Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.8% → 99.9%

Time: 8.9s

Alternatives: 7

Speedup: 1.0×

• Could not converge on a ground truth

  1. x = 4.722513744676484e+122
  2. y = 1.7095488164415817e+157

• 48.9% 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

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

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 89.5%

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

   1. associate-/l* 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 0.5:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\sinh y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 0.5) (* y (/ (sin x) x)) (* x (/ (sinh y) x))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 0.5) {
		tmp = y * (sin(x) / x);
	} else {
		tmp = x * (sinh(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 (sinh(y) <= 0.5d0) then
        tmp = y * (sin(x) / x)
    else
        tmp = x * (sinh(y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 0.5) {
		tmp = y * (Math.sin(x) / x);
	} else {
		tmp = x * (Math.sinh(y) / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 0.5:
		tmp = y * (math.sin(x) / x)
	else:
		tmp = x * (math.sinh(y) / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 0.5)
		tmp = Float64(y * Float64(sin(x) / x));
	else
		tmp = Float64(x * Float64(sinh(y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 0.5)
		tmp = y * (sin(x) / x);
	else
		tmp = x * (sinh(y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 0.5], N[(y * N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Sinh[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 0.5

   1. Initial program 86.3%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 49.7%

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

      1. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   if 0.5 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 65.6%

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

Alternative 3: 73.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

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

   1. associate-/l* 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. Add Preprocessing

5. Taylor expanded in x around 0 72.0%

   \[\leadsto \color{blue}{x} \cdot \frac{\sinh y}{x} \]
6. Add Preprocessing

Alternative 4: 50.3% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.118:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x \cdot \left(y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 0.118)
   (/ x (/ x y))
   (if (<= y 3.2e+220)
     (/ (* x (+ y (* -0.16666666666666666 (* y (* x x))))) x)
     (* x (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 0.118) {
		tmp = x / (x / y);
	} else if (y <= 3.2e+220) {
		tmp = (x * (y + (-0.16666666666666666 * (y * (x * x))))) / 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 <= 0.118d0) then
        tmp = x / (x / y)
    else if (y <= 3.2d+220) then
        tmp = (x * (y + ((-0.16666666666666666d0) * (y * (x * x))))) / 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 <= 0.118) {
		tmp = x / (x / y);
	} else if (y <= 3.2e+220) {
		tmp = (x * (y + (-0.16666666666666666 * (y * (x * x))))) / x;
	} else {
		tmp = x * (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 0.118:
		tmp = x / (x / y)
	elif y <= 3.2e+220:
		tmp = (x * (y + (-0.16666666666666666 * (y * (x * x))))) / x
	else:
		tmp = x * (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 0.118)
		tmp = Float64(x / Float64(x / y));
	elseif (y <= 3.2e+220)
		tmp = Float64(Float64(x * Float64(y + Float64(-0.16666666666666666 * Float64(y * Float64(x * x))))) / x);
	else
		tmp = Float64(x * Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 0.118)
		tmp = x / (x / y);
	elseif (y <= 3.2e+220)
		tmp = (x * (y + (-0.16666666666666666 * (y * (x * x))))) / x;
	else
		tmp = x * (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 0.118], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+220], N[(N[(x * N[(y + N[(-0.16666666666666666 * N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 0.11799999999999999

   1. Initial program 86.2%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in x around 0 74.4%

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

   6. Taylor expanded in y around 0 56.1%

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

      1. clear-num 56.1%

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

      2. un-div-inv 55.2%

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

   8. Applied egg-rr 55.2%

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

   if 0.11799999999999999 < y < 3.19999999999999989e220

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 4.0%

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

   4. Taylor expanded in x around 0 36.1%

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

      1. unpow2 36.1%

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

   6. Applied egg-rr 36.1%

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

   if 3.19999999999999989e220 < y

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 77.8%

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

   6. Taylor expanded in y around 0 67.6%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.118:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x \cdot \left(y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.8% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.2 \lor \neg \left(x \leq 3.4 \cdot 10^{+211}\right):\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot -0.16666666666666666\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x 3.2) (not (<= x 3.4e+211)))
   (* x (/ y x))
   (* (* x x) (* y -0.16666666666666666))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= 3.2) || !(x <= 3.4e+211)) {
		tmp = x * (y / x);
	} else {
		tmp = (x * x) * (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 ((x <= 3.2d0) .or. (.not. (x <= 3.4d+211))) then
        tmp = x * (y / x)
    else
        tmp = (x * x) * (y * (-0.16666666666666666d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= 3.2) || !(x <= 3.4e+211)) {
		tmp = x * (y / x);
	} else {
		tmp = (x * x) * (y * -0.16666666666666666);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= 3.2) or not (x <= 3.4e+211):
		tmp = x * (y / x)
	else:
		tmp = (x * x) * (y * -0.16666666666666666)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= 3.2) || !(x <= 3.4e+211))
		tmp = Float64(x * Float64(y / x));
	else
		tmp = Float64(Float64(x * x) * Float64(y * -0.16666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= 3.2) || ~((x <= 3.4e+211)))
		tmp = x * (y / x);
	else
		tmp = (x * x) * (y * -0.16666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, 3.2], N[Not[LessEqual[x, 3.4e+211]], $MachinePrecision]], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.2000000000000002 or 3.3999999999999999e211 < x

   1. Initial program 87.6%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in x around 0 81.3%

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

   6. Taylor expanded in y around 0 56.1%

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

   if 3.2000000000000002 < x < 3.3999999999999999e211

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 45.0%

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

   4. Taylor expanded in x around 0 34.4%

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

   5. Taylor expanded in x around inf 27.5%

      \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left({x}^{2} \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 27.5%

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

      2. *-commutative 27.5%

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

      3. *-commutative 27.5%

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

      4. associate-*r* 27.5%

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

   7. Simplified 27.5%

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

      1. unpow2 34.4%

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

   9. Applied egg-rr 27.5%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.2 \lor \neg \left(x \leq 3.4 \cdot 10^{+211}\right):\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot -0.16666666666666666\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.8% 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 89.5%

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

   1. associate-/l* 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. Add Preprocessing

5. Taylor expanded in x around 0 72.0%

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

6. Taylor expanded in y around 0 48.9%

   \[\leadsto x \cdot \color{blue}{\frac{y}{x}} \]
7. Add Preprocessing

Alternative 7: 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 89.5%

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

   1. associate-/l* 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. Add Preprocessing

5. Taylor expanded in y around 0 59.9%

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

   1. clear-num 59.5%

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

   2. associate-/r/ 59.7%

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

7. Applied egg-rr 59.7%

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

8. Taylor expanded in x around 0 25.9%

   \[\leadsto \color{blue}{y} \]
9. Add Preprocessing

Developer Target 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]

Reproduce

herbie shell --seed 2024170 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

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

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