Average Error: 29.0 → 11.8
Time: 7.9s
Precision: binary64
\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
↓
\[\begin{array}{l} t_0 := 180 \cdot \frac{1}{\sqrt{\pi}}\\ \mathbf{if}\;C \leq 1.9116610246095172 \cdot 10^{+110}:\\ \;\;\;\;t_0 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\sqrt{\pi}}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\sqrt{\pi}}\\ \end{array} \]
(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
 (let* ((t_0 (* 180.0 (/ 1.0 (sqrt PI)))))
   (if (<= C 1.9116610246095172e+110)
     (* t_0 (/ (atan (/ (- (- C A) (hypot B (- C A))) B)) (sqrt PI)))
     (* t_0 (/ (atan (* -0.5 (/ B C))) (sqrt PI))))))
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 t_0 = 180.0 * (1.0 / sqrt(((double) M_PI)));
	double tmp;
	if (C <= 1.9116610246095172e+110) {
		tmp = t_0 * (atan((((C - A) - hypot(B, (C - A))) / B)) / sqrt(((double) M_PI)));
	} else {
		tmp = t_0 * (atan((-0.5 * (B / C))) / sqrt(((double) M_PI)));
	}
	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 t_0 = 180.0 * (1.0 / Math.sqrt(Math.PI));
	double tmp;
	if (C <= 1.9116610246095172e+110) {
		tmp = t_0 * (Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)) / Math.sqrt(Math.PI));
	} else {
		tmp = t_0 * (Math.atan((-0.5 * (B / C))) / Math.sqrt(Math.PI));
	}
	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):
	t_0 = 180.0 * (1.0 / math.sqrt(math.pi))
	tmp = 0
	if C <= 1.9116610246095172e+110:
		tmp = t_0 * (math.atan((((C - A) - math.hypot(B, (C - A))) / B)) / math.sqrt(math.pi))
	else:
		tmp = t_0 * (math.atan((-0.5 * (B / C))) / math.sqrt(math.pi))
	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)
	t_0 = Float64(180.0 * Float64(1.0 / sqrt(pi)))
	tmp = 0.0
	if (C <= 1.9116610246095172e+110)
		tmp = Float64(t_0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)) / sqrt(pi)));
	else
		tmp = Float64(t_0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / sqrt(pi)));
	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)
	t_0 = 180.0 * (1.0 / sqrt(pi));
	tmp = 0.0;
	if (C <= 1.9116610246095172e+110)
		tmp = t_0 * (atan((((C - A) - hypot(B, (C - A))) / B)) / sqrt(pi));
	else
		tmp = t_0 * (atan((-0.5 * (B / C))) / sqrt(pi));
	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_] := Block[{t$95$0 = N[(180.0 * N[(1.0 / N[Sqrt[Pi], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, 1.9116610246095172e+110], N[(t$95$0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / N[Sqrt[Pi], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Sqrt[Pi], $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}
t_0 := 180 \cdot \frac{1}{\sqrt{\pi}}\\
\mathbf{if}\;C \leq 1.9116610246095172 \cdot 10^{+110}:\\
\;\;\;\;t_0 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\sqrt{\pi}}\\

\mathbf{else}:\\
\;\;\;\;t_0 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\sqrt{\pi}}\\


\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 C < 1.9116610246095172e110

    1. Initial program 24.3

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

    2. Simplified11.0

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

    3. Applied add-sqr-sqrt_binary6411.7

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

    4. Applied *-un-lft-identity_binary6411.7

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

    5. Applied times-frac_binary6411.0

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

    6. Applied associate-*r*_binary6411.0

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

    if 1.9116610246095172e110 < C

    1. Initial program 52.8

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

    2. Simplified28.9

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

    3. Applied add-sqr-sqrt_binary6429.1

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

    4. Applied *-un-lft-identity_binary6429.1

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

    5. Applied times-frac_binary6428.9

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

    6. Applied associate-*r*_binary6428.9

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

    7. Taylor expanded in C around inf 15.8

      \[\leadsto \left(180 \cdot \frac{1}{\sqrt{\pi}}\right) \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\sqrt{\pi}} \]
  3. Recombined 2 regimes into one program.

  4. Final simplification11.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 1.9116610246095172 \cdot 10^{+110}:\\ \;\;\;\;\left(180 \cdot \frac{1}{\sqrt{\pi}}\right) \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\sqrt{\pi}}\\ \mathbf{else}:\\ \;\;\;\;\left(180 \cdot \frac{1}{\sqrt{\pi}}\right) \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\sqrt{\pi}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022137 
(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)))