ABCF->ab-angle angle

Percentage Accurate: 53.1% → 80.9%

Time: 5.5s

Alternatives: 17

Speedup: 2.6×

Specification

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  180.0
  (/
   (atan (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
   PI)))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Initial Program: 53.1% 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: 80.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2.1e+80)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot (- A C) B)) B)) PI))
   (* 180.0 (/ (atan (fma (/ B C) -0.5 (- (/ (* 0.0 A) B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.1e+80) {
		tmp = 180.0 * (atan((((C - A) - hypot((A - C), B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(fma((B / C), -0.5, -((0.0 * A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.1e+80)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(fma(Float64(B / C), -0.5, Float64(-Float64(Float64(0.0 * A) / B)))) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2.1e+80], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5 + (-N[(N[(0.0 * A), $MachinePrecision] / B), $MachinePrecision])), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 2.10000000000000001e80

   1. Initial program 61.3%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 82.7

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

   4. Applied rewrites 82.7%

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

   if 2.10000000000000001e80 < C

   1. Initial program 18.2%

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

   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 73.3

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

   4. Applied rewrites 73.3%

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

Alternative 2: 72.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(fma(-1.0, B, C) - A) / B)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 * atan(fma(Float64(B / C), -0.5, Float64(-Float64(Float64(0.0 * A) / B))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C + B) - A) / B)) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -40.0], N[(180.0 * N[(N[ArcTan[N[(N[(N[(-1.0 * B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 * N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5 + (-N[(N[(0.0 * A), $MachinePrecision] / B), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 86.5

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

   4. Applied rewrites 86.5%

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

   5. Taylor expanded in B around inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate--r+ N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lower-/.f64 74.3

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

   7. Applied rewrites 74.3%

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

   8. Taylor expanded in B around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 75.6

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

   10. Applied rewrites 75.6%

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

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

   1. Initial program 18.1%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 19.4

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

   4. Applied rewrites 19.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 19.4

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

   6. Applied rewrites 19.4%

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

   7. Taylor expanded in C around inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. distribute-rgt1-in N/A

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

      11. metadata-eval N/A

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

      12. lower-*.f64 51.5

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

   9. Applied rewrites 51.5%

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

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

   1. Initial program 58.3%

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

   2. Taylor expanded in 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 75.8

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

   4. Applied rewrites 75.8%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 75.8

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

   7. Applied rewrites 75.8%

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

Alternative 3: 72.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(fma(-1.0, B, C) - A) / B)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(fma(Float64(B / C), -0.5, Float64(-Float64(Float64(0.0 * A) / B)))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C + B) - A) / B)) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -40.0], N[(180.0 * N[(N[ArcTan[N[(N[(N[(-1.0 * B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5 + (-N[(N[(0.0 * A), $MachinePrecision] / B), $MachinePrecision])), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 86.5

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

   4. Applied rewrites 86.5%

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

   5. Taylor expanded in B around inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate--r+ N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lower-/.f64 74.3

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

   7. Applied rewrites 74.3%

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

   8. Taylor expanded in B around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 75.6

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

   10. Applied rewrites 75.6%

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

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

   1. Initial program 18.1%

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

   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 51.5

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

   4. Applied rewrites 51.5%

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

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

   1. Initial program 58.3%

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

   2. Taylor expanded in 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 75.8

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

   4. Applied rewrites 75.8%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 75.8

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

   7. Applied rewrites 75.8%

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

Alternative 4: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 10^{+284}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.5)
     (* 180.0 (/ (atan (/ (- (- B) A) B)) PI))
     (if (<= t_0 0.0)
       (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
       (if (<= t_0 1e+284)
         (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
         (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (atan(((-B - A) / B)) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else if (t_0 <= 1e+284) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (Math.atan(((-B - A) / B)) / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else if (t_0 <= 1e+284) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -0.5:
		tmp = 180.0 * (math.atan(((-B - A) / B)) / math.pi)
	elif t_0 <= 0.0:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	elif t_0 <= 1e+284:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-B) - A) / B)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	elseif (t_0 <= 1e+284)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = 180.0 * (atan(((-B - A) / B)) / pi);
	elseif (t_0 <= 0.0)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	elseif (t_0 <= 1e+284)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(180.0 * N[(N[ArcTan[N[(N[((-B) - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 1e+284], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 59.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 86.5

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

   4. Applied rewrites 86.5%

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

   5. Taylor expanded in B around inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate--r+ N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lower-/.f64 74.3

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

   7. Applied rewrites 74.3%

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

   8. Taylor expanded in B around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 75.6

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

   10. Applied rewrites 75.6%

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

   11. Taylor expanded in B around inf

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

       1. mul-1-neg N/A

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

       2. lower-neg.f64 63.0

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

   13. Applied rewrites 63.0%

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

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

   1. Initial program 18.1%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 19.3

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

   4. Applied rewrites 19.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 19.3

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

   6. Applied rewrites 19.3%

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

   7. Taylor expanded in A around -inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 49.9

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

   9. Applied rewrites 49.9%

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

   if 0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 1.00000000000000008e284

   1. Initial program 95.4%

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

   2. Taylor expanded in 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 93.6

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 77.7

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

   7. Applied rewrites 77.7%

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

   if 1.00000000000000008e284 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 43.5%

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

   2. Taylor expanded in B around -inf

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

      1. 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 68.6

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

   4. Applied rewrites 68.6%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 56.8%

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

Alternative 5: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 10^{+284}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.5)
     (* 180.0 (/ (atan (/ (- (- B) A) B)) PI))
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
       (if (<= t_0 1e+284)
         (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
         (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (atan(((-B - A) / B)) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (t_0 <= 1e+284) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (Math.atan(((-B - A) / B)) / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (t_0 <= 1e+284) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -0.5:
		tmp = 180.0 * (math.atan(((-B - A) / B)) / math.pi)
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif t_0 <= 1e+284:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-B) - A) / B)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (t_0 <= 1e+284)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = 180.0 * (atan(((-B - A) / B)) / pi);
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (t_0 <= 1e+284)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(180.0 * N[(N[ArcTan[N[(N[((-B) - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+284], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 59.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 86.5

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

   4. Applied rewrites 86.5%

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

   5. Taylor expanded in B around inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate--r+ N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lower-/.f64 74.3

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

   7. Applied rewrites 74.3%

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

   8. Taylor expanded in B around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 75.6

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

   10. Applied rewrites 75.6%

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

   11. Taylor expanded in B around inf

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

       1. mul-1-neg N/A

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

       2. lower-neg.f64 63.0

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

   13. Applied rewrites 63.0%

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

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

   1. Initial program 18.1%

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

   2. Taylor expanded in 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 49.9

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

   4. Applied rewrites 49.9%

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

   if 0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 1.00000000000000008e284

   1. Initial program 95.4%

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

   2. Taylor expanded in 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 93.6

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 77.7

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

   7. Applied rewrites 77.7%

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

   if 1.00000000000000008e284 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 43.5%

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

   2. Taylor expanded in B around -inf

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

      1. 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 68.6

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

   4. Applied rewrites 68.6%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 56.8%

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

Alternative 6: 72.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(fma(-1.0, B, C) - A) / B)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C + B) - A) / B)) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -40.0], N[(180.0 * N[(N[ArcTan[N[(N[(N[(-1.0 * B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 86.5

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

   4. Applied rewrites 86.5%

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

   5. Taylor expanded in B around inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate--r+ N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lower-/.f64 74.3

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

   7. Applied rewrites 74.3%

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

   8. Taylor expanded in B around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 75.6

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

   10. Applied rewrites 75.6%

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

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

   1. Initial program 18.1%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 19.4

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

   4. Applied rewrites 19.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 19.4

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

   6. Applied rewrites 19.4%

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

   7. Taylor expanded in A around -inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 49.9

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

   9. Applied rewrites 49.9%

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

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

   1. Initial program 58.3%

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

   2. Taylor expanded in 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 75.8

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

   4. Applied rewrites 75.8%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 75.8

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

   7. Applied rewrites 75.8%

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

Alternative 7: 72.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - B) / B))) / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C + B) - A) / B)) / pi));
	end
	return tmp
end

MATLAB

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

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -40.0], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 86.5

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

   4. Applied rewrites 86.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 86.5

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

   6. Applied rewrites 86.5%

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

   7. Taylor expanded in A around 0

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. pow2 N/A

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

      6. lower-hypot.f64 81.0

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

   9. Applied rewrites 81.0%

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

   10. Taylor expanded in B around inf

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

   12. Applied rewrites 75.6%

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

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

   1. Initial program 18.1%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 19.4

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

   4. Applied rewrites 19.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 19.4

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

   6. Applied rewrites 19.4%

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

   7. Taylor expanded in A around -inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 49.9

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

   9. Applied rewrites 49.9%

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

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

   1. Initial program 58.3%

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

   2. Taylor expanded in 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 75.8

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

   4. Applied rewrites 75.8%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 75.8

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

   7. Applied rewrites 75.8%

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

Alternative 8: 66.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-B) - A) / B)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C + B) - A) / B)) / pi));
	end
	return tmp
end

MATLAB

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

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -40.0], N[(180.0 * N[(N[ArcTan[N[(N[((-B) - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 86.5

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

   4. Applied rewrites 86.5%

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

   5. Taylor expanded in B around inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate--r+ N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lower-/.f64 74.3

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

   7. Applied rewrites 74.3%

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

   8. Taylor expanded in B around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 75.6

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

   10. Applied rewrites 75.6%

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

   11. Taylor expanded in B around inf

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

       1. mul-1-neg N/A

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

       2. lower-neg.f64 63.0

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

   13. Applied rewrites 63.0%

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

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

   1. Initial program 18.1%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 19.4

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

   4. Applied rewrites 19.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 19.4

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

   6. Applied rewrites 19.4%

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

   7. Taylor expanded in A around -inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 49.9

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

   9. Applied rewrites 49.9%

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

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

   1. Initial program 58.3%

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

   2. Taylor expanded in 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 75.8

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

   4. Applied rewrites 75.8%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 75.8

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

   7. Applied rewrites 75.8%

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

Alternative 9: 77.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -8.5 \cdot 10^{-50}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{\mathsf{hypot}\left(A, B\right) + A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -8.5e-50)
   (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
   (if (<= C 1.95e+80)
     (* 180.0 (/ (atan (- (/ (+ (hypot A B) A) B))) PI))
     (* 180.0 (/ (atan (fma (/ B C) -0.5 (- (/ (* 0.0 A) B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -8.5e-50) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else if (C <= 1.95e+80) {
		tmp = 180.0 * (atan(-((hypot(A, B) + A) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(fma((B / C), -0.5, -((0.0 * A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -8.5e-50)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	elseif (C <= 1.95e+80)
		tmp = Float64(180.0 * Float64(atan(Float64(-Float64(Float64(hypot(A, B) + A) / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(fma(Float64(B / C), -0.5, Float64(-Float64(Float64(0.0 * A) / B)))) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -8.5e-50], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.95e+80], N[(180.0 * N[(N[ArcTan[(-N[(N[(N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision] + A), $MachinePrecision] / B), $MachinePrecision])], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5 + (-N[(N[(0.0 * A), $MachinePrecision] / B), $MachinePrecision])), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -8.50000000000000012e-50

   1. Initial program 74.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. unpow2 N/A

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

      6. lower-hypot.f64 86.2

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

   4. Applied rewrites 86.2%

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

   if -8.50000000000000012e-50 < C < 1.94999999999999999e80

   1. Initial program 54.2%

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

   2. Taylor expanded in C around 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. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 74.6

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

   4. Applied rewrites 74.6%

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

   if 1.94999999999999999e80 < C

   1. Initial program 18.2%

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

   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 73.2

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

   4. Applied rewrites 73.2%

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

Alternative 10: 74.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -960000000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \mathsf{fma}\left(\frac{C}{A}, B, B\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 0.0021:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -960000000.0)
   (/ (* 180.0 (atan (/ (* 0.5 (fma (/ C A) B B)) A))) PI)
   (if (<= A 0.0021)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -960000000.0) {
		tmp = (180.0 * atan(((0.5 * fma((C / A), B, B)) / A))) / ((double) M_PI);
	} else if (A <= 0.0021) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -960000000.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * fma(Float64(C / A), B, B)) / A))) / pi);
	elseif (A <= 0.0021)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -960000000.0], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(N[(C / A), $MachinePrecision] * B + B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 0.0021], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.6e8

   1. Initial program 24.2%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 56.7

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

   4. Applied rewrites 56.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 56.7

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

   6. Applied rewrites 56.7%

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

   7. Taylor expanded in A around -inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. distribute-lft-out N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 65.9

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

   9. Applied rewrites 65.9%

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

   10. Taylor expanded in A around inf

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

       1. fp-cancel-sub-sign-inv N/A

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. lower-/.f64 N/A

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

       5. distribute-lft-out N/A

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

       6. associate-*r/ N/A

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

       7. lower-*.f64 N/A

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

       8. +-commutative N/A

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

       9. *-commutative N/A

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

       10. lower-fma.f64 N/A

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

       11. lift-/.f64 65.9

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

   12. Applied rewrites 65.9%

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

   if -9.6e8 < A < 0.00209999999999999987

   1. Initial program 56.4%

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

   2. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. unpow2 N/A

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

      6. lower-hypot.f64 76.9

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

   4. Applied rewrites 76.9%

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

   if 0.00209999999999999987 < A

   1. Initial program 75.7%

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

   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 77.2

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

   4. Applied rewrites 77.2%

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

Alternative 11: 79.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -960000000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5 \cdot \mathsf{fma}\left(\frac{C}{A}, B, B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -960000000.0)
   (/ (* 180.0 (atan (/ (* 0.5 (fma (/ C A) B B)) A))) PI)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot C B)) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -960000000.0) {
		tmp = (180.0 * atan(((0.5 * fma((C / A), B, B)) / A))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(C, B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -960000000.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(0.5 * fma(Float64(C / A), B, B)) / A))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(C, B)) / B)) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -960000000.0], N[(N[(180.0 * N[ArcTan[N[(N[(0.5 * N[(N[(C / A), $MachinePrecision] * B + B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -9.6e8

   1. Initial program 24.2%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 56.7

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

   4. Applied rewrites 56.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 56.7

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

   6. Applied rewrites 56.7%

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

   7. Taylor expanded in A around -inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. distribute-lft-out N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 65.9

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

   9. Applied rewrites 65.9%

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

   10. Taylor expanded in A around inf

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

       1. fp-cancel-sub-sign-inv N/A

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. lower-/.f64 N/A

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

       5. distribute-lft-out N/A

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

       6. associate-*r/ N/A

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

       7. lower-*.f64 N/A

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

       8. +-commutative N/A

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

       9. *-commutative N/A

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

       10. lower-fma.f64 N/A

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

       11. lift-/.f64 65.9

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

   12. Applied rewrites 65.9%

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

   if -9.6e8 < A

   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. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 84.4

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

   4. Applied rewrites 84.4%

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

   5. Taylor expanded in A around 0

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. pow2 N/A

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

      6. lower-hypot.f64 83.7

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

   7. Applied rewrites 83.7%

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

Alternative 12: 50.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.5 \cdot 10^{-214}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.5e-214)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B 1e+20)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.5e-214) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 1e+20) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.5e-214) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 1e+20) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.5e-214:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 1e+20:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.5e-214)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 1e+20)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.5e-214)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 1e+20)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.5e-214], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1e+20], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.5000000000000001e-214

   1. Initial program 51.2%

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

   2. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 68.5

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

   4. Applied rewrites 68.5%

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

   5. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 58.2

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

   7. Applied rewrites 58.2%

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

   if -4.5000000000000001e-214 < B < 1e20

   1. Initial program 59.2%

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

   2. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 47.1

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

   4. Applied rewrites 47.1%

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

   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. lift-/.f64 33.0

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

   7. Applied rewrites 33.0%

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

   if 1e20 < B

   1. Initial program 47.5%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 63.8%

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

Alternative 13: 46.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-68}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.9e-68)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1e+20)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.9e-68) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1e+20) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.9e-68) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1e+20) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.9e-68:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1e+20:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.9e-68)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1e+20)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.9e-68)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1e+20)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.9e-68], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1e+20], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.90000000000000019e-68

   1. Initial program 49.6%

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

   2. Taylor expanded in B around -inf

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

   4. Applied rewrites 54.9%

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

   if -1.90000000000000019e-68 < B < 1e20

   1. Initial program 58.2%

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

   2. 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 48.6

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

   4. Applied rewrites 48.6%

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

   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. lift-/.f64 32.5

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

   7. Applied rewrites 32.5%

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

   if 1e20 < B

   1. Initial program 47.5%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 63.8%

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

Alternative 14: 55.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.15 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.15e-300)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (* 180.0 (/ (atan (/ (- (- B) A) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.15e-300) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((-B - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.15e-300) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((-B - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.15e-300:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((-B - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.15e-300)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-B) - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.15e-300)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((-B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.15e-300], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-B) - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.15e-300

   1. Initial program 52.8%

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

   2. 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 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 55.8%

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

   if -1.15e-300 < B

   1. Initial program 53.5%

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

   2. Taylor expanded in A around 0

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

      1. lower-atan.f64 N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift--.f64 N/A

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

      7. unpow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 N/A

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

      10. lift--.f64 77.8

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

   4. Applied rewrites 77.8%

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

   5. Taylor expanded in B around inf

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate--r+ N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lower-/.f64 64.4

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

   7. Applied rewrites 64.4%

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

   8. Taylor expanded in B around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 65.6

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

   10. Applied rewrites 65.6%

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

   11. Taylor expanded in B around inf

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

       1. mul-1-neg N/A

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

       2. lower-neg.f64 54.9

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

   13. Applied rewrites 54.9%

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

Alternative 15: 50.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 6.5 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 6.5e-132)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 6.5e-132) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 6.5e-132) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 6.5e-132:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 6.5e-132)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 6.5e-132)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 6.5e-132], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 6.49999999999999991e-132

   1. Initial program 54.0%

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

   2. 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 62.7

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

   4. Applied rewrites 62.7%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 51.1%

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

   if 6.49999999999999991e-132 < B

   1. Initial program 51.5%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 50.6%

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

Alternative 16: 39.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 52.9%

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

   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 39.5%

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

   if -4.999999999999985e-310 < B

   1. Initial program 53.4%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 40.0%

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

Alternative 17: 20.9% accurate, 3.1× 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 53.1%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 20.9%

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

Reproduce

herbie shell --seed 2025105 
(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)))