Trigonometry A

Percentage Accurate: 99.8% → 99.8%

Time: 6.9s

Alternatives: 9

Speedup: 1.0×

Specification

\[0 \leq e \land e \leq 1\]

Math

\[\begin{array}{l} \\ \frac{e \cdot \sin v}{1 + e \cdot \cos v} \end{array} \]

FPCore

(FPCore (e v) :precision binary64 (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))

C

double code(double e, double v) {
	return (e * sin(v)) / (1.0 + (e * cos(v)));
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = (e * sin(v)) / (1.0d0 + (e * cos(v)))
end function

Java

public static double code(double e, double v) {
	return (e * Math.sin(v)) / (1.0 + (e * Math.cos(v)));
}

Python

def code(e, v):
	return (e * math.sin(v)) / (1.0 + (e * math.cos(v)))

Julia

function code(e, v)
	return Float64(Float64(e * sin(v)) / Float64(1.0 + Float64(e * cos(v))))
end

MATLAB

function tmp = code(e, v)
	tmp = (e * sin(v)) / (1.0 + (e * cos(v)));
end

Wolfram

code[e_, v_] := N[(N[(e * N[Sin[v], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(e * N[Cos[v], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{e \cdot \sin v}{1 + e \cdot \cos v} \end{array} \]

FPCore

(FPCore (e v) :precision binary64 (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))

C

double code(double e, double v) {
	return (e * sin(v)) / (1.0 + (e * cos(v)));
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = (e * sin(v)) / (1.0d0 + (e * cos(v)))
end function

Java

public static double code(double e, double v) {
	return (e * Math.sin(v)) / (1.0 + (e * Math.cos(v)));
}

Python

def code(e, v):
	return (e * math.sin(v)) / (1.0 + (e * math.cos(v)))

Julia

function code(e, v)
	return Float64(Float64(e * sin(v)) / Float64(1.0 + Float64(e * cos(v))))
end

MATLAB

function tmp = code(e, v)
	tmp = (e * sin(v)) / (1.0 + (e * cos(v)));
end

Wolfram

code[e_, v_] := N[(N[(e * N[Sin[v], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(e * N[Cos[v], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{e \cdot \sin v}{1 + e \cdot \cos v} \end{array} \]

FPCore

(FPCore (e v) :precision binary64 (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))

C

double code(double e, double v) {
	return (e * sin(v)) / (1.0 + (e * cos(v)));
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = (e * sin(v)) / (1.0d0 + (e * cos(v)))
end function

Java

public static double code(double e, double v) {
	return (e * Math.sin(v)) / (1.0 + (e * Math.cos(v)));
}

Python

def code(e, v):
	return (e * math.sin(v)) / (1.0 + (e * math.cos(v)))

Julia

function code(e, v)
	return Float64(Float64(e * sin(v)) / Float64(1.0 + Float64(e * cos(v))))
end

MATLAB

function tmp = code(e, v)
	tmp = (e * sin(v)) / (1.0 + (e * cos(v)));
end

Wolfram

code[e_, v_] := N[(N[(e * N[Sin[v], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(e * N[Cos[v], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

2. Final simplification 99.8%

   \[\leadsto \frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

Alternative 2: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sin v \cdot \left(e - \cos v \cdot \left(e \cdot e\right)\right) \end{array} \]

FPCore

(FPCore (e v) :precision binary64 (* (sin v) (- e (* (cos v) (* e e)))))

C

double code(double e, double v) {
	return sin(v) * (e - (cos(v) * (e * e)));
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = sin(v) * (e - (cos(v) * (e * e)))
end function

Java

public static double code(double e, double v) {
	return Math.sin(v) * (e - (Math.cos(v) * (e * e)));
}

Python

def code(e, v):
	return math.sin(v) * (e - (math.cos(v) * (e * e)))

Julia

function code(e, v)
	return Float64(sin(v) * Float64(e - Float64(cos(v) * Float64(e * e))))
end

MATLAB

function tmp = code(e, v)
	tmp = sin(v) * (e - (cos(v) * (e * e)));
end

Wolfram

code[e_, v_] := N[(N[Sin[v], $MachinePrecision] * N[(e - N[(N[Cos[v], $MachinePrecision] * N[(e * e), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

2. Taylor expanded in e around 0 99.6%

   \[\leadsto \color{blue}{-1 \cdot \left(\sin v \cdot \left(\cos v \cdot {e}^{2}\right)\right) + \sin v \cdot e} \]
3. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\sin v \cdot e + -1 \cdot \left(\sin v \cdot \left(\cos v \cdot {e}^{2}\right)\right)} \]

   2. fma-def 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin v, e, -1 \cdot \left(\sin v \cdot \left(\cos v \cdot {e}^{2}\right)\right)\right)} \]

   3. mul-1-neg 99.6%

      \[\leadsto \mathsf{fma}\left(\sin v, e, \color{blue}{-\sin v \cdot \left(\cos v \cdot {e}^{2}\right)}\right) \]

   4. fma-neg 99.6%

      \[\leadsto \color{blue}{\sin v \cdot e - \sin v \cdot \left(\cos v \cdot {e}^{2}\right)} \]

   5. distribute-lft-out-- 99.7%

      \[\leadsto \color{blue}{\sin v \cdot \left(e - \cos v \cdot {e}^{2}\right)} \]

   6. unpow2 99.7%

      \[\leadsto \sin v \cdot \left(e - \cos v \cdot \color{blue}{\left(e \cdot e\right)}\right) \]

4. Simplified 99.7%

   \[\leadsto \color{blue}{\sin v \cdot \left(e - \cos v \cdot \left(e \cdot e\right)\right)} \]

5. Final simplification 99.7%

   \[\leadsto \sin v \cdot \left(e - \cos v \cdot \left(e \cdot e\right)\right) \]

Alternative 3: 98.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \frac{e}{\frac{e + 1}{\sin v}} \end{array} \]

FPCore

(FPCore (e v) :precision binary64 (/ e (/ (+ e 1.0) (sin v))))

C

double code(double e, double v) {
	return e / ((e + 1.0) / sin(v));
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = e / ((e + 1.0d0) / sin(v))
end function

Java

public static double code(double e, double v) {
	return e / ((e + 1.0) / Math.sin(v));
}

Python

def code(e, v):
	return e / ((e + 1.0) / math.sin(v))

Julia

function code(e, v)
	return Float64(e / Float64(Float64(e + 1.0) / sin(v)))
end

MATLAB

function tmp = code(e, v)
	tmp = e / ((e + 1.0) / sin(v));
end

Wolfram

code[e_, v_] := N[(e / N[(N[(e + 1.0), $MachinePrecision] / N[Sin[v], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

2. Taylor expanded in v around 0 99.5%

   \[\leadsto \frac{e \cdot \sin v}{1 + \color{blue}{e}} \]
3. Step-by-step derivation

   1. clear-num 98.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{1 + e}{e \cdot \sin v}}} \]

   2. inv-pow 98.0%

      \[\leadsto \color{blue}{{\left(\frac{1 + e}{e \cdot \sin v}\right)}^{-1}} \]

   3. +-commutative 98.0%

      \[\leadsto {\left(\frac{\color{blue}{e + 1}}{e \cdot \sin v}\right)}^{-1} \]

4. Applied egg-rr 98.0%

   \[\leadsto \color{blue}{{\left(\frac{e + 1}{e \cdot \sin v}\right)}^{-1}} \]
5. Step-by-step derivation

   1. unpow-1 98.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{e + 1}{e \cdot \sin v}}} \]

   2. associate-/r* 97.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{e + 1}{e}}{\sin v}}} \]

6. Simplified 97.8%

   \[\leadsto \color{blue}{\frac{1}{\frac{\frac{e + 1}{e}}{\sin v}}} \]

7. Taylor expanded in v around inf 99.5%

   \[\leadsto \color{blue}{\frac{\sin v \cdot e}{1 + e}} \]
8. Step-by-step derivation

   1. *-commutative 99.5%

      \[\leadsto \frac{\color{blue}{e \cdot \sin v}}{1 + e} \]

   2. +-commutative 99.5%

      \[\leadsto \frac{e \cdot \sin v}{\color{blue}{e + 1}} \]

   3. associate-/l* 99.3%

      \[\leadsto \color{blue}{\frac{e}{\frac{e + 1}{\sin v}}} \]

9. Simplified 99.3%

   \[\leadsto \color{blue}{\frac{e}{\frac{e + 1}{\sin v}}} \]

10. Final simplification 99.3%

    \[\leadsto \frac{e}{\frac{e + 1}{\sin v}} \]

Alternative 4: 98.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \frac{e \cdot \sin v}{e + 1} \end{array} \]

FPCore

(FPCore (e v) :precision binary64 (/ (* e (sin v)) (+ e 1.0)))

C

double code(double e, double v) {
	return (e * sin(v)) / (e + 1.0);
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = (e * sin(v)) / (e + 1.0d0)
end function

Java

public static double code(double e, double v) {
	return (e * Math.sin(v)) / (e + 1.0);
}

Python

def code(e, v):
	return (e * math.sin(v)) / (e + 1.0)

Julia

function code(e, v)
	return Float64(Float64(e * sin(v)) / Float64(e + 1.0))
end

MATLAB

function tmp = code(e, v)
	tmp = (e * sin(v)) / (e + 1.0);
end

Wolfram

code[e_, v_] := N[(N[(e * N[Sin[v], $MachinePrecision]), $MachinePrecision] / N[(e + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

2. Taylor expanded in v around 0 99.5%

   \[\leadsto \frac{e \cdot \sin v}{1 + \color{blue}{e}} \]

3. Final simplification 99.5%

   \[\leadsto \frac{e \cdot \sin v}{e + 1} \]

Alternative 5: 97.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ e \cdot \sin v \end{array} \]

FPCore

(FPCore (e v) :precision binary64 (* e (sin v)))

C

double code(double e, double v) {
	return e * sin(v);
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = e * sin(v)
end function

Java

public static double code(double e, double v) {
	return e * Math.sin(v);
}

Python

def code(e, v):
	return e * math.sin(v)

Julia

function code(e, v)
	return Float64(e * sin(v))
end

MATLAB

function tmp = code(e, v)
	tmp = e * sin(v);
end

Wolfram

code[e_, v_] := N[(e * N[Sin[v], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

2. Taylor expanded in e around 0 99.6%

   \[\leadsto \color{blue}{-1 \cdot \left(\sin v \cdot \left(\cos v \cdot {e}^{2}\right)\right) + \sin v \cdot e} \]
3. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\sin v \cdot e + -1 \cdot \left(\sin v \cdot \left(\cos v \cdot {e}^{2}\right)\right)} \]

   2. fma-def 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin v, e, -1 \cdot \left(\sin v \cdot \left(\cos v \cdot {e}^{2}\right)\right)\right)} \]

   3. mul-1-neg 99.6%

      \[\leadsto \mathsf{fma}\left(\sin v, e, \color{blue}{-\sin v \cdot \left(\cos v \cdot {e}^{2}\right)}\right) \]

   4. fma-neg 99.6%

      \[\leadsto \color{blue}{\sin v \cdot e - \sin v \cdot \left(\cos v \cdot {e}^{2}\right)} \]

   5. distribute-lft-out-- 99.7%

      \[\leadsto \color{blue}{\sin v \cdot \left(e - \cos v \cdot {e}^{2}\right)} \]

   6. unpow2 99.7%

      \[\leadsto \sin v \cdot \left(e - \cos v \cdot \color{blue}{\left(e \cdot e\right)}\right) \]

4. Simplified 99.7%

   \[\leadsto \color{blue}{\sin v \cdot \left(e - \cos v \cdot \left(e \cdot e\right)\right)} \]

5. Taylor expanded in e around 0 99.3%

   \[\leadsto \color{blue}{\sin v \cdot e} \]

6. Final simplification 99.3%

   \[\leadsto e \cdot \sin v \]

Alternative 6: 52.9% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \frac{e}{0.16666666666666666 \cdot \left(v \cdot \left(e + 1\right)\right) + \left(\frac{e}{v} + \frac{1}{v}\right)} \end{array} \]

FPCore

(FPCore (e v)
 :precision binary64
 (/ e (+ (* 0.16666666666666666 (* v (+ e 1.0))) (+ (/ e v) (/ 1.0 v)))))

C

double code(double e, double v) {
	return e / ((0.16666666666666666 * (v * (e + 1.0))) + ((e / v) + (1.0 / v)));
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = e / ((0.16666666666666666d0 * (v * (e + 1.0d0))) + ((e / v) + (1.0d0 / v)))
end function

Java

public static double code(double e, double v) {
	return e / ((0.16666666666666666 * (v * (e + 1.0))) + ((e / v) + (1.0 / v)));
}

Python

def code(e, v):
	return e / ((0.16666666666666666 * (v * (e + 1.0))) + ((e / v) + (1.0 / v)))

Julia

function code(e, v)
	return Float64(e / Float64(Float64(0.16666666666666666 * Float64(v * Float64(e + 1.0))) + Float64(Float64(e / v) + Float64(1.0 / v))))
end

MATLAB

function tmp = code(e, v)
	tmp = e / ((0.16666666666666666 * (v * (e + 1.0))) + ((e / v) + (1.0 / v)));
end

Wolfram

code[e_, v_] := N[(e / N[(N[(0.16666666666666666 * N[(v * N[(e + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(e / v), $MachinePrecision] + N[(1.0 / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

2. Taylor expanded in v around 0 99.5%

   \[\leadsto \frac{e \cdot \sin v}{1 + \color{blue}{e}} \]
3. Step-by-step derivation

   1. clear-num 98.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{1 + e}{e \cdot \sin v}}} \]

   2. inv-pow 98.0%

      \[\leadsto \color{blue}{{\left(\frac{1 + e}{e \cdot \sin v}\right)}^{-1}} \]

   3. +-commutative 98.0%

      \[\leadsto {\left(\frac{\color{blue}{e + 1}}{e \cdot \sin v}\right)}^{-1} \]

4. Applied egg-rr 98.0%

   \[\leadsto \color{blue}{{\left(\frac{e + 1}{e \cdot \sin v}\right)}^{-1}} \]
5. Step-by-step derivation

   1. unpow-1 98.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{e + 1}{e \cdot \sin v}}} \]

   2. associate-/r* 97.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{e + 1}{e}}{\sin v}}} \]

6. Simplified 97.8%

   \[\leadsto \color{blue}{\frac{1}{\frac{\frac{e + 1}{e}}{\sin v}}} \]

7. Taylor expanded in v around inf 99.5%

   \[\leadsto \color{blue}{\frac{\sin v \cdot e}{1 + e}} \]
8. Step-by-step derivation

   1. *-commutative 99.5%

      \[\leadsto \frac{\color{blue}{e \cdot \sin v}}{1 + e} \]

   2. +-commutative 99.5%

      \[\leadsto \frac{e \cdot \sin v}{\color{blue}{e + 1}} \]

   3. associate-/l* 99.3%

      \[\leadsto \color{blue}{\frac{e}{\frac{e + 1}{\sin v}}} \]

9. Simplified 99.3%

   \[\leadsto \color{blue}{\frac{e}{\frac{e + 1}{\sin v}}} \]

10. Taylor expanded in v around 0 52.7%

    \[\leadsto \frac{e}{\color{blue}{0.16666666666666666 \cdot \left(v \cdot \left(1 + e\right)\right) + \left(\frac{e}{v} + \frac{1}{v}\right)}} \]

11. Final simplification 52.7%

    \[\leadsto \frac{e}{0.16666666666666666 \cdot \left(v \cdot \left(e + 1\right)\right) + \left(\frac{e}{v} + \frac{1}{v}\right)} \]

Alternative 7: 51.3% accurate, 29.9× speedup

Math

\[\begin{array}{l} \\ v \cdot \left(e - e \cdot e\right) \end{array} \]

FPCore

(FPCore (e v) :precision binary64 (* v (- e (* e e))))

C

double code(double e, double v) {
	return v * (e - (e * e));
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = v * (e - (e * e))
end function

Java

public static double code(double e, double v) {
	return v * (e - (e * e));
}

Python

def code(e, v):
	return v * (e - (e * e))

Julia

function code(e, v)
	return Float64(v * Float64(e - Float64(e * e)))
end

MATLAB

function tmp = code(e, v)
	tmp = v * (e - (e * e));
end

Wolfram

code[e_, v_] := N[(v * N[(e - N[(e * e), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

2. Taylor expanded in v around 0 51.5%

   \[\leadsto \color{blue}{\frac{v \cdot e}{1 + e}} \]
3. Step-by-step derivation

   1. associate-/l* 51.4%

      \[\leadsto \color{blue}{\frac{v}{\frac{1 + e}{e}}} \]

   2. associate-/r/ 51.5%

      \[\leadsto \color{blue}{\frac{v}{1 + e} \cdot e} \]

   3. +-commutative 51.5%

      \[\leadsto \frac{v}{\color{blue}{e + 1}} \cdot e \]

4. Simplified 51.5%

   \[\leadsto \color{blue}{\frac{v}{e + 1} \cdot e} \]

5. Taylor expanded in e around 0 51.5%

   \[\leadsto \color{blue}{v \cdot e + -1 \cdot \left(v \cdot {e}^{2}\right)} \]
6. Step-by-step derivation

   1. mul-1-neg 51.5%

      \[\leadsto v \cdot e + \color{blue}{\left(-v \cdot {e}^{2}\right)} \]

   2. unsub-neg 51.5%

      \[\leadsto \color{blue}{v \cdot e - v \cdot {e}^{2}} \]

   3. unpow2 51.5%

      \[\leadsto v \cdot e - v \cdot \color{blue}{\left(e \cdot e\right)} \]

7. Simplified 51.5%

   \[\leadsto \color{blue}{v \cdot e - v \cdot \left(e \cdot e\right)} \]
8. Step-by-step derivation

   1. distribute-lft-out-- 51.5%

      \[\leadsto \color{blue}{v \cdot \left(e - e \cdot e\right)} \]

   2. *-commutative 51.5%

      \[\leadsto \color{blue}{\left(e - e \cdot e\right) \cdot v} \]

9. Applied egg-rr 51.5%

   \[\leadsto \color{blue}{\left(e - e \cdot e\right) \cdot v} \]

10. Final simplification 51.5%

    \[\leadsto v \cdot \left(e - e \cdot e\right) \]

Alternative 8: 50.8% accurate, 69.7× speedup

Math

\[\begin{array}{l} \\ e \cdot v \end{array} \]

FPCore

(FPCore (e v) :precision binary64 (* e v))

C

double code(double e, double v) {
	return e * v;
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = e * v
end function

Java

public static double code(double e, double v) {
	return e * v;
}

Python

def code(e, v):
	return e * v

Julia

function code(e, v)
	return Float64(e * v)
end

MATLAB

function tmp = code(e, v)
	tmp = e * v;
end

Wolfram

code[e_, v_] := N[(e * v), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

2. Taylor expanded in v around 0 51.5%

   \[\leadsto \color{blue}{\frac{v \cdot e}{1 + e}} \]
3. Step-by-step derivation

   1. associate-/l* 51.4%

      \[\leadsto \color{blue}{\frac{v}{\frac{1 + e}{e}}} \]

   2. associate-/r/ 51.5%

      \[\leadsto \color{blue}{\frac{v}{1 + e} \cdot e} \]

   3. +-commutative 51.5%

      \[\leadsto \frac{v}{\color{blue}{e + 1}} \cdot e \]

4. Simplified 51.5%

   \[\leadsto \color{blue}{\frac{v}{e + 1} \cdot e} \]

5. Taylor expanded in e around 0 51.3%

   \[\leadsto \color{blue}{v} \cdot e \]

6. Final simplification 51.3%

   \[\leadsto e \cdot v \]

Alternative 9: 4.5% accurate, 209.0× speedup

Math

\[\begin{array}{l} \\ v \end{array} \]

FPCore

(FPCore (e v) :precision binary64 v)

C

double code(double e, double v) {
	return v;
}

Fortran

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = v
end function

Java

public static double code(double e, double v) {
	return v;
}

Python

def code(e, v):
	return v

Julia

function code(e, v)
	return v
end

MATLAB

function tmp = code(e, v)
	tmp = v;
end

Wolfram

code[e_, v_] := v

Derivation

1. Initial program 99.8%

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

2. Taylor expanded in v around 0 51.5%

   \[\leadsto \color{blue}{\frac{v \cdot e}{1 + e}} \]
3. Step-by-step derivation

   1. associate-/l* 51.4%

      \[\leadsto \color{blue}{\frac{v}{\frac{1 + e}{e}}} \]

   2. associate-/r/ 51.5%

      \[\leadsto \color{blue}{\frac{v}{1 + e} \cdot e} \]

   3. +-commutative 51.5%

      \[\leadsto \frac{v}{\color{blue}{e + 1}} \cdot e \]

4. Simplified 51.5%

   \[\leadsto \color{blue}{\frac{v}{e + 1} \cdot e} \]

5. Taylor expanded in e around inf 2.4%

   \[\leadsto \color{blue}{v + -1 \cdot \frac{v}{e}} \]
6. Step-by-step derivation

   1. mul-1-neg 2.4%

      \[\leadsto v + \color{blue}{\left(-\frac{v}{e}\right)} \]

   2. unsub-neg 2.4%

      \[\leadsto \color{blue}{v - \frac{v}{e}} \]

7. Simplified 2.4%

   \[\leadsto \color{blue}{v - \frac{v}{e}} \]

8. Taylor expanded in e around inf 4.2%

   \[\leadsto \color{blue}{v} \]

9. Final simplification 4.2%

   \[\leadsto v \]

Reproduce

herbie shell --seed 2023187 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (and (<= 0.0 e) (<= e 1.0))
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))