Average Error: 0.7 → 0.7
Time: 6.9s
Precision: binary32
\[\left(10^{-5} \leq x \land x \leq 1\right) \land \left(1 \leq tau \land tau \leq 5\right)\]
\[\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi} \]
↓
\[\begin{array}{l} t_1 := \pi \cdot \left(x \cdot tau\right)\\ t_2 := x \cdot \left(\pi \cdot tau\right)\\ \left(\sqrt[3]{\frac{\sin t_2}{t_2}} \cdot \sqrt[3]{\sqrt{{\left(\frac{\sin t_1}{t_1}\right)}^{4}}}\right) \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi} \end{array} \]
(FPCore (x tau)
 :precision binary32
 (* (/ (sin (* (* x PI) tau)) (* (* x PI) tau)) (/ (sin (* x PI)) (* x PI))))
↓
(FPCore (x tau)
 :precision binary32
 (let* ((t_1 (* PI (* x tau))) (t_2 (* x (* PI tau))))
   (*
    (* (cbrt (/ (sin t_2) t_2)) (cbrt (sqrt (pow (/ (sin t_1) t_1) 4.0))))
    (/ (sin (* x PI)) (* x PI)))))
float code(float x, float tau) {
	return (sinf(((x * ((float) M_PI)) * tau)) / ((x * ((float) M_PI)) * tau)) * (sinf((x * ((float) M_PI))) / (x * ((float) M_PI)));
}
↓
float code(float x, float tau) {
	float t_1 = ((float) M_PI) * (x * tau);
	float t_2 = x * (((float) M_PI) * tau);
	return (cbrtf((sinf(t_2) / t_2)) * cbrtf(sqrtf(powf((sinf(t_1) / t_1), 4.0f)))) * (sinf((x * ((float) M_PI))) / (x * ((float) M_PI)));
}

function code(x, tau)
	return Float32(Float32(sin(Float32(Float32(x * Float32(pi)) * tau)) / Float32(Float32(x * Float32(pi)) * tau)) * Float32(sin(Float32(x * Float32(pi))) / Float32(x * Float32(pi))))
end
↓
function code(x, tau)
	t_1 = Float32(Float32(pi) * Float32(x * tau))
	t_2 = Float32(x * Float32(Float32(pi) * tau))
	return Float32(Float32(cbrt(Float32(sin(t_2) / t_2)) * cbrt(sqrt((Float32(sin(t_1) / t_1) ^ Float32(4.0))))) * Float32(sin(Float32(x * Float32(pi))) / Float32(x * Float32(pi))))
end

\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 := \pi \cdot \left(x \cdot tau\right)\\
t_2 := x \cdot \left(\pi \cdot tau\right)\\
\left(\sqrt[3]{\frac{\sin t_2}{t_2}} \cdot \sqrt[3]{\sqrt{{\left(\frac{\sin t_1}{t_1}\right)}^{4}}}\right) \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

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

  2. Applied egg-rr0.7

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{\sin \left(x \cdot \left(\pi \cdot tau\right)\right)}{x \cdot \left(\pi \cdot tau\right)}} \cdot \sqrt[3]{{\left(\frac{\sin \left(x \cdot \left(\pi \cdot tau\right)\right)}{x \cdot \left(\pi \cdot tau\right)}\right)}^{2}}\right)} \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi} \]

  3. Applied egg-rr0.7

    \[\leadsto \left(\sqrt[3]{\frac{\sin \left(x \cdot \left(\pi \cdot tau\right)\right)}{x \cdot \left(\pi \cdot tau\right)}} \cdot \sqrt[3]{\color{blue}{\sqrt{{\left(\frac{\sin \left(\pi \cdot \left(tau \cdot x\right)\right)}{\pi \cdot \left(tau \cdot x\right)}\right)}^{4}}}}\right) \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi} \]

  4. Final simplification0.7

    \[\leadsto \left(\sqrt[3]{\frac{\sin \left(x \cdot \left(\pi \cdot tau\right)\right)}{x \cdot \left(\pi \cdot tau\right)}} \cdot \sqrt[3]{\sqrt{{\left(\frac{\sin \left(\pi \cdot \left(x \cdot tau\right)\right)}{\pi \cdot \left(x \cdot tau\right)}\right)}^{4}}}\right) \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi} \]

Reproduce

herbie shell --seed 2022200 
(FPCore (x tau)
  :name "Lanczos kernel"
  :precision binary32
  :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))))