Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.8% → 99.9%

Time: 10.0s

Alternatives: 10

Speedup: 1.0×

• 50.3% 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: 88.8% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.0%

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

   1. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.8% 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 90.0%

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

   1. associate-*r/ 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 3: 86.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+16} \lor \neg \left(y \leq 0.00066\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.4e+16) (not (<= y 0.00066))) (sinh y) (* (sin x) (/ y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.4e+16) || !(y <= 0.00066)) {
		tmp = sinh(y);
	} else {
		tmp = sin(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 <= (-2.4d+16)) .or. (.not. (y <= 0.00066d0))) then
        tmp = sinh(y)
    else
        tmp = sin(x) * (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.4e+16) || !(y <= 0.00066)) {
		tmp = Math.sinh(y);
	} else {
		tmp = Math.sin(x) * (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.4e+16) or not (y <= 0.00066):
		tmp = math.sinh(y)
	else:
		tmp = math.sin(x) * (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.4e+16) || !(y <= 0.00066))
		tmp = sinh(y);
	else
		tmp = Float64(sin(x) * Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.4e+16) || ~((y <= 0.00066)))
		tmp = sinh(y);
	else
		tmp = sin(x) * (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.4e+16], N[Not[LessEqual[y, 0.00066]], $MachinePrecision]], N[Sinh[y], $MachinePrecision], N[(N[Sin[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e16 or 6.6e-4 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 72.3%

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

   if -2.4e16 < y < 6.6e-4

   1. Initial program 77.8%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 76.7%

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

      1. associate-/l* 98.7%

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

      2. associate-/r/ 98.6%

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

   6. Simplified 98.6%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+16} \lor \neg \left(y \leq 0.00066\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \end{array} \]

Alternative 4: 86.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+16} \lor \neg \left(y \leq 0.017\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.4e+16) (not (<= y 0.017))) (sinh y) (* (/ (sin x) x) y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.4e+16) || !(y <= 0.017)) {
		tmp = sinh(y);
	} else {
		tmp = (sin(x) / 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 <= (-2.4d+16)) .or. (.not. (y <= 0.017d0))) then
        tmp = sinh(y)
    else
        tmp = (sin(x) / x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.4e+16) || !(y <= 0.017)) {
		tmp = Math.sinh(y);
	} else {
		tmp = (Math.sin(x) / x) * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.4e+16) or not (y <= 0.017):
		tmp = math.sinh(y)
	else:
		tmp = (math.sin(x) / x) * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.4e+16) || !(y <= 0.017))
		tmp = sinh(y);
	else
		tmp = Float64(Float64(sin(x) / x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.4e+16) || ~((y <= 0.017)))
		tmp = sinh(y);
	else
		tmp = (sin(x) / x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.4e+16], N[Not[LessEqual[y, 0.017]], $MachinePrecision]], N[Sinh[y], $MachinePrecision], N[(N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e16 or 0.017000000000000001 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 72.3%

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

   if -2.4e16 < y < 0.017000000000000001

   1. Initial program 77.8%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 76.7%

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

      1. associate-/l* 98.7%

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

   6. Simplified 98.7%

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

      1. div-inv 98.6%

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

      2. *-commutative 98.6%

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

      3. clear-num 98.7%

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

   8. Applied egg-rr 98.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+16} \lor \neg \left(y \leq 0.017\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \end{array} \]

Alternative 5: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+16} \lor \neg \left(y \leq 3.2 \cdot 10^{-8}\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.4e+16) (not (<= y 3.2e-8)))
   (sinh y)
   (* y (/ 1.0 (+ 1.0 (* x (* x 0.16666666666666666)))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.4e+16) || !(y <= 3.2e-8)) {
		tmp = sinh(y);
	} else {
		tmp = y * (1.0 / (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.4d+16)) .or. (.not. (y <= 3.2d-8))) then
        tmp = sinh(y)
    else
        tmp = y * (1.0d0 / (1.0d0 + (x * (x * 0.16666666666666666d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.4e+16) || !(y <= 3.2e-8)) {
		tmp = Math.sinh(y);
	} else {
		tmp = y * (1.0 / (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.4e+16) or not (y <= 3.2e-8):
		tmp = math.sinh(y)
	else:
		tmp = y * (1.0 / (1.0 + (x * (x * 0.16666666666666666))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.4e+16) || !(y <= 3.2e-8))
		tmp = sinh(y);
	else
		tmp = Float64(y * Float64(1.0 / Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.4e+16) || ~((y <= 3.2e-8)))
		tmp = sinh(y);
	else
		tmp = y * (1.0 / (1.0 + (x * (x * 0.16666666666666666))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.4e+16], N[Not[LessEqual[y, 3.2e-8]], $MachinePrecision]], N[Sinh[y], $MachinePrecision], N[(y * N[(1.0 / N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e16 or 3.2000000000000002e-8 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 72.3%

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

   if -2.4e16 < y < 3.2000000000000002e-8

   1. Initial program 77.8%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 76.7%

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

      1. associate-/l* 98.7%

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

      2. associate-/r/ 98.6%

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

   6. Simplified 98.6%

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

      1. associate-/r/ 98.7%

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

      2. div-inv 97.7%

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

      3. associate-/r* 97.6%

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

   8. Applied egg-rr 97.6%

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

   9. Taylor expanded in x around 0 68.8%

      \[\leadsto \frac{\frac{y}{x}}{\color{blue}{0.16666666666666666 \cdot x + \frac{1}{x}}} \]
   10. Step-by-step derivation

       1. associate-/l/ 69.0%

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

       2. div-inv 69.0%

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

       3. *-commutative 69.0%

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

       4. +-commutative 69.0%

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

       5. distribute-rgt-in 69.0%

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

       6. lft-mult-inverse 69.9%

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

       7. *-commutative 69.9%

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

   11. Applied egg-rr 69.9%

       \[\leadsto \color{blue}{y \cdot \frac{1}{1 + \left(x \cdot 0.16666666666666666\right) \cdot x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+16} \lor \neg \left(y \leq 3.2 \cdot 10^{-8}\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}\\ \end{array} \]

Alternative 6: 57.0% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+16} \lor \neg \left(y \leq 190\right):\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.4e+16) (not (<= y 190.0)))
   (/ (/ y x) (* x 0.16666666666666666))
   (* y (/ 1.0 (+ 1.0 (* x (* x 0.16666666666666666)))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.4e+16) || !(y <= 190.0)) {
		tmp = (y / x) / (x * 0.16666666666666666);
	} else {
		tmp = y * (1.0 / (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.4d+16)) .or. (.not. (y <= 190.0d0))) then
        tmp = (y / x) / (x * 0.16666666666666666d0)
    else
        tmp = y * (1.0d0 / (1.0d0 + (x * (x * 0.16666666666666666d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.4e+16) || !(y <= 190.0)) {
		tmp = (y / x) / (x * 0.16666666666666666);
	} else {
		tmp = y * (1.0 / (1.0 + (x * (x * 0.16666666666666666))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.4e+16) or not (y <= 190.0):
		tmp = (y / x) / (x * 0.16666666666666666)
	else:
		tmp = y * (1.0 / (1.0 + (x * (x * 0.16666666666666666))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.4e+16) || !(y <= 190.0))
		tmp = Float64(Float64(y / x) / Float64(x * 0.16666666666666666));
	else
		tmp = Float64(y * Float64(1.0 / Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.4e+16) || ~((y <= 190.0)))
		tmp = (y / x) / (x * 0.16666666666666666);
	else
		tmp = y * (1.0 / (1.0 + (x * (x * 0.16666666666666666))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.4e+16], N[Not[LessEqual[y, 190.0]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] / N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 / N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e16 or 190 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 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 4.6%

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

      1. associate-/l* 4.6%

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

      2. associate-/r/ 30.6%

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

   6. Simplified 30.6%

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

      1. associate-/r/ 4.6%

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

      2. div-inv 4.6%

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

      3. associate-/r* 30.6%

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

   8. Applied egg-rr 30.6%

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

   9. Taylor expanded in x around 0 29.8%

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

   10. Taylor expanded in x around inf 45.1%

       \[\leadsto \frac{\frac{y}{x}}{\color{blue}{0.16666666666666666 \cdot x}} \]
   11. Step-by-step derivation

       1. *-commutative 45.1%

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

   12. Simplified 45.1%

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

   if -2.4e16 < y < 190

   1. Initial program 78.0%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 76.1%

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

      1. associate-/l* 97.9%

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

      2. associate-/r/ 97.8%

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

   6. Simplified 97.8%

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

      1. associate-/r/ 97.9%

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

      2. div-inv 96.9%

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

      3. associate-/r* 96.8%

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

   8. Applied egg-rr 96.8%

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

   9. Taylor expanded in x around 0 68.3%

      \[\leadsto \frac{\frac{y}{x}}{\color{blue}{0.16666666666666666 \cdot x + \frac{1}{x}}} \]
   10. Step-by-step derivation

       1. associate-/l/ 68.5%

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

       2. div-inv 68.5%

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

       3. *-commutative 68.5%

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

       4. +-commutative 68.5%

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

       5. distribute-rgt-in 68.5%

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

       6. lft-mult-inverse 69.4%

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

       7. *-commutative 69.4%

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

   11. Applied egg-rr 69.4%

       \[\leadsto \color{blue}{y \cdot \frac{1}{1 + \left(x \cdot 0.16666666666666666\right) \cdot x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+16} \lor \neg \left(y \leq 190\right):\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}\\ \end{array} \]

Alternative 7: 57.0% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+16} \lor \neg \left(y \leq 300\right):\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.4e+16) (not (<= y 300.0)))
   (/ (/ y x) (* x 0.16666666666666666))
   (/ y (+ 1.0 (* x (* x 0.16666666666666666))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.4e+16) || !(y <= 300.0)) {
		tmp = (y / x) / (x * 0.16666666666666666);
	} else {
		tmp = y / (1.0 + (x * (x * 0.16666666666666666)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.4d+16)) .or. (.not. (y <= 300.0d0))) then
        tmp = (y / x) / (x * 0.16666666666666666d0)
    else
        tmp = y / (1.0d0 + (x * (x * 0.16666666666666666d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.4e+16) || !(y <= 300.0)) {
		tmp = (y / x) / (x * 0.16666666666666666);
	} else {
		tmp = y / (1.0 + (x * (x * 0.16666666666666666)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.4e+16) or not (y <= 300.0):
		tmp = (y / x) / (x * 0.16666666666666666)
	else:
		tmp = y / (1.0 + (x * (x * 0.16666666666666666)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.4e+16) || !(y <= 300.0))
		tmp = Float64(Float64(y / x) / Float64(x * 0.16666666666666666));
	else
		tmp = Float64(y / Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.4e+16) || ~((y <= 300.0)))
		tmp = (y / x) / (x * 0.16666666666666666);
	else
		tmp = y / (1.0 + (x * (x * 0.16666666666666666)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.4e+16], N[Not[LessEqual[y, 300.0]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] / N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision], N[(y / N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e16 or 300 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 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 4.6%

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

      1. associate-/l* 4.6%

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

      2. associate-/r/ 30.6%

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

   6. Simplified 30.6%

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

      1. associate-/r/ 4.6%

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

      2. div-inv 4.6%

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

      3. associate-/r* 30.6%

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

   8. Applied egg-rr 30.6%

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

   9. Taylor expanded in x around 0 29.8%

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

   10. Taylor expanded in x around inf 45.1%

       \[\leadsto \frac{\frac{y}{x}}{\color{blue}{0.16666666666666666 \cdot x}} \]
   11. Step-by-step derivation

       1. *-commutative 45.1%

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

   12. Simplified 45.1%

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

   if -2.4e16 < y < 300

   1. Initial program 78.0%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 76.1%

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

      1. associate-/l* 97.9%

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

      2. associate-/r/ 97.8%

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

   6. Simplified 97.8%

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

      1. associate-/r/ 97.9%

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

      2. div-inv 96.9%

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

      3. associate-/r* 96.8%

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

   8. Applied egg-rr 96.8%

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

   9. Taylor expanded in x around 0 68.3%

      \[\leadsto \frac{\frac{y}{x}}{\color{blue}{0.16666666666666666 \cdot x + \frac{1}{x}}} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 68.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{y}{x}}{0.16666666666666666 \cdot x + \frac{1}{x}}\right)\right)} \]

       2. expm1-udef 26.3%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{y}{x}}{0.16666666666666666 \cdot x + \frac{1}{x}}\right)} - 1} \]

       3. associate-/l/ 26.3%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\left(0.16666666666666666 \cdot x + \frac{1}{x}\right) \cdot x}}\right)} - 1 \]

       4. *-commutative 26.3%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{x \cdot \left(0.16666666666666666 \cdot x + \frac{1}{x}\right)}}\right)} - 1 \]

       5. +-commutative 26.3%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{x \cdot \color{blue}{\left(\frac{1}{x} + 0.16666666666666666 \cdot x\right)}}\right)} - 1 \]

       6. distribute-rgt-in 26.3%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\frac{1}{x} \cdot x + \left(0.16666666666666666 \cdot x\right) \cdot x}}\right)} - 1 \]

       7. lft-mult-inverse 26.3%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{1} + \left(0.16666666666666666 \cdot x\right) \cdot x}\right)} - 1 \]

       8. *-commutative 26.3%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{1 + \color{blue}{\left(x \cdot 0.16666666666666666\right)} \cdot x}\right)} - 1 \]

   11. Applied egg-rr 26.3%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{1 + \left(x \cdot 0.16666666666666666\right) \cdot x}\right)} - 1} \]
   12. Step-by-step derivation

       1. expm1-def 69.4%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{1 + \left(x \cdot 0.16666666666666666\right) \cdot x}\right)\right)} \]

       2. expm1-log1p 69.4%

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

       3. *-commutative 69.4%

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

   13. Simplified 69.4%

       \[\leadsto \color{blue}{\frac{y}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+16} \lor \neg \left(y \leq 300\right):\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}\\ \end{array} \]

Alternative 8: 56.7% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-9} \lor \neg \left(y \leq 270\right):\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.1e-9) (not (<= y 270.0)))
   (/ (/ y x) (* x 0.16666666666666666))
   (/ x (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.1e-9) || !(y <= 270.0)) {
		tmp = (y / x) / (x * 0.16666666666666666);
	} else {
		tmp = x / (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 <= (-3.1d-9)) .or. (.not. (y <= 270.0d0))) then
        tmp = (y / x) / (x * 0.16666666666666666d0)
    else
        tmp = x / (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3.1e-9) || !(y <= 270.0)) {
		tmp = (y / x) / (x * 0.16666666666666666);
	} else {
		tmp = x / (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.1e-9) or not (y <= 270.0):
		tmp = (y / x) / (x * 0.16666666666666666)
	else:
		tmp = x / (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.1e-9) || !(y <= 270.0))
		tmp = Float64(Float64(y / x) / Float64(x * 0.16666666666666666));
	else
		tmp = Float64(x / Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.1e-9) || ~((y <= 270.0)))
		tmp = (y / x) / (x * 0.16666666666666666);
	else
		tmp = x / (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.1e-9], N[Not[LessEqual[y, 270.0]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] / N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000005e-9 or 270 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 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 5.7%

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

      1. associate-/l* 5.7%

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

      2. associate-/r/ 31.1%

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

   6. Simplified 31.1%

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

      1. associate-/r/ 5.7%

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

      2. div-inv 5.7%

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

      3. associate-/r* 31.1%

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

   8. Applied egg-rr 31.1%

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

   9. Taylor expanded in x around 0 29.3%

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

   10. Taylor expanded in x around inf 44.3%

       \[\leadsto \frac{\frac{y}{x}}{\color{blue}{0.16666666666666666 \cdot x}} \]
   11. Step-by-step derivation

       1. *-commutative 44.3%

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

   12. Simplified 44.3%

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

   if -3.10000000000000005e-9 < y < 270

   1. Initial program 77.4%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 76.6%

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

      1. associate-/l* 99.0%

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

      2. associate-/r/ 98.9%

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

   6. Simplified 98.9%

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

   7. Taylor expanded in x around 0 70.1%

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

      1. *-commutative 70.1%

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

      2. clear-num 70.2%

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

      3. un-div-inv 70.4%

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

   9. Applied egg-rr 70.4%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-9} \lor \neg \left(y \leq 270\right):\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \end{array} \]

Alternative 9: 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 90.0%

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

   1. associate-*r/ 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 37.0%

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

   1. associate-/l* 46.9%

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

   2. associate-/r/ 61.1%

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

6. Simplified 61.1%

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

7. Taylor expanded in x around 0 47.5%

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

8. Final simplification 47.5%

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

Alternative 10: 28.0% 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 90.0%

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

   1. associate-*r/ 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 37.0%

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

   1. associate-/l* 46.9%

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

   2. associate-/r/ 61.1%

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

6. Simplified 61.1%

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

7. Taylor expanded in x around 0 24.2%

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

8. Final simplification 24.2%

   \[\leadsto y \]

Developer target: 99.8% 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 2023301 
(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))