Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 89.0% → 99.8%

Time: 8.4s

Alternatives: 9

Speedup: 1.0×

• 50.0% 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: 89.0% 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 88.7%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 2e-7) (/ y (/ x (sin x))) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 2e-7) {
		tmp = y / (x / sin(x));
	} else {
		tmp = 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) <= 2d-7) then
        tmp = y / (x / sin(x))
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 2e-7) {
		tmp = y / (x / Math.sin(x));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 2e-7:
		tmp = y / (x / math.sin(x))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 2e-7)
		tmp = Float64(y / Float64(x / sin(x)));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 2e-7)
		tmp = y / (x / sin(x));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-7], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 1.9999999999999999e-7

   1. Initial program 84.3%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 47.9%

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

      1. associate-/l* 63.5%

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

   7. Simplified 63.5%

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

      1. clear-num 63.5%

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

      2. un-div-inv 63.6%

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

   9. Applied egg-rr 63.6%

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

   if 1.9999999999999999e-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. Taylor expanded in x around 0 80.3%

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

      1. associate-*r/ 80.3%

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

      2. clear-num 80.3%

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

      3. *-commutative 80.3%

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

   7. Applied egg-rr 80.3%

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

      1. associate-/r/ 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-*r* 80.3%

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

      4. unpow-1 80.3%

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

      5. pow-plus 80.3%

         \[\leadsto \color{blue}{{x}^{\left(-1 + 1\right)}} \cdot \sinh y \]

      6. metadata-eval 80.3%

         \[\leadsto {x}^{\color{blue}{0}} \cdot \sinh y \]

      7. metadata-eval 80.3%

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

      8. *-commutative 80.3%

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

      9. *-rgt-identity 80.3%

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

   9. Simplified 80.3%

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

Alternative 3: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 2 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 2e-7) (* y (/ (sin x) x)) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 2e-7) {
		tmp = y * (sin(x) / x);
	} else {
		tmp = 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) <= 2d-7) then
        tmp = y * (sin(x) / x)
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 2e-7) {
		tmp = y * (Math.sin(x) / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 2e-7:
		tmp = y * (math.sin(x) / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 2e-7)
		tmp = Float64(y * Float64(sin(x) / x));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 2e-7)
		tmp = y * (sin(x) / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-7], N[(y * N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 1.9999999999999999e-7

   1. Initial program 84.3%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 47.9%

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

      1. associate-/l* 63.5%

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

   7. Simplified 63.5%

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

   if 1.9999999999999999e-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. Taylor expanded in x around 0 80.3%

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

      1. associate-*r/ 80.3%

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

      2. clear-num 80.3%

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

      3. *-commutative 80.3%

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

   7. Applied egg-rr 80.3%

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

      1. associate-/r/ 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-*r* 80.3%

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

      4. unpow-1 80.3%

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

      5. pow-plus 80.3%

         \[\leadsto \color{blue}{{x}^{\left(-1 + 1\right)}} \cdot \sinh y \]

      6. metadata-eval 80.3%

         \[\leadsto {x}^{\color{blue}{0}} \cdot \sinh y \]

      7. metadata-eval 80.3%

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

      8. *-commutative 80.3%

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

      9. *-rgt-identity 80.3%

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

   9. Simplified 80.3%

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

Alternative 4: 62.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 2e-7) (/ x (/ x y)) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 2e-7) {
		tmp = x / (x / y);
	} else {
		tmp = 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) <= 2d-7) then
        tmp = x / (x / y)
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 2e-7) {
		tmp = x / (x / y);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 2e-7:
		tmp = x / (x / y)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 2e-7)
		tmp = Float64(x / Float64(x / y));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 2e-7)
		tmp = x / (x / y);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-7], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 1.9999999999999999e-7

   1. Initial program 84.3%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 x around 0 76.0%

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

   6. Taylor expanded in y around 0 57.5%

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

      1. clear-num 57.9%

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

      2. un-div-inv 57.1%

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

   8. Applied egg-rr 57.1%

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

   if 1.9999999999999999e-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. Taylor expanded in x around 0 80.3%

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

      1. associate-*r/ 80.3%

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

      2. clear-num 80.3%

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

      3. *-commutative 80.3%

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

   7. Applied egg-rr 80.3%

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

      1. associate-/r/ 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-*r* 80.3%

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

      4. unpow-1 80.3%

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

      5. pow-plus 80.3%

         \[\leadsto \color{blue}{{x}^{\left(-1 + 1\right)}} \cdot \sinh y \]

      6. metadata-eval 80.3%

         \[\leadsto {x}^{\color{blue}{0}} \cdot \sinh y \]

      7. metadata-eval 80.3%

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

      8. *-commutative 80.3%

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

      9. *-rgt-identity 80.3%

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

   9. Simplified 80.3%

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

Alternative 5: 74.3% 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 88.7%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 77.2%

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

Alternative 6: 50.1% accurate, 17.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.4 \cdot 10^{+272}:\\ \;\;\;\;x \cdot \frac{1}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot -0.16666666666666666\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.4e+272)
   (* x (/ 1.0 (/ x y)))
   (* (* x x) (* y -0.16666666666666666))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.4e+272) {
		tmp = x * (1.0 / (x / y));
	} 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 <= 4.4d+272) then
        tmp = x * (1.0d0 / (x / y))
    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 <= 4.4e+272) {
		tmp = x * (1.0 / (x / y));
	} else {
		tmp = (x * x) * (y * -0.16666666666666666);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.4e+272:
		tmp = x * (1.0 / (x / y))
	else:
		tmp = (x * x) * (y * -0.16666666666666666)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.4e+272)
		tmp = Float64(x * Float64(1.0 / Float64(x / y)));
	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 <= 4.4e+272)
		tmp = x * (1.0 / (x / y));
	else
		tmp = (x * x) * (y * -0.16666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.4e+272], N[(x * N[(1.0 / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.40000000000000017e272

   1. Initial program 88.2%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 59.7%

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

      1. clear-num 59.2%

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

      2. associate-/r/ 59.6%

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

   7. Applied egg-rr 59.6%

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

   8. Taylor expanded in x around 0 49.0%

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

      1. associate-/r/ 49.3%

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

   10. Applied egg-rr 49.3%

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

   if 4.40000000000000017e272 < x

   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 y around 0 12.0%

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

   6. Taylor expanded in x around 0 50.0%

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

      1. distribute-rgt-in 50.0%

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

      2. *-lft-identity 50.0%

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

      3. associate-*l* 50.0%

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

      4. unpow2 50.0%

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

      5. unpow3 50.0%

         \[\leadsto \left(x + -0.16666666666666666 \cdot \color{blue}{{x}^{3}}\right) \cdot \frac{y}{x} \]

   8. Simplified 50.0%

      \[\leadsto \color{blue}{\left(x + -0.16666666666666666 \cdot {x}^{3}\right)} \cdot \frac{y}{x} \]

   9. Taylor expanded in x around inf 50.2%

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

       1. *-commutative 50.2%

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

       2. associate-*r* 50.2%

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

   11. Simplified 50.2%

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

       1. unpow2 50.2%

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

   13. Applied egg-rr 50.2%

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

Alternative 7: 50.6% accurate, 29.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.7%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 57.8%

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

   1. clear-num 57.4%

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

   2. associate-/r/ 57.7%

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

7. Applied egg-rr 57.7%

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

8. Taylor expanded in x around 0 47.5%

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

   1. associate-/r/ 47.9%

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

10. Applied egg-rr 47.9%

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

Alternative 8: 50.1% 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 88.7%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 77.2%

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

6. Taylor expanded in y around 0 47.6%

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

Alternative 9: 27.6% 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 88.7%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 77.2%

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

6. Taylor expanded in y around 0 27.1%

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

Developer Target 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]

Reproduce

herbie shell --seed 2024144 
(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))