Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.8% → 96.2%

Time: 14.0s

Alternatives: 16

Speedup: 1.0×

• 63.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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

real(8) function code(x, y, z)
    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

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

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

real(8) function code(x, y, z)
    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: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.5%

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

   1. associate-*r/ 75.5%

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

   2. associate-/r* 77.0%

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

3. Simplified 77.0%

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

   1. *-commutative 77.0%

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

   2. associate-/r* 75.5%

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

   3. associate-/r/ 84.5%

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

   4. associate-/r* 97.3%

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

5. Applied egg-rr 97.3%

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

6. Final simplification 97.3%

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

Alternative 2: 86.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+191}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{z} \cdot \frac{1}{x}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-150} \lor \neg \left(y \leq 7.8 \cdot 10^{-209}\right):\\ \;\;\;\;\frac{\cosh x}{z} \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right) + 1}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2e+191)
   (+ (* 0.5 (/ (* y x) z)) (* (/ y z) (/ 1.0 x)))
   (if (or (<= y -6e-150) (not (<= y 7.8e-209)))
     (* (/ (cosh x) z) (/ y x))
     (* y (/ (+ (* (/ x y) (* y (* x 0.5))) 1.0) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+191) {
		tmp = (0.5 * ((y * x) / z)) + ((y / z) * (1.0 / x));
	} else if ((y <= -6e-150) || !(y <= 7.8e-209)) {
		tmp = (cosh(x) / z) * (y / x);
	} else {
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.2d+191)) then
        tmp = (0.5d0 * ((y * x) / z)) + ((y / z) * (1.0d0 / x))
    else if ((y <= (-6d-150)) .or. (.not. (y <= 7.8d-209))) then
        tmp = (cosh(x) / z) * (y / x)
    else
        tmp = y * ((((x / y) * (y * (x * 0.5d0))) + 1.0d0) / (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+191) {
		tmp = (0.5 * ((y * x) / z)) + ((y / z) * (1.0 / x));
	} else if ((y <= -6e-150) || !(y <= 7.8e-209)) {
		tmp = (Math.cosh(x) / z) * (y / x);
	} else {
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.2e+191:
		tmp = (0.5 * ((y * x) / z)) + ((y / z) * (1.0 / x))
	elif (y <= -6e-150) or not (y <= 7.8e-209):
		tmp = (math.cosh(x) / z) * (y / x)
	else:
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+191)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / z)) + Float64(Float64(y / z) * Float64(1.0 / x)));
	elseif ((y <= -6e-150) || !(y <= 7.8e-209))
		tmp = Float64(Float64(cosh(x) / z) * Float64(y / x));
	else
		tmp = Float64(y * Float64(Float64(Float64(Float64(x / y) * Float64(y * Float64(x * 0.5))) + 1.0) / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.2e+191)
		tmp = (0.5 * ((y * x) / z)) + ((y / z) * (1.0 / x));
	elseif ((y <= -6e-150) || ~((y <= 7.8e-209)))
		tmp = (cosh(x) / z) * (y / x);
	else
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2e+191], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -6e-150], N[Not[LessEqual[y, 7.8e-209]], $MachinePrecision]], N[(N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(N[(x / y), $MachinePrecision] * N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999993e191

   1. Initial program 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l/ 99.9%

         \[\leadsto 0.5 \cdot \frac{x \cdot y}{z} + \color{blue}{\frac{\frac{y}{z}}{x}} \]

      2. div-inv 99.9%

         \[\leadsto 0.5 \cdot \frac{x \cdot y}{z} + \color{blue}{\frac{y}{z} \cdot \frac{1}{x}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{z} + \color{blue}{\frac{y}{z} \cdot \frac{1}{x}} \]

   if -1.19999999999999993e191 < y < -6.0000000000000003e-150 or 7.8000000000000001e-209 < y

   1. Initial program 92.5%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   if -6.0000000000000003e-150 < y < 7.8000000000000001e-209

   1. Initial program 61.6%

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

      1. associate-*r/ 54.4%

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

      2. associate-/r* 61.8%

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

   3. Simplified 61.8%

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

   4. Taylor expanded in x around 0 47.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 47.0%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 47.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 47.0%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 47.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 47.0%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 47.0%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 50.5%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 50.5%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 50.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 50.5%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 50.5%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 50.5%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 50.5%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 50.6%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 50.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 50.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 50.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 50.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 50.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 45.5%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 45.6%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 45.6%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 45.6%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 45.6%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 45.6%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 52.9%

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

      1. add-exp-log_binary64 29.6%

         \[\leadsto \color{blue}{e^{\log \left(\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}\right)}} \]

   10. Applied rewrite-once 29.6%

       \[\leadsto \color{blue}{e^{\log \left(\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}\right)}} \]
   11. Step-by-step derivation

       1. rem-exp-log 52.9%

          \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

       2. *-commutative 52.9%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{\color{blue}{z \cdot x}}{y}} \]

       3. associate-/r/ 80.2%

          \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{z \cdot x} \cdot y} \]

       4. *-commutative 80.2%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{x \cdot z}} \cdot y \]

   12. Simplified 80.2%

       \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{x \cdot z} \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+191}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{z} \cdot \frac{1}{x}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-150} \lor \neg \left(y \leq 7.8 \cdot 10^{-209}\right):\\ \;\;\;\;\frac{\cosh x}{z} \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right) + 1}{x \cdot z}\\ \end{array} \]

Alternative 3: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{\frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right) + 1}{x \cdot z}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+151}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.7e+122)
   (* y (/ (+ (* (/ x y) (* y (* x 0.5))) 1.0) (* x z)))
   (if (<= x 1.08e+151)
     (* (cosh x) (/ y (* x z)))
     (* (/ y x) (/ (+ (* 0.5 (* x x)) 1.0) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e+122) {
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z));
	} else if (x <= 1.08e+151) {
		tmp = cosh(x) * (y / (x * z));
	} else {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.7d+122)) then
        tmp = y * ((((x / y) * (y * (x * 0.5d0))) + 1.0d0) / (x * z))
    else if (x <= 1.08d+151) then
        tmp = cosh(x) * (y / (x * z))
    else
        tmp = (y / x) * (((0.5d0 * (x * x)) + 1.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e+122) {
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z));
	} else if (x <= 1.08e+151) {
		tmp = Math.cosh(x) * (y / (x * z));
	} else {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.7e+122:
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z))
	elif x <= 1.08e+151:
		tmp = math.cosh(x) * (y / (x * z))
	else:
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.7e+122)
		tmp = Float64(y * Float64(Float64(Float64(Float64(x / y) * Float64(y * Float64(x * 0.5))) + 1.0) / Float64(x * z)));
	elseif (x <= 1.08e+151)
		tmp = Float64(cosh(x) * Float64(y / Float64(x * z)));
	else
		tmp = Float64(Float64(y / x) * Float64(Float64(Float64(0.5 * Float64(x * x)) + 1.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.7e+122)
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z));
	elseif (x <= 1.08e+151)
		tmp = cosh(x) * (y / (x * z));
	else
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.7e+122], N[(y * N[(N[(N[(N[(x / y), $MachinePrecision] * N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.08e+151], N[(N[Cosh[x], $MachinePrecision] * N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * N[(N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e122

   1. Initial program 52.4%

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

      1. associate-*r/ 38.1%

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

      2. associate-/r* 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in x around 0 47.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 40.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 40.9%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 40.9%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 40.9%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 40.9%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 40.9%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 40.9%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 40.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 40.9%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 40.9%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 40.9%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 40.9%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 47.4%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 47.4%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 47.4%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 47.4%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 47.4%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 47.4%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 38.1%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 38.1%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 38.1%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 38.1%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 38.1%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 38.1%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 45.2%

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

      1. add-exp-log_binary64 14.3%

         \[\leadsto \color{blue}{e^{\log \left(\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}\right)}} \]

   10. Applied rewrite-once 14.3%

       \[\leadsto \color{blue}{e^{\log \left(\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}\right)}} \]
   11. Step-by-step derivation

       1. rem-exp-log 45.2%

          \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

       2. *-commutative 45.2%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{\color{blue}{z \cdot x}}{y}} \]

       3. associate-/r/ 69.0%

          \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{z \cdot x} \cdot y} \]

       4. *-commutative 69.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{x \cdot z}} \cdot y \]

   12. Simplified 69.0%

       \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{x \cdot z} \cdot y} \]

   if -1.7e122 < x < 1.08000000000000003e151

   1. Initial program 92.7%

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

      1. associate-*r/ 86.2%

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

      2. associate-/r* 87.1%

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

   3. Simplified 87.1%

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

   if 1.08000000000000003e151 < x

   1. Initial program 78.6%

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

      1. associate-*r/ 60.7%

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

      2. associate-/r* 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in x around 0 48.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 45.1%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 45.1%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 45.1%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 45.1%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 45.1%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 45.1%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 45.1%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 45.1%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 45.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 45.1%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 45.1%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 45.1%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 45.1%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 48.4%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 48.4%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 48.4%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 48.4%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 48.4%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 48.4%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 60.8%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 60.8%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 60.8%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 60.8%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 60.8%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 60.8%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 50.1%

      \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

   9. Taylor expanded in y around 0 64.3%

      \[\leadsto \color{blue}{\frac{y \cdot \left(1 + 0.5 \cdot {x}^{2}\right)}{x \cdot z}} \]
   10. Step-by-step derivation

       1. times-frac 75.1%

          \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot {x}^{2}}{z}} \]

       2. unpow2 75.1%

          \[\leadsto \frac{y}{x} \cdot \frac{1 + 0.5 \cdot \color{blue}{\left(x \cdot x\right)}}{z} \]

   11. Simplified 75.1%

       \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{\frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right) + 1}{x \cdot z}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+151}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \end{array} \]

Alternative 4: 77.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ t_1 := \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+77}:\\ \;\;\;\;\frac{t_1 + z \cdot \frac{1}{z}}{x \cdot \frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-151}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \frac{t_1 + 1}{x \cdot z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{\left(x \cdot z\right) \cdot \left(-\frac{x}{2}\right) - y \cdot \frac{z}{y}}{x \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ y x) (/ (+ (* 0.5 (* x x)) 1.0) z)))
        (t_1 (* (/ x y) (* y (* x 0.5)))))
   (if (<= y -1e+77)
     (/ (+ t_1 (* z (/ 1.0 z))) (* x (/ z y)))
     (if (<= y -1.05e-151)
       t_0
       (if (<= y 1.6e-109)
         (* y (/ (+ t_1 1.0) (* x z)))
         (if (<= y 1.5e+74)
           t_0
           (if (<= y 1.55e+92)
             (*
              (/ y z)
              (/ (- (* (* x z) (- (/ x 2.0))) (* y (/ z y))) (* x (- z))))
             (+ (* 0.5 (/ (* y x) z)) (/ y (* x z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	double t_1 = (x / y) * (y * (x * 0.5));
	double tmp;
	if (y <= -1e+77) {
		tmp = (t_1 + (z * (1.0 / z))) / (x * (z / y));
	} else if (y <= -1.05e-151) {
		tmp = t_0;
	} else if (y <= 1.6e-109) {
		tmp = y * ((t_1 + 1.0) / (x * z));
	} else if (y <= 1.5e+74) {
		tmp = t_0;
	} else if (y <= 1.55e+92) {
		tmp = (y / z) * ((((x * z) * -(x / 2.0)) - (y * (z / y))) / (x * -z));
	} else {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (y / x) * (((0.5d0 * (x * x)) + 1.0d0) / z)
    t_1 = (x / y) * (y * (x * 0.5d0))
    if (y <= (-1d+77)) then
        tmp = (t_1 + (z * (1.0d0 / z))) / (x * (z / y))
    else if (y <= (-1.05d-151)) then
        tmp = t_0
    else if (y <= 1.6d-109) then
        tmp = y * ((t_1 + 1.0d0) / (x * z))
    else if (y <= 1.5d+74) then
        tmp = t_0
    else if (y <= 1.55d+92) then
        tmp = (y / z) * ((((x * z) * -(x / 2.0d0)) - (y * (z / y))) / (x * -z))
    else
        tmp = (0.5d0 * ((y * x) / z)) + (y / (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	double t_1 = (x / y) * (y * (x * 0.5));
	double tmp;
	if (y <= -1e+77) {
		tmp = (t_1 + (z * (1.0 / z))) / (x * (z / y));
	} else if (y <= -1.05e-151) {
		tmp = t_0;
	} else if (y <= 1.6e-109) {
		tmp = y * ((t_1 + 1.0) / (x * z));
	} else if (y <= 1.5e+74) {
		tmp = t_0;
	} else if (y <= 1.55e+92) {
		tmp = (y / z) * ((((x * z) * -(x / 2.0)) - (y * (z / y))) / (x * -z));
	} else {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y / x) * (((0.5 * (x * x)) + 1.0) / z)
	t_1 = (x / y) * (y * (x * 0.5))
	tmp = 0
	if y <= -1e+77:
		tmp = (t_1 + (z * (1.0 / z))) / (x * (z / y))
	elif y <= -1.05e-151:
		tmp = t_0
	elif y <= 1.6e-109:
		tmp = y * ((t_1 + 1.0) / (x * z))
	elif y <= 1.5e+74:
		tmp = t_0
	elif y <= 1.55e+92:
		tmp = (y / z) * ((((x * z) * -(x / 2.0)) - (y * (z / y))) / (x * -z))
	else:
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y / x) * Float64(Float64(Float64(0.5 * Float64(x * x)) + 1.0) / z))
	t_1 = Float64(Float64(x / y) * Float64(y * Float64(x * 0.5)))
	tmp = 0.0
	if (y <= -1e+77)
		tmp = Float64(Float64(t_1 + Float64(z * Float64(1.0 / z))) / Float64(x * Float64(z / y)));
	elseif (y <= -1.05e-151)
		tmp = t_0;
	elseif (y <= 1.6e-109)
		tmp = Float64(y * Float64(Float64(t_1 + 1.0) / Float64(x * z)));
	elseif (y <= 1.5e+74)
		tmp = t_0;
	elseif (y <= 1.55e+92)
		tmp = Float64(Float64(y / z) * Float64(Float64(Float64(Float64(x * z) * Float64(-Float64(x / 2.0))) - Float64(y * Float64(z / y))) / Float64(x * Float64(-z))));
	else
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / z)) + Float64(y / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	t_1 = (x / y) * (y * (x * 0.5));
	tmp = 0.0;
	if (y <= -1e+77)
		tmp = (t_1 + (z * (1.0 / z))) / (x * (z / y));
	elseif (y <= -1.05e-151)
		tmp = t_0;
	elseif (y <= 1.6e-109)
		tmp = y * ((t_1 + 1.0) / (x * z));
	elseif (y <= 1.5e+74)
		tmp = t_0;
	elseif (y <= 1.55e+92)
		tmp = (y / z) * ((((x * z) * -(x / 2.0)) - (y * (z / y))) / (x * -z));
	else
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] * N[(N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+77], N[(N[(t$95$1 + N[(z * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.05e-151], t$95$0, If[LessEqual[y, 1.6e-109], N[(y * N[(N[(t$95$1 + 1.0), $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+74], t$95$0, If[LessEqual[y, 1.55e+92], N[(N[(y / z), $MachinePrecision] * N[(N[(N[(N[(x * z), $MachinePrecision] * (-N[(x / 2.0), $MachinePrecision])), $MachinePrecision] - N[(y * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.99999999999999983e76

   1. Initial program 84.7%

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

      1. associate-*r/ 82.6%

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

      2. associate-/r* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around 0 88.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 88.4%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \frac{x \cdot y}{z}} \]

      2. associate-/l/ 88.4%

         \[\leadsto \color{blue}{\frac{\frac{y}{z}}{x}} + 0.5 \cdot \frac{x \cdot y}{z} \]

      3. div-inv 88.3%

         \[\leadsto \frac{\color{blue}{y \cdot \frac{1}{z}}}{x} + 0.5 \cdot \frac{x \cdot y}{z} \]

      4. *-commutative 88.3%

         \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot y}}{x} + 0.5 \cdot \frac{x \cdot y}{z} \]

      5. associate-/l* 74.2%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \frac{x \cdot y}{z} \]

      6. associate-*r/ 74.2%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      7. frac-add 76.1%

         \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(0.5 \cdot \left(x \cdot y\right)\right)}{\frac{x}{y} \cdot z}} \]

      8. associate-*r* 76.1%

         \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \color{blue}{\left(\left(0.5 \cdot x\right) \cdot y\right)}}{\frac{x}{y} \cdot z} \]

      9. *-commutative 76.1%

         \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \color{blue}{\left(y \cdot \left(0.5 \cdot x\right)\right)}}{\frac{x}{y} \cdot z} \]

      10. *-commutative 76.1%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \color{blue}{\left(x \cdot 0.5\right)}\right)}{\frac{x}{y} \cdot z} \]

      11. /-rgt-identity 76.1%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot \color{blue}{\frac{z}{1}}} \]

      12. times-frac 82.0%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{x \cdot z}{y \cdot 1}}} \]

      13. *-commutative 82.0%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{\color{blue}{1 \cdot y}}} \]

      14. times-frac 90.2%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{x}{1} \cdot \frac{z}{y}}} \]

      15. /-rgt-identity 90.2%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{x} \cdot \frac{z}{y}} \]

   6. Applied egg-rr 90.2%

      \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{x \cdot \frac{z}{y}}} \]

   if -9.99999999999999983e76 < y < -1.04999999999999995e-151 or 1.6000000000000001e-109 < y < 1.5e74

   1. Initial program 96.6%

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

      1. associate-*r/ 81.4%

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

      2. associate-/r* 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in x around 0 59.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 59.3%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 59.3%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 59.3%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 59.3%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 59.3%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 59.3%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 61.3%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 61.3%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 61.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 61.2%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 61.3%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 61.3%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 61.3%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 61.3%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 61.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 61.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 61.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 61.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 61.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 63.9%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 63.9%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 63.9%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 63.9%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 63.9%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 63.9%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 63.0%

      \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

   9. Taylor expanded in y around 0 63.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(1 + 0.5 \cdot {x}^{2}\right)}{x \cdot z}} \]
   10. Step-by-step derivation

       1. times-frac 75.7%

          \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot {x}^{2}}{z}} \]

       2. unpow2 75.7%

          \[\leadsto \frac{y}{x} \cdot \frac{1 + 0.5 \cdot \color{blue}{\left(x \cdot x\right)}}{z} \]

   11. Simplified 75.7%

       \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}} \]

   if -1.04999999999999995e-151 < y < 1.6000000000000001e-109

   1. Initial program 64.7%

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

      1. associate-*r/ 55.3%

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

      2. associate-/r* 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in x around 0 46.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 46.0%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 46.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 46.4%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 46.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 46.4%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 46.4%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 52.8%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 52.8%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 52.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 52.8%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 52.8%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 52.8%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 52.8%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 52.8%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 47.6%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 47.7%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 52.1%

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

      1. add-exp-log_binary64 26.5%

         \[\leadsto \color{blue}{e^{\log \left(\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}\right)}} \]

   10. Applied rewrite-once 26.5%

       \[\leadsto \color{blue}{e^{\log \left(\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}\right)}} \]
   11. Step-by-step derivation

       1. rem-exp-log 52.1%

          \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

       2. *-commutative 52.1%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{\color{blue}{z \cdot x}}{y}} \]

       3. associate-/r/ 76.1%

          \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{z \cdot x} \cdot y} \]

       4. *-commutative 76.1%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{x \cdot z}} \cdot y \]

   12. Simplified 76.1%

       \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{x \cdot z} \cdot y} \]

   if 1.5e74 < y < 1.5500000000000001e92

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. associate-/r* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 75.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 75.3%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{y \cdot x}}{z} + \frac{y}{x \cdot z} \]

      2. associate-/l* 75.3%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{z}{x}}} + \frac{y}{x \cdot z} \]

      3. div-inv 75.3%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y \cdot \frac{1}{\frac{z}{x}}\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 75.3%

      \[\leadsto 0.5 \cdot \color{blue}{\left(y \cdot \frac{1}{\frac{z}{x}}\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 75.3%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(y \cdot \frac{1}{\frac{z}{x}}\right)} \]

      2. associate-*r* 75.3%

         \[\leadsto \frac{y}{x \cdot z} + \color{blue}{\left(0.5 \cdot y\right) \cdot \frac{1}{\frac{z}{x}}} \]

      3. clear-num 75.3%

         \[\leadsto \frac{y}{x \cdot z} + \left(0.5 \cdot y\right) \cdot \color{blue}{\frac{x}{z}} \]

      4. associate-*r* 75.3%

         \[\leadsto \frac{y}{x \cdot z} + \color{blue}{0.5 \cdot \left(y \cdot \frac{x}{z}\right)} \]

      5. *-commutative 75.3%

         \[\leadsto \frac{y}{x \cdot z} + 0.5 \cdot \color{blue}{\left(\frac{x}{z} \cdot y\right)} \]

      6. associate-/r/ 75.3%

         \[\leadsto \frac{y}{x \cdot z} + 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} \]

      7. frac-2neg 75.3%

         \[\leadsto \color{blue}{\frac{-y}{-x \cdot z}} + 0.5 \cdot \frac{x}{\frac{z}{y}} \]

      8. associate-*r/ 75.3%

         \[\leadsto \frac{-y}{-x \cdot z} + \color{blue}{\frac{0.5 \cdot x}{\frac{z}{y}}} \]

      9. *-commutative 75.3%

         \[\leadsto \frac{-y}{-x \cdot z} + \frac{\color{blue}{x \cdot 0.5}}{\frac{z}{y}} \]

      10. frac-add 74.2%

          \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot \frac{z}{y} + \left(-x \cdot z\right) \cdot \left(x \cdot 0.5\right)}{\left(-x \cdot z\right) \cdot \frac{z}{y}}} \]

      11. *-commutative 74.2%

          \[\leadsto \frac{\left(-y\right) \cdot \frac{z}{y} + \left(-x \cdot z\right) \cdot \left(x \cdot 0.5\right)}{\color{blue}{\frac{z}{y} \cdot \left(-x \cdot z\right)}} \]

      12. div-inv 74.6%

          \[\leadsto \color{blue}{\left(\left(-y\right) \cdot \frac{z}{y} + \left(-x \cdot z\right) \cdot \left(x \cdot 0.5\right)\right) \cdot \frac{1}{\frac{z}{y} \cdot \left(-x \cdot z\right)}} \]

   8. Applied egg-rr 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-/r/ 74.2%

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

      3. associate-/l* 99.6%

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

      4. associate-/r/ 99.6%

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

      5. associate-/r/ 99.0%

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

      6. associate-*l/ 99.6%

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

      7. *-lft-identity 99.6%

         \[\leadsto \frac{\color{blue}{y}}{z} \cdot \frac{\mathsf{fma}\left(\frac{x}{2}, z \cdot \left(-x\right), \frac{z}{y} \cdot \left(-y\right)\right)}{z \cdot \left(-x\right)} \]

      8. fma-udef 99.6%

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

      9. distribute-rgt-neg-out 99.6%

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

      10. unsub-neg 99.6%

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

      11. distribute-rgt-neg-out 99.6%

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

      12. *-commutative 99.6%

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

      13. distribute-rgt-neg-in 99.6%

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

      14. distribute-rgt-neg-out 99.6%

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

      15. *-commutative 99.6%

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

   10. Simplified 99.6%

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

   if 1.5500000000000001e92 < y

   1. Initial program 92.3%

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

      1. associate-*r/ 89.6%

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

      2. associate-/r* 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in x around 0 89.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right) + z \cdot \frac{1}{z}}{x \cdot \frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-151}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \frac{\frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right) + 1}{x \cdot z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{\left(x \cdot z\right) \cdot \left(-\frac{x}{2}\right) - y \cdot \frac{z}{y}}{x \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \end{array} \]

Alternative 5: 75.1% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+190}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{z} \cdot \frac{1}{x}\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-151} \lor \neg \left(y \leq 2.3 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right) + 1}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+190)
   (+ (* 0.5 (/ (* y x) z)) (* (/ y z) (/ 1.0 x)))
   (if (or (<= y -1.26e-151) (not (<= y 2.3e-110)))
     (* (/ y x) (/ (+ (* 0.5 (* x x)) 1.0) z))
     (* y (/ (+ (* (/ x y) (* y (* x 0.5))) 1.0) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+190) {
		tmp = (0.5 * ((y * x) / z)) + ((y / z) * (1.0 / x));
	} else if ((y <= -1.26e-151) || !(y <= 2.3e-110)) {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	} else {
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9d+190)) then
        tmp = (0.5d0 * ((y * x) / z)) + ((y / z) * (1.0d0 / x))
    else if ((y <= (-1.26d-151)) .or. (.not. (y <= 2.3d-110))) then
        tmp = (y / x) * (((0.5d0 * (x * x)) + 1.0d0) / z)
    else
        tmp = y * ((((x / y) * (y * (x * 0.5d0))) + 1.0d0) / (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+190) {
		tmp = (0.5 * ((y * x) / z)) + ((y / z) * (1.0 / x));
	} else if ((y <= -1.26e-151) || !(y <= 2.3e-110)) {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	} else {
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e+190:
		tmp = (0.5 * ((y * x) / z)) + ((y / z) * (1.0 / x))
	elif (y <= -1.26e-151) or not (y <= 2.3e-110):
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z)
	else:
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+190)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / z)) + Float64(Float64(y / z) * Float64(1.0 / x)));
	elseif ((y <= -1.26e-151) || !(y <= 2.3e-110))
		tmp = Float64(Float64(y / x) * Float64(Float64(Float64(0.5 * Float64(x * x)) + 1.0) / z));
	else
		tmp = Float64(y * Float64(Float64(Float64(Float64(x / y) * Float64(y * Float64(x * 0.5))) + 1.0) / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e+190)
		tmp = (0.5 * ((y * x) / z)) + ((y / z) * (1.0 / x));
	elseif ((y <= -1.26e-151) || ~((y <= 2.3e-110)))
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	else
		tmp = y * ((((x / y) * (y * (x * 0.5))) + 1.0) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+190], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.26e-151], N[Not[LessEqual[y, 2.3e-110]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] * N[(N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(N[(x / y), $MachinePrecision] * N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999999e190

   1. Initial program 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l/ 99.9%

         \[\leadsto 0.5 \cdot \frac{x \cdot y}{z} + \color{blue}{\frac{\frac{y}{z}}{x}} \]

      2. div-inv 99.9%

         \[\leadsto 0.5 \cdot \frac{x \cdot y}{z} + \color{blue}{\frac{y}{z} \cdot \frac{1}{x}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{z} + \color{blue}{\frac{y}{z} \cdot \frac{1}{x}} \]

   if -8.9999999999999999e190 < y < -1.2600000000000001e-151 or 2.3000000000000001e-110 < y

   1. Initial program 94.8%

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

      1. associate-*r/ 84.5%

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

      2. associate-/r* 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in x around 0 68.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 66.5%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 66.5%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 66.5%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 66.5%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 66.5%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 64.6%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 64.6%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 64.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 64.5%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 64.9%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 64.9%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 64.9%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 67.3%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 67.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 67.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 67.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 67.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 67.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 68.8%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 68.8%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 68.8%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 68.8%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 68.8%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 68.8%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 67.1%

      \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

   9. Taylor expanded in y around 0 68.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(1 + 0.5 \cdot {x}^{2}\right)}{x \cdot z}} \]
   10. Step-by-step derivation

       1. times-frac 76.2%

          \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot {x}^{2}}{z}} \]

       2. unpow2 76.2%

          \[\leadsto \frac{y}{x} \cdot \frac{1 + 0.5 \cdot \color{blue}{\left(x \cdot x\right)}}{z} \]

   11. Simplified 76.2%

       \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}} \]

   if -1.2600000000000001e-151 < y < 2.3000000000000001e-110

   1. Initial program 64.7%

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

      1. associate-*r/ 55.3%

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

      2. associate-/r* 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in x around 0 46.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 46.0%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 46.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 46.4%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 46.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 46.4%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 46.4%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 52.8%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 52.8%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 52.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 52.8%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 52.8%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 52.8%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 52.8%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 52.8%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 47.6%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 47.7%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 52.1%

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

      1. add-exp-log_binary64 26.5%

         \[\leadsto \color{blue}{e^{\log \left(\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}\right)}} \]

   10. Applied rewrite-once 26.5%

       \[\leadsto \color{blue}{e^{\log \left(\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}\right)}} \]
   11. Step-by-step derivation

       1. rem-exp-log 52.1%

          \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

       2. *-commutative 52.1%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{\color{blue}{z \cdot x}}{y}} \]

       3. associate-/r/ 76.1%

          \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{z \cdot x} \cdot y} \]

       4. *-commutative 76.1%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{x \cdot z}} \cdot y \]

   12. Simplified 76.1%

       \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{x \cdot z} \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+190}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{z} \cdot \frac{1}{x}\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-151} \lor \neg \left(y \leq 2.3 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right) + 1}{x \cdot z}\\ \end{array} \]

Alternative 6: 75.5% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+77}:\\ \;\;\;\;\frac{t_0 + z \cdot \frac{1}{z}}{x \cdot \frac{z}{y}}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-149} \lor \neg \left(y \leq 6.2 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t_0 + 1}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x y) (* y (* x 0.5)))))
   (if (<= y -5e+77)
     (/ (+ t_0 (* z (/ 1.0 z))) (* x (/ z y)))
     (if (or (<= y -4e-149) (not (<= y 6.2e-110)))
       (* (/ y x) (/ (+ (* 0.5 (* x x)) 1.0) z))
       (* y (/ (+ t_0 1.0) (* x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / y) * (y * (x * 0.5));
	double tmp;
	if (y <= -5e+77) {
		tmp = (t_0 + (z * (1.0 / z))) / (x * (z / y));
	} else if ((y <= -4e-149) || !(y <= 6.2e-110)) {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	} else {
		tmp = y * ((t_0 + 1.0) / (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x / y) * (y * (x * 0.5d0))
    if (y <= (-5d+77)) then
        tmp = (t_0 + (z * (1.0d0 / z))) / (x * (z / y))
    else if ((y <= (-4d-149)) .or. (.not. (y <= 6.2d-110))) then
        tmp = (y / x) * (((0.5d0 * (x * x)) + 1.0d0) / z)
    else
        tmp = y * ((t_0 + 1.0d0) / (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / y) * (y * (x * 0.5));
	double tmp;
	if (y <= -5e+77) {
		tmp = (t_0 + (z * (1.0 / z))) / (x * (z / y));
	} else if ((y <= -4e-149) || !(y <= 6.2e-110)) {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	} else {
		tmp = y * ((t_0 + 1.0) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / y) * (y * (x * 0.5))
	tmp = 0
	if y <= -5e+77:
		tmp = (t_0 + (z * (1.0 / z))) / (x * (z / y))
	elif (y <= -4e-149) or not (y <= 6.2e-110):
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z)
	else:
		tmp = y * ((t_0 + 1.0) / (x * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / y) * Float64(y * Float64(x * 0.5)))
	tmp = 0.0
	if (y <= -5e+77)
		tmp = Float64(Float64(t_0 + Float64(z * Float64(1.0 / z))) / Float64(x * Float64(z / y)));
	elseif ((y <= -4e-149) || !(y <= 6.2e-110))
		tmp = Float64(Float64(y / x) * Float64(Float64(Float64(0.5 * Float64(x * x)) + 1.0) / z));
	else
		tmp = Float64(y * Float64(Float64(t_0 + 1.0) / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / y) * (y * (x * 0.5));
	tmp = 0.0;
	if (y <= -5e+77)
		tmp = (t_0 + (z * (1.0 / z))) / (x * (z / y));
	elseif ((y <= -4e-149) || ~((y <= 6.2e-110)))
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	else
		tmp = y * ((t_0 + 1.0) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] * N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+77], N[(N[(t$95$0 + N[(z * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4e-149], N[Not[LessEqual[y, 6.2e-110]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] * N[(N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t$95$0 + 1.0), $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000004e77

   1. Initial program 84.7%

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

      1. associate-*r/ 82.6%

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

      2. associate-/r* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around 0 88.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 88.4%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \frac{x \cdot y}{z}} \]

      2. associate-/l/ 88.4%

         \[\leadsto \color{blue}{\frac{\frac{y}{z}}{x}} + 0.5 \cdot \frac{x \cdot y}{z} \]

      3. div-inv 88.3%

         \[\leadsto \frac{\color{blue}{y \cdot \frac{1}{z}}}{x} + 0.5 \cdot \frac{x \cdot y}{z} \]

      4. *-commutative 88.3%

         \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot y}}{x} + 0.5 \cdot \frac{x \cdot y}{z} \]

      5. associate-/l* 74.2%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \frac{x \cdot y}{z} \]

      6. associate-*r/ 74.2%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      7. frac-add 76.1%

         \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(0.5 \cdot \left(x \cdot y\right)\right)}{\frac{x}{y} \cdot z}} \]

      8. associate-*r* 76.1%

         \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \color{blue}{\left(\left(0.5 \cdot x\right) \cdot y\right)}}{\frac{x}{y} \cdot z} \]

      9. *-commutative 76.1%

         \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \color{blue}{\left(y \cdot \left(0.5 \cdot x\right)\right)}}{\frac{x}{y} \cdot z} \]

      10. *-commutative 76.1%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \color{blue}{\left(x \cdot 0.5\right)}\right)}{\frac{x}{y} \cdot z} \]

      11. /-rgt-identity 76.1%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot \color{blue}{\frac{z}{1}}} \]

      12. times-frac 82.0%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{x \cdot z}{y \cdot 1}}} \]

      13. *-commutative 82.0%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{\color{blue}{1 \cdot y}}} \]

      14. times-frac 90.2%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{x}{1} \cdot \frac{z}{y}}} \]

      15. /-rgt-identity 90.2%

          \[\leadsto \frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{x} \cdot \frac{z}{y}} \]

   6. Applied egg-rr 90.2%

      \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{x \cdot \frac{z}{y}}} \]

   if -5.00000000000000004e77 < y < -3.99999999999999992e-149 or 6.20000000000000014e-110 < y

   1. Initial program 95.5%

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

      1. associate-*r/ 84.2%

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

      2. associate-/r* 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in x around 0 68.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 66.8%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 66.8%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 66.8%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 66.8%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 66.8%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 66.8%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 66.1%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 66.0%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 66.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 66.0%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 66.0%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 66.0%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 66.0%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 67.5%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 67.5%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 67.5%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 67.5%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 67.5%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 67.5%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 68.5%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 68.5%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 68.5%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 68.5%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 68.5%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 68.5%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 67.0%

      \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

   9. Taylor expanded in y around 0 67.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(1 + 0.5 \cdot {x}^{2}\right)}{x \cdot z}} \]
   10. Step-by-step derivation

       1. times-frac 76.7%

          \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot {x}^{2}}{z}} \]

       2. unpow2 76.7%

          \[\leadsto \frac{y}{x} \cdot \frac{1 + 0.5 \cdot \color{blue}{\left(x \cdot x\right)}}{z} \]

   11. Simplified 76.7%

       \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}} \]

   if -3.99999999999999992e-149 < y < 6.20000000000000014e-110

   1. Initial program 64.7%

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

      1. associate-*r/ 55.3%

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

      2. associate-/r* 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in x around 0 46.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 46.0%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 46.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 46.4%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 46.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 46.4%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 46.4%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 52.8%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 52.8%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 52.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 52.8%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 52.8%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 52.8%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 52.8%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 52.8%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 52.8%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 47.6%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 47.7%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 47.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 52.1%

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

      1. add-exp-log_binary64 26.5%

         \[\leadsto \color{blue}{e^{\log \left(\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}\right)}} \]

   10. Applied rewrite-once 26.5%

       \[\leadsto \color{blue}{e^{\log \left(\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}\right)}} \]
   11. Step-by-step derivation

       1. rem-exp-log 52.1%

          \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

       2. *-commutative 52.1%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{\color{blue}{z \cdot x}}{y}} \]

       3. associate-/r/ 76.1%

          \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{z \cdot x} \cdot y} \]

       4. *-commutative 76.1%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{x \cdot z}} \cdot y \]

   12. Simplified 76.1%

       \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{x \cdot z} \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right) + z \cdot \frac{1}{z}}{x \cdot \frac{z}{y}}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-149} \lor \neg \left(y \leq 6.2 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right) + 1}{x \cdot z}\\ \end{array} \]

Alternative 7: 74.4% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+190}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-105} \lor \neg \left(y \leq 2.7 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + y \cdot \frac{x}{\frac{z}{0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+190)
   (+ (* 0.5 (/ (* y x) z)) (/ y (* x z)))
   (if (or (<= y -8.8e-105) (not (<= y 2.7e-73)))
     (* (/ y x) (/ (+ (* 0.5 (* x x)) 1.0) z))
     (+ (/ (/ y x) z) (* y (/ x (/ z 0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+190) {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	} else if ((y <= -8.8e-105) || !(y <= 2.7e-73)) {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	} else {
		tmp = ((y / x) / z) + (y * (x / (z / 0.5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9d+190)) then
        tmp = (0.5d0 * ((y * x) / z)) + (y / (x * z))
    else if ((y <= (-8.8d-105)) .or. (.not. (y <= 2.7d-73))) then
        tmp = (y / x) * (((0.5d0 * (x * x)) + 1.0d0) / z)
    else
        tmp = ((y / x) / z) + (y * (x / (z / 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+190) {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	} else if ((y <= -8.8e-105) || !(y <= 2.7e-73)) {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	} else {
		tmp = ((y / x) / z) + (y * (x / (z / 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e+190:
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z))
	elif (y <= -8.8e-105) or not (y <= 2.7e-73):
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z)
	else:
		tmp = ((y / x) / z) + (y * (x / (z / 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+190)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / z)) + Float64(y / Float64(x * z)));
	elseif ((y <= -8.8e-105) || !(y <= 2.7e-73))
		tmp = Float64(Float64(y / x) * Float64(Float64(Float64(0.5 * Float64(x * x)) + 1.0) / z));
	else
		tmp = Float64(Float64(Float64(y / x) / z) + Float64(y * Float64(x / Float64(z / 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e+190)
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	elseif ((y <= -8.8e-105) || ~((y <= 2.7e-73)))
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	else
		tmp = ((y / x) / z) + (y * (x / (z / 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+190], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -8.8e-105], N[Not[LessEqual[y, 2.7e-73]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] * N[(N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision] + N[(y * N[(x / N[(z / 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999999e190

   1. Initial program 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]

   if -8.9999999999999999e190 < y < -8.80000000000000016e-105 or 2.69999999999999994e-73 < y

   1. Initial program 95.5%

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

      1. associate-*r/ 84.9%

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

      2. associate-/r* 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around 0 72.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 70.1%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 70.1%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 70.1%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 70.1%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 70.1%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 70.1%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 66.5%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 66.5%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 66.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 66.4%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 66.9%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 66.9%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 66.9%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 69.7%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 69.7%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 69.7%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 69.7%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 69.7%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 69.7%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 70.7%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 70.7%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 70.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 70.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 70.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 70.7%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 70.1%

      \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

   9. Taylor expanded in y around 0 71.6%

      \[\leadsto \color{blue}{\frac{y \cdot \left(1 + 0.5 \cdot {x}^{2}\right)}{x \cdot z}} \]
   10. Step-by-step derivation

       1. times-frac 78.7%

          \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot {x}^{2}}{z}} \]

       2. unpow2 78.7%

          \[\leadsto \frac{y}{x} \cdot \frac{1 + 0.5 \cdot \color{blue}{\left(x \cdot x\right)}}{z} \]

   11. Simplified 78.7%

       \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}} \]

   if -8.80000000000000016e-105 < y < 2.69999999999999994e-73

   1. Initial program 70.7%

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

      1. associate-*r/ 61.3%

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

      2. associate-/r* 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in x around 0 46.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 45.7%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 45.7%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 46.0%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 46.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 46.0%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 46.0%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 52.9%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 52.9%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 52.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 52.8%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 52.9%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 52.9%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 52.9%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 52.9%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 52.9%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 52.9%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 52.9%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 52.9%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 52.9%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 49.8%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 49.9%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 49.9%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 49.9%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 49.9%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 49.9%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 51.4%

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

      1. associate-*r* 51.4%

         \[\leadsto \frac{1 + \color{blue}{\left(\frac{x}{y} \cdot y\right) \cdot \left(x \cdot 0.5\right)}}{\frac{x \cdot z}{y}} \]

      2. div-inv 51.4%

         \[\leadsto \frac{1 + \left(\color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot y\right) \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      3. associate-*l* 49.4%

         \[\leadsto \frac{1 + \color{blue}{\left(x \cdot \left(\frac{1}{y} \cdot y\right)\right)} \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      4. lft-mult-inverse 49.4%

         \[\leadsto \frac{1 + \left(x \cdot \color{blue}{1}\right) \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      5. *-rgt-identity 49.4%

         \[\leadsto \frac{1 + \color{blue}{x} \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      6. rgt-mult-inverse 35.6%

         \[\leadsto \frac{\color{blue}{\frac{y}{z} \cdot \frac{1}{\frac{y}{z}}} + x \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      7. clear-num 35.6%

         \[\leadsto \frac{\frac{y}{z} \cdot \color{blue}{\frac{z}{y}} + x \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      8. associate-/l* 42.4%

         \[\leadsto \frac{\frac{y}{z} \cdot \frac{z}{y} + x \cdot \left(x \cdot 0.5\right)}{\color{blue}{\frac{x}{\frac{y}{z}}}} \]

      9. div-inv 42.4%

         \[\leadsto \frac{\frac{y}{z} \cdot \frac{z}{y} + x \cdot \left(x \cdot 0.5\right)}{\color{blue}{x \cdot \frac{1}{\frac{y}{z}}}} \]

      10. clear-num 42.4%

          \[\leadsto \frac{\frac{y}{z} \cdot \frac{z}{y} + x \cdot \left(x \cdot 0.5\right)}{x \cdot \color{blue}{\frac{z}{y}}} \]

      11. frac-add 46.1%

          \[\leadsto \color{blue}{\frac{\frac{y}{z}}{x} + \frac{x \cdot 0.5}{\frac{z}{y}}} \]

      12. associate-/l/ 45.7%

          \[\leadsto \color{blue}{\frac{y}{x \cdot z}} + \frac{x \cdot 0.5}{\frac{z}{y}} \]

      13. associate-/r* 52.6%

          \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + \frac{x \cdot 0.5}{\frac{z}{y}} \]

      14. associate-/r/ 61.7%

          \[\leadsto \frac{\frac{y}{x}}{z} + \color{blue}{\frac{x \cdot 0.5}{z} \cdot y} \]

      15. *-commutative 61.7%

          \[\leadsto \frac{\frac{y}{x}}{z} + \color{blue}{y \cdot \frac{x \cdot 0.5}{z}} \]

      16. associate-/l* 61.7%

          \[\leadsto \frac{\frac{y}{x}}{z} + y \cdot \color{blue}{\frac{x}{\frac{z}{0.5}}} \]

   10. Applied egg-rr 61.7%

       \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z} + y \cdot \frac{x}{\frac{z}{0.5}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+190}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-105} \lor \neg \left(y \leq 2.7 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + y \cdot \frac{x}{\frac{z}{0.5}}\\ \end{array} \]

Alternative 8: 72.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+77}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \mathbf{elif}\;z \leq 10^{-185}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + y \cdot \frac{x}{\frac{z}{0.5}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+238}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot \frac{x}{2} + 1\right)}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1e+77)
   (+ (* 0.5 (/ (* y x) z)) (/ y (* x z)))
   (if (<= z 1e-185)
     (+ (/ (/ y x) z) (* y (/ x (/ z 0.5))))
     (if (<= z 1.45e+238)
       (/ (* y (+ (* x (/ x 2.0)) 1.0)) (* x z))
       (* (/ y x) (/ (+ (* 0.5 (* x x)) 1.0) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+77) {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	} else if (z <= 1e-185) {
		tmp = ((y / x) / z) + (y * (x / (z / 0.5)));
	} else if (z <= 1.45e+238) {
		tmp = (y * ((x * (x / 2.0)) + 1.0)) / (x * z);
	} else {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1d+77)) then
        tmp = (0.5d0 * ((y * x) / z)) + (y / (x * z))
    else if (z <= 1d-185) then
        tmp = ((y / x) / z) + (y * (x / (z / 0.5d0)))
    else if (z <= 1.45d+238) then
        tmp = (y * ((x * (x / 2.0d0)) + 1.0d0)) / (x * z)
    else
        tmp = (y / x) * (((0.5d0 * (x * x)) + 1.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+77) {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	} else if (z <= 1e-185) {
		tmp = ((y / x) / z) + (y * (x / (z / 0.5)));
	} else if (z <= 1.45e+238) {
		tmp = (y * ((x * (x / 2.0)) + 1.0)) / (x * z);
	} else {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1e+77:
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z))
	elif z <= 1e-185:
		tmp = ((y / x) / z) + (y * (x / (z / 0.5)))
	elif z <= 1.45e+238:
		tmp = (y * ((x * (x / 2.0)) + 1.0)) / (x * z)
	else:
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e+77)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / z)) + Float64(y / Float64(x * z)));
	elseif (z <= 1e-185)
		tmp = Float64(Float64(Float64(y / x) / z) + Float64(y * Float64(x / Float64(z / 0.5))));
	elseif (z <= 1.45e+238)
		tmp = Float64(Float64(y * Float64(Float64(x * Float64(x / 2.0)) + 1.0)) / Float64(x * z));
	else
		tmp = Float64(Float64(y / x) * Float64(Float64(Float64(0.5 * Float64(x * x)) + 1.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1e+77)
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	elseif (z <= 1e-185)
		tmp = ((y / x) / z) + (y * (x / (z / 0.5)));
	elseif (z <= 1.45e+238)
		tmp = (y * ((x * (x / 2.0)) + 1.0)) / (x * z);
	else
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e+77], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-185], N[(N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision] + N[(y * N[(x / N[(z / 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+238], N[(N[(y * N[(N[(x * N[(x / 2.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * N[(N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.99999999999999983e76

   1. Initial program 86.0%

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

      1. associate-*r/ 67.7%

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

      2. associate-/r* 59.2%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in x around 0 56.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]

   if -9.99999999999999983e76 < z < 9.9999999999999999e-186

   1. Initial program 89.7%

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

      1. associate-*r/ 89.7%

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

      2. associate-/r* 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in x around 0 72.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 72.2%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 72.2%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 72.2%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 72.2%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 72.2%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 72.2%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 78.9%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 79.0%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 78.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 78.9%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 78.9%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 78.9%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 78.9%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 78.9%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 78.9%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 78.9%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 78.9%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 78.9%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 78.9%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 75.4%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 75.4%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 75.4%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 75.4%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 75.4%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 75.4%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 74.8%

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

      1. associate-*r* 74.8%

         \[\leadsto \frac{1 + \color{blue}{\left(\frac{x}{y} \cdot y\right) \cdot \left(x \cdot 0.5\right)}}{\frac{x \cdot z}{y}} \]

      2. div-inv 74.8%

         \[\leadsto \frac{1 + \left(\color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot y\right) \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      3. associate-*l* 73.8%

         \[\leadsto \frac{1 + \color{blue}{\left(x \cdot \left(\frac{1}{y} \cdot y\right)\right)} \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      4. lft-mult-inverse 73.8%

         \[\leadsto \frac{1 + \left(x \cdot \color{blue}{1}\right) \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      5. *-rgt-identity 73.8%

         \[\leadsto \frac{1 + \color{blue}{x} \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      6. rgt-mult-inverse 51.3%

         \[\leadsto \frac{\color{blue}{\frac{y}{z} \cdot \frac{1}{\frac{y}{z}}} + x \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      7. clear-num 52.3%

         \[\leadsto \frac{\frac{y}{z} \cdot \color{blue}{\frac{z}{y}} + x \cdot \left(x \cdot 0.5\right)}{\frac{x \cdot z}{y}} \]

      8. associate-/l* 60.0%

         \[\leadsto \frac{\frac{y}{z} \cdot \frac{z}{y} + x \cdot \left(x \cdot 0.5\right)}{\color{blue}{\frac{x}{\frac{y}{z}}}} \]

      9. div-inv 60.1%

         \[\leadsto \frac{\frac{y}{z} \cdot \frac{z}{y} + x \cdot \left(x \cdot 0.5\right)}{\color{blue}{x \cdot \frac{1}{\frac{y}{z}}}} \]

      10. clear-num 60.1%

          \[\leadsto \frac{\frac{y}{z} \cdot \frac{z}{y} + x \cdot \left(x \cdot 0.5\right)}{x \cdot \color{blue}{\frac{z}{y}}} \]

      11. frac-add 78.9%

          \[\leadsto \color{blue}{\frac{\frac{y}{z}}{x} + \frac{x \cdot 0.5}{\frac{z}{y}}} \]

      12. associate-/l/ 72.2%

          \[\leadsto \color{blue}{\frac{y}{x \cdot z}} + \frac{x \cdot 0.5}{\frac{z}{y}} \]

      13. associate-/r* 78.9%

          \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + \frac{x \cdot 0.5}{\frac{z}{y}} \]

      14. associate-/r/ 83.6%

          \[\leadsto \frac{\frac{y}{x}}{z} + \color{blue}{\frac{x \cdot 0.5}{z} \cdot y} \]

      15. *-commutative 83.6%

          \[\leadsto \frac{\frac{y}{x}}{z} + \color{blue}{y \cdot \frac{x \cdot 0.5}{z}} \]

      16. associate-/l* 83.6%

          \[\leadsto \frac{\frac{y}{x}}{z} + y \cdot \color{blue}{\frac{x}{\frac{z}{0.5}}} \]

   10. Applied egg-rr 83.6%

       \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z} + y \cdot \frac{x}{\frac{z}{0.5}}} \]

   if 9.9999999999999999e-186 < z < 1.4500000000000001e238

   1. Initial program 78.8%

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

      1. associate-*r/ 70.2%

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

      2. associate-/r* 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in x around 0 66.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 66.6%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{y \cdot x}}{z} + \frac{y}{x \cdot z} \]

      2. associate-/l* 66.7%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{z}{x}}} + \frac{y}{x \cdot z} \]

      3. div-inv 67.7%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y \cdot \frac{1}{\frac{z}{x}}\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 67.7%

      \[\leadsto 0.5 \cdot \color{blue}{\left(y \cdot \frac{1}{\frac{z}{x}}\right)} + \frac{y}{x \cdot z} \]

   8. Applied egg-rr 65.9%

      \[\leadsto \color{blue}{\frac{-1 - x \cdot \frac{x}{2}}{\frac{z \cdot x}{-y}}} \]
   9. Step-by-step derivation

      1. associate-/r/ 76.6%

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

      2. associate-*l/ 77.7%

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

      3. *-commutative 77.7%

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

   10. Simplified 77.7%

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

   if 1.4500000000000001e238 < z

   1. Initial program 81.3%

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

      1. associate-*r/ 43.8%

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

      2. associate-/r* 49.8%

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

   3. Simplified 49.8%

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

   4. Taylor expanded in x around 0 51.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 50.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 50.9%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 50.9%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 50.9%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 50.9%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 44.9%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 45.1%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 45.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 45.0%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 45.2%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 45.2%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 45.2%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 45.3%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 45.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 45.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 45.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 45.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 45.3%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 44.0%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 44.0%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 44.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 44.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 44.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 44.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 50.0%

      \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

   9. Taylor expanded in y around 0 49.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(1 + 0.5 \cdot {x}^{2}\right)}{x \cdot z}} \]
   10. Step-by-step derivation

       1. times-frac 75.4%

          \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot {x}^{2}}{z}} \]

       2. unpow2 75.4%

          \[\leadsto \frac{y}{x} \cdot \frac{1 + 0.5 \cdot \color{blue}{\left(x \cdot x\right)}}{z} \]

   11. Simplified 75.4%

       \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+77}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \mathbf{elif}\;z \leq 10^{-185}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + y \cdot \frac{x}{\frac{z}{0.5}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+238}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot \frac{x}{2} + 1\right)}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \end{array} \]

Alternative 9: 70.8% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+191}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+191)
   (+ (/ y (* x z)) (* 0.5 (* x (/ y z))))
   (* (/ y x) (/ (+ (* 0.5 (* x x)) 1.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+191) {
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)));
	} else {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.05d+191)) then
        tmp = (y / (x * z)) + (0.5d0 * (x * (y / z)))
    else
        tmp = (y / x) * (((0.5d0 * (x * x)) + 1.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+191) {
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)));
	} else {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+191:
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)))
	else:
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+191)
		tmp = Float64(Float64(y / Float64(x * z)) + Float64(0.5 * Float64(x * Float64(y / z))));
	else
		tmp = Float64(Float64(y / x) * Float64(Float64(Float64(0.5 * Float64(x * x)) + 1.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05e+191)
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)));
	else
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+191], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * N[(N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e191

   1. Initial program 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 86.4%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 86.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 86.4%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 86.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 86.4%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   if -1.05e191 < y

   1. Initial program 85.1%

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

      1. associate-*r/ 75.0%

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

      2. associate-/r* 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in x around 0 61.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 59.8%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 59.8%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 60.0%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 60.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 60.0%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 60.0%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 60.8%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 60.8%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 60.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 60.7%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 61.0%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 61.0%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 61.0%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 62.6%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 62.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 62.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 62.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 62.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 62.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 61.9%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 62.0%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 62.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 62.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 62.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 62.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 62.2%

      \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

   9. Taylor expanded in y around 0 68.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(1 + 0.5 \cdot {x}^{2}\right)}{x \cdot z}} \]
   10. Step-by-step derivation

       1. times-frac 67.3%

          \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot {x}^{2}}{z}} \]

       2. unpow2 67.3%

          \[\leadsto \frac{y}{x} \cdot \frac{1 + 0.5 \cdot \color{blue}{\left(x \cdot x\right)}}{z} \]

   11. Simplified 67.3%

       \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+191}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \end{array} \]

Alternative 10: 71.7% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+190}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+190)
   (+ (* 0.5 (/ (* y x) z)) (/ y (* x z)))
   (* (/ y x) (/ (+ (* 0.5 (* x x)) 1.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+190) {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	} else {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9d+190)) then
        tmp = (0.5d0 * ((y * x) / z)) + (y / (x * z))
    else
        tmp = (y / x) * (((0.5d0 * (x * x)) + 1.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+190) {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	} else {
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e+190:
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z))
	else:
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+190)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / z)) + Float64(y / Float64(x * z)));
	else
		tmp = Float64(Float64(y / x) * Float64(Float64(Float64(0.5 * Float64(x * x)) + 1.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e+190)
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	else
		tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+190], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * N[(N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999999e190

   1. Initial program 80.1%

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

      1. associate-*r/ 80.1%

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

      2. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]

   if -8.9999999999999999e190 < y

   1. Initial program 85.1%

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

      1. associate-*r/ 75.0%

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

      2. associate-/r* 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in x around 0 61.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/l* 59.8%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

      2. div-inv 59.8%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

      3. clear-num 60.0%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

      4. *-commutative 60.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

   6. Applied egg-rr 60.0%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
   7. Step-by-step derivation

      1. +-commutative 60.0%

         \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

      2. associate-/r* 60.8%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      3. div-inv 60.8%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      4. clear-num 60.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      5. metadata-eval 60.7%

         \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      6. associate-*l/ 61.0%

         \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      7. div-inv 61.0%

         \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      8. metadata-eval 61.0%

         \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

      9. associate-*l/ 62.6%

         \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

      10. *-commutative 62.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

      11. associate-*r/ 62.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

      12. associate-*l* 62.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

      13. *-commutative 62.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

      14. *-commutative 62.6%

          \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

      15. frac-add 61.9%

          \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

      16. lft-mult-inverse 62.0%

          \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

      17. remove-double-div 62.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

      18. metadata-eval 62.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

      19. metadata-eval 62.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

      20. metadata-eval 62.0%

          \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

   8. Applied egg-rr 62.2%

      \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

   9. Taylor expanded in y around 0 68.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(1 + 0.5 \cdot {x}^{2}\right)}{x \cdot z}} \]
   10. Step-by-step derivation

       1. times-frac 67.3%

          \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot {x}^{2}}{z}} \]

       2. unpow2 67.3%

          \[\leadsto \frac{y}{x} \cdot \frac{1 + 0.5 \cdot \color{blue}{\left(x \cdot x\right)}}{z} \]

   11. Simplified 67.3%

       \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+190}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z}\\ \end{array} \]

Alternative 11: 66.0% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{+202}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(y \cdot x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 7e+202) (/ (+ (/ y x) (* 0.5 (* y x))) z) (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 7e+202) {
		tmp = ((y / x) + (0.5 * (y * x))) / z;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 7d+202) then
        tmp = ((y / x) + (0.5d0 * (y * x))) / z
    else
        tmp = y / (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 7e+202) {
		tmp = ((y / x) + (0.5 * (y * x))) / z;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 7e+202:
		tmp = ((y / x) + (0.5 * (y * x))) / z
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 7e+202)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(y * x))) / z);
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 7e+202)
		tmp = ((y / x) + (0.5 * (y * x))) / z;
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 7e+202], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.99999999999999975e202

   1. Initial program 86.1%

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

      1. associate-*r/ 79.6%

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

      2. associate-/r* 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in x around 0 66.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]

   5. Taylor expanded in z around 0 67.1%

      \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right) + \frac{y}{x}}{z}} \]

   if 6.99999999999999975e202 < z

   1. Initial program 70.2%

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

      1. associate-*r/ 39.4%

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

      2. associate-/r* 61.4%

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

   3. Simplified 61.4%

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

   4. Taylor expanded in x around 0 62.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{+202}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(y \cdot x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 12: 70.1% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (/ y x) (/ (+ (* 0.5 (* x x)) 1.0) z)))

C

double code(double x, double y, double z) {
	return (y / x) * (((0.5 * (x * x)) + 1.0) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y / x) * (((0.5d0 * (x * x)) + 1.0d0) / z)
end function

Java

public static double code(double x, double y, double z) {
	return (y / x) * (((0.5 * (x * x)) + 1.0) / z);
}

Python

def code(x, y, z):
	return (y / x) * (((0.5 * (x * x)) + 1.0) / z)

Julia

function code(x, y, z)
	return Float64(Float64(y / x) * Float64(Float64(Float64(0.5 * Float64(x * x)) + 1.0) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y / x) * (((0.5 * (x * x)) + 1.0) / z);
end

Wolfram

code[x_, y_, z_] := N[(N[(y / x), $MachinePrecision] * N[(N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.5%

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

   1. associate-*r/ 75.5%

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

   2. associate-/r* 77.0%

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

3. Simplified 77.0%

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

4. Taylor expanded in x around 0 65.8%

   \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
5. Step-by-step derivation

   1. associate-/l* 62.8%

      \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \frac{y}{x \cdot z} \]

   2. div-inv 62.8%

      \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{z}{y}}\right)} + \frac{y}{x \cdot z} \]

   3. clear-num 62.9%

      \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{y}{z}}\right) + \frac{y}{x \cdot z} \]

   4. *-commutative 62.9%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]

6. Applied egg-rr 62.9%

   \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{y}{x \cdot z} \]
7. Step-by-step derivation

   1. +-commutative 62.9%

      \[\leadsto \color{blue}{\frac{y}{x \cdot z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right)} \]

   2. associate-/r* 61.4%

      \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

   3. div-inv 61.4%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

   4. clear-num 61.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{x}{y}}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

   5. metadata-eval 61.4%

      \[\leadsto \frac{\color{blue}{--1}}{\frac{x}{y}} \cdot \frac{1}{z} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

   6. associate-*l/ 61.6%

      \[\leadsto \color{blue}{\frac{\left(--1\right) \cdot \frac{1}{z}}{\frac{x}{y}}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

   7. div-inv 61.6%

      \[\leadsto \frac{\color{blue}{\frac{--1}{z}}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

   8. metadata-eval 61.6%

      \[\leadsto \frac{\frac{\color{blue}{1}}{z}}{\frac{x}{y}} + 0.5 \cdot \left(\frac{y}{z} \cdot x\right) \]

   9. associate-*l/ 64.5%

      \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \color{blue}{\frac{y \cdot x}{z}} \]

   10. *-commutative 64.5%

       \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + 0.5 \cdot \frac{\color{blue}{x \cdot y}}{z} \]

   11. associate-*r/ 64.5%

       \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} \]

   12. associate-*l* 64.5%

       \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{\left(0.5 \cdot x\right) \cdot y}}{z} \]

   13. *-commutative 64.5%

       \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{\color{blue}{y \cdot \left(0.5 \cdot x\right)}}{z} \]

   14. *-commutative 64.5%

       \[\leadsto \frac{\frac{1}{z}}{\frac{x}{y}} + \frac{y \cdot \color{blue}{\left(x \cdot 0.5\right)}}{z} \]

   15. frac-add 63.9%

       \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot z + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z}} \]

   16. lft-mult-inverse 63.9%

       \[\leadsto \frac{\color{blue}{1} + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x}{y} \cdot z} \]

   17. remove-double-div 63.9%

       \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\color{blue}{\frac{1}{\frac{1}{\frac{x}{y} \cdot z}}}} \]

   18. metadata-eval 63.9%

       \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{1 \cdot 1}}{\frac{x}{y} \cdot z}}} \]

   19. metadata-eval 63.9%

       \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\color{blue}{\left(--1\right)} \cdot 1}{\frac{x}{y} \cdot z}}} \]

   20. metadata-eval 63.9%

       \[\leadsto \frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{1}{\frac{\left(--1\right) \cdot \color{blue}{\left(--1\right)}}{\frac{x}{y} \cdot z}}} \]

8. Applied egg-rr 65.6%

   \[\leadsto \color{blue}{\frac{1 + \frac{x}{y} \cdot \left(y \cdot \left(x \cdot 0.5\right)\right)}{\frac{x \cdot z}{y}}} \]

9. Taylor expanded in y around 0 71.0%

   \[\leadsto \color{blue}{\frac{y \cdot \left(1 + 0.5 \cdot {x}^{2}\right)}{x \cdot z}} \]
10. Step-by-step derivation

    1. times-frac 67.3%

       \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot {x}^{2}}{z}} \]

    2. unpow2 67.3%

       \[\leadsto \frac{y}{x} \cdot \frac{1 + 0.5 \cdot \color{blue}{\left(x \cdot x\right)}}{z} \]

11. Simplified 67.3%

    \[\leadsto \color{blue}{\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}} \]

12. Final simplification 67.3%

    \[\leadsto \frac{y}{x} \cdot \frac{0.5 \cdot \left(x \cdot x\right) + 1}{z} \]

Alternative 13: 62.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4) (not (<= x 1.45))) (* 0.5 (* x (/ y z))) (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.45)) {
		tmp = 0.5 * (x * (y / z));
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.4d0)) .or. (.not. (x <= 1.45d0))) then
        tmp = 0.5d0 * (x * (y / z))
    else
        tmp = y / (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.45)) {
		tmp = 0.5 * (x * (y / z));
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4) or not (x <= 1.45):
		tmp = 0.5 * (x * (y / z))
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4) || !(x <= 1.45))
		tmp = Float64(0.5 * Float64(x * Float64(y / z)));
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.4) || ~((x <= 1.45)))
		tmp = 0.5 * (x * (y / z));
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4], N[Not[LessEqual[x, 1.45]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.44999999999999996 < x

   1. Initial program 76.8%

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

      1. associate-*r/ 58.4%

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

      2. associate-/r* 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in x around 0 36.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 36.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y\right)}{z}} + \frac{y}{x \cdot z} \]

      2. frac-2neg 36.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(x \cdot y\right)}{-z}} + \frac{y}{x \cdot z} \]

      3. associate-/r* 36.0%

         \[\leadsto \frac{-0.5 \cdot \left(x \cdot y\right)}{-z} + \color{blue}{\frac{\frac{y}{x}}{z}} \]

      4. div-inv 36.0%

         \[\leadsto \frac{-0.5 \cdot \left(x \cdot y\right)}{-z} + \color{blue}{\frac{y}{x} \cdot \frac{1}{z}} \]

      5. *-commutative 36.0%

         \[\leadsto \frac{-0.5 \cdot \left(x \cdot y\right)}{-z} + \color{blue}{\frac{1}{z} \cdot \frac{y}{x}} \]

      6. frac-2neg 36.0%

         \[\leadsto \frac{-0.5 \cdot \left(x \cdot y\right)}{-z} + \frac{1}{z} \cdot \color{blue}{\frac{-y}{-x}} \]

      7. associate-*r/ 36.0%

         \[\leadsto \frac{-0.5 \cdot \left(x \cdot y\right)}{-z} + \color{blue}{\frac{\frac{1}{z} \cdot \left(-y\right)}{-x}} \]

      8. frac-add 34.5%

         \[\leadsto \color{blue}{\frac{\left(-0.5 \cdot \left(x \cdot y\right)\right) \cdot \left(-x\right) + \left(-z\right) \cdot \left(\frac{1}{z} \cdot \left(-y\right)\right)}{\left(-z\right) \cdot \left(-x\right)}} \]

   6. Applied egg-rr 34.5%

      \[\leadsto \color{blue}{\frac{\left(-y \cdot \left(x \cdot 0.5\right)\right) \cdot \left(-x\right) + \left(-z\right) \cdot \frac{y}{-z}}{\left(-z\right) \cdot \left(-x\right)}} \]
   7. Step-by-step derivation

   8. Simplified 46.7%

      \[\leadsto \color{blue}{\frac{\frac{-y}{-1} + y \cdot \left(x \cdot \left(0.5 \cdot x\right)\right)}{x \cdot z}} \]

   9. Taylor expanded in x around inf 36.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. *-commutative 36.0%

          \[\leadsto 0.5 \cdot \frac{\color{blue}{y \cdot x}}{z} \]

       2. associate-*l/ 30.1%

          \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} \]

       3. *-commutative 30.1%

          \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{z}\right)} \]

   11. Simplified 30.1%

       \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{z}\right)} \]

   if -1.3999999999999999 < x < 1.44999999999999996

   1. Initial program 91.9%

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

      1. associate-*r/ 91.9%

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

      2. associate-/r* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around 0 93.3%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 14: 66.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4) (not (<= x 1.45))) (* 0.5 (* y (/ x z))) (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.45)) {
		tmp = 0.5 * (y * (x / z));
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.4d0)) .or. (.not. (x <= 1.45d0))) then
        tmp = 0.5d0 * (y * (x / z))
    else
        tmp = y / (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.45)) {
		tmp = 0.5 * (y * (x / z));
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4) or not (x <= 1.45):
		tmp = 0.5 * (y * (x / z))
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4) || !(x <= 1.45))
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.4) || ~((x <= 1.45)))
		tmp = 0.5 * (y * (x / z));
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4], N[Not[LessEqual[x, 1.45]], $MachinePrecision]], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.44999999999999996 < x

   1. Initial program 76.8%

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

      1. associate-*r/ 58.4%

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

      2. associate-/r* 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in x around 0 36.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}} \]

   5. Taylor expanded in x around inf 36.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{z}} \]
   6. Step-by-step derivation

      1. *-commutative 36.0%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{y \cdot x}}{z} \]

      2. associate-*r/ 36.8%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y \cdot \frac{x}{z}\right)} \]

   7. Simplified 36.8%

      \[\leadsto \color{blue}{0.5 \cdot \left(y \cdot \frac{x}{z}\right)} \]

   if -1.3999999999999999 < x < 1.44999999999999996

   1. Initial program 91.9%

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

      1. associate-*r/ 91.9%

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

      2. associate-/r* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around 0 93.3%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 15: 55.5% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2e+35) (/ (/ y z) x) (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2e+35) {
		tmp = (y / z) / x;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 2d+35) then
        tmp = (y / z) / x
    else
        tmp = y / (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2e+35) {
		tmp = (y / z) / x;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2e+35:
		tmp = (y / z) / x
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2e+35)
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2e+35)
		tmp = (y / z) / x;
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2e+35], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.9999999999999999e35

   1. Initial program 85.7%

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

      1. associate-*r/ 80.1%

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

      2. associate-/r* 80.1%

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

   3. Simplified 80.1%

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

      1. associate-*r/ 87.8%

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

      2. times-frac 95.6%

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

      3. *-commutative 95.6%

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

      4. clear-num 95.6%

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

      5. un-div-inv 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in x around 0 55.8%

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

   if 1.9999999999999999e35 < z

   1. Initial program 80.8%

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

      1. associate-*r/ 61.1%

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

      2. associate-/r* 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in x around 0 54.9%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 16: 49.8% accurate, 21.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    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 84.5%

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

   1. associate-*r/ 75.5%

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

   2. associate-/r* 77.0%

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

3. Simplified 77.0%

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

4. Taylor expanded in x around 0 50.8%

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

5. Final simplification 50.8%

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

Developer target: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{if}\;y < -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 1.038530535935153 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (/ y z) x) (cosh x))))
   (if (< y -4.618902267687042e-52)
     t_0
     (if (< y 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / z) / x) * cosh(x);
	double tmp;
	if (y < -4.618902267687042e-52) {
		tmp = t_0;
	} else if (y < 1.038530535935153e-39) {
		tmp = ((cosh(x) * y) / x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / z) / x) * cosh(x)
    if (y < (-4.618902267687042d-52)) then
        tmp = t_0
    else if (y < 1.038530535935153d-39) then
        tmp = ((cosh(x) * y) / x) / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / z) / x) * Math.cosh(x);
	double tmp;
	if (y < -4.618902267687042e-52) {
		tmp = t_0;
	} else if (y < 1.038530535935153e-39) {
		tmp = ((Math.cosh(x) * y) / x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / z) / x) * math.cosh(x)
	tmp = 0
	if y < -4.618902267687042e-52:
		tmp = t_0
	elif y < 1.038530535935153e-39:
		tmp = ((math.cosh(x) * y) / x) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / z) / x) * cosh(x))
	tmp = 0.0
	if (y < -4.618902267687042e-52)
		tmp = t_0;
	elseif (y < 1.038530535935153e-39)
		tmp = Float64(Float64(Float64(cosh(x) * y) / x) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / z) / x) * cosh(x);
	tmp = 0.0;
	if (y < -4.618902267687042e-52)
		tmp = t_0;
	elseif (y < 1.038530535935153e-39)
		tmp = ((cosh(x) * y) / x) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision] * N[Cosh[x], $MachinePrecision]), $MachinePrecision]}, If[Less[y, -4.618902267687042e-52], t$95$0, If[Less[y, 1.038530535935153e-39], N[(N[(N[(N[Cosh[x], $MachinePrecision] * y), $MachinePrecision] / x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctan from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y -4.618902267687042e-52) (* (/ (/ y z) x) (cosh x)) (if (< y 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

  (/ (* (cosh x) (/ y x)) z))