Average Error: 0.7 → 0.7
Time: 9.8s
Precision: binary32
\[10^{-05} \leq x \land x \leq 1 \land 1 \leq tau \land tau \leq 5\]
\[\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi}\]
↓
\[\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot e^{\log \left(\frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi}\right)}\]
\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}
↓
\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot e^{\log \left(\frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi}\right)}
(FPCore (x tau)
 :precision binary32
 (* (/ (sin (* (* x PI) tau)) (* (* x PI) tau)) (/ (sin (* x PI)) (* x PI))))
↓
(FPCore (x tau)
 :precision binary32
 (*
  (/ (sin (* (* x PI) tau)) (* (* x PI) tau))
  (exp (log (/ (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) {
	return (sinf((x * ((float) M_PI)) * tau) / ((x * ((float) M_PI)) * tau)) * expf(logf(sinf(x * ((float) M_PI)) / (x * ((float) M_PI))));
}

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 0.7

    \[\frac{\sin \left(\left(x \cdot \pi\right) \cdot tau\right)}{\left(x \cdot \pi\right) \cdot tau} \cdot \frac{\sin \left(x \cdot \pi\right)}{x \cdot \pi}\]
  2. Using strategy rm

  3. Applied add-exp-log_binary320.7

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

  4. Final simplification0.7

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

Reproduce

herbie shell --seed 2021175 
(FPCore (x tau)
  :name "Lanczos kernel"
  :precision binary32
  :pre (and (<= 1e-05 x 1.0) (<= 1.0 tau 5.0))
  (* (/ (sin (* (* x PI) tau)) (* (* x PI) tau)) (/ (sin (* x PI)) (* x PI))))