ABCF->ab-angle angle

Percentage Accurate: 52.5% → 78.5%

Time: 4.7s

Alternatives: 9

Speedup: 2.3×

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: 52.5% 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: 78.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-45}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{0.5 \cdot \mathsf{fma}\left(\frac{C}{A}, B, B\right)}{A}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e-45)
   (/ (* (atan (/ (* 0.5 (fma (/ C A) B B)) A)) 180.0) PI)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot (- C A) B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-45) {
		tmp = (atan(((0.5 * fma((C / A), B, B)) / A)) * 180.0) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e-45)
		tmp = Float64(Float64(atan(Float64(Float64(0.5 * fma(Float64(C / A), B, B)) / A)) * 180.0) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(Float64(C - A), B)))) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e-45], N[(N[(N[ArcTan[N[(N[(0.5 * N[(N[(C / A), $MachinePrecision] * B + B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.34999999999999992e-45

   1. Initial program 52.5%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 33.0

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

   4. Applied rewrites 33.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{\mathsf{fma}\left(-0.5, B, -0.5 \cdot \frac{B \cdot C}{A}\right)}{A}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 33.3%

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

   if -1.34999999999999992e-45 < A

   1. Initial program 52.5%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift--.f64 N/A

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

      11. sqr-neg-rev N/A

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-hypot.f64 77.4

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

   3. Applied rewrites 77.4%

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

Alternative 2: 61.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 3.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} - 1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 3.4e+15)
   (* (/ (atan (- (/ (- C A) B) 1.0)) PI) 180.0)
   (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 3.4e+15) {
		tmp = (atan((((C - A) / B) - 1.0)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 3.4e+15) {
		tmp = (Math.atan((((C - A) / B) - 1.0)) / Math.PI) * 180.0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 3.4e+15:
		tmp = (math.atan((((C - A) / B) - 1.0)) / math.pi) * 180.0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 3.4e+15)
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B) - 1.0)) / pi) * 180.0);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 3.4e+15)
		tmp = (atan((((C - A) / B) - 1.0)) / pi) * 180.0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 3.4e+15], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 3.4e15

   1. Initial program 52.5%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 48.7

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

   4. Applied rewrites 48.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 48.7

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

   6. Applied rewrites 49.7%

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

   if 3.4e15 < C

   1. Initial program 52.5%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 27.0

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

   4. Applied rewrites 27.0%

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

   5. Taylor expanded in A around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 27.0

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

   7. Applied rewrites 27.0%

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

Alternative 3: 55.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-45}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5}{A} \cdot B\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{+131}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e-45)
   (* (atan (* (/ 0.5 A) B)) (/ 180.0 PI))
   (if (<= A 2.4e+131)
     (* (/ (atan (- (/ C B) 1.0)) PI) 180.0)
     (* (/ (atan (* -2.0 (/ A B))) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-45) {
		tmp = atan(((0.5 / A) * B)) * (180.0 / ((double) M_PI));
	} else if (A <= 2.4e+131) {
		tmp = (atan(((C / B) - 1.0)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan((-2.0 * (A / B))) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-45) {
		tmp = Math.atan(((0.5 / A) * B)) * (180.0 / Math.PI);
	} else if (A <= 2.4e+131) {
		tmp = (Math.atan(((C / B) - 1.0)) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan((-2.0 * (A / B))) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.35e-45:
		tmp = math.atan(((0.5 / A) * B)) * (180.0 / math.pi)
	elif A <= 2.4e+131:
		tmp = (math.atan(((C / B) - 1.0)) / math.pi) * 180.0
	else:
		tmp = (math.atan((-2.0 * (A / B))) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e-45)
		tmp = Float64(atan(Float64(Float64(0.5 / A) * B)) * Float64(180.0 / pi));
	elseif (A <= 2.4e+131)
		tmp = Float64(Float64(atan(Float64(Float64(C / B) - 1.0)) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(Float64(-2.0 * Float64(A / B))) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.35e-45)
		tmp = atan(((0.5 / A) * B)) * (180.0 / pi);
	elseif (A <= 2.4e+131)
		tmp = (atan(((C / B) - 1.0)) / pi) * 180.0;
	else
		tmp = (atan((-2.0 * (A / B))) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e-45], N[(N[ArcTan[N[(N[(0.5 / A), $MachinePrecision] * B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.4e+131], N[(N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.34999999999999992e-45

   1. Initial program 52.5%

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

   2. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   3. 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 25.9

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

   4. Applied rewrites 25.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-out N/A

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

      7. lower-*.f64 N/A

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

      8. distribute-lft-neg-out N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 25.9

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

   6. Applied rewrites 25.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\left(0.5 \cdot B\right) \cdot \color{blue}{\frac{1}{A}}\right)}{\pi} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 25.9

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

   8. Applied rewrites 25.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(B \cdot \color{blue}{\frac{0.5}{A}}\right)}{\pi} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

          \[\leadsto \tan^{-1} \left(\frac{\frac{1}{2}}{A} \cdot \color{blue}{B}\right) \cdot \mathsf{Rewrite=>}\left(lower-/.f64, \left(\frac{180}{\pi}\right)\right) \]

   10. Applied rewrites 25.9%

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

   if -1.34999999999999992e-45 < A < 2.3999999999999999e131

   1. Initial program 52.5%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 48.7

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

   4. Applied rewrites 48.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 48.7

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

   6. Applied rewrites 49.7%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 38.7%

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

   if 2.3999999999999999e131 < A

   1. Initial program 52.5%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 48.7

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

   4. Applied rewrites 48.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 48.7

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

   6. Applied rewrites 49.7%

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

   7. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.5

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

   9. Applied rewrites 22.5%

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

Alternative 4: 55.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-45}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5}{A} \cdot B\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{+131}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-A}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e-45)
   (* (atan (* (/ 0.5 A) B)) (/ 180.0 PI))
   (if (<= A 2.4e+131)
     (* (/ (atan (- (/ C B) 1.0)) PI) 180.0)
     (/ (* (atan (/ (- A) B)) 180.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-45) {
		tmp = atan(((0.5 / A) * B)) * (180.0 / ((double) M_PI));
	} else if (A <= 2.4e+131) {
		tmp = (atan(((C / B) - 1.0)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan((-A / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-45) {
		tmp = Math.atan(((0.5 / A) * B)) * (180.0 / Math.PI);
	} else if (A <= 2.4e+131) {
		tmp = (Math.atan(((C / B) - 1.0)) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan((-A / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.35e-45:
		tmp = math.atan(((0.5 / A) * B)) * (180.0 / math.pi)
	elif A <= 2.4e+131:
		tmp = (math.atan(((C / B) - 1.0)) / math.pi) * 180.0
	else:
		tmp = (math.atan((-A / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e-45)
		tmp = Float64(atan(Float64(Float64(0.5 / A) * B)) * Float64(180.0 / pi));
	elseif (A <= 2.4e+131)
		tmp = Float64(Float64(atan(Float64(Float64(C / B) - 1.0)) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(Float64(Float64(-A) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.35e-45)
		tmp = atan(((0.5 / A) * B)) * (180.0 / pi);
	elseif (A <= 2.4e+131)
		tmp = (atan(((C / B) - 1.0)) / pi) * 180.0;
	else
		tmp = (atan((-A / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e-45], N[(N[ArcTan[N[(N[(0.5 / A), $MachinePrecision] * B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.4e+131], N[(N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.34999999999999992e-45

   1. Initial program 52.5%

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

   2. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   3. 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 25.9

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

   4. Applied rewrites 25.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-out N/A

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

      7. lower-*.f64 N/A

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

      8. distribute-lft-neg-out N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 25.9

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

   6. Applied rewrites 25.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\left(0.5 \cdot B\right) \cdot \color{blue}{\frac{1}{A}}\right)}{\pi} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 25.9

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

   8. Applied rewrites 25.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(B \cdot \color{blue}{\frac{0.5}{A}}\right)}{\pi} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

          \[\leadsto \tan^{-1} \left(\frac{\frac{1}{2}}{A} \cdot \color{blue}{B}\right) \cdot \mathsf{Rewrite=>}\left(lower-/.f64, \left(\frac{180}{\pi}\right)\right) \]

   10. Applied rewrites 25.9%

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

   if -1.34999999999999992e-45 < A < 2.3999999999999999e131

   1. Initial program 52.5%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 48.7

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

   4. Applied rewrites 48.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 48.7

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

   6. Applied rewrites 49.7%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 38.7%

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

   if 2.3999999999999999e131 < A

   1. Initial program 52.5%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 48.1

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

   4. Applied rewrites 48.1%

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

   5. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.2

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

   7. Applied rewrites 22.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 22.2%

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

Alternative 5: 44.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq 2.4 \cdot 10^{+131}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-A}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A 2.4e+131)
   (* (/ (atan (- (/ C B) 1.0)) PI) 180.0)
   (/ (* (atan (/ (- A) B)) 180.0) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 2.4e+131) {
		tmp = (atan(((C / B) - 1.0)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan((-A / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 2.4e+131) {
		tmp = (Math.atan(((C / B) - 1.0)) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan((-A / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 2.4e+131:
		tmp = (math.atan(((C / B) - 1.0)) / math.pi) * 180.0
	else:
		tmp = (math.atan((-A / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 2.4e+131)
		tmp = Float64(Float64(atan(Float64(Float64(C / B) - 1.0)) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(Float64(Float64(-A) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 2.4e+131)
		tmp = (atan(((C / B) - 1.0)) / pi) * 180.0;
	else
		tmp = (atan((-A / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, 2.4e+131], N[(N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < 2.3999999999999999e131

   1. Initial program 52.5%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 48.7

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

   4. Applied rewrites 48.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 48.7

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

   6. Applied rewrites 49.7%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 38.7%

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

   if 2.3999999999999999e131 < A

   1. Initial program 52.5%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 48.1

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

   4. Applied rewrites 48.1%

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

   5. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.2

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

   7. Applied rewrites 22.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 22.2%

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

Alternative 6: 36.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -7 \cdot 10^{-23}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} - -1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -7e-23)
   (* (/ (atan (- (/ C B) -1.0)) PI) 180.0)
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -7e-23) {
		tmp = (atan(((C / B) - -1.0)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -7e-23) {
		tmp = (Math.atan(((C / B) - -1.0)) / Math.PI) * 180.0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -7e-23:
		tmp = (math.atan(((C / B) - -1.0)) / math.pi) * 180.0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -7e-23)
		tmp = Float64(Float64(atan(Float64(Float64(C / B) - -1.0)) / pi) * 180.0);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -7e-23)
		tmp = (atan(((C / B) - -1.0)) / pi) * 180.0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -7e-23], N[(N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < -6.99999999999999987e-23

   1. Initial program 52.5%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 48.1

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

   4. Applied rewrites 48.1%

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

   5. Taylor expanded in A around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 38.1

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

   7. Applied rewrites 38.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 38.1

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

   9. Applied rewrites 38.1%

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

   if -6.99999999999999987e-23 < C

   1. Initial program 52.5%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.5%

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

Alternative 7: 32.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq 1.36 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-A}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A 1.36e-16)
   (* 180.0 (/ (atan -1.0) PI))
   (/ (* (atan (/ (- A) B)) 180.0) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 1.36e-16) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = (atan((-A / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 1.36e-16) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = (Math.atan((-A / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 1.36e-16:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = (math.atan((-A / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 1.36e-16)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(-A) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 1.36e-16)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = (atan((-A / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, 1.36e-16], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < 1.3599999999999999e-16

   1. Initial program 52.5%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.5%

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

   if 1.3599999999999999e-16 < A

   1. Initial program 52.5%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 48.1

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

   4. Applied rewrites 48.1%

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

   5. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.2

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

   7. Applied rewrites 22.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 22.2%

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

Alternative 8: 32.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq 1.36 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A 1.36e-16)
   (* 180.0 (/ (atan -1.0) PI))
   (* (/ (atan (/ (- A) B)) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 1.36e-16) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = (atan((-A / B)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 1.36e-16) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = (Math.atan((-A / B)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 1.36e-16:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = (math.atan((-A / B)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 1.36e-16)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(-A) / B)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 1.36e-16)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = (atan((-A / B)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, 1.36e-16], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < 1.3599999999999999e-16

   1. Initial program 52.5%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.5%

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

   if 1.3599999999999999e-16 < A

   1. Initial program 52.5%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 48.1

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

   4. Applied rewrites 48.1%

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

   5. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.2

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

   7. Applied rewrites 22.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 22.2

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

   9. Applied rewrites 22.2%

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

Alternative 9: 21.5% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 52.5%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 21.5%

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

Reproduce

herbie shell --seed 2025156 
(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)))