ABCF->ab-angle angle

Percentage Accurate: 54.1% → 81.8%

Time: 5.7s

Alternatives: 13

Speedup: 2.2×

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: 54.1% 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: 81.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 6.6 \cdot 10^{+51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\left(\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right) \cdot 180\right) \cdot \frac{1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 6.6e+51)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot (- A C) B)))) PI))
   (* (* (atan (fma (/ B C) -0.5 0.0)) 180.0) (/ 1.0 PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 6.6e+51) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((A - C), B)))) / ((double) M_PI));
	} else {
		tmp = (atan(fma((B / C), -0.5, 0.0)) * 180.0) * (1.0 / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 6.6e+51)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(Float64(A - C), B)))) / pi));
	else
		tmp = Float64(Float64(atan(fma(Float64(B / C), -0.5, 0.0)) * 180.0) * Float64(1.0 / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 6.6e+51], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5 + 0.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 6.5999999999999994e51

   1. Initial program 62.8%

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

      1. lift-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. lift-pow.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 84.7

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

   3. Applied rewrites 84.7%

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

   if 6.5999999999999994e51 < C

   1. Initial program 21.1%

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

   2. 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. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 70.6

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 70.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      2. lift-/.f64 N/A

         \[\leadsto 180 \cdot \color{blue}{\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

   6. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right)}{\pi}} \]
   7. Step-by-step derivation

      1. lift-PI.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)}{\mathsf{PI}\left(\right)}} \]

      3. mult-flip N/A

         \[\leadsto \color{blue}{\left(180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}} \]

   8. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\left(\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right) \cdot 180\right) \cdot \frac{1}{\pi}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 81.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 6.6 \cdot 10^{+51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(A, B\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\left(\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right) \cdot 180\right) \cdot \frac{1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 6.6e+51)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot A B)))) PI))
   (* (* (atan (fma (/ B C) -0.5 0.0)) 180.0) (/ 1.0 PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 6.6e+51) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot(A, B)))) / ((double) M_PI));
	} else {
		tmp = (atan(fma((B / C), -0.5, 0.0)) * 180.0) * (1.0 / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 6.6e+51)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(A, B)))) / pi));
	else
		tmp = Float64(Float64(atan(fma(Float64(B / C), -0.5, 0.0)) * 180.0) * Float64(1.0 / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 6.6e+51], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5 + 0.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 6.5999999999999994e51

   1. Initial program 62.8%

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

      1. lift-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. lift-pow.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 84.7

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

   3. Applied rewrites 84.7%

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

   4. Taylor expanded in A around inf

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

   6. Applied rewrites 83.9%

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

   if 6.5999999999999994e51 < C

   1. Initial program 21.1%

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

   2. 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. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 70.6

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 70.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      2. lift-/.f64 N/A

         \[\leadsto 180 \cdot \color{blue}{\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

   6. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right)}{\pi}} \]
   7. Step-by-step derivation

      1. lift-PI.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)}{\mathsf{PI}\left(\right)}} \]

      3. mult-flip N/A

         \[\leadsto \color{blue}{\left(180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}} \]

   8. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\left(\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right) \cdot 180\right) \cdot \frac{1}{\pi}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 79.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -0.0027:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.6 \cdot 10^{+51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-\left(\mathsf{hypot}\left(B, A\right) + A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\left(\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right) \cdot 180\right) \cdot \frac{1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -0.0027)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI))
   (if (<= C 6.6e+51)
     (* 180.0 (/ (atan (/ (- (+ (hypot B A) A)) B)) PI))
     (* (* (atan (fma (/ B C) -0.5 0.0)) 180.0) (/ 1.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -0.0027) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / ((double) M_PI));
	} else if (C <= 6.6e+51) {
		tmp = 180.0 * (atan((-(hypot(B, A) + A) / B)) / ((double) M_PI));
	} else {
		tmp = (atan(fma((B / C), -0.5, 0.0)) * 180.0) * (1.0 / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -0.0027)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - B))) / pi));
	elseif (C <= 6.6e+51)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-Float64(hypot(B, A) + A)) / B)) / pi));
	else
		tmp = Float64(Float64(atan(fma(Float64(B / C), -0.5, 0.0)) * 180.0) * Float64(1.0 / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -0.0027], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.6e+51], N[(180.0 * N[(N[ArcTan[N[((-N[(N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision] + A), $MachinePrecision]) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5 + 0.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -0.0027000000000000001

   1. Initial program 78.2%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 81.1%

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

   if -0.0027000000000000001 < C < 6.5999999999999994e51

   1. Initial program 55.6%

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

   2. Taylor expanded in C around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-fma.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 52.9

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

   4. Applied rewrites 52.9%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. pow2 N/A

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

      5. pow2 N/A

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

      6. +-commutative N/A

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

      7. pow2 N/A

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

      8. pow2 N/A

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

      9. lower-hypot.f64 77.2

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

   6. Applied rewrites 77.2%

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

   if 6.5999999999999994e51 < C

   1. Initial program 21.1%

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

   2. 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. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 70.6

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 70.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      2. lift-/.f64 N/A

         \[\leadsto 180 \cdot \color{blue}{\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

   6. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right)}{\pi}} \]
   7. Step-by-step derivation

      1. lift-PI.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)}{\mathsf{PI}\left(\right)}} \]

      3. mult-flip N/A

         \[\leadsto \color{blue}{\left(180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}} \]

   8. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\left(\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right) \cdot 180\right) \cdot \frac{1}{\pi}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 76.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -92:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \mathsf{hypot}\left(A - C, B\right)\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -92.0)
   (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
   (* 180.0 (/ (atan (* (/ 1.0 B) (- C (hypot (- A C) B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -92.0) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * (C - hypot((A - C), B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -92.0) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((1.0 / B) * (C - Math.hypot((A - C), B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -92.0:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((1.0 / B) * (C - math.hypot((A - C), B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -92.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(C - hypot(Float64(A - C), B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -92.0)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	else
		tmp = 180.0 * (atan(((1.0 / B) * (C - hypot((A - C), B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -92.0], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(C - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -92

   1. Initial program 26.2%

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

   2. 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 64.8

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

   4. Applied rewrites 64.8%

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

   if -92 < A

   1. Initial program 63.1%

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

      1. lift-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. lift-pow.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 85.3

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

   3. Applied rewrites 85.3%

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

   4. Taylor expanded in A around 0

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

   6. Applied rewrites 84.2%

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

Alternative 5: 61.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 3.8 \cdot 10^{+48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\left(\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right) \cdot 180\right) \cdot \frac{1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 3.8e+48)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI))
   (* (* (atan (fma (/ B C) -0.5 0.0)) 180.0) (/ 1.0 PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 3.8e+48) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / ((double) M_PI));
	} else {
		tmp = (atan(fma((B / C), -0.5, 0.0)) * 180.0) * (1.0 / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 3.8e+48)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - B))) / pi));
	else
		tmp = Float64(Float64(atan(fma(Float64(B / C), -0.5, 0.0)) * 180.0) * Float64(1.0 / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 3.8e+48], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5 + 0.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 3.8e48

   1. Initial program 62.9%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 59.5%

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

   if 3.8e48 < C

   1. Initial program 21.4%

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

   2. 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. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 70.1

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 70.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      2. lift-/.f64 N/A

         \[\leadsto 180 \cdot \color{blue}{\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

   6. Applied rewrites 70.1%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right)}{\pi}} \]
   7. Step-by-step derivation

      1. lift-PI.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)}{\mathsf{PI}\left(\right)}} \]

      3. mult-flip N/A

         \[\leadsto \color{blue}{\left(180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}} \]

   8. Applied rewrites 70.1%

      \[\leadsto \color{blue}{\left(\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right) \cdot 180\right) \cdot \frac{1}{\pi}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 57.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.6 \cdot 10^{+122}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C + C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.6 \cdot 10^{+51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\left(\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right) \cdot 180\right) \cdot \frac{1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.6e+122)
   (/ (* 180.0 (atan (/ (+ C C) B))) PI)
   (if (<= C 6.6e+51)
     (* 180.0 (/ (atan (- (/ (- A) B) 1.0)) PI))
     (* (* (atan (fma (/ B C) -0.5 0.0)) 180.0) (/ 1.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.6e+122) {
		tmp = (180.0 * atan(((C + C) / B))) / ((double) M_PI);
	} else if (C <= 6.6e+51) {
		tmp = 180.0 * (atan(((-A / B) - 1.0)) / ((double) M_PI));
	} else {
		tmp = (atan(fma((B / C), -0.5, 0.0)) * 180.0) * (1.0 / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3.6e+122)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C + C) / B))) / pi);
	elseif (C <= 6.6e+51)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) / B) - 1.0)) / pi));
	else
		tmp = Float64(Float64(atan(fma(Float64(B / C), -0.5, 0.0)) * 180.0) * Float64(1.0 / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.6e+122], N[(N[(180.0 * N[ArcTan[N[(N[(C + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 6.6e+51], N[(180.0 * N[(N[ArcTan[N[(N[((-A) / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5 + 0.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -3.6000000000000003e122

   1. Initial program 84.7%

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

   2. Taylor expanded in C around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 82.2

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

   4. Applied rewrites 82.2%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 82.2%

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

   if -3.6000000000000003e122 < C < 6.5999999999999994e51

   1. Initial program 57.7%

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

   2. Taylor expanded in C around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-fma.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 51.8

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

   4. Applied rewrites 51.8%

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

   5. Taylor expanded in A around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. lower-neg.f64 47.2

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

   7. Applied rewrites 47.2%

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

   if 6.5999999999999994e51 < C

   1. Initial program 21.1%

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

   2. 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. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 70.6

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 70.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      2. lift-/.f64 N/A

         \[\leadsto 180 \cdot \color{blue}{\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

   6. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right)}{\pi}} \]
   7. Step-by-step derivation

      1. lift-PI.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)}{\mathsf{PI}\left(\right)}} \]

      3. mult-flip N/A

         \[\leadsto \color{blue}{\left(180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, \frac{0}{B}\right)\right)\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}} \]

   8. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\left(\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right) \cdot 180\right) \cdot \frac{1}{\pi}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 57.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.6 \cdot 10^{+122}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C + C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.6 \cdot 10^{+51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.6e+122)
   (/ (* 180.0 (atan (/ (+ C C) B))) PI)
   (if (<= C 6.6e+51)
     (* 180.0 (/ (atan (- (/ (- A) B) 1.0)) PI))
     (/ (* 180.0 (atan (* (/ B C) -0.5))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.6e+122) {
		tmp = (180.0 * atan(((C + C) / B))) / ((double) M_PI);
	} else if (C <= 6.6e+51) {
		tmp = 180.0 * (atan(((-A / B) - 1.0)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((B / C) * -0.5))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.6e+122) {
		tmp = (180.0 * Math.atan(((C + C) / B))) / Math.PI;
	} else if (C <= 6.6e+51) {
		tmp = 180.0 * (Math.atan(((-A / B) - 1.0)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((B / C) * -0.5))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3.6e+122:
		tmp = (180.0 * math.atan(((C + C) / B))) / math.pi
	elif C <= 6.6e+51:
		tmp = 180.0 * (math.atan(((-A / B) - 1.0)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((B / C) * -0.5))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3.6e+122)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C + C) / B))) / pi);
	elseif (C <= 6.6e+51)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) / B) - 1.0)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / C) * -0.5))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3.6e+122)
		tmp = (180.0 * atan(((C + C) / B))) / pi;
	elseif (C <= 6.6e+51)
		tmp = 180.0 * (atan(((-A / B) - 1.0)) / pi);
	else
		tmp = (180.0 * atan(((B / C) * -0.5))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.6e+122], N[(N[(180.0 * N[ArcTan[N[(N[(C + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 6.6e+51], N[(180.0 * N[(N[ArcTan[N[(N[((-A) / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -3.6000000000000003e122

   1. Initial program 84.7%

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

   2. Taylor expanded in C around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 82.2

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

   4. Applied rewrites 82.2%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 82.2%

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

   if -3.6000000000000003e122 < C < 6.5999999999999994e51

   1. Initial program 57.7%

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

   2. Taylor expanded in C around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-fma.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 51.8

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

   4. Applied rewrites 51.8%

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

   5. Taylor expanded in A around 0

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. lower-neg.f64 47.2

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

   7. Applied rewrites 47.2%

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

   if 6.5999999999999994e51 < C

   1. Initial program 21.1%

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

   2. 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. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 70.6

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 70.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      2. lift-/.f64 N/A

         \[\leadsto 180 \cdot \color{blue}{\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

   6. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right)}{\pi}} \]

   7. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 70.6

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

   9. Applied rewrites 70.6%

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

Alternative 8: 46.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.5)
   (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
   (if (<= A 3.5e-58)
     (* 180.0 (/ (atan -1.0) PI))
     (/ (* 180.0 (atan (* (/ A B) -2.0))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (A <= 3.5e-58) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((A / B) * -2.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (A <= 3.5e-58) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((A / B) * -2.0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.5:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif A <= 3.5e-58:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = (180.0 * math.atan(((A / B) * -2.0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.5)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (A <= 3.5e-58)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(A / B) * -2.0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.5)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (A <= 3.5e-58)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = (180.0 * atan(((A / B) * -2.0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.5], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.5e-58], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.5

   1. Initial program 26.3%

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

   2. 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 64.6

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

   4. Applied rewrites 64.6%

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

   if -1.5 < A < 3.4999999999999999e-58

   1. Initial program 55.9%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 26.7%

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

   if 3.4999999999999999e-58 < A

   1. Initial program 73.6%

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

   2. Taylor expanded in A around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 61.9

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

   4. Applied rewrites 61.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 61.9%

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

Alternative 9: 44.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3 \cdot 10^{+122}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C + C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.5 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3e+122)
   (/ (* 180.0 (atan (/ (+ C C) B))) PI)
   (if (<= C 5.5e-47)
     (* 180.0 (/ (atan -1.0) PI))
     (/ (* 180.0 (atan (* (/ B C) -0.5))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3e+122) {
		tmp = (180.0 * atan(((C + C) / B))) / ((double) M_PI);
	} else if (C <= 5.5e-47) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((B / C) * -0.5))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3e+122) {
		tmp = (180.0 * Math.atan(((C + C) / B))) / Math.PI;
	} else if (C <= 5.5e-47) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((B / C) * -0.5))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3e+122:
		tmp = (180.0 * math.atan(((C + C) / B))) / math.pi
	elif C <= 5.5e-47:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = (180.0 * math.atan(((B / C) * -0.5))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3e+122)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C + C) / B))) / pi);
	elseif (C <= 5.5e-47)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / C) * -0.5))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3e+122)
		tmp = (180.0 * atan(((C + C) / B))) / pi;
	elseif (C <= 5.5e-47)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = (180.0 * atan(((B / C) * -0.5))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3e+122], N[(N[(180.0 * N[ArcTan[N[(N[(C + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 5.5e-47], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.99999999999999986e122

   1. Initial program 84.7%

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

   2. Taylor expanded in C around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 82.2

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

   4. Applied rewrites 82.2%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 82.2%

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

   if -2.99999999999999986e122 < C < 5.5000000000000002e-47

   1. Initial program 59.8%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 26.5%

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

   if 5.5000000000000002e-47 < C

   1. Initial program 27.2%

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

   2. 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. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 61.3

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 61.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      2. lift-/.f64 N/A

         \[\leadsto 180 \cdot \color{blue}{\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi}} \]

   6. Applied rewrites 61.3%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right)}{\pi}} \]

   7. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 61.3

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

   9. Applied rewrites 61.3%

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

Alternative 10: 36.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+260}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5e+260)
   (/ (* 180.0 (atan 0.0)) PI)
   (if (<= A 3.5e-58)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (/ (- A) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5e+260) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (A <= 3.5e-58) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5e+260) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (A <= 3.5e-58) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5e+260:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif A <= 3.5e-58:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5e+260)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (A <= 3.5e-58)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5e+260)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (A <= 3.5e-58)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-A / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5e+260], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 3.5e-58], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.9999999999999996e260

   1. Initial program 6.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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. lift-pow.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 57.2

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

   3. Applied rewrites 57.2%

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

   4. Taylor expanded in C around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(0 \cdot A\right) \cdot -1}{B}\right)}{\pi} \]

      5. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0 \cdot -1}{B}\right)}{\pi} \]

      6. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi} \]

      7. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0 \cdot A}{B}\right)}{\pi} \]

      8. lift-/.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0 \cdot A}{\color{blue}{B}}\right)}{\pi} \]

      9. mul0-lft 50.5

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi} \]

   6. Applied rewrites 50.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}} \]

      2. lift-PI.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      3. lift-/.f64 N/A

         \[\leadsto 180 \cdot \color{blue}{\frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}} \]

   8. Applied rewrites 50.5%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} 0}{\pi}} \]

   if -4.9999999999999996e260 < A < 3.4999999999999999e-58

   1. Initial program 47.7%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 23.4%

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

   if 3.4999999999999999e-58 < A

   1. Initial program 73.6%

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

   2. 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. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 74.4

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

   4. Applied rewrites 74.4%

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

   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. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 61.5

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

   7. Applied rewrites 61.5%

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

Alternative 11: 34.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3 \cdot 10^{+122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.4 \cdot 10^{+220}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3e+122)
   (* 180.0 (/ (atan (/ C B)) PI))
   (if (<= C 8.4e+220)
     (* 180.0 (/ (atan -1.0) PI))
     (/ (* 180.0 (atan 0.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3e+122) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= 8.4e+220) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3e+122) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= 8.4e+220) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3e+122:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= 8.4e+220:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3e+122)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= 8.4e+220)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3e+122)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= 8.4e+220)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = (180.0 * atan(0.0)) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3e+122], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8.4e+220], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.99999999999999986e122

   1. Initial program 84.7%

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

   2. 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. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 87.2

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

   4. Applied rewrites 87.2%

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

   5. Taylor expanded in C around inf

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

      1. lower-/.f64 81.7

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

   7. Applied rewrites 81.7%

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

   if -2.99999999999999986e122 < C < 8.40000000000000027e220

   1. Initial program 52.7%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 24.1%

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

   if 8.40000000000000027e220 < C

   1. Initial program 7.7%

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

      1. lift-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. lift-pow.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 55.6

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

   3. Applied rewrites 55.6%

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

   4. Taylor expanded in C around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(0 \cdot A\right) \cdot -1}{B}\right)}{\pi} \]

      5. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0 \cdot -1}{B}\right)}{\pi} \]

      6. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi} \]

      7. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0 \cdot A}{B}\right)}{\pi} \]

      8. lift-/.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0 \cdot A}{\color{blue}{B}}\right)}{\pi} \]

      9. mul0-lft 46.1

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi} \]

   6. Applied rewrites 46.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}} \]

      2. lift-PI.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      3. lift-/.f64 N/A

         \[\leadsto 180 \cdot \color{blue}{\frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}} \]

   8. Applied rewrites 46.1%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} 0}{\pi}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 24.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 8.4 \cdot 10^{+220}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 8.4e+220) (* 180.0 (/ (atan -1.0) PI)) (/ (* 180.0 (atan 0.0)) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 8.4e+220) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 8.4e+220) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 8.4e+220:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 8.4e+220)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 8.4e+220)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = (180.0 * atan(0.0)) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 8.4e+220], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 8.40000000000000027e220

   1. Initial program 57.8%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 22.5%

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

   if 8.40000000000000027e220 < C

   1. Initial program 7.7%

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

      1. lift-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. lift-pow.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 55.6

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

   3. Applied rewrites 55.6%

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

   4. Taylor expanded in C around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(0 \cdot A\right) \cdot -1}{B}\right)}{\pi} \]

      5. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0 \cdot -1}{B}\right)}{\pi} \]

      6. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi} \]

      7. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0 \cdot A}{B}\right)}{\pi} \]

      8. lift-/.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0 \cdot A}{\color{blue}{B}}\right)}{\pi} \]

      9. mul0-lft 46.1

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi} \]

   6. Applied rewrites 46.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}} \]

      2. lift-PI.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      3. lift-/.f64 N/A

         \[\leadsto 180 \cdot \color{blue}{\frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}} \]

   8. Applied rewrites 46.1%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} 0}{\pi}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 21.4% 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 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. Taylor expanded in B around inf

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

4. Applied rewrites 21.4%

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

Reproduce

herbie shell --seed 2025128 
(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)))