Average Error: 20.5 → 20.4
Time: 13.9s
Precision: binary64
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]
↓
\[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \log e\right)}^{2} \]
{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2}
↓
{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \log e\right)}^{2}

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
  (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)))
↓
(FPCore (a b angle)
 :precision binary64
 (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (log E)) 2.0)))
double code(double a, double b, double angle) {
	return pow((a * sin((angle / 180.0) * ((double) M_PI))), 2.0) + pow((b * cos((angle / 180.0) * ((double) M_PI))), 2.0);
}
↓
double code(double a, double b, double angle) {
	return pow((a * sin((angle / 180.0) * ((double) M_PI))), 2.0) + pow((b * log((double) M_E)), 2.0);
}

Error

Bits error versus a

Bits error versus b

Bits error versus angle

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 20.5

    \[{\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} \]
  2. Using strategy rm

  3. Applied add-log-exp_binary6420.5

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \color{blue}{\log \left(e^{\cos \left(\frac{angle}{180} \cdot \pi\right)}\right)}\right)}^{2} \]

  4. Simplified20.4

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \log \color{blue}{\left(e^{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}\right)}^{2} \]

  5. Taylor expanded around 0 20.4

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \log \left(e^{\color{blue}{1}}\right)\right)}^{2} \]

  6. Final simplification20.4

    \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \log e\right)}^{2} \]

Reproduce

herbie shell --seed 2021207 
(FPCore (a b angle)
  :name "ab-angle->ABCF A"
  :precision binary64
  (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)))