Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.8% → 99.8%

Time: 5.7s

Alternatives: 10

Speedup: 0.5×

• 35.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \cosh \left(\left|x\right|\right)\\ t_1 := \frac{t\_0 \cdot \frac{\left|y\right|}{\left|x\right|}}{\left|z\right|}\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, z\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 100000000000000002309309130269787154892983822485169927543056457815484218967945768886576179686795076111078238543825857419659919011313587350687602971665369018571203143144663564875896666980352:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-\left|y\right|\right) \cdot \frac{t\_0}{\left|z\right|}}{-\left|x\right|}\\ \end{array}\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (cosh (fabs x)))
       (t_1 (/ (* t_0 (/ (fabs y) (fabs x))) (fabs z))))
  (*
   (copysign 1 x)
   (*
    (copysign 1 y)
    (*
     (copysign 1 z)
     (if (<=
          t_1
          100000000000000002309309130269787154892983822485169927543056457815484218967945768886576179686795076111078238543825857419659919011313587350687602971665369018571203143144663564875896666980352)
       t_1
       (/ (* (- (fabs y)) (/ t_0 (fabs z))) (- (fabs x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(fabs(x));
	double t_1 = (t_0 * (fabs(y) / fabs(x))) / fabs(z);
	double tmp;
	if (t_1 <= 1e+188) {
		tmp = t_1;
	} else {
		tmp = (-fabs(y) * (t_0 / fabs(z))) / -fabs(x);
	}
	return copysign(1.0, x) * (copysign(1.0, y) * (copysign(1.0, z) * tmp));
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cosh(Math.abs(x));
	double t_1 = (t_0 * (Math.abs(y) / Math.abs(x))) / Math.abs(z);
	double tmp;
	if (t_1 <= 1e+188) {
		tmp = t_1;
	} else {
		tmp = (-Math.abs(y) * (t_0 / Math.abs(z))) / -Math.abs(x);
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * (Math.copySign(1.0, z) * tmp));
}

Python

def code(x, y, z):
	t_0 = math.cosh(math.fabs(x))
	t_1 = (t_0 * (math.fabs(y) / math.fabs(x))) / math.fabs(z)
	tmp = 0
	if t_1 <= 1e+188:
		tmp = t_1
	else:
		tmp = (-math.fabs(y) * (t_0 / math.fabs(z))) / -math.fabs(x)
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * (math.copysign(1.0, z) * tmp))

Julia

function code(x, y, z)
	t_0 = cosh(abs(x))
	t_1 = Float64(Float64(t_0 * Float64(abs(y) / abs(x))) / abs(z))
	tmp = 0.0
	if (t_1 <= 1e+188)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-abs(y)) * Float64(t_0 / abs(z))) / Float64(-abs(x)));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * Float64(copysign(1.0, z) * tmp)))
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(abs(x));
	t_1 = (t_0 * (abs(y) / abs(x))) / abs(z);
	tmp = 0.0;
	if (t_1 <= 1e+188)
		tmp = t_1;
	else
		tmp = (-abs(y) * (t_0 / abs(z))) / -abs(x);
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * ((sign(z) * abs(1.0)) * tmp));
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Cosh[N[Abs[x], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(t$95$0 * N[(N[Abs[y], $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Abs[z], $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, 100000000000000002309309130269787154892983822485169927543056457815484218967945768886576179686795076111078238543825857419659919011313587350687602971665369018571203143144663564875896666980352], t$95$1, N[(N[((-N[Abs[y], $MachinePrecision]) * N[(t$95$0 / N[Abs[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-N[Abs[x], $MachinePrecision])), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 1e188

   1. Initial program 84.8%

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

   if 1e188 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(y\right)}{\mathsf{neg}\left(x\right)}} \cdot \left(\cosh x \cdot \frac{1}{z}\right) \]

      8. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\cosh x \cdot \frac{1}{z}\right)}{\mathsf{neg}\left(x\right)}} \]

      9. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\cosh x \cdot \frac{1}{z}\right)}{\mathsf{neg}\left(x\right)}} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\cosh x \cdot \frac{1}{z}\right)}}{\mathsf{neg}\left(x\right)} \]

      11. lower-neg.f64 N/A

          \[\leadsto \frac{\color{blue}{\left(-y\right)} \cdot \left(\cosh x \cdot \frac{1}{z}\right)}{\mathsf{neg}\left(x\right)} \]

      12. mult-flip-rev N/A

          \[\leadsto \frac{\left(-y\right) \cdot \color{blue}{\frac{\cosh x}{z}}}{\mathsf{neg}\left(x\right)} \]

      13. lower-/.f64 N/A

          \[\leadsto \frac{\left(-y\right) \cdot \color{blue}{\frac{\cosh x}{z}}}{\mathsf{neg}\left(x\right)} \]

      14. lower-neg.f64 96.1%

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

   3. Applied rewrites 96.1%

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

Alternative 2: 99.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \cosh \left(\left|x\right|\right)\\ t_1 := \frac{t\_0 \cdot \frac{\left|y\right|}{\left|x\right|}}{\left|z\right|}\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, z\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 8000000000000000106300440576:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left|y\right| \cdot t\_0}{\left|z\right|}}{\left|x\right|}\\ \end{array}\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (cosh (fabs x)))
       (t_1 (/ (* t_0 (/ (fabs y) (fabs x))) (fabs z))))
  (*
   (copysign 1 x)
   (*
    (copysign 1 y)
    (*
     (copysign 1 z)
     (if (<= t_1 8000000000000000106300440576)
       t_1
       (/ (/ (* (fabs y) t_0) (fabs z)) (fabs x))))))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(fabs(x));
	double t_1 = (t_0 * (fabs(y) / fabs(x))) / fabs(z);
	double tmp;
	if (t_1 <= 8e+27) {
		tmp = t_1;
	} else {
		tmp = ((fabs(y) * t_0) / fabs(z)) / fabs(x);
	}
	return copysign(1.0, x) * (copysign(1.0, y) * (copysign(1.0, z) * tmp));
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cosh(Math.abs(x));
	double t_1 = (t_0 * (Math.abs(y) / Math.abs(x))) / Math.abs(z);
	double tmp;
	if (t_1 <= 8e+27) {
		tmp = t_1;
	} else {
		tmp = ((Math.abs(y) * t_0) / Math.abs(z)) / Math.abs(x);
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * (Math.copySign(1.0, z) * tmp));
}

Python

def code(x, y, z):
	t_0 = math.cosh(math.fabs(x))
	t_1 = (t_0 * (math.fabs(y) / math.fabs(x))) / math.fabs(z)
	tmp = 0
	if t_1 <= 8e+27:
		tmp = t_1
	else:
		tmp = ((math.fabs(y) * t_0) / math.fabs(z)) / math.fabs(x)
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * (math.copysign(1.0, z) * tmp))

Julia

function code(x, y, z)
	t_0 = cosh(abs(x))
	t_1 = Float64(Float64(t_0 * Float64(abs(y) / abs(x))) / abs(z))
	tmp = 0.0
	if (t_1 <= 8e+27)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(abs(y) * t_0) / abs(z)) / abs(x));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * Float64(copysign(1.0, z) * tmp)))
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(abs(x));
	t_1 = (t_0 * (abs(y) / abs(x))) / abs(z);
	tmp = 0.0;
	if (t_1 <= 8e+27)
		tmp = t_1;
	else
		tmp = ((abs(y) * t_0) / abs(z)) / abs(x);
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * ((sign(z) * abs(1.0)) * tmp));
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Cosh[N[Abs[x], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(t$95$0 * N[(N[Abs[y], $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Abs[z], $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, 8000000000000000106300440576], t$95$1, N[(N[(N[(N[Abs[y], $MachinePrecision] * t$95$0), $MachinePrecision] / N[Abs[z], $MachinePrecision]), $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 8.0000000000000001e27

   1. Initial program 84.8%

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

   if 8.0000000000000001e27 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 96.1%

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

   3. Applied rewrites 96.1%

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

Alternative 3: 92.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{if}\;t\_0 \leq \infty:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{z \cdot x}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (/ (* (cosh x) (/ y x)) z)))
  (if (<= t_0 INFINITY) t_0 (* y (/ (cosh x) (* z x))))))

C

double code(double x, double y, double z) {
	double t_0 = (cosh(x) * (y / x)) / z;
	double tmp;
	if (t_0 <= ((double) INFINITY)) {
		tmp = t_0;
	} else {
		tmp = y * (cosh(x) / (z * x));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (Math.cosh(x) * (y / x)) / z;
	double tmp;
	if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = t_0;
	} else {
		tmp = y * (Math.cosh(x) / (z * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.cosh(x) * (y / x)) / z
	tmp = 0
	if t_0 <= math.inf:
		tmp = t_0
	else:
		tmp = y * (math.cosh(x) / (z * x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(cosh(x) * Float64(y / x)) / z)
	tmp = 0.0
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(cosh(x) / Float64(z * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (cosh(x) * (y / x)) / z;
	tmp = 0.0;
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = y * (cosh(x) / (z * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$0, Infinity], t$95$0, N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < +inf.0

   1. Initial program 84.8%

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

   if +inf.0 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. associate-/l/ N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 82.4%

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

   3. Applied rewrites 82.4%

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

Alternative 4: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \cosh \left(\left|x\right|\right)\\ t_1 := \frac{\left|y\right|}{\left|x\right|}\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;t\_0 \cdot t\_1 \leq 39999999999999999563482447285636784507139225041605435780720061858901209596441032595416451225830520245186635713283815594336131046093817348450418688:\\ \;\;\;\;\frac{t\_1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|y\right| \cdot t\_0}{z \cdot \left|x\right|}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (cosh (fabs x))) (t_1 (/ (fabs y) (fabs x))))
  (*
   (copysign 1 x)
   (*
    (copysign 1 y)
    (if (<=
         (* t_0 t_1)
         39999999999999999563482447285636784507139225041605435780720061858901209596441032595416451225830520245186635713283815594336131046093817348450418688)
      (/ t_1 z)
      (/ (* (fabs y) t_0) (* z (fabs x))))))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(fabs(x));
	double t_1 = fabs(y) / fabs(x);
	double tmp;
	if ((t_0 * t_1) <= 4e+145) {
		tmp = t_1 / z;
	} else {
		tmp = (fabs(y) * t_0) / (z * fabs(x));
	}
	return copysign(1.0, x) * (copysign(1.0, y) * tmp);
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cosh(Math.abs(x));
	double t_1 = Math.abs(y) / Math.abs(x);
	double tmp;
	if ((t_0 * t_1) <= 4e+145) {
		tmp = t_1 / z;
	} else {
		tmp = (Math.abs(y) * t_0) / (z * Math.abs(x));
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * tmp);
}

Python

def code(x, y, z):
	t_0 = math.cosh(math.fabs(x))
	t_1 = math.fabs(y) / math.fabs(x)
	tmp = 0
	if (t_0 * t_1) <= 4e+145:
		tmp = t_1 / z
	else:
		tmp = (math.fabs(y) * t_0) / (z * math.fabs(x))
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * tmp)

Julia

function code(x, y, z)
	t_0 = cosh(abs(x))
	t_1 = Float64(abs(y) / abs(x))
	tmp = 0.0
	if (Float64(t_0 * t_1) <= 4e+145)
		tmp = Float64(t_1 / z);
	else
		tmp = Float64(Float64(abs(y) * t_0) / Float64(z * abs(x)));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * tmp))
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(abs(x));
	t_1 = abs(y) / abs(x);
	tmp = 0.0;
	if ((t_0 * t_1) <= 4e+145)
		tmp = t_1 / z;
	else
		tmp = (abs(y) * t_0) / (z * abs(x));
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * tmp);
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Cosh[N[Abs[x], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[y], $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(t$95$0 * t$95$1), $MachinePrecision], 39999999999999999563482447285636784507139225041605435780720061858901209596441032595416451225830520245186635713283815594336131046093817348450418688], N[(t$95$1 / z), $MachinePrecision], N[(N[(N[Abs[y], $MachinePrecision] * t$95$0), $MachinePrecision] / N[(z * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (cosh.f64 x) (/.f64 y x)) < 4e145

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 48.1%

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

   4. Applied rewrites 48.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 48.0%

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

   6. Applied rewrites 48.0%

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

   if 4e145 < (*.f64 (cosh.f64 x) (/.f64 y x))

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. associate-/l/ N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 82.8%

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

   3. Applied rewrites 82.8%

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

Alternative 5: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \cosh \left(\left|x\right|\right)\\ t_1 := \frac{\left|y\right|}{\left|x\right|}\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;t\_0 \cdot t\_1 \leq 39999999999999999563482447285636784507139225041605435780720061858901209596441032595416451225830520245186635713283815594336131046093817348450418688:\\ \;\;\;\;\frac{t\_1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left|y\right| \cdot \frac{t\_0}{z \cdot \left|x\right|}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (cosh (fabs x))) (t_1 (/ (fabs y) (fabs x))))
  (*
   (copysign 1 x)
   (*
    (copysign 1 y)
    (if (<=
         (* t_0 t_1)
         39999999999999999563482447285636784507139225041605435780720061858901209596441032595416451225830520245186635713283815594336131046093817348450418688)
      (/ t_1 z)
      (* (fabs y) (/ t_0 (* z (fabs x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(fabs(x));
	double t_1 = fabs(y) / fabs(x);
	double tmp;
	if ((t_0 * t_1) <= 4e+145) {
		tmp = t_1 / z;
	} else {
		tmp = fabs(y) * (t_0 / (z * fabs(x)));
	}
	return copysign(1.0, x) * (copysign(1.0, y) * tmp);
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cosh(Math.abs(x));
	double t_1 = Math.abs(y) / Math.abs(x);
	double tmp;
	if ((t_0 * t_1) <= 4e+145) {
		tmp = t_1 / z;
	} else {
		tmp = Math.abs(y) * (t_0 / (z * Math.abs(x)));
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * tmp);
}

Python

def code(x, y, z):
	t_0 = math.cosh(math.fabs(x))
	t_1 = math.fabs(y) / math.fabs(x)
	tmp = 0
	if (t_0 * t_1) <= 4e+145:
		tmp = t_1 / z
	else:
		tmp = math.fabs(y) * (t_0 / (z * math.fabs(x)))
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * tmp)

Julia

function code(x, y, z)
	t_0 = cosh(abs(x))
	t_1 = Float64(abs(y) / abs(x))
	tmp = 0.0
	if (Float64(t_0 * t_1) <= 4e+145)
		tmp = Float64(t_1 / z);
	else
		tmp = Float64(abs(y) * Float64(t_0 / Float64(z * abs(x))));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * tmp))
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(abs(x));
	t_1 = abs(y) / abs(x);
	tmp = 0.0;
	if ((t_0 * t_1) <= 4e+145)
		tmp = t_1 / z;
	else
		tmp = abs(y) * (t_0 / (z * abs(x)));
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * tmp);
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Cosh[N[Abs[x], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[y], $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(t$95$0 * t$95$1), $MachinePrecision], 39999999999999999563482447285636784507139225041605435780720061858901209596441032595416451225830520245186635713283815594336131046093817348450418688], N[(t$95$1 / z), $MachinePrecision], N[(N[Abs[y], $MachinePrecision] * N[(t$95$0 / N[(z * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (cosh.f64 x) (/.f64 y x)) < 4e145

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 48.1%

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

   4. Applied rewrites 48.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 48.0%

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

   6. Applied rewrites 48.0%

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

   if 4e145 < (*.f64 (cosh.f64 x) (/.f64 y x))

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. associate-/l/ N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 82.4%

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

   3. Applied rewrites 82.4%

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

Alternative 6: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := z \cdot \left|x\right|\\ t_1 := \left|x\right| \cdot z\\ \mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;\left|x\right| \leq \frac{1770887431076117}{36893488147419103232}:\\ \;\;\;\;\frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\left|x\right| \cdot \left(z + \left|x\right| \cdot \left(\frac{-1}{2} \cdot z + \left(\frac{1}{2} \cdot z + \frac{1}{2} \cdot t\_1\right)\right)\right)}{t\_0 \cdot t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (* z (fabs x))) (t_1 (* (fabs x) z)))
  (*
   (copysign 1 x)
   (if (<= (fabs x) 1770887431076117/36893488147419103232)
     (/ y t_1)
     (*
      y
      (/
       (*
        (fabs x)
        (+ z (* (fabs x) (+ (* -1/2 z) (+ (* 1/2 z) (* 1/2 t_1))))))
       (* t_0 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * fabs(x);
	double t_1 = fabs(x) * z;
	double tmp;
	if (fabs(x) <= 4.8e-5) {
		tmp = y / t_1;
	} else {
		tmp = y * ((fabs(x) * (z + (fabs(x) * ((-0.5 * z) + ((0.5 * z) + (0.5 * t_1)))))) / (t_0 * t_0));
	}
	return copysign(1.0, x) * tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.abs(x);
	double t_1 = Math.abs(x) * z;
	double tmp;
	if (Math.abs(x) <= 4.8e-5) {
		tmp = y / t_1;
	} else {
		tmp = y * ((Math.abs(x) * (z + (Math.abs(x) * ((-0.5 * z) + ((0.5 * z) + (0.5 * t_1)))))) / (t_0 * t_0));
	}
	return Math.copySign(1.0, x) * tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.fabs(x)
	t_1 = math.fabs(x) * z
	tmp = 0
	if math.fabs(x) <= 4.8e-5:
		tmp = y / t_1
	else:
		tmp = y * ((math.fabs(x) * (z + (math.fabs(x) * ((-0.5 * z) + ((0.5 * z) + (0.5 * t_1)))))) / (t_0 * t_0))
	return math.copysign(1.0, x) * tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * abs(x))
	t_1 = Float64(abs(x) * z)
	tmp = 0.0
	if (abs(x) <= 4.8e-5)
		tmp = Float64(y / t_1);
	else
		tmp = Float64(y * Float64(Float64(abs(x) * Float64(z + Float64(abs(x) * Float64(Float64(-0.5 * z) + Float64(Float64(0.5 * z) + Float64(0.5 * t_1)))))) / Float64(t_0 * t_0)));
	end
	return Float64(copysign(1.0, x) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * abs(x);
	t_1 = abs(x) * z;
	tmp = 0.0;
	if (abs(x) <= 4.8e-5)
		tmp = y / t_1;
	else
		tmp = y * ((abs(x) * (z + (abs(x) * ((-0.5 * z) + ((0.5 * z) + (0.5 * t_1)))))) / (t_0 * t_0));
	end
	tmp_2 = (sign(x) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Abs[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[x], $MachinePrecision] * z), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[x], $MachinePrecision], 1770887431076117/36893488147419103232], N[(y / t$95$1), $MachinePrecision], N[(y * N[(N[(N[Abs[x], $MachinePrecision] * N[(z + N[(N[Abs[x], $MachinePrecision] * N[(N[(-1/2 * z), $MachinePrecision] + N[(N[(1/2 * z), $MachinePrecision] + N[(1/2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 4.8000000000000001e-5

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 48.1%

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

   4. Applied rewrites 48.1%

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

   if 4.8000000000000001e-5 < x

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. associate-/l/ N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 82.4%

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

   3. Applied rewrites 82.4%

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

      1. lift-/.f64 N/A

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

      2. lift-cosh.f64 N/A

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

      3. cosh-def N/A

         \[\leadsto y \cdot \frac{\color{blue}{\frac{e^{x} + e^{\mathsf{neg}\left(x\right)}}{2}}}{z \cdot x} \]

      4. div-add N/A

         \[\leadsto y \cdot \frac{\color{blue}{\frac{e^{x}}{2} + \frac{e^{\mathsf{neg}\left(x\right)}}{2}}}{z \cdot x} \]

      5. div-add N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{\frac{e^{x}}{2}}{z \cdot x} + \frac{\frac{e^{\mathsf{neg}\left(x\right)}}{2}}{z \cdot x}\right)} \]

      6. frac-add N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{e^{x}}{2} \cdot \left(z \cdot x\right) + \left(z \cdot x\right) \cdot \frac{e^{\mathsf{neg}\left(x\right)}}{2}}{\left(z \cdot x\right) \cdot \left(z \cdot x\right)}} \]

      7. lower-/.f64 N/A

         \[\leadsto y \cdot \color{blue}{\frac{\frac{e^{x}}{2} \cdot \left(z \cdot x\right) + \left(z \cdot x\right) \cdot \frac{e^{\mathsf{neg}\left(x\right)}}{2}}{\left(z \cdot x\right) \cdot \left(z \cdot x\right)}} \]

   5. Applied rewrites 52.9%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 45.7%

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

   8. Applied rewrites 45.7%

      \[\leadsto y \cdot \frac{\color{blue}{x \cdot \left(z + x \cdot \left(\frac{-1}{2} \cdot z + \left(\frac{1}{2} \cdot z + \frac{1}{2} \cdot \left(x \cdot z\right)\right)\right)\right)}}{\left(z \cdot x\right) \cdot \left(z \cdot x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 55.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{\left|y\right|}{\left|x\right|}\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;\cosh \left(\left|x\right|\right) \cdot t\_0 \leq 499999999999999960548416541607351328777021384687611118643325884835920630831966800139023707085267707205518204055907116200520239285727065764214062887637864581182125170853648392988706023732518458057027666759600481533739104277734798607669877628825763840:\\ \;\;\;\;\frac{t\_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|y\right| \cdot \frac{1}{z}}{\left|x\right|}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (/ (fabs y) (fabs x))))
  (*
   (copysign 1 x)
   (*
    (copysign 1 y)
    (if (<=
         (* (cosh (fabs x)) t_0)
         499999999999999960548416541607351328777021384687611118643325884835920630831966800139023707085267707205518204055907116200520239285727065764214062887637864581182125170853648392988706023732518458057027666759600481533739104277734798607669877628825763840)
      (/ t_0 z)
      (/ (* (fabs y) (/ 1 z)) (fabs x)))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(y) / fabs(x);
	double tmp;
	if ((cosh(fabs(x)) * t_0) <= 5e+248) {
		tmp = t_0 / z;
	} else {
		tmp = (fabs(y) * (1.0 / z)) / fabs(x);
	}
	return copysign(1.0, x) * (copysign(1.0, y) * tmp);
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(y) / Math.abs(x);
	double tmp;
	if ((Math.cosh(Math.abs(x)) * t_0) <= 5e+248) {
		tmp = t_0 / z;
	} else {
		tmp = (Math.abs(y) * (1.0 / z)) / Math.abs(x);
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * tmp);
}

Python

def code(x, y, z):
	t_0 = math.fabs(y) / math.fabs(x)
	tmp = 0
	if (math.cosh(math.fabs(x)) * t_0) <= 5e+248:
		tmp = t_0 / z
	else:
		tmp = (math.fabs(y) * (1.0 / z)) / math.fabs(x)
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * tmp)

Julia

function code(x, y, z)
	t_0 = Float64(abs(y) / abs(x))
	tmp = 0.0
	if (Float64(cosh(abs(x)) * t_0) <= 5e+248)
		tmp = Float64(t_0 / z);
	else
		tmp = Float64(Float64(abs(y) * Float64(1.0 / z)) / abs(x));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * tmp))
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(y) / abs(x);
	tmp = 0.0;
	if ((cosh(abs(x)) * t_0) <= 5e+248)
		tmp = t_0 / z;
	else
		tmp = (abs(y) * (1.0 / z)) / abs(x);
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * tmp);
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[y], $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[Cosh[N[Abs[x], $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision], 499999999999999960548416541607351328777021384687611118643325884835920630831966800139023707085267707205518204055907116200520239285727065764214062887637864581182125170853648392988706023732518458057027666759600481533739104277734798607669877628825763840], N[(t$95$0 / z), $MachinePrecision], N[(N[(N[Abs[y], $MachinePrecision] * N[(1 / z), $MachinePrecision]), $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (cosh.f64 x) (/.f64 y x)) < 4.9999999999999996e248

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 48.1%

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

   4. Applied rewrites 48.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 48.0%

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

   6. Applied rewrites 48.0%

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

   if 4.9999999999999996e248 < (*.f64 (cosh.f64 x) (/.f64 y x))

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 48.0%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. mult-flip-rev N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 51.8%

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

   6. Applied rewrites 51.8%

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

Alternative 8: 55.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{\left|y\right|}{\left|x\right|}\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, z\right) \cdot \begin{array}{l} \mathbf{if}\;\frac{\cosh \left(\left|x\right|\right) \cdot t\_0}{\left|z\right|} \leq 8000000000000000106300440576:\\ \;\;\;\;\frac{t\_0}{\left|z\right|}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left|y\right|}{\left|z\right|}}{\left|x\right|}\\ \end{array}\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (/ (fabs y) (fabs x))))
  (*
   (copysign 1 x)
   (*
    (copysign 1 y)
    (*
     (copysign 1 z)
     (if (<=
          (/ (* (cosh (fabs x)) t_0) (fabs z))
          8000000000000000106300440576)
       (/ t_0 (fabs z))
       (/ (/ (fabs y) (fabs z)) (fabs x))))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(y) / fabs(x);
	double tmp;
	if (((cosh(fabs(x)) * t_0) / fabs(z)) <= 8e+27) {
		tmp = t_0 / fabs(z);
	} else {
		tmp = (fabs(y) / fabs(z)) / fabs(x);
	}
	return copysign(1.0, x) * (copysign(1.0, y) * (copysign(1.0, z) * tmp));
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(y) / Math.abs(x);
	double tmp;
	if (((Math.cosh(Math.abs(x)) * t_0) / Math.abs(z)) <= 8e+27) {
		tmp = t_0 / Math.abs(z);
	} else {
		tmp = (Math.abs(y) / Math.abs(z)) / Math.abs(x);
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * (Math.copySign(1.0, z) * tmp));
}

Python

def code(x, y, z):
	t_0 = math.fabs(y) / math.fabs(x)
	tmp = 0
	if ((math.cosh(math.fabs(x)) * t_0) / math.fabs(z)) <= 8e+27:
		tmp = t_0 / math.fabs(z)
	else:
		tmp = (math.fabs(y) / math.fabs(z)) / math.fabs(x)
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * (math.copysign(1.0, z) * tmp))

Julia

function code(x, y, z)
	t_0 = Float64(abs(y) / abs(x))
	tmp = 0.0
	if (Float64(Float64(cosh(abs(x)) * t_0) / abs(z)) <= 8e+27)
		tmp = Float64(t_0 / abs(z));
	else
		tmp = Float64(Float64(abs(y) / abs(z)) / abs(x));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * Float64(copysign(1.0, z) * tmp)))
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(y) / abs(x);
	tmp = 0.0;
	if (((cosh(abs(x)) * t_0) / abs(z)) <= 8e+27)
		tmp = t_0 / abs(z);
	else
		tmp = (abs(y) / abs(z)) / abs(x);
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * ((sign(z) * abs(1.0)) * tmp));
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[y], $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[(N[Cosh[N[Abs[x], $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision] / N[Abs[z], $MachinePrecision]), $MachinePrecision], 8000000000000000106300440576], N[(t$95$0 / N[Abs[z], $MachinePrecision]), $MachinePrecision], N[(N[(N[Abs[y], $MachinePrecision] / N[Abs[z], $MachinePrecision]), $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 8.0000000000000001e27

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 48.1%

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

   4. Applied rewrites 48.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 48.0%

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

   6. Applied rewrites 48.0%

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

   if 8.0000000000000001e27 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 84.8%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. associate-*l/ N/A

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

      7. lower-/.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 96.1%

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

   3. Applied rewrites 96.1%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 51.9%

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

Alternative 9: 51.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{\left|y\right|}{\left|x\right|}\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \begin{array}{l} \mathbf{if}\;\cosh \left(\left|x\right|\right) \cdot t\_0 \leq 50000000000000002216397832979173719250214483304318128040098968915481738541309455929792089182585038346225505444281420986050205132811653363414864588844456074162727639905052485516551288455999908458318119026366376053636438477835715215872973713965056:\\ \;\;\;\;\frac{t\_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|y\right|}{\left|x\right| \cdot z}\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (/ (fabs y) (fabs x))))
  (*
   (copysign 1 x)
   (*
    (copysign 1 y)
    (if (<=
         (* (cosh (fabs x)) t_0)
         50000000000000002216397832979173719250214483304318128040098968915481738541309455929792089182585038346225505444281420986050205132811653363414864588844456074162727639905052485516551288455999908458318119026366376053636438477835715215872973713965056)
      (/ t_0 z)
      (/ (fabs y) (* (fabs x) z)))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(y) / fabs(x);
	double tmp;
	if ((cosh(fabs(x)) * t_0) <= 5e+244) {
		tmp = t_0 / z;
	} else {
		tmp = fabs(y) / (fabs(x) * z);
	}
	return copysign(1.0, x) * (copysign(1.0, y) * tmp);
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(y) / Math.abs(x);
	double tmp;
	if ((Math.cosh(Math.abs(x)) * t_0) <= 5e+244) {
		tmp = t_0 / z;
	} else {
		tmp = Math.abs(y) / (Math.abs(x) * z);
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * tmp);
}

Python

def code(x, y, z):
	t_0 = math.fabs(y) / math.fabs(x)
	tmp = 0
	if (math.cosh(math.fabs(x)) * t_0) <= 5e+244:
		tmp = t_0 / z
	else:
		tmp = math.fabs(y) / (math.fabs(x) * z)
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * tmp)

Julia

function code(x, y, z)
	t_0 = Float64(abs(y) / abs(x))
	tmp = 0.0
	if (Float64(cosh(abs(x)) * t_0) <= 5e+244)
		tmp = Float64(t_0 / z);
	else
		tmp = Float64(abs(y) / Float64(abs(x) * z));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * tmp))
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(y) / abs(x);
	tmp = 0.0;
	if ((cosh(abs(x)) * t_0) <= 5e+244)
		tmp = t_0 / z;
	else
		tmp = abs(y) / (abs(x) * z);
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * tmp);
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[y], $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[Cosh[N[Abs[x], $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision], 50000000000000002216397832979173719250214483304318128040098968915481738541309455929792089182585038346225505444281420986050205132811653363414864588844456074162727639905052485516551288455999908458318119026366376053636438477835715215872973713965056], N[(t$95$0 / z), $MachinePrecision], N[(N[Abs[y], $MachinePrecision] / N[(N[Abs[x], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (cosh.f64 x) (/.f64 y x)) < 5.0000000000000002e244

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 48.1%

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

   4. Applied rewrites 48.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 48.0%

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

   6. Applied rewrites 48.0%

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

   if 5.0000000000000002e244 < (*.f64 (cosh.f64 x) (/.f64 y x))

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 48.1%

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

   4. Applied rewrites 48.1%

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

Alternative 10: 48.1% accurate, 7.5× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

2. Taylor expanded in x around 0

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 48.1%

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

4. Applied rewrites 48.1%

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

Reproduce

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