Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 89.5% → 99.9%

Time: 12.9s

Alternatives: 6

Speedup: 1.0×

• 50.0% 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
  (/ (* (sin x) (sinh y)) x))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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]

Initial Program: 89.5% accurate, 1.0× speedup

Math

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

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

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

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. mult-flip-rev N/A

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

   9. lower-/.f64 99.9%

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

3. Applied rewrites 99.9%

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

Alternative 2: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \sinh \left(\left|y\right|\right)\\ t_1 := \frac{\sin x \cdot t\_0}{x}\\ \mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(1 + \frac{-1}{6} \cdot {x}^{2}\right) \cdot t\_0\\ \mathbf{elif}\;t\_1 \leq \frac{7482888383134223}{374144419156711147060143317175368453031918731001856}:\\ \;\;\;\;\frac{\left|y\right|}{x} \cdot \sin x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (sinh (fabs y))) (t_1 (/ (* (sin x) t_0) x)))
  (*
   (copysign 1 y)
   (if (<= t_1 (- INFINITY))
     (* (+ 1 (* -1/6 (pow x 2))) t_0)
     (if (<=
          t_1
          7482888383134223/374144419156711147060143317175368453031918731001856)
       (* (/ (fabs y) x) (sin x))
       (* 1 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 = (1.0 + (-0.16666666666666666 * pow(x, 2.0))) * t_0;
	} else if (t_1 <= 2e-35) {
		tmp = (fabs(y) / x) * sin(x);
	} else {
		tmp = 1.0 * t_0;
	}
	return copysign(1.0, y) * tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = Math.sinh(Math.abs(y));
	double t_1 = (Math.sin(x) * t_0) / x;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (1.0 + (-0.16666666666666666 * Math.pow(x, 2.0))) * t_0;
	} else if (t_1 <= 2e-35) {
		tmp = (Math.abs(y) / x) * Math.sin(x);
	} else {
		tmp = 1.0 * t_0;
	}
	return Math.copySign(1.0, y) * tmp;
}

Python

def code(x, y):
	t_0 = math.sinh(math.fabs(y))
	t_1 = (math.sin(x) * t_0) / x
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (1.0 + (-0.16666666666666666 * math.pow(x, 2.0))) * t_0
	elif t_1 <= 2e-35:
		tmp = (math.fabs(y) / x) * math.sin(x)
	else:
		tmp = 1.0 * t_0
	return math.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(Float64(1.0 + Float64(-0.16666666666666666 * (x ^ 2.0))) * t_0);
	elseif (t_1 <= 2e-35)
		tmp = Float64(Float64(abs(y) / x) * sin(x));
	else
		tmp = Float64(1.0 * t_0);
	end
	return Float64(copysign(1.0, y) * tmp)
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sinh(abs(y));
	t_1 = (sin(x) * t_0) / x;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (1.0 + (-0.16666666666666666 * (x ^ 2.0))) * t_0;
	elseif (t_1 <= 2e-35)
		tmp = (abs(y) / x) * sin(x);
	else
		tmp = 1.0 * t_0;
	end
	tmp_2 = (sign(y) * abs(1.0)) * 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], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, (-Infinity)], N[(N[(1 + N[(-1/6 * N[Power[x, 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[t$95$1, 7482888383134223/374144419156711147060143317175368453031918731001856], N[(N[(N[Abs[y], $MachinePrecision] / x), $MachinePrecision] * N[Sin[x], $MachinePrecision]), $MachinePrecision], N[(1 * t$95$0), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 89.5%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 99.9%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

         \[\leadsto \left(1 + \color{blue}{\frac{-1}{6} \cdot {x}^{2}}\right) \cdot \sinh y \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 + \frac{-1}{6} \cdot \color{blue}{{x}^{2}}\right) \cdot \sinh y \]

      3. lower-pow.f64 62.9%

         \[\leadsto \left(1 + \frac{-1}{6} \cdot {x}^{\color{blue}{2}}\right) \cdot \sinh y \]

   6. Applied rewrites 62.9%

      \[\leadsto \color{blue}{\left(1 + \frac{-1}{6} \cdot {x}^{2}\right)} \cdot \sinh y \]

   if -inf.0 < (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x) < 2e-35

   1. Initial program 89.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8%

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in y around 0

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

      1. lower-/.f64 62.9%

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

   6. Applied rewrites 62.9%

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

   if 2e-35 < (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x)

   1. Initial program 89.5%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 99.9%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 63.2%

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

Alternative 3: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \sinh \left(\left|y\right|\right)\\ t_1 := \frac{\sin x \cdot t\_0}{x}\\ \mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot x\right) \cdot \frac{-1}{6} - -1\right) \cdot x\right) \cdot \left|y\right|}{x}\\ \mathbf{elif}\;t\_1 \leq \frac{7482888383134223}{374144419156711147060143317175368453031918731001856}:\\ \;\;\;\;\frac{\left|y\right|}{x} \cdot \sin x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (sinh (fabs y))) (t_1 (/ (* (sin x) t_0) x)))
  (*
   (copysign 1 y)
   (if (<= t_1 (- INFINITY))
     (/ (* (* (- (* (* x x) -1/6) -1) x) (fabs y)) x)
     (if (<=
          t_1
          7482888383134223/374144419156711147060143317175368453031918731001856)
       (* (/ (fabs y) x) (sin x))
       (* 1 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 = (((((x * x) * -0.16666666666666666) - -1.0) * x) * fabs(y)) / x;
	} else if (t_1 <= 2e-35) {
		tmp = (fabs(y) / x) * sin(x);
	} else {
		tmp = 1.0 * t_0;
	}
	return copysign(1.0, y) * tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = Math.sinh(Math.abs(y));
	double t_1 = (Math.sin(x) * t_0) / x;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * Math.abs(y)) / x;
	} else if (t_1 <= 2e-35) {
		tmp = (Math.abs(y) / x) * Math.sin(x);
	} else {
		tmp = 1.0 * t_0;
	}
	return Math.copySign(1.0, y) * tmp;
}

Python

def code(x, y):
	t_0 = math.sinh(math.fabs(y))
	t_1 = (math.sin(x) * t_0) / x
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * math.fabs(y)) / x
	elif t_1 <= 2e-35:
		tmp = (math.fabs(y) / x) * math.sin(x)
	else:
		tmp = 1.0 * t_0
	return math.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(Float64(Float64(Float64(Float64(Float64(x * x) * -0.16666666666666666) - -1.0) * x) * abs(y)) / x);
	elseif (t_1 <= 2e-35)
		tmp = Float64(Float64(abs(y) / x) * sin(x));
	else
		tmp = Float64(1.0 * t_0);
	end
	return Float64(copysign(1.0, y) * tmp)
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sinh(abs(y));
	t_1 = (sin(x) * t_0) / x;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * abs(y)) / x;
	elseif (t_1 <= 2e-35)
		tmp = (abs(y) / x) * sin(x);
	else
		tmp = 1.0 * t_0;
	end
	tmp_2 = (sign(y) * abs(1.0)) * 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], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(N[(N[(x * x), $MachinePrecision] * -1/6), $MachinePrecision] - -1), $MachinePrecision] * x), $MachinePrecision] * N[Abs[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[t$95$1, 7482888383134223/374144419156711147060143317175368453031918731001856], N[(N[(N[Abs[y], $MachinePrecision] / x), $MachinePrecision] * N[Sin[x], $MachinePrecision]), $MachinePrecision], N[(1 * t$95$0), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 89.5%

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

   2. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-sin.f64 40.7%

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

   4. Applied rewrites 40.7%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 40.6%

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

   6. Applied rewrites 40.6%

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

   7. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \color{blue}{\frac{-1}{6} \cdot {x}^{2}}\right)\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot \color{blue}{{x}^{2}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{\color{blue}{2}}\right)\right)\right) \]

      4. lower-pow.f64 26.2%

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right) \]

   9. Applied rewrites 26.2%

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

       1. lift-*.f64 N/A

          \[\leadsto \color{blue}{\frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right) \cdot \frac{1}{x}} \]

       3. lift-/.f64 N/A

          \[\leadsto \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right) \cdot \color{blue}{\frac{1}{x}} \]

       4. mult-flip-rev N/A

          \[\leadsto \color{blue}{\frac{y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)}{x}} \]

       5. lower-/.f64 26.2%

          \[\leadsto \color{blue}{\frac{y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)}{x}} \]

   11. Applied rewrites 26.2%

       \[\leadsto \color{blue}{\frac{\left(\left(\left(x \cdot x\right) \cdot \frac{-1}{6} - -1\right) \cdot x\right) \cdot y}{x}} \]

   if -inf.0 < (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x) < 2e-35

   1. Initial program 89.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8%

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in y around 0

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

      1. lower-/.f64 62.9%

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

   6. Applied rewrites 62.9%

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

   if 2e-35 < (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x)

   1. Initial program 89.5%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 99.9%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 63.2%

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

Alternative 4: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \sinh \left(\left|y\right|\right)\\ \mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;\frac{\sin x \cdot t\_0}{x} \leq \frac{-3366486976990959}{168324348849547952231711676252164117297610873690341563503944988898199428937506586307637329160882830439263455003397702966816621832005881723620090072660860187198567157476110227142133240252298326952681384055545004032}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot x\right) \cdot \frac{-1}{6} - -1\right) \cdot x\right) \cdot \left|y\right|}{x}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (sinh (fabs y))))
  (*
   (copysign 1 y)
   (if (<=
        (/ (* (sin x) t_0) x)
        -3366486976990959/168324348849547952231711676252164117297610873690341563503944988898199428937506586307637329160882830439263455003397702966816621832005881723620090072660860187198567157476110227142133240252298326952681384055545004032)
     (/ (* (* (- (* (* x x) -1/6) -1) x) (fabs y)) x)
     (* 1 t_0)))))

C

double code(double x, double y) {
	double t_0 = sinh(fabs(y));
	double tmp;
	if (((sin(x) * t_0) / x) <= -2e-197) {
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * fabs(y)) / x;
	} else {
		tmp = 1.0 * t_0;
	}
	return copysign(1.0, y) * tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = Math.sinh(Math.abs(y));
	double tmp;
	if (((Math.sin(x) * t_0) / x) <= -2e-197) {
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * Math.abs(y)) / x;
	} else {
		tmp = 1.0 * t_0;
	}
	return Math.copySign(1.0, y) * tmp;
}

Python

def code(x, y):
	t_0 = math.sinh(math.fabs(y))
	tmp = 0
	if ((math.sin(x) * t_0) / x) <= -2e-197:
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * math.fabs(y)) / x
	else:
		tmp = 1.0 * t_0
	return math.copysign(1.0, y) * tmp

Julia

function code(x, y)
	t_0 = sinh(abs(y))
	tmp = 0.0
	if (Float64(Float64(sin(x) * t_0) / x) <= -2e-197)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(x * x) * -0.16666666666666666) - -1.0) * x) * abs(y)) / x);
	else
		tmp = Float64(1.0 * t_0);
	end
	return Float64(copysign(1.0, y) * tmp)
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sinh(abs(y));
	tmp = 0.0;
	if (((sin(x) * t_0) / x) <= -2e-197)
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * abs(y)) / x;
	else
		tmp = 1.0 * t_0;
	end
	tmp_2 = (sign(y) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[Sinh[N[Abs[y], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[(N[Sin[x], $MachinePrecision] * t$95$0), $MachinePrecision] / x), $MachinePrecision], -3366486976990959/168324348849547952231711676252164117297610873690341563503944988898199428937506586307637329160882830439263455003397702966816621832005881723620090072660860187198567157476110227142133240252298326952681384055545004032], N[(N[(N[(N[(N[(N[(x * x), $MachinePrecision] * -1/6), $MachinePrecision] - -1), $MachinePrecision] * x), $MachinePrecision] * N[Abs[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(1 * t$95$0), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x) < -2e-197

   1. Initial program 89.5%

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

   2. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-sin.f64 40.7%

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

   4. Applied rewrites 40.7%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 40.6%

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

   6. Applied rewrites 40.6%

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

   7. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \color{blue}{\frac{-1}{6} \cdot {x}^{2}}\right)\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot \color{blue}{{x}^{2}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{\color{blue}{2}}\right)\right)\right) \]

      4. lower-pow.f64 26.2%

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right) \]

   9. Applied rewrites 26.2%

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

       1. lift-*.f64 N/A

          \[\leadsto \color{blue}{\frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right) \cdot \frac{1}{x}} \]

       3. lift-/.f64 N/A

          \[\leadsto \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right) \cdot \color{blue}{\frac{1}{x}} \]

       4. mult-flip-rev N/A

          \[\leadsto \color{blue}{\frac{y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)}{x}} \]

       5. lower-/.f64 26.2%

          \[\leadsto \color{blue}{\frac{y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)}{x}} \]

   11. Applied rewrites 26.2%

       \[\leadsto \color{blue}{\frac{\left(\left(\left(x \cdot x\right) \cdot \frac{-1}{6} - -1\right) \cdot x\right) \cdot y}{x}} \]

   if -2e-197 < (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x)

   1. Initial program 89.5%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 99.9%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 63.2%

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

Alternative 5: 33.3% accurate, 0.6× speedup

Math

\[\mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;\frac{\sin x \cdot \sinh \left(\left|y\right|\right)}{x} \leq \frac{-3366486976990959}{168324348849547952231711676252164117297610873690341563503944988898199428937506586307637329160882830439263455003397702966816621832005881723620090072660860187198567157476110227142133240252298326952681384055545004032}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot x\right) \cdot \frac{-1}{6} - -1\right) \cdot x\right) \cdot \left|y\right|}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left|y\right|}{x}\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (*
 (copysign 1 y)
 (if (<=
      (/ (* (sin x) (sinh (fabs y))) x)
      -3366486976990959/168324348849547952231711676252164117297610873690341563503944988898199428937506586307637329160882830439263455003397702966816621832005881723620090072660860187198567157476110227142133240252298326952681384055545004032)
   (/ (* (* (- (* (* x x) -1/6) -1) x) (fabs y)) x)
   (/ (* x (fabs y)) x))))

C

double code(double x, double y) {
	double tmp;
	if (((sin(x) * sinh(fabs(y))) / x) <= -2e-197) {
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * fabs(y)) / x;
	} 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-197) {
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * Math.abs(y)) / x;
	} 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-197:
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * math.fabs(y)) / x
	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-197)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(x * x) * -0.16666666666666666) - -1.0) * x) * abs(y)) / x);
	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-197)
		tmp = (((((x * x) * -0.16666666666666666) - -1.0) * x) * abs(y)) / x;
	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], 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], -3366486976990959/168324348849547952231711676252164117297610873690341563503944988898199428937506586307637329160882830439263455003397702966816621832005881723620090072660860187198567157476110227142133240252298326952681384055545004032], N[(N[(N[(N[(N[(N[(x * x), $MachinePrecision] * -1/6), $MachinePrecision] - -1), $MachinePrecision] * x), $MachinePrecision] * N[Abs[y], $MachinePrecision]), $MachinePrecision] / x), $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) < -2e-197

   1. Initial program 89.5%

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

   2. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-sin.f64 40.7%

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

   4. Applied rewrites 40.7%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 40.6%

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

   6. Applied rewrites 40.6%

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

   7. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \color{blue}{\frac{-1}{6} \cdot {x}^{2}}\right)\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot \color{blue}{{x}^{2}}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{\color{blue}{2}}\right)\right)\right) \]

      4. lower-pow.f64 26.2%

         \[\leadsto \frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right) \]

   9. Applied rewrites 26.2%

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

       1. lift-*.f64 N/A

          \[\leadsto \color{blue}{\frac{1}{x} \cdot \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right) \cdot \frac{1}{x}} \]

       3. lift-/.f64 N/A

          \[\leadsto \left(y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)\right) \cdot \color{blue}{\frac{1}{x}} \]

       4. mult-flip-rev N/A

          \[\leadsto \color{blue}{\frac{y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)}{x}} \]

       5. lower-/.f64 26.2%

          \[\leadsto \color{blue}{\frac{y \cdot \left(x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)\right)}{x}} \]

   11. Applied rewrites 26.2%

       \[\leadsto \color{blue}{\frac{\left(\left(\left(x \cdot x\right) \cdot \frac{-1}{6} - -1\right) \cdot x\right) \cdot y}{x}} \]

   if -2e-197 < (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x)

   1. Initial program 89.5%

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

   2. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-sin.f64 40.7%

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

   4. Applied rewrites 40.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 22.7%

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

   7. Applied rewrites 22.7%

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

Alternative 6: 22.7% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y)
use fmin_fmax_functions
    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(Float64(x * y) / x)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

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

2. Taylor expanded in y around 0

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

   1. lower-*.f64 N/A

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

   2. lower-sin.f64 40.7%

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

4. Applied rewrites 40.7%

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

5. Taylor expanded in x around 0

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

   1. lower-*.f64 22.7%

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

7. Applied rewrites 22.7%

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

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64
  (/ (* (sin x) (sinh y)) x))