Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Percentage Accurate: 95.7% → 97.4%

Time: 8.4s

Alternatives: 13

Speedup: 0.9×

• 28.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+111}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7e+111)
   (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))
   (+ x (* -0.3333333333333333 (/ (- y (/ t y)) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e+111) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-7d+111)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    else
        tmp = x + ((-0.3333333333333333d0) * ((y - (t / y)) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e+111) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7e+111:
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	else:
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7e+111)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7e+111)
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	else
		tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7e+111], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.0000000000000004e111

   1. Initial program 99.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   if -7.0000000000000004e111 < t

   1. Initial program 94.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+111}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \]

Alternative 2: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_2 := -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* y z))))
        (t_2 (* -0.3333333333333333 (/ y z))))
   (if (<= y -1.65e+87)
     t_2
     (if (<= y -4.8e+56)
       x
       (if (<= y -1.1e+46)
         t_2
         (if (<= y 7.4e-223)
           t_1
           (if (<= y 1.95e-190) x (if (<= y 2.15e-48) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double t_2 = -0.3333333333333333 * (y / z);
	double tmp;
	if (y <= -1.65e+87) {
		tmp = t_2;
	} else if (y <= -4.8e+56) {
		tmp = x;
	} else if (y <= -1.1e+46) {
		tmp = t_2;
	} else if (y <= 7.4e-223) {
		tmp = t_1;
	} else if (y <= 1.95e-190) {
		tmp = x;
	} else if (y <= 2.15e-48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 * (t / (y * z))
    t_2 = (-0.3333333333333333d0) * (y / z)
    if (y <= (-1.65d+87)) then
        tmp = t_2
    else if (y <= (-4.8d+56)) then
        tmp = x
    else if (y <= (-1.1d+46)) then
        tmp = t_2
    else if (y <= 7.4d-223) then
        tmp = t_1
    else if (y <= 1.95d-190) then
        tmp = x
    else if (y <= 2.15d-48) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double t_2 = -0.3333333333333333 * (y / z);
	double tmp;
	if (y <= -1.65e+87) {
		tmp = t_2;
	} else if (y <= -4.8e+56) {
		tmp = x;
	} else if (y <= -1.1e+46) {
		tmp = t_2;
	} else if (y <= 7.4e-223) {
		tmp = t_1;
	} else if (y <= 1.95e-190) {
		tmp = x;
	} else if (y <= 2.15e-48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (y * z))
	t_2 = -0.3333333333333333 * (y / z)
	tmp = 0
	if y <= -1.65e+87:
		tmp = t_2
	elif y <= -4.8e+56:
		tmp = x
	elif y <= -1.1e+46:
		tmp = t_2
	elif y <= 7.4e-223:
		tmp = t_1
	elif y <= 1.95e-190:
		tmp = x
	elif y <= 2.15e-48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(y * z)))
	t_2 = Float64(-0.3333333333333333 * Float64(y / z))
	tmp = 0.0
	if (y <= -1.65e+87)
		tmp = t_2;
	elseif (y <= -4.8e+56)
		tmp = x;
	elseif (y <= -1.1e+46)
		tmp = t_2;
	elseif (y <= 7.4e-223)
		tmp = t_1;
	elseif (y <= 1.95e-190)
		tmp = x;
	elseif (y <= 2.15e-48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (y * z));
	t_2 = -0.3333333333333333 * (y / z);
	tmp = 0.0;
	if (y <= -1.65e+87)
		tmp = t_2;
	elseif (y <= -4.8e+56)
		tmp = x;
	elseif (y <= -1.1e+46)
		tmp = t_2;
	elseif (y <= 7.4e-223)
		tmp = t_1;
	elseif (y <= 1.95e-190)
		tmp = x;
	elseif (y <= 2.15e-48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+87], t$95$2, If[LessEqual[y, -4.8e+56], x, If[LessEqual[y, -1.1e+46], t$95$2, If[LessEqual[y, 7.4e-223], t$95$1, If[LessEqual[y, 1.95e-190], x, If[LessEqual[y, 2.15e-48], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6500000000000001e87 or -4.80000000000000027e56 < y < -1.1e46 or 2.15e-48 < y

   1. Initial program 99.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} + x} \]

   5. Taylor expanded in z around 0 77.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}} \]

   6. Taylor expanded in y around inf 72.0%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   7. Step-by-step derivation

      1. *-commutative 72.0%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

   8. Simplified 72.0%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

   if -1.6500000000000001e87 < y < -4.80000000000000027e56 or 7.3999999999999997e-223 < y < 1.94999999999999997e-190

   1. Initial program 100.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around inf 91.7%

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

   if -1.1e46 < y < 7.3999999999999997e-223 or 1.94999999999999997e-190 < y < 2.15e-48

   1. Initial program 92.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around 0 92.2%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} + x} \]

   5. Taylor expanded in z around 0 70.0%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}} \]

   6. Taylor expanded in y around 0 65.8%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+87}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+46}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-223}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-48}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 75.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_2 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* y z))))
        (t_2 (+ x (/ y (* z -3.0)))))
   (if (<= y -4.3e-17)
     t_2
     (if (<= y 7.4e-223)
       t_1
       (if (<= y 1.95e-190) x (if (<= y 1.9e-49) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double t_2 = x + (y / (z * -3.0));
	double tmp;
	if (y <= -4.3e-17) {
		tmp = t_2;
	} else if (y <= 7.4e-223) {
		tmp = t_1;
	} else if (y <= 1.95e-190) {
		tmp = x;
	} else if (y <= 1.9e-49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 * (t / (y * z))
    t_2 = x + (y / (z * (-3.0d0)))
    if (y <= (-4.3d-17)) then
        tmp = t_2
    else if (y <= 7.4d-223) then
        tmp = t_1
    else if (y <= 1.95d-190) then
        tmp = x
    else if (y <= 1.9d-49) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double t_2 = x + (y / (z * -3.0));
	double tmp;
	if (y <= -4.3e-17) {
		tmp = t_2;
	} else if (y <= 7.4e-223) {
		tmp = t_1;
	} else if (y <= 1.95e-190) {
		tmp = x;
	} else if (y <= 1.9e-49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (y * z))
	t_2 = x + (y / (z * -3.0))
	tmp = 0
	if y <= -4.3e-17:
		tmp = t_2
	elif y <= 7.4e-223:
		tmp = t_1
	elif y <= 1.95e-190:
		tmp = x
	elif y <= 1.9e-49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(y * z)))
	t_2 = Float64(x + Float64(y / Float64(z * -3.0)))
	tmp = 0.0
	if (y <= -4.3e-17)
		tmp = t_2;
	elseif (y <= 7.4e-223)
		tmp = t_1;
	elseif (y <= 1.95e-190)
		tmp = x;
	elseif (y <= 1.9e-49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (y * z));
	t_2 = x + (y / (z * -3.0));
	tmp = 0.0;
	if (y <= -4.3e-17)
		tmp = t_2;
	elseif (y <= 7.4e-223)
		tmp = t_1;
	elseif (y <= 1.95e-190)
		tmp = x;
	elseif (y <= 1.9e-49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e-17], t$95$2, If[LessEqual[y, 7.4e-223], t$95$1, If[LessEqual[y, 1.95e-190], x, If[LessEqual[y, 1.9e-49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.30000000000000023e-17 or 1.8999999999999999e-49 < y

   1. Initial program 99.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]

   5. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
   6. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   7. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   8. Taylor expanded in y around inf 91.8%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   9. Step-by-step derivation

      1. *-commutative 91.8%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-/r/ 91.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{-0.3333333333333333}}} \]

      3. metadata-eval 91.8%

         \[\leadsto x + \frac{y}{\frac{z}{\color{blue}{\frac{1}{-3}}}} \]

      4. associate-/l* 91.9%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{z \cdot -3}{1}}} \]

      5. /-rgt-identity 91.9%

         \[\leadsto x + \frac{y}{\color{blue}{z \cdot -3}} \]

   10. Simplified 91.9%

       \[\leadsto x + \color{blue}{\frac{y}{z \cdot -3}} \]

   if -4.30000000000000023e-17 < y < 7.3999999999999997e-223 or 1.94999999999999997e-190 < y < 1.8999999999999999e-49

   1. Initial program 91.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around 0 91.5%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} + x} \]

   5. Taylor expanded in z around 0 70.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}} \]

   6. Taylor expanded in y around 0 67.9%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]

   if 7.3999999999999997e-223 < y < 1.94999999999999997e-190

   1. Initial program 100.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around inf 85.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-223}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-49}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 4: 75.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* y z)))))
   (if (<= y -3.6e-17)
     (- x (/ (* y 0.3333333333333333) z))
     (if (<= y 7.4e-223)
       t_1
       (if (<= y 1.2e-187)
         x
         (if (<= y 1.3e-53) t_1 (+ x (/ y (* z -3.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double tmp;
	if (y <= -3.6e-17) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 7.4e-223) {
		tmp = t_1;
	} else if (y <= 1.2e-187) {
		tmp = x;
	} else if (y <= 1.3e-53) {
		tmp = t_1;
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 * (t / (y * z))
    if (y <= (-3.6d-17)) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else if (y <= 7.4d-223) then
        tmp = t_1
    else if (y <= 1.2d-187) then
        tmp = x
    else if (y <= 1.3d-53) then
        tmp = t_1
    else
        tmp = x + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double tmp;
	if (y <= -3.6e-17) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 7.4e-223) {
		tmp = t_1;
	} else if (y <= 1.2e-187) {
		tmp = x;
	} else if (y <= 1.3e-53) {
		tmp = t_1;
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (y * z))
	tmp = 0
	if y <= -3.6e-17:
		tmp = x - ((y * 0.3333333333333333) / z)
	elif y <= 7.4e-223:
		tmp = t_1
	elif y <= 1.2e-187:
		tmp = x
	elif y <= 1.3e-53:
		tmp = t_1
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(y * z)))
	tmp = 0.0
	if (y <= -3.6e-17)
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	elseif (y <= 7.4e-223)
		tmp = t_1;
	elseif (y <= 1.2e-187)
		tmp = x;
	elseif (y <= 1.3e-53)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (y * z));
	tmp = 0.0;
	if (y <= -3.6e-17)
		tmp = x - ((y * 0.3333333333333333) / z);
	elseif (y <= 7.4e-223)
		tmp = t_1;
	elseif (y <= 1.2e-187)
		tmp = x;
	elseif (y <= 1.3e-53)
		tmp = t_1;
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e-17], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4e-223], t$95$1, If[LessEqual[y, 1.2e-187], x, If[LessEqual[y, 1.3e-53], t$95$1, N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.59999999999999995e-17

   1. Initial program 98.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 92.4%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 92.5%

         \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

   4. Applied egg-rr 92.5%

      \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

   if -3.59999999999999995e-17 < y < 7.3999999999999997e-223 or 1.20000000000000007e-187 < y < 1.29999999999999998e-53

   1. Initial program 91.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around 0 91.5%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} + x} \]

   5. Taylor expanded in z around 0 70.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}} \]

   6. Taylor expanded in y around 0 67.9%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]

   if 7.3999999999999997e-223 < y < 1.20000000000000007e-187

   1. Initial program 100.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around inf 85.8%

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

   if 1.29999999999999998e-53 < y

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. clear-num 99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

      2. inv-pow 99.6%

         \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]

   5. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
   6. Step-by-step derivation

      1. unpow-1 99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   7. Simplified 99.6%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   8. Taylor expanded in y around inf 91.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   9. Step-by-step derivation

      1. *-commutative 91.2%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-/r/ 91.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{-0.3333333333333333}}} \]

      3. metadata-eval 91.3%

         \[\leadsto x + \frac{y}{\frac{z}{\color{blue}{\frac{1}{-3}}}} \]

      4. associate-/l* 91.4%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{z \cdot -3}{1}}} \]

      5. /-rgt-identity 91.4%

         \[\leadsto x + \frac{y}{\color{blue}{z \cdot -3}} \]

   10. Simplified 91.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-223}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-53}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 5: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-223}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\frac{-t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-52}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e-17)
   (- x (/ (* y 0.3333333333333333) z))
   (if (<= y 7.4e-223)
     (* -0.3333333333333333 (/ (/ (- t) y) z))
     (if (<= y 1.95e-190)
       x
       (if (<= y 2.9e-52)
         (* 0.3333333333333333 (/ t (* y z)))
         (+ x (/ y (* z -3.0))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e-17) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 7.4e-223) {
		tmp = -0.3333333333333333 * ((-t / y) / z);
	} else if (y <= 1.95e-190) {
		tmp = x;
	} else if (y <= 2.9e-52) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.2d-17)) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else if (y <= 7.4d-223) then
        tmp = (-0.3333333333333333d0) * ((-t / y) / z)
    else if (y <= 1.95d-190) then
        tmp = x
    else if (y <= 2.9d-52) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = x + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e-17) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 7.4e-223) {
		tmp = -0.3333333333333333 * ((-t / y) / z);
	} else if (y <= 1.95e-190) {
		tmp = x;
	} else if (y <= 2.9e-52) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2e-17:
		tmp = x - ((y * 0.3333333333333333) / z)
	elif y <= 7.4e-223:
		tmp = -0.3333333333333333 * ((-t / y) / z)
	elif y <= 1.95e-190:
		tmp = x
	elif y <= 2.9e-52:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2e-17)
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	elseif (y <= 7.4e-223)
		tmp = Float64(-0.3333333333333333 * Float64(Float64(Float64(-t) / y) / z));
	elseif (y <= 1.95e-190)
		tmp = x;
	elseif (y <= 2.9e-52)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.2e-17)
		tmp = x - ((y * 0.3333333333333333) / z);
	elseif (y <= 7.4e-223)
		tmp = -0.3333333333333333 * ((-t / y) / z);
	elseif (y <= 1.95e-190)
		tmp = x;
	elseif (y <= 2.9e-52)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2e-17], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4e-223], N[(-0.3333333333333333 * N[(N[((-t) / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-190], x, If[LessEqual[y, 2.9e-52], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.2000000000000002e-17

   1. Initial program 98.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 92.4%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 92.5%

         \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

   4. Applied egg-rr 92.5%

      \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

   if -3.2000000000000002e-17 < y < 7.3999999999999997e-223

   1. Initial program 92.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around 0 93.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} + x} \]

   5. Taylor expanded in z around 0 70.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}} \]

   6. Taylor expanded in y around 0 68.6%

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(-1 \cdot \frac{t}{y \cdot z}\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 68.6%

         \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(-\frac{t}{y \cdot z}\right)} \]

      2. associate-/r* 69.7%

         \[\leadsto -0.3333333333333333 \cdot \left(-\color{blue}{\frac{\frac{t}{y}}{z}}\right) \]

      3. distribute-neg-frac 69.7%

         \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{-\frac{t}{y}}{z}} \]

   8. Simplified 69.7%

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{-\frac{t}{y}}{z}} \]

   if 7.3999999999999997e-223 < y < 1.94999999999999997e-190

   1. Initial program 100.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around inf 85.8%

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

   if 1.94999999999999997e-190 < y < 2.9000000000000002e-52

   1. Initial program 86.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around 0 82.4%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} + x} \]

   5. Taylor expanded in z around 0 70.4%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}} \]

   6. Taylor expanded in y around 0 65.0%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]

   if 2.9000000000000002e-52 < y

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. clear-num 99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

      2. inv-pow 99.6%

         \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]

   5. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
   6. Step-by-step derivation

      1. unpow-1 99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   7. Simplified 99.6%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   8. Taylor expanded in y around inf 91.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   9. Step-by-step derivation

      1. *-commutative 91.2%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-/r/ 91.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{-0.3333333333333333}}} \]

      3. metadata-eval 91.3%

         \[\leadsto x + \frac{y}{\frac{z}{\color{blue}{\frac{1}{-3}}}} \]

      4. associate-/l* 91.4%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{z \cdot -3}{1}}} \]

      5. /-rgt-identity 91.4%

         \[\leadsto x + \frac{y}{\color{blue}{z \cdot -3}} \]

   10. Simplified 91.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-223}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\frac{-t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-52}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 6: 81.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+105}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e+53)
   (+ x (/ y (* z -3.0)))
   (if (<= z 1.85e+105)
     (* -0.3333333333333333 (/ (- y (/ t y)) z))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+53) {
		tmp = x + (y / (z * -3.0));
	} else if (z <= 1.85e+105) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.5d+53)) then
        tmp = x + (y / (z * (-3.0d0)))
    else if (z <= 1.85d+105) then
        tmp = (-0.3333333333333333d0) * ((y - (t / y)) / z)
    else
        tmp = x - (0.3333333333333333d0 * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+53) {
		tmp = x + (y / (z * -3.0));
	} else if (z <= 1.85e+105) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e+53:
		tmp = x + (y / (z * -3.0))
	elif z <= 1.85e+105:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e+53)
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	elseif (z <= 1.85e+105)
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	else
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.5e+53)
		tmp = x + (y / (z * -3.0));
	elseif (z <= 1.85e+105)
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e+53], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+105], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999975e53

   1. Initial program 98.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. clear-num 87.9%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

      2. inv-pow 87.9%

         \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]

   5. Applied egg-rr 87.9%

      \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
   6. Step-by-step derivation

      1. unpow-1 87.9%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   7. Simplified 87.9%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   8. Taylor expanded in y around inf 77.8%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   9. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-/r/ 77.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{-0.3333333333333333}}} \]

      3. metadata-eval 77.9%

         \[\leadsto x + \frac{y}{\frac{z}{\color{blue}{\frac{1}{-3}}}} \]

      4. associate-/l* 78.0%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{z \cdot -3}{1}}} \]

      5. /-rgt-identity 78.0%

         \[\leadsto x + \frac{y}{\color{blue}{z \cdot -3}} \]

   10. Simplified 78.0%

       \[\leadsto x + \color{blue}{\frac{y}{z \cdot -3}} \]

   if -5.49999999999999975e53 < z < 1.84999999999999992e105

   1. Initial program 93.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} + x} \]

   5. Taylor expanded in z around 0 90.4%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}} \]

   if 1.84999999999999992e105 < z

   1. Initial program 99.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 75.2%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+105}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 7: 88.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+44}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e+44)
   (- x (/ (* y 0.3333333333333333) z))
   (if (<= y 3.2e-46)
     (+ x (* (/ t y) (/ 0.3333333333333333 z)))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e+44) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 3.2e-46) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5d+44)) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else if (y <= 3.2d-46) then
        tmp = x + ((t / y) * (0.3333333333333333d0 / z))
    else
        tmp = x + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e+44) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 3.2e-46) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5e+44:
		tmp = x - ((y * 0.3333333333333333) / z)
	elif y <= 3.2e-46:
		tmp = x + ((t / y) * (0.3333333333333333 / z))
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e+44)
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	elseif (y <= 3.2e-46)
		tmp = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e+44)
		tmp = x - ((y * 0.3333333333333333) / z);
	elseif (y <= 3.2e-46)
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5e+44], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-46], N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999996e44

   1. Initial program 98.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 98.4%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 98.5%

         \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

   4. Applied egg-rr 98.5%

      \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

   if -4.9999999999999996e44 < y < 3.1999999999999999e-46

   1. Initial program 92.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in y around 0 89.6%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 89.5%

         \[\leadsto x + \color{blue}{\frac{0.3333333333333333 \cdot t}{y \cdot z}} \]

      2. *-commutative 89.5%

         \[\leadsto x + \frac{0.3333333333333333 \cdot t}{\color{blue}{z \cdot y}} \]

      3. times-frac 89.0%

         \[\leadsto x + \color{blue}{\frac{0.3333333333333333}{z} \cdot \frac{t}{y}} \]

      4. *-commutative 89.0%

         \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]

   6. Simplified 89.0%

      \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]

   if 3.1999999999999999e-46 < y

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. clear-num 99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

      2. inv-pow 99.6%

         \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]

   5. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
   6. Step-by-step derivation

      1. unpow-1 99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   7. Simplified 99.6%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   8. Taylor expanded in y around inf 91.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   9. Step-by-step derivation

      1. *-commutative 91.2%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-/r/ 91.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{-0.3333333333333333}}} \]

      3. metadata-eval 91.3%

         \[\leadsto x + \frac{y}{\frac{z}{\color{blue}{\frac{1}{-3}}}} \]

      4. associate-/l* 91.4%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{z \cdot -3}{1}}} \]

      5. /-rgt-identity 91.4%

         \[\leadsto x + \frac{y}{\color{blue}{z \cdot -3}} \]

   10. Simplified 91.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+44}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 8: 89.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-47}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e+50)
   (- x (/ (* y 0.3333333333333333) z))
   (if (<= y 2.6e-47)
     (+ x (* 0.3333333333333333 (/ t (* y z))))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e+50) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 2.6e-47) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.6d+50)) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else if (y <= 2.6d-47) then
        tmp = x + (0.3333333333333333d0 * (t / (y * z)))
    else
        tmp = x + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e+50) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 2.6e-47) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e+50:
		tmp = x - ((y * 0.3333333333333333) / z)
	elif y <= 2.6e-47:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e+50)
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	elseif (y <= 2.6e-47)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	else
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.6e+50)
		tmp = x - ((y * 0.3333333333333333) / z);
	elseif (y <= 2.6e-47)
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e+50], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-47], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999991e50

   1. Initial program 98.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 98.4%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 98.5%

         \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

   4. Applied egg-rr 98.5%

      \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

   if -1.59999999999999991e50 < y < 2.6e-47

   1. Initial program 92.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in y around 0 89.6%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z} + x} \]

   if 2.6e-47 < y

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. clear-num 99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

      2. inv-pow 99.6%

         \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]

   5. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
   6. Step-by-step derivation

      1. unpow-1 99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   7. Simplified 99.6%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   8. Taylor expanded in y around inf 91.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   9. Step-by-step derivation

      1. *-commutative 91.2%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-/r/ 91.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{-0.3333333333333333}}} \]

      3. metadata-eval 91.3%

         \[\leadsto x + \frac{y}{\frac{z}{\color{blue}{\frac{1}{-3}}}} \]

      4. associate-/l* 91.4%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{z \cdot -3}{1}}} \]

      5. /-rgt-identity 91.4%

         \[\leadsto x + \frac{y}{\color{blue}{z \cdot -3}} \]

   10. Simplified 91.4%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-47}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 9: 91.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+40}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+40)
   (- x (/ (* y 0.3333333333333333) z))
   (if (<= y 3.2e-46)
     (+ x (/ 0.3333333333333333 (* y (/ z t))))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+40) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 3.2e-46) {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.7d+40)) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else if (y <= 3.2d-46) then
        tmp = x + (0.3333333333333333d0 / (y * (z / t)))
    else
        tmp = x + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+40) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 3.2e-46) {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+40:
		tmp = x - ((y * 0.3333333333333333) / z)
	elif y <= 3.2e-46:
		tmp = x + (0.3333333333333333 / (y * (z / t)))
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+40)
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	elseif (y <= 3.2e-46)
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y * Float64(z / t))));
	else
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+40)
		tmp = x - ((y * 0.3333333333333333) / z);
	elseif (y <= 3.2e-46)
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+40], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-46], N[(x + N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999994e40

   1. Initial program 98.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0 98.4%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 98.5%

         \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

   4. Applied egg-rr 98.5%

      \[\leadsto x - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}} \]

   if -1.69999999999999994e40 < y < 3.1999999999999999e-46

   1. Initial program 92.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in y around 0 89.6%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z} + x} \]
   5. Step-by-step derivation

      1. associate-*r/ 89.5%

         \[\leadsto \color{blue}{\frac{0.3333333333333333 \cdot t}{y \cdot z}} + x \]

      2. *-commutative 89.5%

         \[\leadsto \frac{0.3333333333333333 \cdot t}{\color{blue}{z \cdot y}} + x \]

      3. associate-/l/ 88.9%

         \[\leadsto \color{blue}{\frac{\frac{0.3333333333333333 \cdot t}{y}}{z}} + x \]

      4. div-inv 89.0%

         \[\leadsto \color{blue}{\frac{0.3333333333333333 \cdot t}{y} \cdot \frac{1}{z}} + x \]

      5. associate-/l* 88.9%

         \[\leadsto \color{blue}{\frac{0.3333333333333333}{\frac{y}{t}}} \cdot \frac{1}{z} + x \]

      6. frac-times 89.7%

         \[\leadsto \color{blue}{\frac{0.3333333333333333 \cdot 1}{\frac{y}{t} \cdot z}} + x \]

      7. metadata-eval 89.7%

         \[\leadsto \frac{\color{blue}{0.3333333333333333}}{\frac{y}{t} \cdot z} + x \]

   6. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{\frac{0.3333333333333333}{\frac{y}{t} \cdot z}} + x \]

   7. Taylor expanded in y around 0 89.5%

      \[\leadsto \frac{0.3333333333333333}{\color{blue}{\frac{y \cdot z}{t}}} + x \]
   8. Step-by-step derivation

      1. *-commutative 89.5%

         \[\leadsto \frac{0.3333333333333333}{\frac{\color{blue}{z \cdot y}}{t}} + x \]

      2. associate-*l/ 94.1%

         \[\leadsto \frac{0.3333333333333333}{\color{blue}{\frac{z}{t} \cdot y}} + x \]

      3. *-commutative 94.1%

         \[\leadsto \frac{0.3333333333333333}{\color{blue}{y \cdot \frac{z}{t}}} + x \]

   9. Simplified 94.1%

      \[\leadsto \frac{0.3333333333333333}{\color{blue}{y \cdot \frac{z}{t}}} + x \]

   if 3.1999999999999999e-46 < y

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
   4. Step-by-step derivation

      1. clear-num 99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

      2. inv-pow 99.6%

         \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]

   5. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
   6. Step-by-step derivation

      1. unpow-1 99.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   7. Simplified 99.6%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   8. Taylor expanded in y around inf 91.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   9. Step-by-step derivation

      1. *-commutative 91.2%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-/r/ 91.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{-0.3333333333333333}}} \]

      3. metadata-eval 91.3%

         \[\leadsto x + \frac{y}{\frac{z}{\color{blue}{\frac{1}{-3}}}} \]

      4. associate-/l* 91.4%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{z \cdot -3}{1}}} \]

      5. /-rgt-identity 91.4%

         \[\leadsto x + \frac{y}{\color{blue}{z \cdot -3}} \]

   10. Simplified 91.4%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+40}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 10: 95.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z))))

C

double code(double x, double y, double z, double t) {
	return x + ((y - (t / y)) * (-0.3333333333333333 / z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - (t / y)) * ((-0.3333333333333333d0) / z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - (t / y)) * (-0.3333333333333333 / z));
}

Python

def code(x, y, z, t):
	return x + ((y - (t / y)) * (-0.3333333333333333 / z))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.8%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

3. Simplified 96.1%

   \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

4. Final simplification 96.1%

   \[\leadsto x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z} \]

Alternative 11: 95.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (* -0.3333333333333333 (/ (- y (/ t y)) z))))

C

double code(double x, double y, double z, double t) {
	return x + (-0.3333333333333333 * ((y - (t / y)) / z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((-0.3333333333333333d0) * ((y - (t / y)) / z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (-0.3333333333333333 * ((y - (t / y)) / z));
}

Python

def code(x, y, z, t):
	return x + (-0.3333333333333333 * ((y - (t / y)) / z))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (-0.3333333333333333 * ((y - (t / y)) / z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.8%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

3. Simplified 96.1%

   \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

4. Taylor expanded in x around 0 96.1%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} + x} \]

5. Final simplification 96.1%

   \[\leadsto x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} \]

Alternative 12: 47.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+88} \lor \neg \left(y \leq 5.5 \cdot 10^{-26}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.25e+88) (not (<= y 5.5e-26)))
   (* -0.3333333333333333 (/ y z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e+88) || !(y <= 5.5e-26)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.25d+88)) .or. (.not. (y <= 5.5d-26))) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e+88) || !(y <= 5.5e-26)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.25e+88) or not (y <= 5.5e-26):
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.25e+88) || !(y <= 5.5e-26))
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.25e+88) || ~((y <= 5.5e-26)))
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.25e+88], N[Not[LessEqual[y, 5.5e-26]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999999e88 or 5.5000000000000005e-26 < y

   1. Initial program 99.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} + x} \]

   5. Taylor expanded in z around 0 79.1%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}} \]

   6. Taylor expanded in y around inf 73.1%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   7. Step-by-step derivation

      1. *-commutative 73.1%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

   8. Simplified 73.1%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

   if -1.24999999999999999e88 < y < 5.5000000000000005e-26

   1. Initial program 93.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 93.1%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

   4. Taylor expanded in x around inf 31.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+88} \lor \neg \left(y \leq 5.5 \cdot 10^{-26}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 30.5% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 95.8%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

3. Simplified 96.1%

   \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]

4. Taylor expanded in x around inf 27.4%

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

5. Final simplification 27.4%

   \[\leadsto x \]

Developer target: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y)))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - (y / (z * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))