rsin A (should all be same)

Percentage Accurate: 76.3% → 99.5%

Time: 13.6s

Alternatives: 10

Speedup: 0.4×

Specification

Math

\[\begin{array}{l} \\ \frac{r \cdot \sin b}{\cos \left(a + b\right)} \end{array} \]

FPCore

(FPCore (r a b) :precision binary64 (/ (* r (sin b)) (cos (+ a b))))

C

double code(double r, double a, double b) {
	return (r * sin(b)) / cos((a + b));
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (r * sin(b)) / cos((a + b))
end function

Java

public static double code(double r, double a, double b) {
	return (r * Math.sin(b)) / Math.cos((a + b));
}

Python

def code(r, a, b):
	return (r * math.sin(b)) / math.cos((a + b))

Julia

function code(r, a, b)
	return Float64(Float64(r * sin(b)) / cos(Float64(a + b)))
end

MATLAB

function tmp = code(r, a, b)
	tmp = (r * sin(b)) / cos((a + b));
end

Wolfram

code[r_, a_, b_] := N[(N[(r * N[Sin[b], $MachinePrecision]), $MachinePrecision] / N[Cos[N[(a + b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{r \cdot \sin b}{\cos \left(a + b\right)} \end{array} \]

FPCore

(FPCore (r a b) :precision binary64 (/ (* r (sin b)) (cos (+ a b))))

C

double code(double r, double a, double b) {
	return (r * sin(b)) / cos((a + b));
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (r * sin(b)) / cos((a + b))
end function

Java

public static double code(double r, double a, double b) {
	return (r * Math.sin(b)) / Math.cos((a + b));
}

Python

def code(r, a, b):
	return (r * math.sin(b)) / math.cos((a + b))

Julia

function code(r, a, b)
	return Float64(Float64(r * sin(b)) / cos(Float64(a + b)))
end

MATLAB

function tmp = code(r, a, b)
	tmp = (r * sin(b)) / cos((a + b));
end

Wolfram

code[r_, a_, b_] := N[(N[(r * N[Sin[b], $MachinePrecision]), $MachinePrecision] / N[Cos[N[(a + b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin b \cdot \sin a} \end{array} \]

FPCore

(FPCore (r a b)
 :precision binary64
 (* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))))

C

double code(double r, double a, double b) {
	return r * (sin(b) / ((cos(b) * cos(a)) - (sin(b) * sin(a))));
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = r * (sin(b) / ((cos(b) * cos(a)) - (sin(b) * sin(a))))
end function

Java

public static double code(double r, double a, double b) {
	return r * (Math.sin(b) / ((Math.cos(b) * Math.cos(a)) - (Math.sin(b) * Math.sin(a))));
}

Python

def code(r, a, b):
	return r * (math.sin(b) / ((math.cos(b) * math.cos(a)) - (math.sin(b) * math.sin(a))))

Julia

function code(r, a, b)
	return Float64(r * Float64(sin(b) / Float64(Float64(cos(b) * cos(a)) - Float64(sin(b) * sin(a)))))
end

MATLAB

function tmp = code(r, a, b)
	tmp = r * (sin(b) / ((cos(b) * cos(a)) - (sin(b) * sin(a))));
end

Wolfram

code[r_, a_, b_] := N[(r * N[(N[Sin[b], $MachinePrecision] / N[(N[(N[Cos[b], $MachinePrecision] * N[Cos[a], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[b], $MachinePrecision] * N[Sin[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-/l* 80.4%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

   2. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

   3. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

   4. +-commutative 80.4%

      \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

3. Simplified 80.4%

   \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. cos-sum 99.5%

      \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}} \]

6. Applied egg-rr 99.5%

   \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}} \]
7. Add Preprocessing

Alternative 2: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00054 \lor \neg \left(b \leq 0.0085\right):\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \end{array} \end{array} \]

FPCore

(FPCore (r a b)
 :precision binary64
 (if (or (<= b -0.00054) (not (<= b 0.0085)))
   (* r (/ (sin b) (cos b)))
   (* b (/ r (cos a)))))

C

double code(double r, double a, double b) {
	double tmp;
	if ((b <= -0.00054) || !(b <= 0.0085)) {
		tmp = r * (sin(b) / cos(b));
	} else {
		tmp = b * (r / cos(a));
	}
	return tmp;
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-0.00054d0)) .or. (.not. (b <= 0.0085d0))) then
        tmp = r * (sin(b) / cos(b))
    else
        tmp = b * (r / cos(a))
    end if
    code = tmp
end function

Java

public static double code(double r, double a, double b) {
	double tmp;
	if ((b <= -0.00054) || !(b <= 0.0085)) {
		tmp = r * (Math.sin(b) / Math.cos(b));
	} else {
		tmp = b * (r / Math.cos(a));
	}
	return tmp;
}

Python

def code(r, a, b):
	tmp = 0
	if (b <= -0.00054) or not (b <= 0.0085):
		tmp = r * (math.sin(b) / math.cos(b))
	else:
		tmp = b * (r / math.cos(a))
	return tmp

Julia

function code(r, a, b)
	tmp = 0.0
	if ((b <= -0.00054) || !(b <= 0.0085))
		tmp = Float64(r * Float64(sin(b) / cos(b)));
	else
		tmp = Float64(b * Float64(r / cos(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(r, a, b)
	tmp = 0.0;
	if ((b <= -0.00054) || ~((b <= 0.0085)))
		tmp = r * (sin(b) / cos(b));
	else
		tmp = b * (r / cos(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[r_, a_, b_] := If[Or[LessEqual[b, -0.00054], N[Not[LessEqual[b, 0.0085]], $MachinePrecision]], N[(r * N[(N[Sin[b], $MachinePrecision] / N[Cos[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(r / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.40000000000000007e-4 or 0.0085000000000000006 < b

   1. Initial program 59.7%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 59.7%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 59.7%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 59.7%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 59.7%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 59.9%

      \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos b}} \]

   if -5.40000000000000007e-4 < b < 0.0085000000000000006

   1. Initial program 98.2%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 98.3%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 98.3%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 98.3%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 98.2%

      \[\leadsto r \cdot \color{blue}{\frac{b}{\cos a}} \]
   6. Step-by-step derivation

      1. clear-num 98.1%

         \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos a}{b}}} \]

      2. un-div-inv 98.1%

         \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]

   7. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 98.2%

         \[\leadsto \color{blue}{\frac{r}{\cos a} \cdot b} \]

   9. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{r}{\cos a} \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00054 \lor \neg \left(b \leq 0.0085\right):\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\cos b}{\sin b}\\ \mathbf{if}\;b \leq -0.00054:\\ \;\;\;\;r \cdot \frac{1}{t\_0}\\ \mathbf{elif}\;b \leq 0.0085:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\frac{r}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (r a b)
 :precision binary64
 (let* ((t_0 (/ (cos b) (sin b))))
   (if (<= b -0.00054)
     (* r (/ 1.0 t_0))
     (if (<= b 0.0085) (* b (/ r (cos a))) (/ r t_0)))))

C

double code(double r, double a, double b) {
	double t_0 = cos(b) / sin(b);
	double tmp;
	if (b <= -0.00054) {
		tmp = r * (1.0 / t_0);
	} else if (b <= 0.0085) {
		tmp = b * (r / cos(a));
	} else {
		tmp = r / t_0;
	}
	return tmp;
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos(b) / sin(b)
    if (b <= (-0.00054d0)) then
        tmp = r * (1.0d0 / t_0)
    else if (b <= 0.0085d0) then
        tmp = b * (r / cos(a))
    else
        tmp = r / t_0
    end if
    code = tmp
end function

Java

public static double code(double r, double a, double b) {
	double t_0 = Math.cos(b) / Math.sin(b);
	double tmp;
	if (b <= -0.00054) {
		tmp = r * (1.0 / t_0);
	} else if (b <= 0.0085) {
		tmp = b * (r / Math.cos(a));
	} else {
		tmp = r / t_0;
	}
	return tmp;
}

Python

def code(r, a, b):
	t_0 = math.cos(b) / math.sin(b)
	tmp = 0
	if b <= -0.00054:
		tmp = r * (1.0 / t_0)
	elif b <= 0.0085:
		tmp = b * (r / math.cos(a))
	else:
		tmp = r / t_0
	return tmp

Julia

function code(r, a, b)
	t_0 = Float64(cos(b) / sin(b))
	tmp = 0.0
	if (b <= -0.00054)
		tmp = Float64(r * Float64(1.0 / t_0));
	elseif (b <= 0.0085)
		tmp = Float64(b * Float64(r / cos(a)));
	else
		tmp = Float64(r / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(r, a, b)
	t_0 = cos(b) / sin(b);
	tmp = 0.0;
	if (b <= -0.00054)
		tmp = r * (1.0 / t_0);
	elseif (b <= 0.0085)
		tmp = b * (r / cos(a));
	else
		tmp = r / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[r_, a_, b_] := Block[{t$95$0 = N[(N[Cos[b], $MachinePrecision] / N[Sin[b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.00054], N[(r * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0085], N[(b * N[(r / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(r / t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.40000000000000007e-4

   1. Initial program 56.8%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 56.9%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 56.9%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 56.9%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 56.9%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 56.9%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. cos-sum 99.3%

         \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}} \]

   6. Applied egg-rr 99.3%

      \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}} \]
   7. Step-by-step derivation

      1. cos-sum 56.9%

         \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos \left(b + a\right)}} \]

      2. clear-num 56.9%

         \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

      3. inv-pow 56.9%

         \[\leadsto r \cdot \color{blue}{{\left(\frac{\cos \left(b + a\right)}{\sin b}\right)}^{-1}} \]

   8. Applied egg-rr 56.9%

      \[\leadsto r \cdot \color{blue}{{\left(\frac{\cos \left(b + a\right)}{\sin b}\right)}^{-1}} \]
   9. Step-by-step derivation

      1. unpow-1 56.9%

         \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

   10. Simplified 56.9%

       \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

   11. Taylor expanded in a around 0 57.3%

       \[\leadsto r \cdot \frac{1}{\color{blue}{\frac{\cos b}{\sin b}}} \]

   if -5.40000000000000007e-4 < b < 0.0085000000000000006

   1. Initial program 98.2%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 98.3%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 98.3%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 98.3%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 98.2%

      \[\leadsto r \cdot \color{blue}{\frac{b}{\cos a}} \]
   6. Step-by-step derivation

      1. clear-num 98.1%

         \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos a}{b}}} \]

      2. un-div-inv 98.1%

         \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]

   7. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 98.2%

         \[\leadsto \color{blue}{\frac{r}{\cos a} \cdot b} \]

   9. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{r}{\cos a} \cdot b} \]

   if 0.0085000000000000006 < b

   1. Initial program 62.5%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 62.4%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 62.4%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 62.4%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 62.4%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 62.4%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 62.5%

         \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

      2. un-div-inv 62.7%

         \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

   6. Applied egg-rr 62.7%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

   7. Taylor expanded in a around 0 62.6%

      \[\leadsto \frac{r}{\frac{\color{blue}{\cos b}}{\sin b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00054:\\ \;\;\;\;r \cdot \frac{1}{\frac{\cos b}{\sin b}}\\ \mathbf{elif}\;b \leq 0.0085:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\frac{r}{\frac{\cos b}{\sin b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00058:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{elif}\;b \leq 0.0085:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\frac{r}{\frac{\cos b}{\sin b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (r a b)
 :precision binary64
 (if (<= b -0.00058)
   (* r (/ (sin b) (cos b)))
   (if (<= b 0.0085) (* b (/ r (cos a))) (/ r (/ (cos b) (sin b))))))

C

double code(double r, double a, double b) {
	double tmp;
	if (b <= -0.00058) {
		tmp = r * (sin(b) / cos(b));
	} else if (b <= 0.0085) {
		tmp = b * (r / cos(a));
	} else {
		tmp = r / (cos(b) / sin(b));
	}
	return tmp;
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-0.00058d0)) then
        tmp = r * (sin(b) / cos(b))
    else if (b <= 0.0085d0) then
        tmp = b * (r / cos(a))
    else
        tmp = r / (cos(b) / sin(b))
    end if
    code = tmp
end function

Java

public static double code(double r, double a, double b) {
	double tmp;
	if (b <= -0.00058) {
		tmp = r * (Math.sin(b) / Math.cos(b));
	} else if (b <= 0.0085) {
		tmp = b * (r / Math.cos(a));
	} else {
		tmp = r / (Math.cos(b) / Math.sin(b));
	}
	return tmp;
}

Python

def code(r, a, b):
	tmp = 0
	if b <= -0.00058:
		tmp = r * (math.sin(b) / math.cos(b))
	elif b <= 0.0085:
		tmp = b * (r / math.cos(a))
	else:
		tmp = r / (math.cos(b) / math.sin(b))
	return tmp

Julia

function code(r, a, b)
	tmp = 0.0
	if (b <= -0.00058)
		tmp = Float64(r * Float64(sin(b) / cos(b)));
	elseif (b <= 0.0085)
		tmp = Float64(b * Float64(r / cos(a)));
	else
		tmp = Float64(r / Float64(cos(b) / sin(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(r, a, b)
	tmp = 0.0;
	if (b <= -0.00058)
		tmp = r * (sin(b) / cos(b));
	elseif (b <= 0.0085)
		tmp = b * (r / cos(a));
	else
		tmp = r / (cos(b) / sin(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[r_, a_, b_] := If[LessEqual[b, -0.00058], N[(r * N[(N[Sin[b], $MachinePrecision] / N[Cos[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0085], N[(b * N[(r / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(r / N[(N[Cos[b], $MachinePrecision] / N[Sin[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.8e-4

   1. Initial program 56.8%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 56.9%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 56.9%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 56.9%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 56.9%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 56.9%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 57.3%

      \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos b}} \]

   if -5.8e-4 < b < 0.0085000000000000006

   1. Initial program 98.2%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 98.3%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 98.3%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 98.3%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 98.2%

      \[\leadsto r \cdot \color{blue}{\frac{b}{\cos a}} \]
   6. Step-by-step derivation

      1. clear-num 98.1%

         \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos a}{b}}} \]

      2. un-div-inv 98.1%

         \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]

   7. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 98.2%

         \[\leadsto \color{blue}{\frac{r}{\cos a} \cdot b} \]

   9. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{r}{\cos a} \cdot b} \]

   if 0.0085000000000000006 < b

   1. Initial program 62.5%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 62.4%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 62.4%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 62.4%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 62.4%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 62.4%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 62.5%

         \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

      2. un-div-inv 62.7%

         \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

   6. Applied egg-rr 62.7%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos \left(b + a\right)}{\sin b}}} \]

   7. Taylor expanded in a around 0 62.6%

      \[\leadsto \frac{r}{\frac{\color{blue}{\cos b}}{\sin b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00058:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{elif}\;b \leq 0.0085:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\frac{r}{\frac{\cos b}{\sin b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00054:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{elif}\;b \leq 0.0085:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\sin b \cdot \frac{r}{\cos b}\\ \end{array} \end{array} \]

FPCore

(FPCore (r a b)
 :precision binary64
 (if (<= b -0.00054)
   (* r (/ (sin b) (cos b)))
   (if (<= b 0.0085) (* b (/ r (cos a))) (* (sin b) (/ r (cos b))))))

C

double code(double r, double a, double b) {
	double tmp;
	if (b <= -0.00054) {
		tmp = r * (sin(b) / cos(b));
	} else if (b <= 0.0085) {
		tmp = b * (r / cos(a));
	} else {
		tmp = sin(b) * (r / cos(b));
	}
	return tmp;
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-0.00054d0)) then
        tmp = r * (sin(b) / cos(b))
    else if (b <= 0.0085d0) then
        tmp = b * (r / cos(a))
    else
        tmp = sin(b) * (r / cos(b))
    end if
    code = tmp
end function

Java

public static double code(double r, double a, double b) {
	double tmp;
	if (b <= -0.00054) {
		tmp = r * (Math.sin(b) / Math.cos(b));
	} else if (b <= 0.0085) {
		tmp = b * (r / Math.cos(a));
	} else {
		tmp = Math.sin(b) * (r / Math.cos(b));
	}
	return tmp;
}

Python

def code(r, a, b):
	tmp = 0
	if b <= -0.00054:
		tmp = r * (math.sin(b) / math.cos(b))
	elif b <= 0.0085:
		tmp = b * (r / math.cos(a))
	else:
		tmp = math.sin(b) * (r / math.cos(b))
	return tmp

Julia

function code(r, a, b)
	tmp = 0.0
	if (b <= -0.00054)
		tmp = Float64(r * Float64(sin(b) / cos(b)));
	elseif (b <= 0.0085)
		tmp = Float64(b * Float64(r / cos(a)));
	else
		tmp = Float64(sin(b) * Float64(r / cos(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(r, a, b)
	tmp = 0.0;
	if (b <= -0.00054)
		tmp = r * (sin(b) / cos(b));
	elseif (b <= 0.0085)
		tmp = b * (r / cos(a));
	else
		tmp = sin(b) * (r / cos(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[r_, a_, b_] := If[LessEqual[b, -0.00054], N[(r * N[(N[Sin[b], $MachinePrecision] / N[Cos[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0085], N[(b * N[(r / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sin[b], $MachinePrecision] * N[(r / N[Cos[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.40000000000000007e-4

   1. Initial program 56.8%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 56.9%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 56.9%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 56.9%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 56.9%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 56.9%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 57.3%

      \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos b}} \]

   if -5.40000000000000007e-4 < b < 0.0085000000000000006

   1. Initial program 98.2%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 98.3%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 98.3%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 98.3%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 98.2%

      \[\leadsto r \cdot \color{blue}{\frac{b}{\cos a}} \]
   6. Step-by-step derivation

      1. clear-num 98.1%

         \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos a}{b}}} \]

      2. un-div-inv 98.1%

         \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]

   7. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 98.2%

         \[\leadsto \color{blue}{\frac{r}{\cos a} \cdot b} \]

   9. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{r}{\cos a} \cdot b} \]

   if 0.0085000000000000006 < b

   1. Initial program 62.5%

      \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
   2. Step-by-step derivation

      1. associate-/l* 62.4%

         \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

      2. remove-double-neg 62.4%

         \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

      3. remove-double-neg 62.4%

         \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

      4. +-commutative 62.4%

         \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

   3. Simplified 62.4%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 62.5%

      \[\leadsto \color{blue}{\frac{r \cdot \sin b}{\cos b}} \]
   6. Step-by-step derivation

      1. *-commutative 62.5%

         \[\leadsto \frac{\color{blue}{\sin b \cdot r}}{\cos b} \]

      2. associate-/l* 62.4%

         \[\leadsto \color{blue}{\sin b \cdot \frac{r}{\cos b}} \]

   7. Simplified 62.4%

      \[\leadsto \color{blue}{\sin b \cdot \frac{r}{\cos b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00054:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{elif}\;b \leq 0.0085:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\sin b \cdot \frac{r}{\cos b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ r \cdot \frac{\sin b}{\cos \left(b + a\right)} \end{array} \]

FPCore

(FPCore (r a b) :precision binary64 (* r (/ (sin b) (cos (+ b a)))))

C

double code(double r, double a, double b) {
	return r * (sin(b) / cos((b + a)));
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = r * (sin(b) / cos((b + a)))
end function

Java

public static double code(double r, double a, double b) {
	return r * (Math.sin(b) / Math.cos((b + a)));
}

Python

def code(r, a, b):
	return r * (math.sin(b) / math.cos((b + a)))

Julia

function code(r, a, b)
	return Float64(r * Float64(sin(b) / cos(Float64(b + a))))
end

MATLAB

function tmp = code(r, a, b)
	tmp = r * (sin(b) / cos((b + a)));
end

Wolfram

code[r_, a_, b_] := N[(r * N[(N[Sin[b], $MachinePrecision] / N[Cos[N[(b + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-/l* 80.4%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

   2. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

   3. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

   4. +-commutative 80.4%

      \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

3. Simplified 80.4%

   \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 7: 55.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ r \cdot \frac{\sin b}{\cos a} \end{array} \]

FPCore

(FPCore (r a b) :precision binary64 (* r (/ (sin b) (cos a))))

C

double code(double r, double a, double b) {
	return r * (sin(b) / cos(a));
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = r * (sin(b) / cos(a))
end function

Java

public static double code(double r, double a, double b) {
	return r * (Math.sin(b) / Math.cos(a));
}

Python

def code(r, a, b):
	return r * (math.sin(b) / math.cos(a))

Julia

function code(r, a, b)
	return Float64(r * Float64(sin(b) / cos(a)))
end

MATLAB

function tmp = code(r, a, b)
	tmp = r * (sin(b) / cos(a));
end

Wolfram

code[r_, a_, b_] := N[(r * N[(N[Sin[b], $MachinePrecision] / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-/l* 80.4%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

   2. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

   3. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

   4. +-commutative 80.4%

      \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

3. Simplified 80.4%

   \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
4. Add Preprocessing

5. Taylor expanded in b around 0 58.0%

   \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a}} \]
6. Add Preprocessing

Alternative 8: 51.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ b \cdot \frac{r}{\cos a} \end{array} \]

FPCore

(FPCore (r a b) :precision binary64 (* b (/ r (cos a))))

C

double code(double r, double a, double b) {
	return b * (r / cos(a));
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = b * (r / cos(a))
end function

Java

public static double code(double r, double a, double b) {
	return b * (r / Math.cos(a));
}

Python

def code(r, a, b):
	return b * (r / math.cos(a))

Julia

function code(r, a, b)
	return Float64(b * Float64(r / cos(a)))
end

MATLAB

function tmp = code(r, a, b)
	tmp = b * (r / cos(a));
end

Wolfram

code[r_, a_, b_] := N[(b * N[(r / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-/l* 80.4%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

   2. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

   3. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

   4. +-commutative 80.4%

      \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

3. Simplified 80.4%

   \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
4. Add Preprocessing

5. Taylor expanded in b around 0 54.4%

   \[\leadsto r \cdot \color{blue}{\frac{b}{\cos a}} \]
6. Step-by-step derivation

   1. clear-num 54.3%

      \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos a}{b}}} \]

   2. un-div-inv 54.3%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]

7. Applied egg-rr 54.3%

   \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]
8. Step-by-step derivation

   1. associate-/r/ 54.4%

      \[\leadsto \color{blue}{\frac{r}{\cos a} \cdot b} \]

9. Simplified 54.4%

   \[\leadsto \color{blue}{\frac{r}{\cos a} \cdot b} \]

10. Final simplification 54.4%

    \[\leadsto b \cdot \frac{r}{\cos a} \]
11. Add Preprocessing

Alternative 9: 51.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ r \cdot \frac{b}{\cos a} \end{array} \]

FPCore

(FPCore (r a b) :precision binary64 (* r (/ b (cos a))))

C

double code(double r, double a, double b) {
	return r * (b / cos(a));
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = r * (b / cos(a))
end function

Java

public static double code(double r, double a, double b) {
	return r * (b / Math.cos(a));
}

Python

def code(r, a, b):
	return r * (b / math.cos(a))

Julia

function code(r, a, b)
	return Float64(r * Float64(b / cos(a)))
end

MATLAB

function tmp = code(r, a, b)
	tmp = r * (b / cos(a));
end

Wolfram

code[r_, a_, b_] := N[(r * N[(b / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-/l* 80.4%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

   2. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

   3. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

   4. +-commutative 80.4%

      \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

3. Simplified 80.4%

   \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
4. Add Preprocessing

5. Taylor expanded in b around 0 54.4%

   \[\leadsto r \cdot \color{blue}{\frac{b}{\cos a}} \]
6. Add Preprocessing

Alternative 10: 34.6% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ r \cdot b \end{array} \]

FPCore

(FPCore (r a b) :precision binary64 (* r b))

C

double code(double r, double a, double b) {
	return r * b;
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = r * b
end function

Java

public static double code(double r, double a, double b) {
	return r * b;
}

Python

def code(r, a, b):
	return r * b

Julia

function code(r, a, b)
	return Float64(r * b)
end

MATLAB

function tmp = code(r, a, b)
	tmp = r * b;
end

Wolfram

code[r_, a_, b_] := N[(r * b), $MachinePrecision]

Derivation

1. Initial program 80.3%

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
2. Step-by-step derivation

   1. associate-/l* 80.4%

      \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(a + b\right)}} \]

   2. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\left(-\left(-\frac{\sin b}{\cos \left(a + b\right)}\right)\right)} \]

   3. remove-double-neg 80.4%

      \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos \left(a + b\right)}} \]

   4. +-commutative 80.4%

      \[\leadsto r \cdot \frac{\sin b}{\cos \color{blue}{\left(b + a\right)}} \]

3. Simplified 80.4%

   \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}} \]
4. Add Preprocessing

5. Taylor expanded in b around 0 54.4%

   \[\leadsto r \cdot \color{blue}{\frac{b}{\cos a}} \]

6. Taylor expanded in a around 0 34.5%

   \[\leadsto r \cdot \color{blue}{b} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024097 
(FPCore (r a b)
  :name "rsin A (should all be same)"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))