Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 89.4% → 99.8%

Time: 6.9s

Alternatives: 7

Speedup: 1.0×

• 50.7% 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: 89.4% 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: 99.8% 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 87.2%

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

   1. associate-/l* 99.5%

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

3. Simplified 99.5%

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

Alternative 2: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.001:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\log \left(e^{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 0.001) (/ y (/ x (sin x))) (log (exp y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 0.001) {
		tmp = y / (x / sin(x));
	} else {
		tmp = log(exp(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 <= 0.001d0) then
        tmp = y / (x / sin(x))
    else
        tmp = log(exp(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 0.001) {
		tmp = y / (x / Math.sin(x));
	} else {
		tmp = Math.log(Math.exp(y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 0.001:
		tmp = y / (x / math.sin(x))
	else:
		tmp = math.log(math.exp(y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 0.001)
		tmp = Float64(y / Float64(x / sin(x)));
	else
		tmp = log(exp(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 0.001)
		tmp = y / (x / sin(x));
	else
		tmp = log(exp(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 0.001], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Log[N[Exp[y], $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1e-3

   1. Initial program 82.2%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 y around 0 54.9%

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

      1. associate-/l* 72.6%

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

   7. Simplified 72.6%

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

      1. clear-num 72.7%

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

      2. un-div-inv 72.7%

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

   9. Applied egg-rr 72.7%

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

   if 1e-3 < y

   1. Initial program 100.0%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 4.8%

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

      1. associate-/l* 4.8%

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

   7. Simplified 4.8%

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

      1. associate-*r/ 4.8%

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

      2. *-commutative 4.8%

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

      3. clear-num 4.8%

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

      4. *-commutative 4.8%

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

      5. associate-/r* 26.7%

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

   9. Applied egg-rr 26.7%

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

   10. Taylor expanded in x around 0 4.4%

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

       1. remove-double-div 4.4%

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

       2. add-log-exp 68.6%

          \[\leadsto \color{blue}{\log \left(e^{y}\right)} \]

   12. Applied egg-rr 68.6%

       \[\leadsto \color{blue}{\log \left(e^{y}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 56.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{\frac{1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 3.4e+79) (* y (/ (sin x) x)) (/ (/ y x) (/ 1.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.4e+79) {
		tmp = y * (sin(x) / x);
	} else {
		tmp = (y / x) / (1.0 / 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 <= 3.4d+79) then
        tmp = y * (sin(x) / x)
    else
        tmp = (y / x) / (1.0d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 3.4e+79) {
		tmp = y * (Math.sin(x) / x);
	} else {
		tmp = (y / x) / (1.0 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.4e+79:
		tmp = y * (math.sin(x) / x)
	else:
		tmp = (y / x) / (1.0 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.4e+79)
		tmp = Float64(y * Float64(sin(x) / x));
	else
		tmp = Float64(Float64(y / x) / Float64(1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3.4e+79)
		tmp = y * (sin(x) / x);
	else
		tmp = (y / x) / (1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.4e+79], N[(y * N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.40000000000000032e79

   1. Initial program 84.0%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
   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* 65.6%

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

   7. Simplified 65.6%

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

   if 3.40000000000000032e79 < 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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. associate-/r/ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 35.9%

      \[\leadsto \sin x \cdot \left(\frac{1}{x} \cdot \color{blue}{y}\right) \]
   8. Step-by-step derivation

      1. *-commutative 35.9%

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

      2. associate-*l/ 35.9%

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

      3. *-un-lft-identity 35.9%

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

      4. associate-/r/ 4.9%

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

      5. div-inv 4.9%

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

      6. associate-/r* 35.9%

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

   9. Applied egg-rr 35.9%

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

   10. Taylor expanded in x around 0 35.8%

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

Alternative 4: 62.7% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

   1. associate-/l* 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in y around 0 64.5%

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

Alternative 5: 30.2% accurate, 20.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 5e-17) y (/ (* x y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 5e-17) {
		tmp = y;
	} 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 <= 5d-17) then
        tmp = y
    else
        tmp = (x * y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 5e-17) {
		tmp = y;
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 5e-17:
		tmp = y
	else:
		tmp = (x * y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 5e-17)
		tmp = y;
	else
		tmp = Float64(Float64(x * y) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 5e-17)
		tmp = y;
	else
		tmp = (x * y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 5e-17], y, N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.9999999999999999e-17

   1. Initial program 82.1%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 54.7%

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

      1. associate-/l* 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in x around 0 39.1%

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

   if 4.9999999999999999e-17 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 6.0%

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

   4. Taylor expanded in x around 0 16.0%

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

      1. *-commutative 16.0%

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

   6. Simplified 16.0%

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

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.5% accurate, 29.3× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{y}{x}}{\frac{1}{x}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (/ y x) (/ 1.0 x)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (y / x) / (1.0 / x)

Julia

function code(x, y)
	return Float64(Float64(y / x) / Float64(1.0 / x))
end

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(y / x), $MachinePrecision] / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.2%

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

   1. associate-/l* 99.5%

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

3. Simplified 99.5%

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

   1. clear-num 99.2%

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

   2. associate-/r/ 99.5%

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

6. Applied egg-rr 99.5%

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

7. Taylor expanded in y around 0 64.4%

   \[\leadsto \sin x \cdot \left(\frac{1}{x} \cdot \color{blue}{y}\right) \]
8. Step-by-step derivation

   1. *-commutative 64.4%

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

   2. associate-*l/ 64.5%

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

   3. *-un-lft-identity 64.5%

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

   4. associate-/r/ 53.6%

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

   5. div-inv 53.5%

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

   6. associate-/r* 64.3%

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

9. Applied egg-rr 64.3%

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

10. Taylor expanded in x around 0 51.6%

    \[\leadsto \frac{\frac{y}{x}}{\color{blue}{\frac{1}{x}}} \]
11. Add Preprocessing

Alternative 7: 27.3% 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 87.2%

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

   1. associate-/l* 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in y around 0 40.8%

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

   1. associate-/l* 53.5%

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

7. Simplified 53.5%

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

8. Taylor expanded in x around 0 29.5%

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

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 2024096 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

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

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