Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.9% → 99.9%

Time: 8.5s

Alternatives: 9

Speedup: 1.0×

• 50.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\sin x \cdot \sinh y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (sin x) (sinh y)) x))

C

double code(double x, double y) {
	return (sin(x) * sinh(y)) / x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (sin(x) * sinh(y)) / x
end function

Java

public static double code(double x, double y) {
	return (Math.sin(x) * Math.sinh(y)) / x;
}

Python

def code(x, y):
	return (math.sin(x) * math.sinh(y)) / x

Julia

function code(x, y)
	return Float64(Float64(sin(x) * sinh(y)) / x)
end

MATLAB

function tmp = code(x, y)
	tmp = (sin(x) * sinh(y)) / x;
end

Wolfram

code[x_, y_] := N[(N[(N[Sin[x], $MachinePrecision] * N[Sinh[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]

Initial Program: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\sin x \cdot \sinh y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (sin x) (sinh y)) x))

C

double code(double x, double y) {
	return (sin(x) * sinh(y)) / x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (sin(x) * sinh(y)) / x
end function

Java

public static double code(double x, double y) {
	return (Math.sin(x) * Math.sinh(y)) / x;
}

Python

def code(x, y):
	return (math.sin(x) * math.sinh(y)) / x

Julia

function code(x, y)
	return Float64(Float64(sin(x) * sinh(y)) / x)
end

MATLAB

function tmp = code(x, y)
	tmp = (sin(x) * sinh(y)) / x;
end

Wolfram

code[x_, y_] := N[(N[(N[Sin[x], $MachinePrecision] * N[Sinh[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sin x \cdot \frac{\sinh y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) x)))

C

double code(double x, double y) {
	return sin(x) * (sinh(y) / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sin(x) * (sinh(y) / x)
end function

Java

public static double code(double x, double y) {
	return Math.sin(x) * (Math.sinh(y) / x);
}

Python

def code(x, y):
	return math.sin(x) * (math.sinh(y) / x)

Julia

function code(x, y)
	return Float64(sin(x) * Float64(sinh(y) / x))
end

MATLAB

function tmp = code(x, y)
	tmp = sin(x) * (sinh(y) / x);
end

Wolfram

code[x_, y_] := N[(N[Sin[x], $MachinePrecision] * N[(N[Sinh[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.0%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. *-commutative 91.0%

      \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

   2. associate-*l/ 99.9%

      \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

   3. *-commutative 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

4. Final simplification 99.9%

   \[\leadsto \sin x \cdot \frac{\sinh y}{x} \]

Alternative 2: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 12.5:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(\mathsf{expm1}\left(y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 12.5) (* (sin x) (/ y x)) (log1p (expm1 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 12.5) {
		tmp = sin(x) * (y / x);
	} else {
		tmp = log1p(expm1(y));
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 12.5) {
		tmp = Math.sin(x) * (y / x);
	} else {
		tmp = Math.log1p(Math.expm1(y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 12.5:
		tmp = math.sin(x) * (y / x)
	else:
		tmp = math.log1p(math.expm1(y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 12.5)
		tmp = Float64(sin(x) * Float64(y / x));
	else
		tmp = log1p(expm1(y));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, 12.5], N[(N[Sin[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision], N[Log[1 + N[(Exp[y] - 1), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 12.5

   1. Initial program 87.4%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. *-commutative 87.4%

         \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

      3. *-commutative 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 50.7%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 63.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 70.9%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 70.9%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   if 12.5 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]

   2. Taylor expanded in y around 0 4.4%

      \[\leadsto \frac{\sin x \cdot \color{blue}{y}}{x} \]

   3. Taylor expanded in x around 0 19.4%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{x} \]
   4. Step-by-step derivation

      1. *-commutative 19.4%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]

   5. Simplified 19.4%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. div-inv 19.4%

         \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{1}{x}} \]

      2. associate-*l* 4.2%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot \frac{1}{x}\right)} \]

      3. div-inv 4.2%

         \[\leadsto y \cdot \color{blue}{\frac{x}{x}} \]

      4. *-inverses 4.2%

         \[\leadsto y \cdot \color{blue}{1} \]

      5. *-commutative 4.2%

         \[\leadsto \color{blue}{1 \cdot y} \]

      6. *-un-lft-identity 4.2%

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

      7. log1p-expm1-u 71.4%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(y\right)\right)} \]

   7. Applied egg-rr 71.4%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 12.5:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(\mathsf{expm1}\left(y\right)\right)\\ \end{array} \]

Alternative 3: 61.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1600000000:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+88}:\\ \;\;\;\;\frac{y \cdot \left(x + -0.16666666666666666 \cdot {x}^{3}\right)}{x}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+202}:\\ \;\;\;\;\frac{\frac{y}{x}}{\frac{1}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{x \cdot y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1600000000.0)
   (* (sin x) (/ y x))
   (if (<= y 6e+88)
     (/ (* y (+ x (* -0.16666666666666666 (pow x 3.0)))) x)
     (if (<= y 2.2e+202)
       (/ (/ y x) (/ 1.0 (sin x)))
       (/ 1.0 (* x (/ 1.0 (* x y))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1600000000.0) {
		tmp = sin(x) * (y / x);
	} else if (y <= 6e+88) {
		tmp = (y * (x + (-0.16666666666666666 * pow(x, 3.0)))) / x;
	} else if (y <= 2.2e+202) {
		tmp = (y / x) / (1.0 / sin(x));
	} else {
		tmp = 1.0 / (x * (1.0 / (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1600000000.0d0) then
        tmp = sin(x) * (y / x)
    else if (y <= 6d+88) then
        tmp = (y * (x + ((-0.16666666666666666d0) * (x ** 3.0d0)))) / x
    else if (y <= 2.2d+202) then
        tmp = (y / x) / (1.0d0 / sin(x))
    else
        tmp = 1.0d0 / (x * (1.0d0 / (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1600000000.0) {
		tmp = Math.sin(x) * (y / x);
	} else if (y <= 6e+88) {
		tmp = (y * (x + (-0.16666666666666666 * Math.pow(x, 3.0)))) / x;
	} else if (y <= 2.2e+202) {
		tmp = (y / x) / (1.0 / Math.sin(x));
	} else {
		tmp = 1.0 / (x * (1.0 / (x * y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1600000000.0:
		tmp = math.sin(x) * (y / x)
	elif y <= 6e+88:
		tmp = (y * (x + (-0.16666666666666666 * math.pow(x, 3.0)))) / x
	elif y <= 2.2e+202:
		tmp = (y / x) / (1.0 / math.sin(x))
	else:
		tmp = 1.0 / (x * (1.0 / (x * y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1600000000.0)
		tmp = Float64(sin(x) * Float64(y / x));
	elseif (y <= 6e+88)
		tmp = Float64(Float64(y * Float64(x + Float64(-0.16666666666666666 * (x ^ 3.0)))) / x);
	elseif (y <= 2.2e+202)
		tmp = Float64(Float64(y / x) / Float64(1.0 / sin(x)));
	else
		tmp = Float64(1.0 / Float64(x * Float64(1.0 / Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1600000000.0)
		tmp = sin(x) * (y / x);
	elseif (y <= 6e+88)
		tmp = (y * (x + (-0.16666666666666666 * (x ^ 3.0)))) / x;
	elseif (y <= 2.2e+202)
		tmp = (y / x) / (1.0 / sin(x));
	else
		tmp = 1.0 / (x * (1.0 / (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1600000000.0], N[(N[Sin[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+88], N[(N[(y * N[(x + N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[y, 2.2e+202], N[(N[(y / x), $MachinePrecision] / N[(1.0 / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(x * N[(1.0 / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 1.6e9

   1. Initial program 87.6%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. *-commutative 87.6%

         \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

      3. *-commutative 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 50.0%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 62.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 70.4%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 70.4%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   if 1.6e9 < y < 6.00000000000000011e88

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]

   2. Taylor expanded in y around 0 3.1%

      \[\leadsto \frac{\sin x \cdot \color{blue}{y}}{x} \]

   3. Taylor expanded in x around 0 30.2%

      \[\leadsto \frac{\color{blue}{-0.16666666666666666 \cdot \left({x}^{3} \cdot y\right) + x \cdot y}}{x} \]
   4. Step-by-step derivation

      1. +-commutative 30.2%

         \[\leadsto \frac{\color{blue}{x \cdot y + -0.16666666666666666 \cdot \left({x}^{3} \cdot y\right)}}{x} \]

      2. associate-*r* 30.2%

         \[\leadsto \frac{x \cdot y + \color{blue}{\left(-0.16666666666666666 \cdot {x}^{3}\right) \cdot y}}{x} \]

      3. distribute-rgt-out 30.2%

         \[\leadsto \frac{\color{blue}{y \cdot \left(x + -0.16666666666666666 \cdot {x}^{3}\right)}}{x} \]

   5. Simplified 30.2%

      \[\leadsto \frac{\color{blue}{y \cdot \left(x + -0.16666666666666666 \cdot {x}^{3}\right)}}{x} \]

   if 6.00000000000000011e88 < y < 2.19999999999999978e202

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

      2. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 4.0%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 4.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 45.4%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 45.4%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]
   7. Step-by-step derivation

      1. associate-/r/ 4.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. div-inv 4.0%

         \[\leadsto \frac{y}{\color{blue}{x \cdot \frac{1}{\sin x}}} \]

      3. associate-/r* 45.4%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{\frac{1}{\sin x}}} \]

   8. Applied egg-rr 45.4%

      \[\leadsto \color{blue}{\frac{\frac{y}{x}}{\frac{1}{\sin x}}} \]

   if 2.19999999999999978e202 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

      2. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 5.6%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 5.6%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 30.5%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 30.5%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]
   7. Step-by-step derivation

      1. *-commutative 30.5%

         \[\leadsto \color{blue}{\sin x \cdot \frac{y}{x}} \]

      2. associate-*r/ 5.6%

         \[\leadsto \color{blue}{\frac{\sin x \cdot y}{x}} \]

      3. clear-num 5.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{\sin x \cdot y}}} \]

      4. *-commutative 5.6%

         \[\leadsto \frac{1}{\frac{x}{\color{blue}{y \cdot \sin x}}} \]

   8. Applied egg-rr 5.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{x}{y \cdot \sin x}}} \]
   9. Step-by-step derivation

      1. div-inv 5.6%

         \[\leadsto \frac{1}{\color{blue}{x \cdot \frac{1}{y \cdot \sin x}}} \]

      2. *-commutative 5.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{y \cdot \sin x} \cdot x}} \]

      3. associate-/r* 5.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{y}}{\sin x}} \cdot x} \]

   10. Applied egg-rr 5.6%

       \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{y}}{\sin x} \cdot x}} \]

   11. Taylor expanded in x around 0 43.3%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{x \cdot y}} \cdot x} \]
   12. Step-by-step derivation

       1. *-commutative 43.3%

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{y \cdot x}} \cdot x} \]

   13. Simplified 43.3%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{y \cdot x}} \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1600000000:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+88}:\\ \;\;\;\;\frac{y \cdot \left(x + -0.16666666666666666 \cdot {x}^{3}\right)}{x}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+202}:\\ \;\;\;\;\frac{\frac{y}{x}}{\frac{1}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{x \cdot y}}\\ \end{array} \]

Alternative 4: 61.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+202}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{x \cdot y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.7e+202) (* (sin x) (/ y x)) (/ 1.0 (* x (/ 1.0 (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.7e+202) {
		tmp = sin(x) * (y / x);
	} else {
		tmp = 1.0 / (x * (1.0 / (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1.7d+202) then
        tmp = sin(x) * (y / x)
    else
        tmp = 1.0d0 / (x * (1.0d0 / (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.7e+202) {
		tmp = Math.sin(x) * (y / x);
	} else {
		tmp = 1.0 / (x * (1.0 / (x * y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.7e+202:
		tmp = math.sin(x) * (y / x)
	else:
		tmp = 1.0 / (x * (1.0 / (x * y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.7e+202)
		tmp = Float64(sin(x) * Float64(y / x));
	else
		tmp = Float64(1.0 / Float64(x * Float64(1.0 / Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.7e+202)
		tmp = sin(x) * (y / x);
	else
		tmp = 1.0 / (x * (1.0 / (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.7e+202], N[(N[Sin[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(x * N[(1.0 / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.7e202

   1. Initial program 90.2%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. *-commutative 90.2%

         \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

      3. *-commutative 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 40.5%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 50.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 62.4%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 62.4%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   if 1.7e202 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

      2. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 5.6%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 5.6%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 30.5%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 30.5%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]
   7. Step-by-step derivation

      1. *-commutative 30.5%

         \[\leadsto \color{blue}{\sin x \cdot \frac{y}{x}} \]

      2. associate-*r/ 5.6%

         \[\leadsto \color{blue}{\frac{\sin x \cdot y}{x}} \]

      3. clear-num 5.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{\sin x \cdot y}}} \]

      4. *-commutative 5.6%

         \[\leadsto \frac{1}{\frac{x}{\color{blue}{y \cdot \sin x}}} \]

   8. Applied egg-rr 5.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{x}{y \cdot \sin x}}} \]
   9. Step-by-step derivation

      1. div-inv 5.6%

         \[\leadsto \frac{1}{\color{blue}{x \cdot \frac{1}{y \cdot \sin x}}} \]

      2. *-commutative 5.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{y \cdot \sin x} \cdot x}} \]

      3. associate-/r* 5.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{y}}{\sin x}} \cdot x} \]

   10. Applied egg-rr 5.6%

       \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{y}}{\sin x} \cdot x}} \]

   11. Taylor expanded in x around 0 43.3%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{x \cdot y}} \cdot x} \]
   12. Step-by-step derivation

       1. *-commutative 43.3%

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{y \cdot x}} \cdot x} \]

   13. Simplified 43.3%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{y \cdot x}} \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+202}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{x \cdot y}}\\ \end{array} \]

Alternative 5: 49.1% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666 + \frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{x \cdot y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 4.2e+191)
   (/ (/ y x) (+ (* x 0.16666666666666666) (/ 1.0 x)))
   (/ 1.0 (* x (/ 1.0 (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.2e+191) {
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	} else {
		tmp = 1.0 / (x * (1.0 / (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 4.2d+191) then
        tmp = (y / x) / ((x * 0.16666666666666666d0) + (1.0d0 / x))
    else
        tmp = 1.0d0 / (x * (1.0d0 / (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4.2e+191) {
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	} else {
		tmp = 1.0 / (x * (1.0 / (x * y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.2e+191:
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x))
	else:
		tmp = 1.0 / (x * (1.0 / (x * y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.2e+191)
		tmp = Float64(Float64(y / x) / Float64(Float64(x * 0.16666666666666666) + Float64(1.0 / x)));
	else
		tmp = Float64(1.0 / Float64(x * Float64(1.0 / Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4.2e+191)
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	else
		tmp = 1.0 / (x * (1.0 / (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.2e+191], N[(N[(y / x), $MachinePrecision] / N[(N[(x * 0.16666666666666666), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(x * N[(1.0 / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.2000000000000001e191

   1. Initial program 90.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. *-commutative 90.0%

         \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

      3. *-commutative 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 41.1%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 51.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 63.0%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 63.0%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]
   7. Step-by-step derivation

      1. associate-/r/ 51.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. div-inv 51.0%

         \[\leadsto \frac{y}{\color{blue}{x \cdot \frac{1}{\sin x}}} \]

      3. associate-/r* 62.9%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{\frac{1}{\sin x}}} \]

   8. Applied egg-rr 62.9%

      \[\leadsto \color{blue}{\frac{\frac{y}{x}}{\frac{1}{\sin x}}} \]

   9. Taylor expanded in x around 0 48.8%

      \[\leadsto \frac{\frac{y}{x}}{\color{blue}{0.16666666666666666 \cdot x + \frac{1}{x}}} \]

   if 4.2000000000000001e191 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

      2. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 5.4%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 5.4%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 30.0%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 30.0%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]
   7. Step-by-step derivation

      1. *-commutative 30.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{y}{x}} \]

      2. associate-*r/ 5.4%

         \[\leadsto \color{blue}{\frac{\sin x \cdot y}{x}} \]

      3. clear-num 5.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{\sin x \cdot y}}} \]

      4. *-commutative 5.4%

         \[\leadsto \frac{1}{\frac{x}{\color{blue}{y \cdot \sin x}}} \]

   8. Applied egg-rr 5.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{x}{y \cdot \sin x}}} \]
   9. Step-by-step derivation

      1. div-inv 5.4%

         \[\leadsto \frac{1}{\color{blue}{x \cdot \frac{1}{y \cdot \sin x}}} \]

      2. *-commutative 5.4%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{y \cdot \sin x} \cdot x}} \]

      3. associate-/r* 5.4%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{y}}{\sin x}} \cdot x} \]

   10. Applied egg-rr 5.4%

       \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{y}}{\sin x} \cdot x}} \]

   11. Taylor expanded in x around 0 40.7%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{x \cdot y}} \cdot x} \]
   12. Step-by-step derivation

       1. *-commutative 40.7%

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{y \cdot x}} \cdot x} \]

   13. Simplified 40.7%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{y \cdot x}} \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666 + \frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{x \cdot y}}\\ \end{array} \]

Alternative 6: 48.7% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{x \cdot y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 6.6e+222) (* x (/ y x)) (/ 1.0 (* x (/ 1.0 (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 6.6e+222) {
		tmp = x * (y / x);
	} else {
		tmp = 1.0 / (x * (1.0 / (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 6.6d+222) then
        tmp = x * (y / x)
    else
        tmp = 1.0d0 / (x * (1.0d0 / (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 6.6e+222) {
		tmp = x * (y / x);
	} else {
		tmp = 1.0 / (x * (1.0 / (x * y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 6.6e+222:
		tmp = x * (y / x)
	else:
		tmp = 1.0 / (x * (1.0 / (x * y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 6.6e+222)
		tmp = Float64(x * Float64(y / x));
	else
		tmp = Float64(1.0 / Float64(x * Float64(1.0 / Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 6.6e+222)
		tmp = x * (y / x);
	else
		tmp = 1.0 / (x * (1.0 / (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 6.6e+222], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(x * N[(1.0 / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.59999999999999967e222

   1. Initial program 90.3%

      \[\frac{\sin x \cdot \sinh y}{x} \]

   2. Taylor expanded in y around 0 39.9%

      \[\leadsto \frac{\sin x \cdot \color{blue}{y}}{x} \]

   3. Taylor expanded in x around 0 22.5%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{x} \]
   4. Step-by-step derivation

      1. *-commutative 22.5%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]

   5. Simplified 22.5%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. associate-/l* 25.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{x}}} \]

      2. associate-/r/ 48.0%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   7. Applied egg-rr 48.0%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   if 6.59999999999999967e222 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

      2. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 5.9%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 5.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 25.8%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 25.8%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]
   7. Step-by-step derivation

      1. *-commutative 25.8%

         \[\leadsto \color{blue}{\sin x \cdot \frac{y}{x}} \]

      2. associate-*r/ 5.9%

         \[\leadsto \color{blue}{\frac{\sin x \cdot y}{x}} \]

      3. clear-num 5.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{\sin x \cdot y}}} \]

      4. *-commutative 5.9%

         \[\leadsto \frac{1}{\frac{x}{\color{blue}{y \cdot \sin x}}} \]

   8. Applied egg-rr 5.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{x}{y \cdot \sin x}}} \]
   9. Step-by-step derivation

      1. div-inv 5.9%

         \[\leadsto \frac{1}{\color{blue}{x \cdot \frac{1}{y \cdot \sin x}}} \]

      2. *-commutative 5.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{y \cdot \sin x} \cdot x}} \]

      3. associate-/r* 5.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{y}}{\sin x}} \cdot x} \]

   10. Applied egg-rr 5.9%

       \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1}{y}}{\sin x} \cdot x}} \]

   11. Taylor expanded in x around 0 46.7%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{x \cdot y}} \cdot x} \]
   12. Step-by-step derivation

       1. *-commutative 46.7%

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{y \cdot x}} \cdot x} \]

   13. Simplified 46.7%

       \[\leadsto \frac{1}{\color{blue}{\frac{1}{y \cdot x}} \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{x \cdot y}}\\ \end{array} \]

Alternative 7: 48.7% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.25e+222) (* x (/ y x)) (/ (* x y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.25e+222) {
		tmp = x * (y / x);
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1.25d+222) then
        tmp = x * (y / x)
    else
        tmp = (x * y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.25e+222) {
		tmp = x * (y / x);
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.25e+222:
		tmp = x * (y / x)
	else:
		tmp = (x * y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.25e+222)
		tmp = Float64(x * Float64(y / x));
	else
		tmp = Float64(Float64(x * y) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.25e+222)
		tmp = x * (y / x);
	else
		tmp = (x * y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.25e+222], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.25000000000000006e222

   1. Initial program 90.3%

      \[\frac{\sin x \cdot \sinh y}{x} \]

   2. Taylor expanded in y around 0 39.9%

      \[\leadsto \frac{\sin x \cdot \color{blue}{y}}{x} \]

   3. Taylor expanded in x around 0 22.5%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{x} \]
   4. Step-by-step derivation

      1. *-commutative 22.5%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]

   5. Simplified 22.5%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. associate-/l* 25.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{x}}} \]

      2. associate-/r/ 48.0%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   7. Applied egg-rr 48.0%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   if 1.25000000000000006e222 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]

   2. Taylor expanded in y around 0 5.9%

      \[\leadsto \frac{\sin x \cdot \color{blue}{y}}{x} \]

   3. Taylor expanded in x around 0 46.7%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{x} \]
   4. Step-by-step derivation

      1. *-commutative 46.7%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]

   5. Simplified 46.7%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \]

Alternative 8: 49.7% accurate, 41.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (/ y x)))

C

double code(double x, double y) {
	return x * (y / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (y / x)
end function

Java

public static double code(double x, double y) {
	return x * (y / x);
}

Python

def code(x, y):
	return x * (y / x)

Julia

function code(x, y)
	return Float64(x * Float64(y / x))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (y / x);
end

Wolfram

code[x_, y_] := N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.0%

   \[\frac{\sin x \cdot \sinh y}{x} \]

2. Taylor expanded in y around 0 37.5%

   \[\leadsto \frac{\sin x \cdot \color{blue}{y}}{x} \]

3. Taylor expanded in x around 0 24.2%

   \[\leadsto \frac{\color{blue}{x \cdot y}}{x} \]
4. Step-by-step derivation

   1. *-commutative 24.2%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]

5. Simplified 24.2%

   \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
6. Step-by-step derivation

   1. associate-/l* 24.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{x}{x}}} \]

   2. associate-/r/ 46.5%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

7. Applied egg-rr 46.5%

   \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

8. Final simplification 46.5%

   \[\leadsto x \cdot \frac{y}{x} \]

Alternative 9: 27.9% accurate, 205.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 y)

C

double code(double x, double y) {
	return y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y
end function

Java

public static double code(double x, double y) {
	return y;
}

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

function tmp = code(x, y)
	tmp = y;
end

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 91.0%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. *-commutative 91.0%

      \[\leadsto \frac{\color{blue}{\sinh y \cdot \sin x}}{x} \]

   2. associate-*l/ 99.9%

      \[\leadsto \color{blue}{\frac{\sinh y}{x} \cdot \sin x} \]

   3. *-commutative 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

4. Taylor expanded in y around 0 37.5%

   \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
5. Step-by-step derivation

   1. associate-/l* 46.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

   2. associate-/r/ 59.7%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

6. Simplified 59.7%

   \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

7. Taylor expanded in x around 0 24.4%

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

8. Final simplification 24.4%

   \[\leadsto y \]

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sin x \cdot \frac{\sinh y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) x)))

C

double code(double x, double y) {
	return sin(x) * (sinh(y) / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sin(x) * (sinh(y) / x)
end function

Java

public static double code(double x, double y) {
	return Math.sin(x) * (Math.sinh(y) / x);
}

Python

def code(x, y):
	return math.sin(x) * (math.sinh(y) / x)

Julia

function code(x, y)
	return Float64(sin(x) * Float64(sinh(y) / x))
end

MATLAB

function tmp = code(x, y)
	tmp = sin(x) * (sinh(y) / x);
end

Wolfram

code[x_, y_] := N[(N[Sin[x], $MachinePrecision] * N[(N[Sinh[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023332 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))