ABCF->ab-angle angle

Percentage Accurate: 53.4% → 88.2%

Time: 12.6s

Alternatives: 15

Speedup: 0.6×

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: 53.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)\right)\right)}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 0.0002:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{\frac{\mathsf{fma}\left(-0.5, \frac{B \cdot B}{C - A}, \left(C - A\right) \cdot -2\right)}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot (- C A) B)))) PI)))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -4e-22)
     t_0
     (if (<= t_1 0.0002)
       (*
        180.0
        (/
         (atan (/ 1.0 (/ (fma -0.5 (/ (* B B) (- C A)) (* (- C A) -2.0)) B)))
         PI))
       t_0))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / ((double) M_PI));
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_1 <= -4e-22) {
		tmp = t_0;
	} else if (t_1 <= 0.0002) {
		tmp = 180.0 * (atan((1.0 / (fma(-0.5, ((B * B) / (C - A)), ((C - A) * -2.0)) / B))) / ((double) M_PI));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(Float64(C - A), B)))) / pi))
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_1 <= -4e-22)
		tmp = t_0;
	elseif (t_1 <= 0.0002)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 / Float64(fma(-0.5, Float64(Float64(B * B) / Float64(C - A)), Float64(Float64(C - A) * -2.0)) / B))) / pi));
	else
		tmp = t_0;
	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[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-22], t$95$0, If[LessEqual[t$95$1, 0.0002], N[(180.0 * N[(N[ArcTan[N[(1.0 / N[(N[(-0.5 * N[(N[(B * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision] + N[(N[(C - A), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 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)))))) < -4.0000000000000002e-22 or 2.0000000000000001e-4 < (*.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 61.5%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 91.5%

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

   if -4.0000000000000002e-22 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.0000000000000001e-4

   1. Initial program 22.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 22.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. clear-num N/A

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

      5. lower-/.f64 N/A

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

      6. *-lft-identity N/A

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

      7. lower-/.f64 22.2

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

      8. lift-hypot.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lower-fma.f64 22.2

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

   6. Applied rewrites 22.2%

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

   7. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 99.2

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{\frac{\mathsf{fma}\left(-0.5, \frac{B \cdot B}{C - A}, \color{blue}{\left(C - A\right)} \cdot -2\right)}{B}}\right)}{\pi} \]

   9. Applied rewrites 99.2%

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

Alternative 2: 79.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.0002:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{\frac{\mathsf{fma}\left(-0.5, \frac{B \cdot B}{C - A}, \left(C - A\right) \cdot -2\right)}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{\mathsf{fma}\left(-0.5, \left(A - C\right) \cdot \frac{A - C}{B}, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

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 -4e-22)
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI))
     (if (<= t_0 0.0002)
       (*
        180.0
        (/
         (atan (/ 1.0 (/ (fma -0.5 (/ (* B B) (- C A)) (* (- C A) -2.0)) B)))
         PI))
       (*
        180.0
        (/
         (atan (- 1.0 (/ (fma -0.5 (* (- A C) (/ (- A C) B)) (- A 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 <= -4e-22) {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (atan((1.0 / (fma(-0.5, ((B * B) / (C - A)), ((C - A) * -2.0)) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (fma(-0.5, ((A - C) * ((A - C) / B)), (A - C)) / B))) / ((double) M_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 <= -4e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	elseif (t_0 <= 0.0002)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 / Float64(fma(-0.5, Float64(Float64(B * B) / Float64(C - A)), Float64(Float64(C - A) * -2.0)) / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(fma(-0.5, Float64(Float64(A - C) * Float64(Float64(A - C) / B)), Float64(A - C)) / B))) / pi));
	end
	return 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, -4e-22], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0002], N[(180.0 * N[(N[ArcTan[N[(1.0 / N[(N[(-0.5 * N[(N[(B * B), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision] + N[(N[(C - A), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(N[(-0.5 * N[(N[(A - C), $MachinePrecision] * N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision] + N[(A - C), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.0000000000000002e-22

   1. Initial program 62.0%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 84.8

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

   5. Applied rewrites 84.8%

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

   if -4.0000000000000002e-22 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.0000000000000001e-4

   1. Initial program 22.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 22.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. clear-num N/A

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

      5. lower-/.f64 N/A

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

      6. *-lft-identity N/A

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

      7. lower-/.f64 22.2

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

      8. lift-hypot.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lower-fma.f64 22.2

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

   6. Applied rewrites 22.2%

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

   7. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 99.2

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{\frac{\mathsf{fma}\left(-0.5, \frac{B \cdot B}{C - A}, \color{blue}{\left(C - A\right)} \cdot -2\right)}{B}}\right)}{\pi} \]

   9. Applied rewrites 99.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{\color{blue}{\frac{\mathsf{fma}\left(-0.5, \frac{B \cdot B}{C - A}, \left(C - A\right) \cdot -2\right)}{B}}}\right)}{\pi} \]

   if 2.0000000000000001e-4 < (*.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 61.0%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 11.1

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

   5. Applied rewrites 11.1%

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

   6. Taylor expanded in B around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   8. Applied rewrites 79.4%

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

Alternative 3: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.0002:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{\mathsf{fma}\left(-0.5, \left(A - C\right) \cdot \frac{A - C}{B}, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

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 -4e-22)
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI))
     (if (<= t_0 0.0002)
       (/ (* 180.0 (atan (* -0.5 (/ B (- C A))))) PI)
       (*
        180.0
        (/
         (atan (- 1.0 (/ (fma -0.5 (* (- A C) (/ (- A C) B)) (- A 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 <= -4e-22) {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0002) {
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((1.0 - (fma(-0.5, ((A - C) * ((A - C) / B)), (A - C)) / B))) / ((double) M_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 <= -4e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	elseif (t_0 <= 0.0002)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / Float64(C - A))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(fma(-0.5, Float64(Float64(A - C) * Float64(Float64(A - C) / B)), Float64(A - C)) / B))) / pi));
	end
	return 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, -4e-22], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0002], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(N[(-0.5 * N[(N[(A - C), $MachinePrecision] * N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision] + N[(A - C), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.0000000000000002e-22

   1. Initial program 62.0%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 84.8

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

   5. Applied rewrites 84.8%

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

   if -4.0000000000000002e-22 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.0000000000000001e-4

   1. Initial program 22.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 22.2%

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

   5. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 98.3

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

   7. Applied rewrites 98.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 98.5

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

   9. Applied rewrites 98.5%

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

   if 2.0000000000000001e-4 < (*.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 61.0%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 11.1

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

   5. Applied rewrites 11.1%

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

   6. Taylor expanded in B around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   8. Applied rewrites 79.4%

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

Alternative 4: 79.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \frac{C - A}{B}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_1 + -1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.0002:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_1\right)}{\pi}\\ \end{array} \end{array} \]

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))))))
        (t_1 (/ (- C A) B)))
   (if (<= t_0 -4e-22)
     (* 180.0 (/ (atan (+ t_1 -1.0)) PI))
     (if (<= t_0 0.0002)
       (/ (* 180.0 (atan (* -0.5 (/ B (- C A))))) PI)
       (* 180.0 (/ (atan (+ 1.0 t_1)) 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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -4e-22) {
		tmp = 180.0 * (atan((t_1 + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0002) {
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((1.0 + t_1)) / ((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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -4e-22) {
		tmp = 180.0 * (Math.atan((t_1 + -1.0)) / Math.PI);
	} else if (t_0 <= 0.0002) {
		tmp = (180.0 * Math.atan((-0.5 * (B / (C - A))))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((1.0 + t_1)) / 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))))
	t_1 = (C - A) / B
	tmp = 0
	if t_0 <= -4e-22:
		tmp = 180.0 * (math.atan((t_1 + -1.0)) / math.pi)
	elif t_0 <= 0.0002:
		tmp = (180.0 * math.atan((-0.5 * (B / (C - A))))) / math.pi
	else:
		tmp = 180.0 * (math.atan((1.0 + t_1)) / 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)))))
	t_1 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (t_0 <= -4e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(t_1 + -1.0)) / pi));
	elseif (t_0 <= 0.0002)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / Float64(C - A))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / 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))));
	t_1 = (C - A) / B;
	tmp = 0.0;
	if (t_0 <= -4e-22)
		tmp = 180.0 * (atan((t_1 + -1.0)) / pi);
	elseif (t_0 <= 0.0002)
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / pi;
	else
		tmp = 180.0 * (atan((1.0 + t_1)) / 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]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[t$95$0, -4e-22], N[(180.0 * N[(N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0002], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.0000000000000002e-22

   1. Initial program 62.0%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 84.8

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

   5. Applied rewrites 84.8%

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

   if -4.0000000000000002e-22 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.0000000000000001e-4

   1. Initial program 22.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 22.2%

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

   5. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 98.3

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

   7. Applied rewrites 98.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 98.5

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

   9. Applied rewrites 98.5%

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

   if 2.0000000000000001e-4 < (*.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 61.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 78.9

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

   5. Applied rewrites 78.9%

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

Alternative 5: 78.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \frac{C - A}{B}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_1 + -1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.0002:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_1\right)}{\pi}\\ \end{array} \end{array} \]

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))))))
        (t_1 (/ (- C A) B)))
   (if (<= t_0 -4e-22)
     (* 180.0 (/ (atan (+ t_1 -1.0)) PI))
     (if (<= t_0 0.0002)
       (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))
       (* 180.0 (/ (atan (+ 1.0 t_1)) 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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -4e-22) {
		tmp = 180.0 * (atan((t_1 + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + t_1)) / ((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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -4e-22) {
		tmp = 180.0 * (Math.atan((t_1 + -1.0)) / Math.PI);
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + t_1)) / 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))))
	t_1 = (C - A) / B
	tmp = 0
	if t_0 <= -4e-22:
		tmp = 180.0 * (math.atan((t_1 + -1.0)) / math.pi)
	elif t_0 <= 0.0002:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + t_1)) / 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)))))
	t_1 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (t_0 <= -4e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(t_1 + -1.0)) / pi));
	elseif (t_0 <= 0.0002)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / 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))));
	t_1 = (C - A) / B;
	tmp = 0.0;
	if (t_0 <= -4e-22)
		tmp = 180.0 * (atan((t_1 + -1.0)) / pi);
	elseif (t_0 <= 0.0002)
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	else
		tmp = 180.0 * (atan((1.0 + t_1)) / 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]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[t$95$0, -4e-22], N[(180.0 * N[(N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0002], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.0000000000000002e-22

   1. Initial program 62.0%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 84.8

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

   5. Applied rewrites 84.8%

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

   if -4.0000000000000002e-22 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.0000000000000001e-4

   1. Initial program 22.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 22.2%

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

   5. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 98.3

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

   7. Applied rewrites 98.3%

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

   if 2.0000000000000001e-4 < (*.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 61.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 78.9

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

   5. Applied rewrites 78.9%

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

Alternative 6: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \frac{C - A}{B}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_1 + -1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.0002:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(B, \frac{-0.5}{C}, 0\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_1\right)}{\pi}\\ \end{array} \end{array} \]

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))))))
        (t_1 (/ (- C A) B)))
   (if (<= t_0 -4e-22)
     (* 180.0 (/ (atan (+ t_1 -1.0)) PI))
     (if (<= t_0 0.0002)
       (* 180.0 (/ (atan (fma B (/ -0.5 C) 0.0)) PI))
       (* 180.0 (/ (atan (+ 1.0 t_1)) 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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -4e-22) {
		tmp = 180.0 * (atan((t_1 + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (atan(fma(B, (-0.5 / C), 0.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + t_1)) / ((double) M_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)))))
	t_1 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (t_0 <= -4e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(t_1 + -1.0)) / pi));
	elseif (t_0 <= 0.0002)
		tmp = Float64(180.0 * Float64(atan(fma(B, Float64(-0.5 / C), 0.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / pi));
	end
	return 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]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[t$95$0, -4e-22], N[(180.0 * N[(N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0002], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision] + 0.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.0000000000000002e-22

   1. Initial program 62.0%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 84.8

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

   5. Applied rewrites 84.8%

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

   if -4.0000000000000002e-22 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.0000000000000001e-4

   1. Initial program 22.2%

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

   3. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-rgt1-in N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. div0 N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 57.5

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

   5. Applied rewrites 57.5%

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

   if 2.0000000000000001e-4 < (*.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 61.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 78.9

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

   5. Applied rewrites 78.9%

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

Alternative 7: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \frac{C - A}{B}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_1 + -1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.0002:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_1\right)}{\pi}\\ \end{array} \end{array} \]

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))))))
        (t_1 (/ (- C A) B)))
   (if (<= t_0 -4e-22)
     (* 180.0 (/ (atan (+ t_1 -1.0)) PI))
     (if (<= t_0 0.0002)
       (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
       (* 180.0 (/ (atan (+ 1.0 t_1)) 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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -4e-22) {
		tmp = 180.0 * (atan((t_1 + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + t_1)) / ((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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -4e-22) {
		tmp = 180.0 * (Math.atan((t_1 + -1.0)) / Math.PI);
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + t_1)) / 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))))
	t_1 = (C - A) / B
	tmp = 0
	if t_0 <= -4e-22:
		tmp = 180.0 * (math.atan((t_1 + -1.0)) / math.pi)
	elif t_0 <= 0.0002:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + t_1)) / 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)))))
	t_1 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (t_0 <= -4e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(t_1 + -1.0)) / pi));
	elseif (t_0 <= 0.0002)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / 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))));
	t_1 = (C - A) / B;
	tmp = 0.0;
	if (t_0 <= -4e-22)
		tmp = 180.0 * (atan((t_1 + -1.0)) / pi);
	elseif (t_0 <= 0.0002)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + t_1)) / 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]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[t$95$0, -4e-22], N[(180.0 * N[(N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0002], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.0000000000000002e-22

   1. Initial program 62.0%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 84.8

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

   5. Applied rewrites 84.8%

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

   if -4.0000000000000002e-22 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.0000000000000001e-4

   1. Initial program 22.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 22.2%

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

   5. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 98.3

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

   7. Applied rewrites 98.3%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 57.5%

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

   if 2.0000000000000001e-4 < (*.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 61.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 78.9

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

   5. Applied rewrites 78.9%

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

Alternative 8: 67.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.0002:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -4e-22)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (if (<= t_0 0.0002)
       (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
       (* 180.0 (/ (atan (+ 1.0 (/ (- C A) 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 <= -4e-22) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / 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 <= -4e-22) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / 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 <= -4e-22:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif t_0 <= 0.0002:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / 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 <= -4e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (t_0 <= 0.0002)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / 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 <= -4e-22)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (t_0 <= 0.0002)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / 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, -4e-22], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0002], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $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 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.0000000000000002e-22

   1. Initial program 62.0%

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

   3. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-sqrt.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 49.2

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

   5. Applied rewrites 49.2%

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

   7. Applied rewrites 76.5%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 69.3%

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

   if -4.0000000000000002e-22 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.0000000000000001e-4

   1. Initial program 22.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 22.2%

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

   5. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 98.3

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

   7. Applied rewrites 98.3%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 57.5%

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

   if 2.0000000000000001e-4 < (*.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 61.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 78.9

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

   5. Applied rewrites 78.9%

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

Alternative 9: 62.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.0002:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

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 -4e-22)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (if (<= t_0 0.0002)
       (* 180.0 (/ (atan (/ (* B -0.5) C)) 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 <= -4e-22) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((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 <= -4e-22) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / 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 <= -4e-22:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif t_0 <= 0.0002:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / 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 <= -4e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (t_0 <= 0.0002)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / 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 <= -4e-22)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (t_0 <= 0.0002)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / 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, -4e-22], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0002], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $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 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.0000000000000002e-22

   1. Initial program 62.0%

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

   3. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-sqrt.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 49.2

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

   5. Applied rewrites 49.2%

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

   7. Applied rewrites 76.5%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 69.3%

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

   if -4.0000000000000002e-22 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.0000000000000001e-4

   1. Initial program 22.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 22.2%

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

   5. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 98.3

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

   7. Applied rewrites 98.3%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 57.5%

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

   if 2.0000000000000001e-4 < (*.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 61.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in C around inf

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

   8. Applied rewrites 63.7%

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

Alternative 10: 57.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.0002:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

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 -4e-22)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (if (<= t_0 0.0002)
       (* 180.0 (/ (atan 0.0) 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 <= -4e-22) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (atan(0.0) / ((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 <= -4e-22) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (t_0 <= 0.0002) {
		tmp = 180.0 * (Math.atan(0.0) / 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 <= -4e-22:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif t_0 <= 0.0002:
		tmp = 180.0 * (math.atan(0.0) / 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 <= -4e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (t_0 <= 0.0002)
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= -4e-22)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (t_0 <= 0.0002)
		tmp = 180.0 * (atan(0.0) / 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, -4e-22], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0002], N[(180.0 * N[(N[ArcTan[0.0], $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 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.0000000000000002e-22

   1. Initial program 62.0%

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

   3. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-sqrt.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 49.2

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

   5. Applied rewrites 49.2%

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

   7. Applied rewrites 76.5%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 69.3%

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

   if -4.0000000000000002e-22 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.0000000000000001e-4

   1. Initial program 22.2%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 20.8

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

   5. Applied rewrites 20.8%

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

   if 2.0000000000000001e-4 < (*.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 61.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in C around inf

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

   8. Applied rewrites 63.7%

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

Alternative 11: 57.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

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 -4e-22)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan 0.0) PI))
       (* 180.0 (/ (atan (- 1.0 (/ A 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 <= -4e-22) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / 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 <= -4e-22) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / 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 <= -4e-22:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / 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 <= -4e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / 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 <= -4e-22)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / 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, -4e-22], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.0000000000000002e-22

   1. Initial program 62.0%

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

   3. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-sqrt.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 49.2

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

   5. Applied rewrites 49.2%

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

   7. Applied rewrites 76.5%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 69.3%

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

   if -4.0000000000000002e-22 < (*.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 21.2%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 21.2

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

   5. Applied rewrites 21.2%

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

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

   1. Initial program 61.0%

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

   3. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-sqrt.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 47.6

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

   5. Applied rewrites 47.6%

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

   6. Taylor expanded in B around -inf

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

   8. Applied rewrites 61.9%

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

Alternative 12: 50.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1900000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1900000.0)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1900000.0) {
		tmp = 180.0 * (atan((1.0 - (A / 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 <= 1900000.0) {
		tmp = 180.0 * (Math.atan((1.0 - (A / 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 <= 1900000.0:
		tmp = 180.0 * (math.atan((1.0 - (A / 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 <= 1900000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / 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 <= 1900000.0)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1900000.0], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / 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 < 1.9e6

   1. Initial program 59.6%

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

   3. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-sqrt.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 42.5

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

   5. Applied rewrites 42.5%

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

   6. Taylor expanded in B around -inf

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

   8. Applied rewrites 45.2%

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

   if 1.9e6 < B

   1. Initial program 36.7%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 76.3%

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

Alternative 13: 43.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.5e-111)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.6e-238)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.5e-111) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.6e-238) {
		tmp = 180.0 * (atan(0.0) / ((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 <= -2.5e-111) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.6e-238) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.5e-111:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.6e-238:
		tmp = 180.0 * (math.atan(0.0) / 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 <= -2.5e-111)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.6e-238)
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= -2.5e-111)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.6e-238)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.5e-111], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.6e-238], N[(180.0 * N[(N[ArcTan[0.0], $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 < -2.5000000000000001e-111

   1. Initial program 53.0%

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

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 51.4%

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

   if -2.5000000000000001e-111 < B < 4.60000000000000009e-238

   1. Initial program 58.1%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 33.9

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

   5. Applied rewrites 33.9%

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

   if 4.60000000000000009e-238 < B

   1. Initial program 54.8%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 48.9%

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

Alternative 14: 28.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 4.6 \cdot 10^{-238}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 4.6e-238) (* 180.0 (/ (atan 0.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 4.6e-238) {
		tmp = 180.0 * (atan(0.0) / ((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 <= 4.6e-238) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 4.6e-238:
		tmp = 180.0 * (math.atan(0.0) / 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 <= 4.6e-238)
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= 4.6e-238)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 4.6e-238], N[(180.0 * N[(N[ArcTan[0.0], $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 < 4.60000000000000009e-238

   1. Initial program 55.0%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 16.8

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

   5. Applied rewrites 16.8%

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

   if 4.60000000000000009e-238 < B

   1. Initial program 54.8%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 48.9%

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

Alternative 15: 20.8% 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 54.9%

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

3. Taylor expanded in B around inf

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
4. Step-by-step derivation

5. Applied rewrites 22.8%

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

Reproduce

herbie shell --seed 2024233 
(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)))