Average Error: 0.1 → 0.1
Time: 12.8s
Precision: binary64
\[\left|\left(ew \cdot \cos t\right) \cdot \cos \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right) - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right)\right|\]
↓
\[\left|\left(ew \cdot \cos t\right) \cdot \log \left(e^{\cos \tan^{-1} \left(-\frac{eh \cdot \tan t}{ew}\right)}\right) - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(-\frac{eh \cdot \tan t}{ew}\right)\right|\]
\left|\left(ew \cdot \cos t\right) \cdot \cos \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right) - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right)\right|
↓
\left|\left(ew \cdot \cos t\right) \cdot \log \left(e^{\cos \tan^{-1} \left(-\frac{eh \cdot \tan t}{ew}\right)}\right) - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(-\frac{eh \cdot \tan t}{ew}\right)\right|
(FPCore (eh ew t)
 :precision binary64
 (fabs
  (-
   (* (* ew (cos t)) (cos (atan (/ (* (- eh) (tan t)) ew))))
   (* (* eh (sin t)) (sin (atan (/ (* (- eh) (tan t)) ew)))))))
↓
(FPCore (eh ew t)
 :precision binary64
 (fabs
  (-
   (* (* ew (cos t)) (log (exp (cos (atan (- (/ (* eh (tan t)) ew)))))))
   (* (* eh (sin t)) (sin (atan (- (/ (* eh (tan t)) ew))))))))
double code(double eh, double ew, double t) {
	return fabs(((ew * cos(t)) * cos(atan((-eh * tan(t)) / ew))) - ((eh * sin(t)) * sin(atan((-eh * tan(t)) / ew))));
}
↓
double code(double eh, double ew, double t) {
	return fabs(((ew * cos(t)) * log(exp(cos(atan(-((eh * tan(t)) / ew)))))) - ((eh * sin(t)) * sin(atan(-((eh * tan(t)) / ew)))));
}

Error

Bits error versus eh

Bits error versus ew

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left|\left(ew \cdot \cos t\right) \cdot \cos \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right) - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right)\right|\]
  2. Using strategy rm

  3. Applied add-log-exp_binary64_28450.1

    \[\leadsto \left|\left(ew \cdot \cos t\right) \cdot \color{blue}{\log \left(e^{\cos \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right)}\right)} - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right)\right|\]

  4. Simplified0.1

    \[\leadsto \left|\left(ew \cdot \cos t\right) \cdot \log \color{blue}{\left(e^{\cos \tan^{-1} \left(-\frac{eh \cdot \tan t}{ew}\right)}\right)} - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right)\right|\]

  5. Final simplification0.1

    \[\leadsto \left|\left(ew \cdot \cos t\right) \cdot \log \left(e^{\cos \tan^{-1} \left(-\frac{eh \cdot \tan t}{ew}\right)}\right) - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(-\frac{eh \cdot \tan t}{ew}\right)\right|\]

Reproduce

herbie shell --seed 2021027 
(FPCore (eh ew t)
  :name "Example 2 from Robby"
  :precision binary64
  (fabs (- (* (* ew (cos t)) (cos (atan (/ (* (- eh) (tan t)) ew)))) (* (* eh (sin t)) (sin (atan (/ (* (- eh) (tan t)) ew)))))))