Linear.Quaternion:$csinh from linear-1.19.1.3

Percentage Accurate: 99.9% → 99.9%

Time: 8.1s

Alternatives: 7

Speedup: 1.0×

• Could not converge on a ground truth

  1. x = 3.234625241379351e+269
  2. y = 2.0589407775864308e+290

• 48.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

   \[\cosh x \cdot \frac{\sin y}{y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 86.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cosh x \leq 1.0001:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (cosh x) 1.0001) (/ (sin y) y) (cosh x)))

C

double code(double x, double y) {
	double tmp;
	if (cosh(x) <= 1.0001) {
		tmp = sin(y) / y;
	} else {
		tmp = cosh(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (cosh(x) <= 1.0001d0) then
        tmp = sin(y) / y
    else
        tmp = cosh(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.cosh(x) <= 1.0001) {
		tmp = Math.sin(y) / y;
	} else {
		tmp = Math.cosh(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.cosh(x) <= 1.0001:
		tmp = math.sin(y) / y
	else:
		tmp = math.cosh(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (cosh(x) <= 1.0001)
		tmp = Float64(sin(y) / y);
	else
		tmp = cosh(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (cosh(x) <= 1.0001)
		tmp = sin(y) / y;
	else
		tmp = cosh(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Cosh[x], $MachinePrecision], 1.0001], N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision], N[Cosh[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cosh.f64 x) < 1.00009999999999999

   1. Initial program 99.8%

      \[\cosh x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.9%

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

   if 1.00009999999999999 < (cosh.f64 x)

   1. Initial program 99.3%

      \[\cosh x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r/ 99.3%

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

      2. associate-*l/ 99.3%

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

      3. *-commutative 99.3%

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

      4. clear-num 99.3%

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

      5. un-div-inv 99.3%

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in y around 0 74.9%

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

      1. div-inv 74.9%

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

      2. clear-num 74.9%

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

   7. Applied egg-rr 74.9%

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

      1. associate-*r/ 74.9%

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

      2. *-commutative 74.9%

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

      3. associate-/l* 74.9%

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

      4. *-inverses 74.9%

         \[\leadsto \cosh x \cdot \color{blue}{1} \]

      5. *-rgt-identity 74.9%

         \[\leadsto \color{blue}{\cosh x} \]

   9. Simplified 74.9%

      \[\leadsto \color{blue}{\cosh x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 62.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \cosh x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (cosh x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return math.cosh(x)

Julia

function code(x, y)
	return cosh(x)
end

MATLAB

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

Wolfram

code[x_, y_] := N[Cosh[x], $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\cosh x \cdot \frac{\sin y}{y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-*r/ 99.5%

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

   2. associate-*l/ 99.5%

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

   3. *-commutative 99.5%

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

   4. clear-num 99.5%

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

   5. un-div-inv 99.5%

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

4. Applied egg-rr 99.5%

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

5. Taylor expanded in y around 0 60.1%

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

   1. div-inv 60.1%

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

   2. clear-num 60.1%

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

7. Applied egg-rr 60.1%

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

   1. associate-*r/ 60.1%

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

   2. *-commutative 60.1%

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

   3. associate-/l* 60.1%

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

   4. *-inverses 60.1%

      \[\leadsto \cosh x \cdot \color{blue}{1} \]

   5. *-rgt-identity 60.1%

      \[\leadsto \color{blue}{\cosh x} \]

9. Simplified 60.1%

   \[\leadsto \color{blue}{\cosh x} \]
10. Add Preprocessing

Alternative 4: 34.7% accurate, 15.8× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (/ 1.0 (/ y (* y (+ 1.0 (* (* y y) -0.16666666666666666))))))

C

double code(double x, double y) {
	return 1.0 / (y / (y * (1.0 + ((y * y) * -0.16666666666666666))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 / (y / (y * (1.0d0 + ((y * y) * (-0.16666666666666666d0)))))
end function

Java

public static double code(double x, double y) {
	return 1.0 / (y / (y * (1.0 + ((y * y) * -0.16666666666666666))));
}

Python

def code(x, y):
	return 1.0 / (y / (y * (1.0 + ((y * y) * -0.16666666666666666))))

Julia

function code(x, y)
	return Float64(1.0 / Float64(y / Float64(y * Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666)))))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 / (y / (y * (1.0 + ((y * y) * -0.16666666666666666))));
end

Wolfram

code[x_, y_] := N[(1.0 / N[(y / N[(y * N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. *-commutative 99.5%

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

   2. associate-*l/ 99.5%

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

   3. associate-/l* 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\sin y \cdot \frac{\cosh x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 45.3%

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

   1. un-div-inv 45.4%

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

   2. clear-num 45.3%

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

7. Applied egg-rr 45.3%

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

8. Taylor expanded in y around 0 26.8%

   \[\leadsto \frac{1}{\frac{y}{\color{blue}{y \cdot \left(1 + -0.16666666666666666 \cdot {y}^{2}\right)}}} \]
9. Step-by-step derivation

   1. *-commutative 26.8%

      \[\leadsto \frac{1}{\frac{y}{y \cdot \left(1 + \color{blue}{{y}^{2} \cdot -0.16666666666666666}\right)}} \]

10. Simplified 26.8%

    \[\leadsto \frac{1}{\frac{y}{\color{blue}{y \cdot \left(1 + {y}^{2} \cdot -0.16666666666666666\right)}}} \]
11. Step-by-step derivation

    1. unpow2 26.8%

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

12. Applied egg-rr 26.8%

    \[\leadsto \frac{1}{\frac{y}{y \cdot \left(1 + \color{blue}{\left(y \cdot y\right)} \cdot -0.16666666666666666\right)}} \]
13. Add Preprocessing

Alternative 5: 34.7% accurate, 15.8× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (* (* y (+ 1.0 (* (* y y) -0.16666666666666666))) (/ 1.0 y)))

C

double code(double x, double y) {
	return (y * (1.0 + ((y * y) * -0.16666666666666666))) * (1.0 / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y * (1.0d0 + ((y * y) * (-0.16666666666666666d0)))) * (1.0d0 / y)
end function

Java

public static double code(double x, double y) {
	return (y * (1.0 + ((y * y) * -0.16666666666666666))) * (1.0 / y);
}

Python

def code(x, y):
	return (y * (1.0 + ((y * y) * -0.16666666666666666))) * (1.0 / y)

Julia

function code(x, y)
	return Float64(Float64(y * Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666))) * Float64(1.0 / y))
end

MATLAB

function tmp = code(x, y)
	tmp = (y * (1.0 + ((y * y) * -0.16666666666666666))) * (1.0 / y);
end

Wolfram

code[x_, y_] := N[(N[(y * N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. *-commutative 99.5%

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

   2. associate-*l/ 99.5%

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

   3. associate-/l* 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\sin y \cdot \frac{\cosh x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 45.3%

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

6. Taylor expanded in y around 0 26.8%

   \[\leadsto \color{blue}{\left(y \cdot \left(1 + -0.16666666666666666 \cdot {y}^{2}\right)\right)} \cdot \frac{1}{y} \]
7. Step-by-step derivation

   1. *-commutative 26.8%

      \[\leadsto \frac{1}{\frac{y}{y \cdot \left(1 + \color{blue}{{y}^{2} \cdot -0.16666666666666666}\right)}} \]

8. Simplified 26.8%

   \[\leadsto \color{blue}{\left(y \cdot \left(1 + {y}^{2} \cdot -0.16666666666666666\right)\right)} \cdot \frac{1}{y} \]
9. Step-by-step derivation

   1. unpow2 26.8%

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

10. Applied egg-rr 26.8%

    \[\leadsto \left(y \cdot \left(1 + \color{blue}{\left(y \cdot y\right)} \cdot -0.16666666666666666\right)\right) \cdot \frac{1}{y} \]
11. Add Preprocessing

Alternative 6: 29.8% accurate, 20.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot -0.16666666666666666\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 4.8e+160) 1.0 (* (* y y) -0.16666666666666666)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.8e+160) {
		tmp = 1.0;
	} else {
		tmp = (y * y) * -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 <= 4.8d+160) then
        tmp = 1.0d0
    else
        tmp = (y * y) * (-0.16666666666666666d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4.8e+160) {
		tmp = 1.0;
	} else {
		tmp = (y * y) * -0.16666666666666666;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.8e+160:
		tmp = 1.0
	else:
		tmp = (y * y) * -0.16666666666666666
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.8e+160)
		tmp = 1.0;
	else
		tmp = Float64(Float64(y * y) * -0.16666666666666666);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4.8e+160)
		tmp = 1.0;
	else
		tmp = (y * y) * -0.16666666666666666;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.8e+160], 1.0, N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.8000000000000003e160

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 99.5%

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

      3. associate-/l* 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\sin y \cdot \frac{\cosh x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 46.0%

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

   6. Taylor expanded in y around 0 22.4%

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

   if 4.8000000000000003e160 < y

   1. Initial program 99.9%

      \[\cosh x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 40.4%

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

   4. Taylor expanded in y around 0 21.9%

      \[\leadsto \frac{\color{blue}{y \cdot \left(1 + -0.16666666666666666 \cdot {y}^{2}\right)}}{y} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 21.9%

         \[\leadsto \frac{\color{blue}{1 \cdot y + \left(-0.16666666666666666 \cdot {y}^{2}\right) \cdot y}}{y} \]

      2. *-lft-identity 21.9%

         \[\leadsto \frac{\color{blue}{y} + \left(-0.16666666666666666 \cdot {y}^{2}\right) \cdot y}{y} \]

      3. associate-*l* 21.9%

         \[\leadsto \frac{y + \color{blue}{-0.16666666666666666 \cdot \left({y}^{2} \cdot y\right)}}{y} \]

      4. unpow2 21.9%

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

      5. unpow3 21.9%

         \[\leadsto \frac{y + -0.16666666666666666 \cdot \color{blue}{{y}^{3}}}{y} \]

   6. Simplified 21.9%

      \[\leadsto \frac{\color{blue}{y + -0.16666666666666666 \cdot {y}^{3}}}{y} \]

   7. Taylor expanded in y around inf 21.9%

      \[\leadsto \color{blue}{-0.16666666666666666 \cdot {y}^{2}} \]
   8. Step-by-step derivation

      1. unpow2 21.9%

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

   9. Applied egg-rr 21.9%

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

4. Final simplification 22.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot -0.16666666666666666\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 27.0% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 99.5%

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

   1. *-commutative 99.5%

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

   2. associate-*l/ 99.5%

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

   3. associate-/l* 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\sin y \cdot \frac{\cosh x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 45.3%

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

6. Taylor expanded in y around 0 19.8%

   \[\leadsto \color{blue}{1} \]
7. Add Preprocessing

Developer Target 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024185 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (* (cosh x) (sin y)) y))

  (* (cosh x) (/ (sin y) y)))