Average Error: 0.6 → 0.7
Time: 7.2s
Precision: binary32
\[\left(10^{-5} \leq x \land x \leq 1\right) \land \left(1 \leq tau \land tau \leq 5\right)\]
\[\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi} \]
↓
\[\begin{array}{l} t_1 := \sqrt[3]{{x}^{3} \cdot {\pi}^{3}}\\ \frac{\sin \left(t_1 \cdot tau\right)}{tau \cdot \left(x \cdot \pi\right)} \cdot \frac{\sin \left(x \cdot \pi\right)}{t_1} \end{array} \]
(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 (cbrt (* (pow x 3.0) (pow PI 3.0)))))
   (* (/ (sin (* t_1 tau)) (* tau (* x PI))) (/ (sin (* x PI)) t_1))))
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 = cbrtf((powf(x, 3.0f) * powf(((float) M_PI), 3.0f)));
	return (sinf((t_1 * tau)) / (tau * (x * ((float) M_PI)))) * (sinf((x * ((float) M_PI))) / t_1);
}

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 = cbrt(Float32((x ^ Float32(3.0)) * (Float32(pi) ^ Float32(3.0))))
	return Float32(Float32(sin(Float32(t_1 * tau)) / Float32(tau * Float32(x * Float32(pi)))) * Float32(sin(Float32(x * Float32(pi))) / t_1))
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 := \sqrt[3]{{x}^{3} \cdot {\pi}^{3}}\\
\frac{\sin \left(t_1 \cdot tau\right)}{tau \cdot \left(x \cdot \pi\right)} \cdot \frac{\sin \left(x \cdot \pi\right)}{t_1}
\end{array}

Error

Bits error versus x

Bits error versus tau

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

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

  2. Applied egg-rr0.7

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

  3. Applied egg-rr0.7

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

  4. Final simplification0.7

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

Reproduce

herbie shell --seed 2022153 
(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))))