Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.9% → 99.9%

Time: 8.1s

Alternatives: 7

Speedup: 1.0×

• 49.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{\sinh y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 1e-6) (/ y (/ x (sin x))) (/ 1.0 (/ 1.0 (sinh y)))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 1e-6) {
		tmp = y / (x / sin(x));
	} else {
		tmp = 1.0 / (1.0 / sinh(y));
	}
	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) <= 1d-6) then
        tmp = y / (x / sin(x))
    else
        tmp = 1.0d0 / (1.0d0 / sinh(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 1e-6) {
		tmp = y / (x / Math.sin(x));
	} else {
		tmp = 1.0 / (1.0 / Math.sinh(y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 1e-6:
		tmp = y / (x / math.sin(x))
	else:
		tmp = 1.0 / (1.0 / math.sinh(y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 1e-6)
		tmp = Float64(y / Float64(x / sin(x)));
	else
		tmp = Float64(1.0 / Float64(1.0 / sinh(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 1e-6)
		tmp = y / (x / sin(x));
	else
		tmp = 1.0 / (1.0 / sinh(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 1e-6], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(1.0 / N[Sinh[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 9.99999999999999955e-7

   1. Initial program 86.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 52.8%

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

      1. associate-/l* 66.7%

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

   7. Simplified 66.7%

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

      1. clear-num 66.7%

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

      2. un-div-inv 66.7%

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

   9. Applied egg-rr 66.7%

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

   if 9.99999999999999955e-7 < (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. Step-by-step derivation

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/r* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 75.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{2}{e^{y} - \frac{1}{e^{y}}}}} \]
   8. Step-by-step derivation

      1. metadata-eval 75.5%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot 2}}{e^{y} - \frac{1}{e^{y}}}} \]

      2. associate-*l/ 75.5%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{e^{y} - \frac{1}{e^{y}}} \cdot 2}} \]

      3. associate-/r/ 75.5%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{e^{y} - \frac{1}{e^{y}}}{2}}}} \]

      4. rec-exp 75.5%

         \[\leadsto \frac{1}{\frac{1}{\frac{e^{y} - \color{blue}{e^{-y}}}{2}}} \]

      5. sinh-def 75.5%

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

   9. Simplified 75.5%

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

Alternative 3: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 10^{-6}:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{\sinh y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 1e-6) (* y (/ (sin x) x)) (/ 1.0 (/ 1.0 (sinh y)))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 1e-6) {
		tmp = y * (sin(x) / x);
	} else {
		tmp = 1.0 / (1.0 / sinh(y));
	}
	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) <= 1d-6) then
        tmp = y * (sin(x) / x)
    else
        tmp = 1.0d0 / (1.0d0 / sinh(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 1e-6) {
		tmp = y * (Math.sin(x) / x);
	} else {
		tmp = 1.0 / (1.0 / Math.sinh(y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 1e-6:
		tmp = y * (math.sin(x) / x)
	else:
		tmp = 1.0 / (1.0 / math.sinh(y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 1e-6)
		tmp = Float64(y * Float64(sin(x) / x));
	else
		tmp = Float64(1.0 / Float64(1.0 / sinh(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 1e-6)
		tmp = y * (sin(x) / x);
	else
		tmp = 1.0 / (1.0 / sinh(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 1e-6], N[(y * N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(1.0 / N[Sinh[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 9.99999999999999955e-7

   1. Initial program 86.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 52.8%

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

      1. associate-/l* 66.7%

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

   7. Simplified 66.7%

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

   if 9.99999999999999955e-7 < (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. Step-by-step derivation

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/r* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 75.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{2}{e^{y} - \frac{1}{e^{y}}}}} \]
   8. Step-by-step derivation

      1. metadata-eval 75.5%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot 2}}{e^{y} - \frac{1}{e^{y}}}} \]

      2. associate-*l/ 75.5%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{e^{y} - \frac{1}{e^{y}}} \cdot 2}} \]

      3. associate-/r/ 75.5%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{e^{y} - \frac{1}{e^{y}}}{2}}}} \]

      4. rec-exp 75.5%

         \[\leadsto \frac{1}{\frac{1}{\frac{e^{y} - \color{blue}{e^{-y}}}{2}}} \]

      5. sinh-def 75.5%

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

   9. Simplified 75.5%

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

Alternative 4: 57.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.8 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 7.8e-5) (* x (/ y x)) (* y (/ (sin x) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 7.8e-5) {
		tmp = x * (y / x);
	} else {
		tmp = y * (sin(x) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 7.8d-5) then
        tmp = x * (y / x)
    else
        tmp = y * (sin(x) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 7.8e-5) {
		tmp = x * (y / x);
	} else {
		tmp = y * (Math.sin(x) / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 7.8e-5:
		tmp = x * (y / x)
	else:
		tmp = y * (math.sin(x) / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 7.8e-5)
		tmp = Float64(x * Float64(y / x));
	else
		tmp = Float64(y * Float64(sin(x) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 7.8e-5)
		tmp = x * (y / x);
	else
		tmp = y * (sin(x) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 7.8e-5], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.7999999999999999e-5

   1. Initial program 85.6%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 y around 0 37.2%

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

      1. associate-/l* 51.6%

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

   7. Simplified 51.6%

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

      1. associate-*r/ 37.2%

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

      2. *-commutative 37.2%

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

      3. clear-num 36.9%

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

   9. Applied egg-rr 36.9%

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

   10. Taylor expanded in x around 0 24.6%

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

       1. *-commutative 24.6%

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

   12. Simplified 24.6%

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

       1. associate-/r* 62.6%

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

       2. associate-/r/ 64.9%

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

       3. clear-num 64.3%

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

   14. Applied egg-rr 64.3%

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

   if 7.7999999999999999e-5 < x

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 61.0%

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

      1. associate-/l* 60.9%

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

   7. Simplified 60.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.8 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.0% 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 88.9%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 68.0%

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

Alternative 6: 51.0% 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 88.9%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 42.8%

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

   1. associate-/l* 53.8%

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

7. Simplified 53.8%

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

   1. associate-*r/ 42.8%

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

   2. *-commutative 42.8%

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

   3. clear-num 41.9%

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

9. Applied egg-rr 41.9%

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

10. Taylor expanded in x around 0 20.9%

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

    1. *-commutative 20.9%

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

12. Simplified 20.9%

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

    1. associate-/r* 54.1%

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

    2. associate-/r/ 55.8%

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

    3. clear-num 54.6%

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

14. Applied egg-rr 54.6%

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

15. Final simplification 54.6%

    \[\leadsto x \cdot \frac{y}{x} \]
16. Add Preprocessing

Alternative 7: 28.3% 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 88.9%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 42.8%

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

   1. associate-/l* 53.8%

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

7. Simplified 53.8%

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

8. Taylor expanded in x around 0 28.9%

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

Developer target: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024088 
(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))