ABCF->ab-angle angle

Percentage Accurate: 53.6% → 88.4%

Time: 5.8s

Alternatives: 13

Speedup: 2.5×

Specification

Math

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

FPCore

(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)))

C

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));
}

Java

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);
}

Python

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)

Julia

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

MATLAB

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

Wolfram

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]

Initial Program: 53.6% accurate, 1.0× speedup

Math

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

FPCore

(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)))

C

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));
}

Java

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);
}

Python

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)

Julia

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

MATLAB

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

Wolfram

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]

Alternative 1: 88.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right) \cdot 180}{\pi}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI)))
        (t_1 (/ (* (atan (/ (- (- C A) (hypot (- A C) B)) B)) 180.0) PI)))
   (if (<= t_0 -1e-28)
     t_1
     (if (<= t_0 0.0) (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI)) t_1))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double t_1 = (atan((((C - A) - hypot((A - C), B)) / B)) * 180.0) / ((double) M_PI);
	double tmp;
	if (t_0 <= -1e-28) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double t_1 = (Math.atan((((C - A) - Math.hypot((A - C), B)) / B)) * 180.0) / Math.PI;
	double tmp;
	if (t_0 <= -1e-28) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	t_1 = (math.atan((((C - A) - math.hypot((A - C), B)) / B)) * 180.0) / math.pi
	tmp = 0
	if t_0 <= -1e-28:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	else:
		tmp = t_1
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	t_1 = Float64(Float64(atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B)) * 180.0) / pi)
	tmp = 0.0
	if (t_0 <= -1e-28)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	t_1 = (atan((((C - A) - hypot((A - C), B)) / B)) * 180.0) / pi;
	tmp = 0.0;
	if (t_0 <= -1e-28)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, Block[{t$95$1 = N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-28], t$95$1, If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -9.99999999999999971e-29 or -0.0 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 59.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 86.9%

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

   if -9.99999999999999971e-29 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -0.0

   1. Initial program 18.4%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 18.4

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 18.4

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

   3. Applied rewrites 18.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)\right)}{\pi} \]
   4. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-negate2 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. lift-+.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. sub-negate2 N/A

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

      9. difference-of-squares-rev N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 17.5

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

   5. Applied rewrites 17.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\color{blue}{\frac{\left(A + C\right) \cdot \left(C - A\right)}{A + C}} - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}\right)\right)}{\pi} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate2 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. lift-+.f64 N/A

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

      8. distribute-neg-frac N/A

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

      9. sub-negate2 N/A

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

      10. difference-of-squares-rev N/A

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

      11. +-commutative N/A

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

      12. lift-+.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. lower-/.f64 N/A

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

   7. Applied rewrites 8.9%

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

   8. Taylor expanded in B around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 98.5

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

   10. Applied rewrites 98.5%

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

Alternative 2: 70.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right) \cdot 180}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_2 := \frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{if}\;t\_1 \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+297}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* (atan (/ (- C (+ B A)) B)) 180.0) PI))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
        (t_2 (/ (* (atan 1.0) 180.0) PI)))
   (if (<= t_1 -0.5)
     t_0
     (if (<= t_1 2e-40)
       (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))
       (if (<= t_1 2.0) t_2 (if (<= t_1 4e+297) t_0 t_2))))))

C

double code(double A, double B, double C) {
	double t_0 = (atan(((C - (B + A)) / B)) * 180.0) / ((double) M_PI);
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double t_2 = (atan(1.0) * 180.0) / ((double) M_PI);
	double tmp;
	if (t_1 <= -0.5) {
		tmp = t_0;
	} else if (t_1 <= 2e-40) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else if (t_1 <= 2.0) {
		tmp = t_2;
	} else if (t_1 <= 4e+297) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (Math.atan(((C - (B + A)) / B)) * 180.0) / Math.PI;
	double t_1 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double t_2 = (Math.atan(1.0) * 180.0) / Math.PI;
	double tmp;
	if (t_1 <= -0.5) {
		tmp = t_0;
	} else if (t_1 <= 2e-40) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	} else if (t_1 <= 2.0) {
		tmp = t_2;
	} else if (t_1 <= 4e+297) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (math.atan(((C - (B + A)) / B)) * 180.0) / math.pi
	t_1 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	t_2 = (math.atan(1.0) * 180.0) / math.pi
	tmp = 0
	if t_1 <= -0.5:
		tmp = t_0
	elif t_1 <= 2e-40:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	elif t_1 <= 2.0:
		tmp = t_2
	elif t_1 <= 4e+297:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) * 180.0) / pi)
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	t_2 = Float64(Float64(atan(1.0) * 180.0) / pi)
	tmp = 0.0
	if (t_1 <= -0.5)
		tmp = t_0;
	elseif (t_1 <= 2e-40)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	elseif (t_1 <= 2.0)
		tmp = t_2;
	elseif (t_1 <= 4e+297)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (atan(((C - (B + A)) / B)) * 180.0) / pi;
	t_1 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	t_2 = (atan(1.0) * 180.0) / pi;
	tmp = 0.0;
	if (t_1 <= -0.5)
		tmp = t_0;
	elseif (t_1 <= 2e-40)
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	elseif (t_1 <= 2.0)
		tmp = t_2;
	elseif (t_1 <= 4e+297)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = 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]}, Block[{t$95$2 = N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[t$95$1, -0.5], t$95$0, If[LessEqual[t$95$1, 2e-40], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], t$95$2, If[LessEqual[t$95$1, 4e+297], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.5 or 2 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 4.0000000000000001e297

   1. Initial program 64.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 88.2%

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

   5. Applied rewrites 87.9%

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

   7. Applied rewrites 84.3%

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

   8. Taylor expanded in B around inf

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(\color{blue}{B} + A\right)}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 78.7%

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

   if -0.5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 1.9999999999999999e-40

   1. Initial program 19.0%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 19.0

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 19.0

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

   3. Applied rewrites 19.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)\right)}{\pi} \]
   4. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-negate2 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. lift-+.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. sub-negate2 N/A

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

      9. difference-of-squares-rev N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 18.0

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

   5. Applied rewrites 18.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\color{blue}{\frac{\left(A + C\right) \cdot \left(C - A\right)}{A + C}} - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}\right)\right)}{\pi} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate2 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. lift-+.f64 N/A

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

      8. distribute-neg-frac N/A

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

      9. sub-negate2 N/A

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

      10. difference-of-squares-rev N/A

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

      11. +-commutative N/A

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

      12. lift-+.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. lower-/.f64 N/A

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

   7. Applied rewrites 9.4%

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

   8. Taylor expanded in B around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 96.7

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

   10. Applied rewrites 96.7%

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

   if 1.9999999999999999e-40 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2 or 4.0000000000000001e297 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 52.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 85.3%

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

   5. Applied rewrites 84.8%

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

   7. Applied rewrites 79.9%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 50.6%

       \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(\frac{C - \left(\mathsf{hypot}\left(B, A - C\right) + A\right)}{B}\right) \cdot 180}{\pi}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI)))
        (t_1 (/ (* (atan (/ (- C (+ (hypot B (- A C)) A)) B)) 180.0) PI)))
   (if (<= t_0 -1e-28)
     t_1
     (if (<= t_0 0.0) (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI)) t_1))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double t_1 = (atan(((C - (hypot(B, (A - C)) + A)) / B)) * 180.0) / ((double) M_PI);
	double tmp;
	if (t_0 <= -1e-28) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double t_1 = (Math.atan(((C - (Math.hypot(B, (A - C)) + A)) / B)) * 180.0) / Math.PI;
	double tmp;
	if (t_0 <= -1e-28) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	t_1 = (math.atan(((C - (math.hypot(B, (A - C)) + A)) / B)) * 180.0) / math.pi
	tmp = 0
	if t_0 <= -1e-28:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	else:
		tmp = t_1
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	t_1 = Float64(Float64(atan(Float64(Float64(C - Float64(hypot(B, Float64(A - C)) + A)) / B)) * 180.0) / pi)
	tmp = 0.0
	if (t_0 <= -1e-28)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	t_1 = (atan(((C - (hypot(B, (A - C)) + A)) / B)) * 180.0) / pi;
	tmp = 0.0;
	if (t_0 <= -1e-28)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, Block[{t$95$1 = N[(N[(N[ArcTan[N[(N[(C - N[(N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision] + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-28], t$95$1, If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -9.99999999999999971e-29 or -0.0 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 59.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 86.9%

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

   5. Applied rewrites 82.4%

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

   if -9.99999999999999971e-29 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -0.0

   1. Initial program 18.4%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 18.4

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 18.4

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

   3. Applied rewrites 18.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)\right)}{\pi} \]
   4. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-negate2 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. lift-+.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. sub-negate2 N/A

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

      9. difference-of-squares-rev N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 17.5

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

   5. Applied rewrites 17.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\color{blue}{\frac{\left(A + C\right) \cdot \left(C - A\right)}{A + C}} - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}\right)\right)}{\pi} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate2 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. lift-+.f64 N/A

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

      8. distribute-neg-frac N/A

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

      9. sub-negate2 N/A

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

      10. difference-of-squares-rev N/A

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

      11. +-commutative N/A

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

      12. lift-+.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. lower-/.f64 N/A

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

   7. Applied rewrites 8.9%

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

   8. Taylor expanded in B around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 98.5

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

   10. Applied rewrites 98.5%

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

Alternative 4: 79.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(\frac{C - \left(\mathsf{hypot}\left(A, B\right) + A\right)}{B}\right) \cdot 180}{\pi}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI)))
        (t_1 (/ (* (atan (/ (- C (+ (hypot A B) A)) B)) 180.0) PI)))
   (if (<= t_0 -1e-28)
     t_1
     (if (<= t_0 0.0) (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI)) t_1))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double t_1 = (atan(((C - (hypot(A, B) + A)) / B)) * 180.0) / ((double) M_PI);
	double tmp;
	if (t_0 <= -1e-28) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double t_1 = (Math.atan(((C - (Math.hypot(A, B) + A)) / B)) * 180.0) / Math.PI;
	double tmp;
	if (t_0 <= -1e-28) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	t_1 = (math.atan(((C - (math.hypot(A, B) + A)) / B)) * 180.0) / math.pi
	tmp = 0
	if t_0 <= -1e-28:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	else:
		tmp = t_1
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	t_1 = Float64(Float64(atan(Float64(Float64(C - Float64(hypot(A, B) + A)) / B)) * 180.0) / pi)
	tmp = 0.0
	if (t_0 <= -1e-28)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	t_1 = (atan(((C - (hypot(A, B) + A)) / B)) * 180.0) / pi;
	tmp = 0.0;
	if (t_0 <= -1e-28)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, Block[{t$95$1 = N[(N[(N[ArcTan[N[(N[(C - N[(N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision] + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-28], t$95$1, If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -9.99999999999999971e-29 or -0.0 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 59.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 86.9%

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

   5. Applied rewrites 86.6%

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

   7. Applied rewrites 82.4%

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

   8. Taylor expanded in A around inf

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(\mathsf{hypot}\left(\color{blue}{A}, B\right) + A\right)}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 76.8%

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

   if -9.99999999999999971e-29 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -0.0

   1. Initial program 18.4%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 18.4

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 18.4

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

   3. Applied rewrites 18.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)\right)}{\pi} \]
   4. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-negate2 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. lift-+.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. sub-negate2 N/A

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

      9. difference-of-squares-rev N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 17.5

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

   5. Applied rewrites 17.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\color{blue}{\frac{\left(A + C\right) \cdot \left(C - A\right)}{A + C}} - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}\right)\right)}{\pi} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate2 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. lift-+.f64 N/A

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

      8. distribute-neg-frac N/A

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

      9. sub-negate2 N/A

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

      10. difference-of-squares-rev N/A

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

      11. +-commutative N/A

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

      12. lift-+.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. lower-/.f64 N/A

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

   7. Applied rewrites 8.9%

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

   8. Taylor expanded in B around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 98.5

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

   10. Applied rewrites 98.5%

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

Alternative 5: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -40:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;t\_0 \leq 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI))))
   (if (<= t_0 -40.0)
     (/ (* (atan (/ (- C (+ B A)) B)) 180.0) PI)
     (if (<= t_0 1e-23)
       (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))
       (*
        180.0
        (/
         (atan (* (/ 1.0 B) (- (- C A) (sqrt (fma (- C A) (- C A) (* B B))))))
         PI))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double tmp;
	if (t_0 <= -40.0) {
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / ((double) M_PI);
	} else if (t_0 <= 1e-23) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt(fma((C - A), (C - A), (B * B)))))) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) * 180.0) / pi);
	elseif (t_0 <= 1e-23)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(fma(Float64(C - A), Float64(C - A), Float64(B * B)))))) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -40.0], N[(N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 1e-23], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[(C - A), $MachinePrecision] * N[(C - A), $MachinePrecision] + N[(B * B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -40

   1. Initial program 59.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 87.2%

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

   5. Applied rewrites 86.9%

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

   7. Applied rewrites 82.7%

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

   8. Taylor expanded in B around inf

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(\color{blue}{B} + A\right)}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 76.7%

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

   if -40 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < 9.9999999999999996e-24

   1. Initial program 19.0%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 19.0

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 19.0

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

   3. Applied rewrites 19.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)\right)}{\pi} \]
   4. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-negate2 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. lift-+.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. sub-negate2 N/A

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

      9. difference-of-squares-rev N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 18.1

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

   5. Applied rewrites 18.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\color{blue}{\frac{\left(A + C\right) \cdot \left(C - A\right)}{A + C}} - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}\right)\right)}{\pi} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate2 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. lift-+.f64 N/A

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

      8. distribute-neg-frac N/A

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

      9. sub-negate2 N/A

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

      10. difference-of-squares-rev N/A

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

      11. +-commutative N/A

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

      12. lift-+.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. lower-/.f64 N/A

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

   7. Applied rewrites 9.4%

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

   8. Taylor expanded in B around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 96.3

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

   10. Applied rewrites 96.3%

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

   if 9.9999999999999996e-24 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 58.3%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 58.3

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 58.3

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

   3. Applied rewrites 58.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)\right)}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -40:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI))))
   (if (<= t_0 -40.0)
     (/ (* (atan (/ (- C B) B)) 180.0) PI)
     (if (<= t_0 0.0)
       (/ (* (atan (* 0.5 (/ B A))) 180.0) PI)
       (/ (* (atan 1.0) 180.0) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double tmp;
	if (t_0 <= -40.0) {
		tmp = (atan(((C - B) / B)) * 180.0) / ((double) M_PI);
	} else if (t_0 <= 0.0) {
		tmp = (atan((0.5 * (B / A))) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double tmp;
	if (t_0 <= -40.0) {
		tmp = (Math.atan(((C - B) / B)) * 180.0) / Math.PI;
	} else if (t_0 <= 0.0) {
		tmp = (Math.atan((0.5 * (B / A))) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	tmp = 0
	if t_0 <= -40.0:
		tmp = (math.atan(((C - B) / B)) * 180.0) / math.pi
	elif t_0 <= 0.0:
		tmp = (math.atan((0.5 * (B / A))) * 180.0) / math.pi
	else:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(Float64(atan(Float64(Float64(C - B) / B)) * 180.0) / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(atan(Float64(0.5 * Float64(B / A))) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	tmp = 0.0;
	if (t_0 <= -40.0)
		tmp = (atan(((C - B) / B)) * 180.0) / pi;
	elseif (t_0 <= 0.0)
		tmp = (atan((0.5 * (B / A))) * 180.0) / pi;
	else
		tmp = (atan(1.0) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -40.0], N[(N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -40

   1. Initial program 59.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 87.2%

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

   5. Applied rewrites 86.9%

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

   7. Applied rewrites 82.7%

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

   8. Taylor expanded in B around inf

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \color{blue}{B}}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 64.6%

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

   if -40 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -0.0

   1. Initial program 19.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 20.8%

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

   5. Applied rewrites 19.9%

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

   7. Applied rewrites 13.6%

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

   8. Taylor expanded in A around -inf

      \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)} \cdot 180}{\pi} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-/.f64 52.8

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

   10. Applied rewrites 52.8%

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

   if -0.0 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 58.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 86.7%

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

   5. Applied rewrites 86.3%

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

   7. Applied rewrites 82.1%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 45.9%

       \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -40:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI))))
   (if (<= t_0 -40.0)
     (/ (* (atan (/ (- C B) B)) 180.0) PI)
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
       (/ (* (atan 1.0) 180.0) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double tmp;
	if (t_0 <= -40.0) {
		tmp = (atan(((C - B) / B)) * 180.0) / ((double) M_PI);
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double tmp;
	if (t_0 <= -40.0) {
		tmp = (Math.atan(((C - B) / B)) * 180.0) / Math.PI;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	tmp = 0
	if t_0 <= -40.0:
		tmp = (math.atan(((C - B) / B)) * 180.0) / math.pi
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(Float64(atan(Float64(Float64(C - B) / B)) * 180.0) / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	tmp = 0.0;
	if (t_0 <= -40.0)
		tmp = (atan(((C - B) / B)) * 180.0) / pi;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = (atan(1.0) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -40.0], N[(N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -40

   1. Initial program 59.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 87.2%

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

   5. Applied rewrites 86.9%

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

   7. Applied rewrites 82.7%

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

   8. Taylor expanded in B around inf

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \color{blue}{B}}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 64.6%

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

   if -40 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -0.0

   1. Initial program 19.1%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 19.1

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 19.1

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

   3. Applied rewrites 19.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)\right)}{\pi} \]
   4. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-negate2 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. lift-+.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. sub-negate2 N/A

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

      9. difference-of-squares-rev N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 18.2

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

   5. Applied rewrites 18.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\color{blue}{\frac{\left(A + C\right) \cdot \left(C - A\right)}{A + C}} - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}\right)\right)}{\pi} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate2 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. lift-+.f64 N/A

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

      8. distribute-neg-frac N/A

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

      9. sub-negate2 N/A

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

      10. difference-of-squares-rev N/A

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

      11. +-commutative N/A

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

      12. lift-+.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. lower-/.f64 N/A

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

   7. Applied rewrites 9.4%

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

   8. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-/.f64 52.8

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

   10. Applied rewrites 52.8%

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

   if -0.0 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 58.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 86.7%

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

   5. Applied rewrites 86.3%

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

   7. Applied rewrites 82.1%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 45.9%

       \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.5)
     (/ (* (atan (/ (- C (+ B A)) B)) 180.0) PI)
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))
       (/ (* (atan (/ (- C (hypot B C)) B)) 180.0) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / ((double) M_PI);
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else {
		tmp = (atan(((C - hypot(B, C)) / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = (Math.atan(((C - (B + A)) / B)) * 180.0) / Math.PI;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	} else {
		tmp = (Math.atan(((C - Math.hypot(B, C)) / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -0.5:
		tmp = (math.atan(((C - (B + A)) / B)) * 180.0) / math.pi
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	else:
		tmp = (math.atan(((C - math.hypot(B, C)) / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) * 180.0) / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / pi;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	else
		tmp = (atan(((C - hypot(B, C)) / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -0.5], N[(N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.5

   1. Initial program 59.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 87.2%

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

   5. Applied rewrites 86.9%

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

   7. Applied rewrites 82.8%

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

   8. Taylor expanded in B around inf

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(\color{blue}{B} + A\right)}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 76.7%

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

   if -0.5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.0

   1. Initial program 19.0%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 19.0

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 19.0

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

   3. Applied rewrites 19.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)\right)}{\pi} \]
   4. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-negate2 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. lift-+.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. sub-negate2 N/A

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

      9. difference-of-squares-rev N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 18.1

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

   5. Applied rewrites 18.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\color{blue}{\frac{\left(A + C\right) \cdot \left(C - A\right)}{A + C}} - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}\right)\right)}{\pi} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate2 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. lift-+.f64 N/A

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

      8. distribute-neg-frac N/A

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

      9. sub-negate2 N/A

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

      10. difference-of-squares-rev N/A

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

      11. +-commutative N/A

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

      12. lift-+.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. lower-/.f64 N/A

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

   7. Applied rewrites 9.5%

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

   8. Taylor expanded in B around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 97.2

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

   10. Applied rewrites 97.2%

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

   if -0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 58.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 86.7%

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

   5. Applied rewrites 86.3%

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

   7. Applied rewrites 82.1%

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

   8. Taylor expanded in A around 0

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \color{blue}{\sqrt{{B}^{2} + {C}^{2}}}}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

      1. pow2 N/A

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

      2. unpow2 N/A

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

      3. lower-hypot.f64 71.2

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

   10. Applied rewrites 71.2%

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

Alternative 9: 56.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{+23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.3 \cdot 10^{+44}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-2 \cdot A}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.5e+23)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 5.3e+44)
     (/ (* (atan (/ (- C B) B)) 180.0) PI)
     (/ (* (atan (/ (* -2.0 A) B)) 180.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.5e+23) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 5.3e+44) {
		tmp = (atan(((C - B) / B)) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(((-2.0 * A) / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.5e+23) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 5.3e+44) {
		tmp = (Math.atan(((C - B) / B)) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan(((-2.0 * A) / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.5e+23:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 5.3e+44:
		tmp = (math.atan(((C - B) / B)) * 180.0) / math.pi
	else:
		tmp = (math.atan(((-2.0 * A) / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9.5e+23)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 5.3e+44)
		tmp = Float64(Float64(atan(Float64(Float64(C - B) / B)) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(Float64(Float64(-2.0 * A) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9.5e+23)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 5.3e+44)
		tmp = (atan(((C - B) / B)) * 180.0) / pi;
	else
		tmp = (atan(((-2.0 * A) / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.5e+23], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.3e+44], N[(N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(-2.0 * A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.50000000000000038e23

   1. Initial program 23.7%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 23.7

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 23.7

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

   3. Applied rewrites 23.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)\right)}{\pi} \]
   4. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-negate2 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. lift-+.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. sub-negate2 N/A

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

      9. difference-of-squares-rev N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 19.9

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

   5. Applied rewrites 19.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\color{blue}{\frac{\left(A + C\right) \cdot \left(C - A\right)}{A + C}} - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}\right)\right)}{\pi} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate2 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. lift-+.f64 N/A

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

      8. distribute-neg-frac N/A

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

      9. sub-negate2 N/A

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

      10. difference-of-squares-rev N/A

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

      11. +-commutative N/A

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

      12. lift-+.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r/ N/A

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

      16. lower-/.f64 N/A

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

   7. Applied rewrites 15.7%

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

   8. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-/.f64 68.9

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

   10. Applied rewrites 68.9%

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

   if -9.50000000000000038e23 < A < 5.2999999999999999e44

   1. Initial program 57.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 80.9%

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

   5. Applied rewrites 80.9%

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

   7. Applied rewrites 80.8%

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

   8. Taylor expanded in B around inf

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \color{blue}{B}}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 46.2%

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

   if 5.2999999999999999e44 < A

   1. Initial program 77.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 94.5%

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

   5. Applied rewrites 94.2%

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

   7. Applied rewrites 94.5%

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

   8. Taylor expanded in A around inf

      \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{-2 \cdot A}}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

      1. lower-*.f64 70.6

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

   10. Applied rewrites 70.6%

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

Alternative 10: 60.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.8e+40)
   (/ (* (atan 1.0) 180.0) PI)
   (/ (* (atan (/ (- C (+ B A)) B)) 180.0) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.8e+40) {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.8e+40) {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan(((C - (B + A)) / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.8e+40:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	else:
		tmp = (math.atan(((C - (B + A)) / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.8e+40)
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.8e+40)
		tmp = (atan(1.0) * 180.0) / pi;
	else
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.8e+40], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.79999999999999998e40

   1. Initial program 47.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 83.0%

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

   5. Applied rewrites 83.0%

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

   7. Applied rewrites 83.0%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 66.5%

       \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]

   if -1.79999999999999998e40 < B

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 76.5%

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

   5. Applied rewrites 75.9%

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

   7. Applied rewrites 70.2%

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

   8. Taylor expanded in B around inf

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(\color{blue}{B} + A\right)}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 58.3%

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

Alternative 11: 51.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.4e-27)
   (/ (* (atan 1.0) 180.0) PI)
   (/ (* (atan (/ (- C B) B)) 180.0) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.4e-27) {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(((C - B) / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.4e-27) {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan(((C - B) / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.4e-27:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	else:
		tmp = (math.atan(((C - B) / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.4e-27)
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - B) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.4e-27)
		tmp = (atan(1.0) * 180.0) / pi;
	else
		tmp = (atan(((C - B) / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.4e-27], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -2.40000000000000002e-27

   1. Initial program 50.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   5. Applied rewrites 79.7%

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

   7. Applied rewrites 79.6%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 60.5%

       \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]

   if -2.40000000000000002e-27 < B

   1. Initial program 54.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 77.2%

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

   5. Applied rewrites 76.7%

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

   7. Applied rewrites 70.6%

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

   8. Taylor expanded in B around inf

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \color{blue}{B}}{B}\right) \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 48.2%

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

Alternative 12: 40.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1 \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4e-310) (/ (* (atan 1.0) 180.0) PI) (/ (* (atan -1.0) 180.0) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4e-310) {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(-1.0) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4e-310) {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan(-1.0) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4e-310:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	else:
		tmp = (math.atan(-1.0) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4e-310)
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(-1.0) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4e-310)
		tmp = (atan(1.0) * 180.0) / pi;
	else
		tmp = (atan(-1.0) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4e-310], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[-1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -3.999999999999988e-310

   1. Initial program 53.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 77.8%

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

   5. Applied rewrites 77.3%

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

   7. Applied rewrites 72.9%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 40.7%

       \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]

   if -3.999999999999988e-310 < B

   1. Initial program 54.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 78.0%

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

   5. Applied rewrites 77.7%

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

   7. Applied rewrites 73.2%

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

   8. Taylor expanded in B around inf

      \[\leadsto \frac{\tan^{-1} \color{blue}{-1} \cdot 180}{\pi} \]
   9. Step-by-step derivation

   10. Applied rewrites 40.9%

       \[\leadsto \frac{\tan^{-1} \color{blue}{-1} \cdot 180}{\pi} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 21.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \frac{\tan^{-1} -1 \cdot 180}{\pi} \end{array} \]

FPCore

(FPCore (A B C) :precision binary64 (/ (* (atan -1.0) 180.0) PI))

C

double code(double A, double B, double C) {
	return (atan(-1.0) * 180.0) / ((double) M_PI);
}

Java

public static double code(double A, double B, double C) {
	return (Math.atan(-1.0) * 180.0) / Math.PI;
}

Python

def code(A, B, C):
	return (math.atan(-1.0) * 180.0) / math.pi

Julia

function code(A, B, C)
	return Float64(Float64(atan(-1.0) * 180.0) / pi)
end

MATLAB

function tmp = code(A, B, C)
	tmp = (atan(-1.0) * 180.0) / pi;
end

Wolfram

code[A_, B_, C_] := N[(N[(N[ArcTan[-1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]

Derivation

1. Initial program 53.6%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-*r/ N/A

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

   4. lower-/.f64 N/A

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

3. Applied rewrites 77.9%

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

5. Applied rewrites 77.5%

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

7. Applied rewrites 73.0%

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

8. Taylor expanded in B around inf

   \[\leadsto \frac{\tan^{-1} \color{blue}{-1} \cdot 180}{\pi} \]
9. Step-by-step derivation

10. Applied rewrites 21.5%

    \[\leadsto \frac{\tan^{-1} \color{blue}{-1} \cdot 180}{\pi} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025107 
(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)))