rsin B (should all be same)

Percentage Accurate: 76.7% → 99.5%

Time: 35.7s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

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(r * Float64(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[(r * N[(N[Sin[b], $MachinePrecision] / N[Cos[N[(a + b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.7% accurate, 1.0× speedup

Math

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

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(r * Float64(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[(r * N[(N[Sin[b], $MachinePrecision] / N[Cos[N[(a + b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.0%

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

   1. associate-*r/ 77.1%

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

   2. +-commutative 77.1%

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

3. Simplified 77.1%

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

   1. cos-sum 99.5%

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

   2. cancel-sign-sub-inv 99.5%

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

   3. fma-define 99.5%

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

6. Applied egg-rr 99.5%

   \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\mathsf{fma}\left(\cos b, \cos a, \left(-\sin b\right) \cdot \sin a\right)}} \]
7. Add Preprocessing

Alternative 2: 99.5% accurate, 0.4× speedup

Math

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

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(Float64(r * 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[(N[(r * N[Sin[b], $MachinePrecision]), $MachinePrecision] / N[(N[(N[Cos[b], $MachinePrecision] * N[Cos[a], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[b], $MachinePrecision] * N[Sin[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.0%

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

   1. associate-*r/ 77.1%

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

   2. +-commutative 77.1%

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

3. Simplified 77.1%

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

   1. cos-sum 99.5%

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

6. Applied egg-rr 99.5%

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

Alternative 3: 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 77.0%

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

   1. +-commutative 77.0%

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

3. Simplified 77.0%

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

   1. cos-sum 99.5%

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

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 4: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\cos b \cdot \frac{\cos a}{r \cdot \sin b} - \frac{\sin a}{r}} \end{array} \]

FPCore

(FPCore (r a b)
 :precision binary64
 (/ 1.0 (- (* (cos b) (/ (cos a) (* r (sin b)))) (/ (sin a) r))))

C

double code(double r, double a, double b) {
	return 1.0 / ((cos(b) * (cos(a) / (r * sin(b)))) - (sin(a) / r));
}

Fortran

real(8) function code(r, a, b)
    real(8), intent (in) :: r
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = 1.0d0 / ((cos(b) * (cos(a) / (r * sin(b)))) - (sin(a) / r))
end function

Java

public static double code(double r, double a, double b) {
	return 1.0 / ((Math.cos(b) * (Math.cos(a) / (r * Math.sin(b)))) - (Math.sin(a) / r));
}

Python

def code(r, a, b):
	return 1.0 / ((math.cos(b) * (math.cos(a) / (r * math.sin(b)))) - (math.sin(a) / r))

Julia

function code(r, a, b)
	return Float64(1.0 / Float64(Float64(cos(b) * Float64(cos(a) / Float64(r * sin(b)))) - Float64(sin(a) / r)))
end

MATLAB

function tmp = code(r, a, b)
	tmp = 1.0 / ((cos(b) * (cos(a) / (r * sin(b)))) - (sin(a) / r));
end

Wolfram

code[r_, a_, b_] := N[(1.0 / N[(N[(N[Cos[b], $MachinePrecision] * N[(N[Cos[a], $MachinePrecision] / N[(r * N[Sin[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Sin[a], $MachinePrecision] / r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.0%

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

   1. +-commutative 77.0%

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

3. Simplified 77.0%

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

   1. associate-*r/ 77.1%

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

   2. clear-num 76.5%

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

   3. *-commutative 76.5%

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

6. Applied egg-rr 76.5%

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

   1. cos-sum 99.0%

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

   2. div-sub 91.1%

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

8. Applied egg-rr 91.1%

   \[\leadsto \frac{1}{\color{blue}{\frac{\cos b \cdot \cos a}{\sin b \cdot r} - \frac{\sin b \cdot \sin a}{\sin b \cdot r}}} \]
9. Step-by-step derivation

   1. associate-/l* 91.2%

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

   2. remove-double-neg 91.2%

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

   3. neg-mul-1 91.2%

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

   4. *-commutative 91.2%

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

   5. distribute-rgt-neg-in 91.2%

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

   6. distribute-frac-neg 91.2%

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

   7. associate-*r* 91.2%

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

   8. *-commutative 91.2%

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

   9. neg-mul-1 91.2%

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

   10. distribute-neg-frac 91.2%

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

   11. times-frac 99.0%

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

   12. *-inverses 99.0%

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

   13. distribute-lft-neg-in 99.0%

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

   14. metadata-eval 99.0%

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

   15. associate-*r/ 99.0%

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

10. Simplified 99.0%

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

11. Final simplification 99.0%

    \[\leadsto \frac{1}{\cos b \cdot \frac{\cos a}{r \cdot \sin b} - \frac{\sin a}{r}} \]
12. Add Preprocessing

Alternative 5: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00072 \lor \neg \left(b \leq 48000000000000\right):\\ \;\;\;\;r \cdot \tan b\\ \mathbf{else}:\\ \;\;\;\;\sin b \cdot \frac{r}{\cos a}\\ \end{array} \end{array} \]

FPCore

(FPCore (r a b)
 :precision binary64
 (if (or (<= b -0.00072) (not (<= b 48000000000000.0)))
   (* r (tan b))
   (* (sin b) (/ r (cos a)))))

C

double code(double r, double a, double b) {
	double tmp;
	if ((b <= -0.00072) || !(b <= 48000000000000.0)) {
		tmp = r * tan(b);
	} else {
		tmp = sin(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 <= (-0.00072d0)) .or. (.not. (b <= 48000000000000.0d0))) then
        tmp = r * tan(b)
    else
        tmp = sin(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 <= -0.00072) || !(b <= 48000000000000.0)) {
		tmp = r * Math.tan(b);
	} else {
		tmp = Math.sin(b) * (r / Math.cos(a));
	}
	return tmp;
}

Python

def code(r, a, b):
	tmp = 0
	if (b <= -0.00072) or not (b <= 48000000000000.0):
		tmp = r * math.tan(b)
	else:
		tmp = math.sin(b) * (r / math.cos(a))
	return tmp

Julia

function code(r, a, b)
	tmp = 0.0
	if ((b <= -0.00072) || !(b <= 48000000000000.0))
		tmp = Float64(r * tan(b));
	else
		tmp = Float64(sin(b) * Float64(r / cos(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(r, a, b)
	tmp = 0.0;
	if ((b <= -0.00072) || ~((b <= 48000000000000.0)))
		tmp = r * tan(b);
	else
		tmp = sin(b) * (r / cos(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[r_, a_, b_] := If[Or[LessEqual[b, -0.00072], N[Not[LessEqual[b, 48000000000000.0]], $MachinePrecision]], N[(r * N[Tan[b], $MachinePrecision]), $MachinePrecision], N[(N[Sin[b], $MachinePrecision] * N[(r / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.20000000000000045e-4 or 4.8e13 < b

   1. Initial program 52.7%

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

      1. associate-*r/ 52.7%

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

      2. +-commutative 52.7%

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

   3. Simplified 52.7%

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

   5. Taylor expanded in a around 0 52.8%

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

      1. associate-/l* 52.7%

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

      2. quot-tan 52.8%

         \[\leadsto r \cdot \color{blue}{\tan b} \]

   7. Applied egg-rr 52.8%

      \[\leadsto \color{blue}{r \cdot \tan b} \]

   if -7.20000000000000045e-4 < b < 4.8e13

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

   3. Simplified 97.5%

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

      1. associate-*r/ 97.5%

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

      2. clear-num 96.6%

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

      3. *-commutative 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in b around 0 96.6%

      \[\leadsto \frac{1}{\frac{\cos \color{blue}{a}}{\sin b \cdot r}} \]
   8. Step-by-step derivation

      1. clear-num 97.5%

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

      2. associate-/l* 97.5%

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

   9. Applied egg-rr 97.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00072 \lor \neg \left(b \leq 48000000000000\right):\\ \;\;\;\;r \cdot \tan b\\ \mathbf{else}:\\ \;\;\;\;\sin b \cdot \frac{r}{\cos a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00072:\\ \;\;\;\;r \cdot \tan b\\ \mathbf{elif}\;b \leq 48000000000000:\\ \;\;\;\;\sin b \cdot \frac{r}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\frac{r \cdot \sin b}{\cos b}\\ \end{array} \end{array} \]

FPCore

(FPCore (r a b)
 :precision binary64
 (if (<= b -0.00072)
   (* r (tan b))
   (if (<= b 48000000000000.0)
     (* (sin b) (/ r (cos a)))
     (/ (* r (sin b)) (cos b)))))

C

double code(double r, double a, double b) {
	double tmp;
	if (b <= -0.00072) {
		tmp = r * tan(b);
	} else if (b <= 48000000000000.0) {
		tmp = sin(b) * (r / cos(a));
	} else {
		tmp = (r * sin(b)) / 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 <= (-0.00072d0)) then
        tmp = r * tan(b)
    else if (b <= 48000000000000.0d0) then
        tmp = sin(b) * (r / cos(a))
    else
        tmp = (r * sin(b)) / cos(b)
    end if
    code = tmp
end function

Java

public static double code(double r, double a, double b) {
	double tmp;
	if (b <= -0.00072) {
		tmp = r * Math.tan(b);
	} else if (b <= 48000000000000.0) {
		tmp = Math.sin(b) * (r / Math.cos(a));
	} else {
		tmp = (r * Math.sin(b)) / Math.cos(b);
	}
	return tmp;
}

Python

def code(r, a, b):
	tmp = 0
	if b <= -0.00072:
		tmp = r * math.tan(b)
	elif b <= 48000000000000.0:
		tmp = math.sin(b) * (r / math.cos(a))
	else:
		tmp = (r * math.sin(b)) / math.cos(b)
	return tmp

Julia

function code(r, a, b)
	tmp = 0.0
	if (b <= -0.00072)
		tmp = Float64(r * tan(b));
	elseif (b <= 48000000000000.0)
		tmp = Float64(sin(b) * Float64(r / cos(a)));
	else
		tmp = Float64(Float64(r * sin(b)) / cos(b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(r, a, b)
	tmp = 0.0;
	if (b <= -0.00072)
		tmp = r * tan(b);
	elseif (b <= 48000000000000.0)
		tmp = sin(b) * (r / cos(a));
	else
		tmp = (r * sin(b)) / cos(b);
	end
	tmp_2 = tmp;
end

Wolfram

code[r_, a_, b_] := If[LessEqual[b, -0.00072], N[(r * N[Tan[b], $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 48000000000000.0], N[(N[Sin[b], $MachinePrecision] * N[(r / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(r * N[Sin[b], $MachinePrecision]), $MachinePrecision] / N[Cos[b], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.20000000000000045e-4

   1. Initial program 60.2%

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

      1. associate-*r/ 60.4%

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

      2. +-commutative 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in a around 0 60.6%

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

      1. associate-/l* 60.5%

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

      2. quot-tan 60.6%

         \[\leadsto r \cdot \color{blue}{\tan b} \]

   7. Applied egg-rr 60.6%

      \[\leadsto \color{blue}{r \cdot \tan b} \]

   if -7.20000000000000045e-4 < b < 4.8e13

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

   3. Simplified 97.5%

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

      1. associate-*r/ 97.5%

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

      2. clear-num 96.6%

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

      3. *-commutative 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in b around 0 96.6%

      \[\leadsto \frac{1}{\frac{\cos \color{blue}{a}}{\sin b \cdot r}} \]
   8. Step-by-step derivation

      1. clear-num 97.5%

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

      2. associate-/l* 97.5%

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

   9. Applied egg-rr 97.5%

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

   if 4.8e13 < b

   1. Initial program 46.2%

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

      1. associate-*r/ 46.2%

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

      2. +-commutative 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in a around 0 46.1%

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

Alternative 7: 76.7% accurate, 1.0× speedup

Math

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

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(Float64(r * 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[(N[(r * N[Sin[b], $MachinePrecision]), $MachinePrecision] / N[Cos[N[(b + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.0%

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

   1. associate-*r/ 77.1%

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

   2. +-commutative 77.1%

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

3. Simplified 77.1%

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

Alternative 8: 76.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double r, double a, double b) {
	return sin(b) * (r / 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 = sin(b) * (r / cos((b + a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.0%

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

   1. associate-*r/ 77.1%

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

   2. +-commutative 77.1%

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

3. Simplified 77.1%

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

   1. *-commutative 77.1%

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

   2. associate-/l* 77.0%

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

6. Applied egg-rr 77.0%

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

Alternative 9: 76.7% 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 77.0%

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

3. Final simplification 77.0%

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

Alternative 10: 76.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00092 \lor \neg \left(b \leq 200\right):\\ \;\;\;\;r \cdot \tan b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \end{array} \end{array} \]

FPCore

(FPCore (r a b)
 :precision binary64
 (if (or (<= b -0.00092) (not (<= b 200.0)))
   (* r (tan b))
   (* b (/ r (cos a)))))

C

double code(double r, double a, double b) {
	double tmp;
	if ((b <= -0.00092) || !(b <= 200.0)) {
		tmp = r * tan(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 <= (-0.00092d0)) .or. (.not. (b <= 200.0d0))) then
        tmp = r * tan(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 <= -0.00092) || !(b <= 200.0)) {
		tmp = r * Math.tan(b);
	} else {
		tmp = b * (r / Math.cos(a));
	}
	return tmp;
}

Python

def code(r, a, b):
	tmp = 0
	if (b <= -0.00092) or not (b <= 200.0):
		tmp = r * math.tan(b)
	else:
		tmp = b * (r / math.cos(a))
	return tmp

Julia

function code(r, a, b)
	tmp = 0.0
	if ((b <= -0.00092) || !(b <= 200.0))
		tmp = Float64(r * tan(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 <= -0.00092) || ~((b <= 200.0)))
		tmp = r * tan(b);
	else
		tmp = b * (r / cos(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[r_, a_, b_] := If[Or[LessEqual[b, -0.00092], N[Not[LessEqual[b, 200.0]], $MachinePrecision]], N[(r * N[Tan[b], $MachinePrecision]), $MachinePrecision], N[(b * N[(r / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.2000000000000003e-4 or 200 < b

   1. Initial program 52.4%

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

      1. associate-*r/ 52.4%

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

      2. +-commutative 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in a around 0 52.4%

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

      1. associate-/l* 52.3%

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

      2. quot-tan 52.4%

         \[\leadsto r \cdot \color{blue}{\tan b} \]

   7. Applied egg-rr 52.4%

      \[\leadsto \color{blue}{r \cdot \tan b} \]

   if -9.2000000000000003e-4 < b < 200

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in b around 0 98.1%

      \[\leadsto r \cdot \color{blue}{\frac{b}{\cos a}} \]
   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 98.0%

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

   7. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{\frac{r}{\frac{\cos a}{b}}} \]
   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 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00092 \lor \neg \left(b \leq 200\right):\\ \;\;\;\;r \cdot \tan b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00076 \lor \neg \left(b \leq 200\right):\\ \;\;\;\;r \cdot \tan b\\ \mathbf{else}:\\ \;\;\;\;r \cdot \frac{b}{\cos a}\\ \end{array} \end{array} \]

FPCore

(FPCore (r a b)
 :precision binary64
 (if (or (<= b -0.00076) (not (<= b 200.0)))
   (* r (tan b))
   (* r (/ b (cos a)))))

C

double code(double r, double a, double b) {
	double tmp;
	if ((b <= -0.00076) || !(b <= 200.0)) {
		tmp = r * tan(b);
	} else {
		tmp = r * (b / 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 <= (-0.00076d0)) .or. (.not. (b <= 200.0d0))) then
        tmp = r * tan(b)
    else
        tmp = r * (b / cos(a))
    end if
    code = tmp
end function

Java

public static double code(double r, double a, double b) {
	double tmp;
	if ((b <= -0.00076) || !(b <= 200.0)) {
		tmp = r * Math.tan(b);
	} else {
		tmp = r * (b / Math.cos(a));
	}
	return tmp;
}

Python

def code(r, a, b):
	tmp = 0
	if (b <= -0.00076) or not (b <= 200.0):
		tmp = r * math.tan(b)
	else:
		tmp = r * (b / math.cos(a))
	return tmp

Julia

function code(r, a, b)
	tmp = 0.0
	if ((b <= -0.00076) || !(b <= 200.0))
		tmp = Float64(r * tan(b));
	else
		tmp = Float64(r * Float64(b / cos(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(r, a, b)
	tmp = 0.0;
	if ((b <= -0.00076) || ~((b <= 200.0)))
		tmp = r * tan(b);
	else
		tmp = r * (b / cos(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[r_, a_, b_] := If[Or[LessEqual[b, -0.00076], N[Not[LessEqual[b, 200.0]], $MachinePrecision]], N[(r * N[Tan[b], $MachinePrecision]), $MachinePrecision], N[(r * N[(b / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.6000000000000004e-4 or 200 < b

   1. Initial program 52.4%

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

      1. associate-*r/ 52.4%

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

      2. +-commutative 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in a around 0 52.4%

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

      1. associate-/l* 52.3%

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

      2. quot-tan 52.4%

         \[\leadsto r \cdot \color{blue}{\tan b} \]

   7. Applied egg-rr 52.4%

      \[\leadsto \color{blue}{r \cdot \tan b} \]

   if -7.6000000000000004e-4 < b < 200

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in b around 0 98.1%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00076 \lor \neg \left(b \leq 200\right):\\ \;\;\;\;r \cdot \tan b\\ \mathbf{else}:\\ \;\;\;\;r \cdot \frac{b}{\cos a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double r, double a, double b) {
	return r * tan(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 * tan(b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.0%

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

   1. associate-*r/ 77.1%

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

   2. +-commutative 77.1%

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

3. Simplified 77.1%

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

5. Taylor expanded in a around 0 59.9%

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

   1. associate-/l* 59.8%

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

   2. quot-tan 59.9%

      \[\leadsto r \cdot \color{blue}{\tan b} \]

7. Applied egg-rr 59.9%

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

Alternative 13: 34.9% 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 77.0%

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

   1. +-commutative 77.0%

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

3. Simplified 77.0%

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

5. Taylor expanded in b around 0 54.6%

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

6. Taylor expanded in a around 0 37.3%

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

Reproduce

herbie shell --seed 2024123 
(FPCore (r a b)
  :name "rsin B (should all be same)"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))