Average Error: 29.6 → 11.7
Time: 9.4s
Precision: binary64
\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
↓
\[\begin{array}{l} \mathbf{if}\;A \leq -3.205797192814889 \cdot 10^{+139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{C}{\frac{A \cdot A}{B}} + \frac{B}{A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}}\\ \end{array} \]
(FPCore (A B C)
 :precision binary64
 (*
  180.0
  (/
   (atan (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
   PI)))
↓
(FPCore (A B C)
 :precision binary64
 (if (<= A -3.205797192814889e+139)
   (* 180.0 (/ (atan (* 0.5 (+ (/ C (/ (* A A) B)) (/ B A)))) PI))
   (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot B (- C A))) B))))))
double code(double A, double B, double C) {
	return 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
}
↓
double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.205797192814889e+139) {
		tmp = 180.0 * (atan((0.5 * ((C / ((A * A) / B)) + (B / A)))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot(B, (C - A))) / B)));
	}
	return tmp;
}

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
}
↓
public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.205797192814889e+139) {
		tmp = 180.0 * (Math.atan((0.5 * ((C / ((A * A) / B)) + (B / A)))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)));
	}
	return tmp;
}

def code(A, B, C):
	return 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
↓
def code(A, B, C):
	tmp = 0
	if A <= -3.205797192814889e+139:
		tmp = 180.0 * (math.atan((0.5 * ((C / ((A * A) / B)) + (B / A)))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot(B, (C - A))) / B)))
	return tmp

function code(A, B, C)
	return Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
end
↓
function code(A, B, C)
	tmp = 0.0
	if (A <= -3.205797192814889e+139)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(C / Float64(Float64(A * A) / B)) + Float64(B / A)))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B))));
	end
	return tmp
end

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
end
↓
function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.205797192814889e+139)
		tmp = 180.0 * (atan((0.5 * ((C / ((A * A) / B)) + (B / A)))) / pi);
	else
		tmp = 180.0 / (pi / atan((((C - A) - hypot(B, (C - A))) / B)));
	end
	tmp_2 = tmp;
end

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]
↓
code[A_, B_, C_] := If[LessEqual[A, -3.205797192814889e+139], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(C / N[(N[(A * A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision] + N[(B / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}
↓
\begin{array}{l}
\mathbf{if}\;A \leq -3.205797192814889 \cdot 10^{+139}:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{C}{\frac{A \cdot A}{B}} + \frac{B}{A}\right)\right)}{\pi}\\

\mathbf{else}:\\
\;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}}\\


\end{array}

Error

Bits error versus A

Bits error versus B

Bits error versus C

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if A < -3.20579719281488916e139

    1. Initial program 55.4

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

    2. Simplified28.3

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]

    3. Taylor expanded in A around -inf 16.3

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{C \cdot B}{{A}^{2}} + 0.5 \cdot \frac{B}{A}\right)}}{\pi} \]

    4. Simplified13.5

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \left(\frac{C}{\frac{A \cdot A}{B}} + \frac{B}{A}\right)\right)}}{\pi} \]

    5. Applied *-un-lft-identity_binary6413.5

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{C}{\frac{A \cdot A}{B}} + \frac{B}{A}\right)\right)}{\color{blue}{1 \cdot \pi}} \]

    6. Applied associate-/r*_binary6413.5

      \[\leadsto 180 \cdot \color{blue}{\frac{\frac{\tan^{-1} \left(0.5 \cdot \left(\frac{C}{\frac{A \cdot A}{B}} + \frac{B}{A}\right)\right)}{1}}{\pi}} \]

    if -3.20579719281488916e139 < A

    1. Initial program 25.4

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

    2. Simplified11.4

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi}} \]

    3. Applied clear-num_binary6411.4

      \[\leadsto 180 \cdot \color{blue}{\frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}}} \]

    4. Applied un-div-inv_binary6411.4

      \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}}} \]
  3. Recombined 2 regimes into one program.

  4. Final simplification11.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.205797192814889 \cdot 10^{+139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{C}{\frac{A \cdot A}{B}} + \frac{B}{A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022131 
(FPCore (A B C)
  :name "ABCF->ab-angle angle"
  :precision binary64
  (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))) PI)))