ((double) M_PI)) * tau;
	return (sin(t_1) / t_1) * (sin((x * ((double) M_PI))) / (x * ((double) M_PI)));
}

public static double code(double x, double tau) {
	return (Math.sin(((x * Math.PI) * tau)) / ((x * Math.PI) * tau)) * (Math.sin((x * Math.PI)) / (x * Math.PI));
}
↓
public static double code(double x, double tau) {
	double t_1 = (x * Math.PI) * tau;
	return (Math.sin(t_1) / t_1) * (Math.sin((x * Math.PI)) / (x * Math.PI));
}

def code(x, tau):
	return (math.sin(((x * math.pi) * tau)) / ((x * math.pi) * tau)) * (math.sin((x * math.pi)) / (x * math.pi))
↓
def code(x, tau):
	t_1 = (x * math.pi) * tau
	return (math.sin(t_1) / t_1) * (math.sin((x * math.pi)) / (x * math.pi))

function code(x, tau)
	return Float64(Float64(sin(Float64(Float64(x * pi) * tau)) / Float64(Float64(x * pi) * tau)) * Float64(sin(Float64(x * pi)) / Float64(x * pi)))
end
↓
function code(x, tau)
	t_1 = Float64(Float64(x * pi) * tau)
	return Float64(Float64(sin(t_1) / t_1) * Float64(sin(Float64(x * pi)) / Float64(x * pi)))
end

function tmp = code(x, tau)
	tmp = (sin(((x * pi) * tau)) / ((x * pi) * tau)) * (sin((x * pi)) / (x * pi));
end
↓
function tmp = code(x, tau)
	t_1 = (x * pi) * tau;
	tmp = (sin(t_1) / t_1) * (sin((x * pi)) / (x * pi));
end

code[x_, tau_] := N[(N[(N[Sin[N[(N[(x * Pi), $MachinePrecision] * tau), $MachinePrecision]], $MachinePrecision] / N[(N[(x * Pi), $MachinePrecision] * tau), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[N[(x * Pi), $MachinePrecision]], $MachinePrecision] / N[(x * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, tau_] := Block[{t$95$1 = N[(N[(x * Pi), $MachinePrecision] * tau), $MachinePrecision]}, N[(N[(N[Sin[t$95$1], $MachinePrecision] / t$95$1), $MachinePrecision] * N[(N[Sin[N[(x * Pi), $MachinePrecision]], $MachinePrecision] / N[(x * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi}
↓
\begin{array}{l}
t_1 := \left(x \cdot \pi\right) \cdot tau\\
\frac{\sin t_1}{t_1} \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi}
\end{array}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.7

    \[\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi} \]

Alternatives

Alternative 1
Error0.9
Cost39232
\[\frac{\sin \left(x \cdot \pi\right)}{{\left(x \cdot \pi\right)}^{2} \cdot tau} \cdot \sin \left(\left(x \cdot \pi\right) \cdot tau\right) \]
Alternative 2
Error0.9
Cost39232
\[\frac{\sin \left(\left(x \cdot tau\right) \cdot \pi\right)}{{\left(x \cdot \pi\right)}^{2}} \cdot \frac{\sin \left(x \cdot \pi\right)}{tau} \]
Alternative 3
Error0.9
Cost39232
\[\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{tau} \cdot \frac{\sin \left(x \cdot \pi\right)}{{\left(x \cdot \pi\right)}^{2}} \]
Alternative 4
Error0.9
Cost39232
\[\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{{\left(x \cdot \pi\right)}^{2}} \cdot \frac{\sin \left(x \cdot \pi\right)}{tau} \]
Alternative 5
Error37.0
Cost32832
\[\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{{\left({\left(x \cdot \pi\right)}^{3}\right)}^{0.3333333333333333} \cdot tau} \cdot 1 \]
Alternative 6
Error37.0
Cost32768
\[\begin{array}{l} t_1 := \left(x \cdot \pi\right) \cdot tau\\ \frac{\sin \left(\sqrt[3]{{t_1}^{3}}\right)}{t_1} \cdot 1 \end{array} \]
Alternative 7
Error37.0
Cost32768
\[\frac{\sin \left(\sqrt[3]{{\left(x \cdot \pi\right)}^{3}} \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot 1 \]
Alternative 8
Error37.0
Cost32768
\[\frac{\sin \left({\left(\sqrt[3]{x \cdot \pi}\right)}^{3} \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot 1 \]
Alternative 9
Error37.0
Cost20224
\[\left(3 - \left(3 + \frac{\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{x \cdot \pi}}{-tau}\right)\right) \cdot 1 \]
Alternative 10
Error37.0
Cost19904
\[\begin{array}{l} t_1 := \left(x \cdot tau\right) \cdot \pi\\ \frac{\sin t_1}{t_1} \cdot 1 \end{array} \]
Alternative 11
Error37.0
Cost19904
\[\frac{\sin \left(\left(\pi \cdot tau\right) \cdot x\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot 1 \]
Alternative 12
Error37.6
Cost13504
\[\left(1 + {\left(x \cdot \left(\pi \cdot tau\right)\right)}^{2} \cdot -0.16666666666666666\right) \cdot 1 \]
Alternative 13
Error40.2
Cost64
\[1 \]

Error

Reproduce?

herbie shell --seed 2023033 
(FPCore (x tau)
  :name "Lanczos kernel"
  :precision binary64
  :pre (and (and (<= 1e-5 x) (<= x 1.0)) (and (<= 1.0 tau) (<= tau 5.0)))
  (* (/ (sin (* (* x PI) tau)) (* (* x PI) tau)) (/ (sin (* x PI)) (* x PI))))