Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.9% → 99.9%

Time: 2.4s

Alternatives: 10

Speedup: 1.0×

• 49.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (* (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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((sin(x)) * (((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y)))))) / x
END code

Initial Program: 88.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (* (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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((sin(x)) * (((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y)))))) / x
END code

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y))))) * ((sin(x)) / x)
END code

Derivation

1. Initial program 88.9%

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

3. Applied rewrites 99.9%

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

Alternative 2: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \sinh \left(\left|y\right|\right)\\ t_1 := \frac{\sin x \cdot t\_0}{x}\\ \mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_0 \cdot \mathsf{fma}\left(x \cdot x, -0.16666666666666666, 1\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-46}:\\ \;\;\;\;\sin x \cdot \frac{\left|y\right|}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (sinh (fabs y))) (t_1 (/ (* (sin x) t_0) x)))
  (*
   (copysign 1.0 y)
   (if (<= t_1 (- INFINITY))
     (* t_0 (fma (* x x) -0.16666666666666666 1.0))
     (if (<= t_1 4e-46) (* (sin x) (/ (fabs y) x)) t_0)))))

C

double code(double x, double y) {
	double t_0 = sinh(fabs(y));
	double t_1 = (sin(x) * t_0) / x;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_0 * fma((x * x), -0.16666666666666666, 1.0);
	} else if (t_1 <= 4e-46) {
		tmp = sin(x) * (fabs(y) / x);
	} else {
		tmp = t_0;
	}
	return copysign(1.0, y) * tmp;
}

Julia

function code(x, y)
	t_0 = sinh(abs(y))
	t_1 = Float64(Float64(sin(x) * t_0) / x)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t_0 * fma(Float64(x * x), -0.16666666666666666, 1.0));
	elseif (t_1 <= 4e-46)
		tmp = Float64(sin(x) * Float64(abs(y) / x));
	else
		tmp = t_0;
	end
	return Float64(copysign(1.0, y) * tmp)
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[Sinh[N[Abs[y], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[Sin[x], $MachinePrecision] * t$95$0), $MachinePrecision] / x), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, (-Infinity)], N[(t$95$0 * N[(N[(x * x), $MachinePrecision] * -0.16666666666666666 + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-46], N[(N[Sin[x], $MachinePrecision] * N[(N[Abs[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$0]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x) < -inf.0

   1. Initial program 88.9%

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

   3. Applied rewrites 99.9%

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \sinh y \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 62.9%

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

   10. Applied rewrites 62.9%

       \[\leadsto \sinh y \cdot \mathsf{fma}\left(x \cdot x, -0.16666666666666666, 1\right) \]

   if -inf.0 < (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x) < 4.0000000000000001e-46

   1. Initial program 88.9%

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 62.9%

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

   if 4.0000000000000001e-46 < (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x)

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 64.8%

      \[\leadsto \sinh y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 75.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := e^{\left|y\right|}\\ t_1 := \sinh \left(\left|y\right|\right)\\ \mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 6.575218410636739 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\left|x\right| \leq 2.9174093151562287 \cdot 10^{+89}:\\ \;\;\;\;t\_1 \cdot \mathsf{fma}\left(\left|x\right| \cdot \left|x\right|, -0.16666666666666666, 1\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(t\_0 - \frac{1}{t\_0}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (exp (fabs y))) (t_1 (sinh (fabs y))))
  (*
   (copysign 1.0 y)
   (if (<= (fabs x) 6.575218410636739e+75)
     t_1
     (if (<= (fabs x) 2.9174093151562287e+89)
       (* t_1 (fma (* (fabs x) (fabs x)) -0.16666666666666666 1.0))
       (* 0.5 (- t_0 (/ 1.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = exp(fabs(y));
	double t_1 = sinh(fabs(y));
	double tmp;
	if (fabs(x) <= 6.575218410636739e+75) {
		tmp = t_1;
	} else if (fabs(x) <= 2.9174093151562287e+89) {
		tmp = t_1 * fma((fabs(x) * fabs(x)), -0.16666666666666666, 1.0);
	} else {
		tmp = 0.5 * (t_0 - (1.0 / t_0));
	}
	return copysign(1.0, y) * tmp;
}

Julia

function code(x, y)
	t_0 = exp(abs(y))
	t_1 = sinh(abs(y))
	tmp = 0.0
	if (abs(x) <= 6.575218410636739e+75)
		tmp = t_1;
	elseif (abs(x) <= 2.9174093151562287e+89)
		tmp = Float64(t_1 * fma(Float64(abs(x) * abs(x)), -0.16666666666666666, 1.0));
	else
		tmp = Float64(0.5 * Float64(t_0 - Float64(1.0 / t_0)));
	end
	return Float64(copysign(1.0, y) * tmp)
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[Exp[N[Abs[y], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sinh[N[Abs[y], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[x], $MachinePrecision], 6.575218410636739e+75], t$95$1, If[LessEqual[N[Abs[x], $MachinePrecision], 2.9174093151562287e+89], N[(t$95$1 * N[(N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * -0.16666666666666666 + 1.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(t$95$0 - N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 6.5752184106367389e75

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 64.8%

      \[\leadsto \sinh y \]

   if 6.5752184106367389e75 < x < 2.9174093151562287e89

   1. Initial program 88.9%

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

   3. Applied rewrites 99.9%

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \sinh y \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 62.9%

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

   10. Applied rewrites 62.9%

       \[\leadsto \sinh y \cdot \mathsf{fma}\left(x \cdot x, -0.16666666666666666, 1\right) \]

   if 2.9174093151562287e89 < x

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := \sinh \left(\left|y\right|\right)\\ \mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 6.575218410636739 \cdot 10^{+75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\left|x\right| \leq 2.9174093151562287 \cdot 10^{+89}:\\ \;\;\;\;t\_0 \cdot \mathsf{fma}\left(\left|x\right| \cdot \left|x\right|, -0.16666666666666666, 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(e^{\left|y\right|} - \left(1 - \left|y\right|\right)\right) \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (sinh (fabs y))))
  (*
   (copysign 1.0 y)
   (if (<= (fabs x) 6.575218410636739e+75)
     t_0
     (if (<= (fabs x) 2.9174093151562287e+89)
       (* t_0 (fma (* (fabs x) (fabs x)) -0.16666666666666666 1.0))
       (* (- (exp (fabs y)) (- 1.0 (fabs y))) 0.5))))))

C

double code(double x, double y) {
	double t_0 = sinh(fabs(y));
	double tmp;
	if (fabs(x) <= 6.575218410636739e+75) {
		tmp = t_0;
	} else if (fabs(x) <= 2.9174093151562287e+89) {
		tmp = t_0 * fma((fabs(x) * fabs(x)), -0.16666666666666666, 1.0);
	} else {
		tmp = (exp(fabs(y)) - (1.0 - fabs(y))) * 0.5;
	}
	return copysign(1.0, y) * tmp;
}

Julia

function code(x, y)
	t_0 = sinh(abs(y))
	tmp = 0.0
	if (abs(x) <= 6.575218410636739e+75)
		tmp = t_0;
	elseif (abs(x) <= 2.9174093151562287e+89)
		tmp = Float64(t_0 * fma(Float64(abs(x) * abs(x)), -0.16666666666666666, 1.0));
	else
		tmp = Float64(Float64(exp(abs(y)) - Float64(1.0 - abs(y))) * 0.5);
	end
	return Float64(copysign(1.0, y) * tmp)
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[Sinh[N[Abs[y], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[x], $MachinePrecision], 6.575218410636739e+75], t$95$0, If[LessEqual[N[Abs[x], $MachinePrecision], 2.9174093151562287e+89], N[(t$95$0 * N[(N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * -0.16666666666666666 + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[Exp[N[Abs[y], $MachinePrecision]], $MachinePrecision] - N[(1.0 - N[Abs[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if x < 6.5752184106367389e75

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 64.8%

      \[\leadsto \sinh y \]

   if 6.5752184106367389e75 < x < 2.9174093151562287e89

   1. Initial program 88.9%

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

   3. Applied rewrites 99.9%

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \sinh y \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 62.9%

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

   10. Applied rewrites 62.9%

       \[\leadsto \sinh y \cdot \mathsf{fma}\left(x \cdot x, -0.16666666666666666, 1\right) \]

   if 2.9174093151562287e89 < x

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \left(e^{y} - \left(1 + -1 \cdot y\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.5%

      \[\leadsto 0.5 \cdot \left(e^{y} - \left(1 + -1 \cdot y\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 35.5%

      \[\leadsto \left(e^{y} - \left(1 - y\right)\right) \cdot 0.5 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.9% accurate, 1.7× speedup

Math

\[\mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 1.3074546278004367 \cdot 10^{+39}:\\ \;\;\;\;\sinh \left(\left|y\right|\right)\\ \mathbf{else}:\\ \;\;\;\;\left(e^{\left|y\right|} - \left(1 - \left|y\right|\right)\right) \cdot 0.5\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (*
 (copysign 1.0 y)
 (if (<= (fabs x) 1.3074546278004367e+39)
   (sinh (fabs y))
   (* (- (exp (fabs y)) (- 1.0 (fabs y))) 0.5))))

C

double code(double x, double y) {
	double tmp;
	if (fabs(x) <= 1.3074546278004367e+39) {
		tmp = sinh(fabs(y));
	} else {
		tmp = (exp(fabs(y)) - (1.0 - fabs(y))) * 0.5;
	}
	return copysign(1.0, y) * tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.abs(x) <= 1.3074546278004367e+39) {
		tmp = Math.sinh(Math.abs(y));
	} else {
		tmp = (Math.exp(Math.abs(y)) - (1.0 - Math.abs(y))) * 0.5;
	}
	return Math.copySign(1.0, y) * tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.fabs(x) <= 1.3074546278004367e+39:
		tmp = math.sinh(math.fabs(y))
	else:
		tmp = (math.exp(math.fabs(y)) - (1.0 - math.fabs(y))) * 0.5
	return math.copysign(1.0, y) * tmp

Julia

function code(x, y)
	tmp = 0.0
	if (abs(x) <= 1.3074546278004367e+39)
		tmp = sinh(abs(y));
	else
		tmp = Float64(Float64(exp(abs(y)) - Float64(1.0 - abs(y))) * 0.5);
	end
	return Float64(copysign(1.0, y) * tmp)
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (abs(x) <= 1.3074546278004367e+39)
		tmp = sinh(abs(y));
	else
		tmp = (exp(abs(y)) - (1.0 - abs(y))) * 0.5;
	end
	tmp_2 = (sign(y) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[x], $MachinePrecision], 1.3074546278004367e+39], N[Sinh[N[Abs[y], $MachinePrecision]], $MachinePrecision], N[(N[(N[Exp[N[Abs[y], $MachinePrecision]], $MachinePrecision] - N[(1.0 - N[Abs[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.3074546278004367e39

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 64.8%

      \[\leadsto \sinh y \]

   if 1.3074546278004367e39 < x

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \left(e^{y} - \left(1 + -1 \cdot y\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.5%

      \[\leadsto 0.5 \cdot \left(e^{y} - \left(1 + -1 \cdot y\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 35.5%

      \[\leadsto \left(e^{y} - \left(1 - y\right)\right) \cdot 0.5 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 70.7% accurate, 1.7× speedup

Math

\[\mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 4.414482953417929 \cdot 10^{+77}:\\ \;\;\;\;\sinh \left(\left|y\right|\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(0.5, \left|y\right|, 1\right), \left|y\right|, 1\right) - \left(1 - \left|y\right|\right)\right) \cdot 0.5\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (*
 (copysign 1.0 y)
 (if (<= (fabs x) 4.414482953417929e+77)
   (sinh (fabs y))
   (*
    (- (fma (fma 0.5 (fabs y) 1.0) (fabs y) 1.0) (- 1.0 (fabs y)))
    0.5))))

C

double code(double x, double y) {
	double tmp;
	if (fabs(x) <= 4.414482953417929e+77) {
		tmp = sinh(fabs(y));
	} else {
		tmp = (fma(fma(0.5, fabs(y), 1.0), fabs(y), 1.0) - (1.0 - fabs(y))) * 0.5;
	}
	return copysign(1.0, y) * tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (abs(x) <= 4.414482953417929e+77)
		tmp = sinh(abs(y));
	else
		tmp = Float64(Float64(fma(fma(0.5, abs(y), 1.0), abs(y), 1.0) - Float64(1.0 - abs(y))) * 0.5);
	end
	return Float64(copysign(1.0, y) * tmp)
end

Wolfram

code[x_, y_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[x], $MachinePrecision], 4.414482953417929e+77], N[Sinh[N[Abs[y], $MachinePrecision]], $MachinePrecision], N[(N[(N[(N[(0.5 * N[Abs[y], $MachinePrecision] + 1.0), $MachinePrecision] * N[Abs[y], $MachinePrecision] + 1.0), $MachinePrecision] - N[(1.0 - N[Abs[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 4.414482953417929e77

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 64.8%

      \[\leadsto \sinh y \]

   if 4.414482953417929e77 < x

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \left(e^{y} - \left(1 + -1 \cdot y\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.5%

      \[\leadsto 0.5 \cdot \left(e^{y} - \left(1 + -1 \cdot y\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \left(\left(1 + y \cdot \left(1 + \frac{1}{2} \cdot y\right)\right) - \left(1 + -1 \cdot y\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 28.3%

       \[\leadsto 0.5 \cdot \left(\left(1 + y \cdot \left(1 + 0.5 \cdot y\right)\right) - \left(1 + -1 \cdot y\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 28.3%

       \[\leadsto \left(\mathsf{fma}\left(\mathsf{fma}\left(0.5, y, 1\right), y, 1\right) - \left(1 - y\right)\right) \cdot 0.5 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 66.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left|x\right| \leq 1.538824596465832 \cdot 10^{+138}:\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - -1\right) - \left(1 - y\right)\right) \cdot 0.5\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (fabs x) 1.538824596465832e+138)
  (sinh y)
  (* (- (- y -1.0) (- 1.0 y)) 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (fabs(x) <= 1.538824596465832e+138) {
		tmp = sinh(y);
	} else {
		tmp = ((y - -1.0) - (1.0 - y)) * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (abs(x) <= 1.538824596465832d+138) then
        tmp = sinh(y)
    else
        tmp = ((y - (-1.0d0)) - (1.0d0 - y)) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.abs(x) <= 1.538824596465832e+138) {
		tmp = Math.sinh(y);
	} else {
		tmp = ((y - -1.0) - (1.0 - y)) * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.fabs(x) <= 1.538824596465832e+138:
		tmp = math.sinh(y)
	else:
		tmp = ((y - -1.0) - (1.0 - y)) * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (abs(x) <= 1.538824596465832e+138)
		tmp = sinh(y);
	else
		tmp = Float64(Float64(Float64(y - -1.0) - Float64(1.0 - y)) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (abs(x) <= 1.538824596465832e+138)
		tmp = sinh(y);
	else
		tmp = ((y - -1.0) - (1.0 - y)) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Abs[x], $MachinePrecision], 1.538824596465832e+138], N[Sinh[y], $MachinePrecision], N[(N[(N[(y - -1.0), $MachinePrecision] - N[(1.0 - y), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF ((abs(x)) <= (1538824596465832064834429787659023318790986286200578955760090637805956879730743687518287917823051291161627589587803539258046338137333956608)) THEN (((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y))))) ELSE (((y - (-1)) - ((1) - y)) * (5e-1)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 1.5388245964658321e138

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 64.8%

      \[\leadsto \sinh y \]

   if 1.5388245964658321e138 < x

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \left(e^{y} - \left(1 + -1 \cdot y\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.5%

      \[\leadsto 0.5 \cdot \left(e^{y} - \left(1 + -1 \cdot y\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \left(\left(1 + y\right) - \left(1 + -1 \cdot y\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.6%

       \[\leadsto 0.5 \cdot \left(\left(1 + y\right) - \left(1 + -1 \cdot y\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 16.6%

       \[\leadsto \left(\left(y - -1\right) - \left(1 - y\right)\right) \cdot 0.5 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 39.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left|x\right| \leq 9.508742156060054 \cdot 10^{+42}:\\ \;\;\;\;\left(y + y\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - -1\right) - \left(1 - y\right)\right) \cdot 0.5\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (fabs x) 9.508742156060054e+42)
  (* (+ y y) 0.5)
  (* (- (- y -1.0) (- 1.0 y)) 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (fabs(x) <= 9.508742156060054e+42) {
		tmp = (y + y) * 0.5;
	} else {
		tmp = ((y - -1.0) - (1.0 - y)) * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (abs(x) <= 9.508742156060054d+42) then
        tmp = (y + y) * 0.5d0
    else
        tmp = ((y - (-1.0d0)) - (1.0d0 - y)) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.abs(x) <= 9.508742156060054e+42) {
		tmp = (y + y) * 0.5;
	} else {
		tmp = ((y - -1.0) - (1.0 - y)) * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.fabs(x) <= 9.508742156060054e+42:
		tmp = (y + y) * 0.5
	else:
		tmp = ((y - -1.0) - (1.0 - y)) * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (abs(x) <= 9.508742156060054e+42)
		tmp = Float64(Float64(y + y) * 0.5);
	else
		tmp = Float64(Float64(Float64(y - -1.0) - Float64(1.0 - y)) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (abs(x) <= 9.508742156060054e+42)
		tmp = (y + y) * 0.5;
	else
		tmp = ((y - -1.0) - (1.0 - y)) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Abs[x], $MachinePrecision], 9.508742156060054e+42], N[(N[(y + y), $MachinePrecision] * 0.5), $MachinePrecision], N[(N[(N[(y - -1.0), $MachinePrecision] - N[(1.0 - y), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF ((abs(x)) <= (9508742156060053731629728907426303123128320)) THEN ((y + y) * (5e-1)) ELSE (((y - (-1)) - ((1) - y)) * (5e-1)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 9.5087421560600537e42

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \left(2 \cdot y\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 28.3%

      \[\leadsto 0.5 \cdot \left(2 \cdot y\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 28.3%

      \[\leadsto \left(y + y\right) \cdot 0.5 \]

   if 9.5087421560600537e42 < x

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \left(e^{y} - \left(1 + -1 \cdot y\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 35.5%

      \[\leadsto 0.5 \cdot \left(e^{y} - \left(1 + -1 \cdot y\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \left(\left(1 + y\right) - \left(1 + -1 \cdot y\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 16.6%

       \[\leadsto 0.5 \cdot \left(\left(1 + y\right) - \left(1 + -1 \cdot y\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 16.6%

       \[\leadsto \left(\left(y - -1\right) - \left(1 - y\right)\right) \cdot 0.5 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 34.6% accurate, 0.8× speedup

Math

\[\mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;\frac{\sin x \cdot \sinh \left(\left|y\right|\right)}{x} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\left(\left|y\right| + \left|y\right|\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left|y\right|}{x}\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (*
 (copysign 1.0 y)
 (if (<= (/ (* (sin x) (sinh (fabs y))) x) 2e-10)
   (* (+ (fabs y) (fabs y)) 0.5)
   (/ (* x (fabs y)) x))))

C

double code(double x, double y) {
	double tmp;
	if (((sin(x) * sinh(fabs(y))) / x) <= 2e-10) {
		tmp = (fabs(y) + fabs(y)) * 0.5;
	} else {
		tmp = (x * fabs(y)) / x;
	}
	return copysign(1.0, y) * tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (((Math.sin(x) * Math.sinh(Math.abs(y))) / x) <= 2e-10) {
		tmp = (Math.abs(y) + Math.abs(y)) * 0.5;
	} else {
		tmp = (x * Math.abs(y)) / x;
	}
	return Math.copySign(1.0, y) * tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((math.sin(x) * math.sinh(math.fabs(y))) / x) <= 2e-10:
		tmp = (math.fabs(y) + math.fabs(y)) * 0.5
	else:
		tmp = (x * math.fabs(y)) / x
	return math.copysign(1.0, y) * tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(sin(x) * sinh(abs(y))) / x) <= 2e-10)
		tmp = Float64(Float64(abs(y) + abs(y)) * 0.5);
	else
		tmp = Float64(Float64(x * abs(y)) / x);
	end
	return Float64(copysign(1.0, y) * tmp)
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((sin(x) * sinh(abs(y))) / x) <= 2e-10)
		tmp = (abs(y) + abs(y)) * 0.5;
	else
		tmp = (x * abs(y)) / x;
	end
	tmp_2 = (sign(y) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[(N[Sin[x], $MachinePrecision] * N[Sinh[N[Abs[y], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], 2e-10], N[(N[(N[Abs[y], $MachinePrecision] + N[Abs[y], $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], N[(N[(x * N[Abs[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x) < 2.0000000000000001e-10

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.1%

      \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \left(2 \cdot y\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 28.3%

      \[\leadsto 0.5 \cdot \left(2 \cdot y\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 28.3%

      \[\leadsto \left(y + y\right) \cdot 0.5 \]

   if 2.0000000000000001e-10 < (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x)

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 40.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 23.5%

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

Alternative 10: 28.3% accurate, 8.4× speedup

Math

\[\left(y + y\right) \cdot 0.5 \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* (+ y y) 0.5))

C

double code(double x, double y) {
	return (y + y) * 0.5;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + y) * 0.5d0
end function

Java

public static double code(double x, double y) {
	return (y + y) * 0.5;
}

Python

def code(x, y):
	return (y + y) * 0.5

Julia

function code(x, y)
	return Float64(Float64(y + y) * 0.5)
end

MATLAB

function tmp = code(x, y)
	tmp = (y + y) * 0.5;
end

Wolfram

code[x_, y_] := N[(N[(y + y), $MachinePrecision] * 0.5), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(y + y) * (5e-1)
END code

Derivation

1. Initial program 88.9%

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

2. Taylor expanded in x around 0

   \[\leadsto \frac{1}{2} \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]
3. Step-by-step derivation

4. Applied rewrites 53.1%

   \[\leadsto 0.5 \cdot \left(e^{y} - \frac{1}{e^{y}}\right) \]

5. Taylor expanded in y around 0

   \[\leadsto 0.5 \cdot \left(2 \cdot y\right) \]
6. Step-by-step derivation

7. Applied rewrites 28.3%

   \[\leadsto 0.5 \cdot \left(2 \cdot y\right) \]
8. Step-by-step derivation

9. Applied rewrites 28.3%

   \[\leadsto \left(y + y\right) \cdot 0.5 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64
  (/ (* (sin x) (sinh y)) x))