Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Percentage Accurate: 98.0% → 98.1%

Time: 14.1s

Alternatives: 14

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 10^{+68}:\\ \;\;\;\;x + y \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 1e+68) (+ x (* y t_1)) (+ x (/ (* z y) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 1e+68) {
		tmp = x + (y * t_1);
	} else {
		tmp = x + ((z * y) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= 1d+68) then
        tmp = x + (y * t_1)
    else
        tmp = x + ((z * y) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 1e+68) {
		tmp = x + (y * t_1);
	} else {
		tmp = x + ((z * y) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= 1e+68:
		tmp = x + (y * t_1)
	else:
		tmp = x + ((z * y) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 1e+68)
		tmp = Float64(x + Float64(y * t_1));
	else
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= 1e+68)
		tmp = x + (y * t_1);
	else
		tmp = x + ((z * y) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+68], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999953e67

   1. Initial program 98.5%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   if 9.99999999999999953e67 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 85.1%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 97.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 10^{+68}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-253}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+78} \lor \neg \left(t \leq 1.9 \cdot 10^{+152}\right) \land t \leq 1.2 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- a t))))))
   (if (<= t -1.9e+108)
     (+ x y)
     (if (<= t -2e-87)
       t_1
       (if (<= t -7.8e-253)
         (+ x (/ (* z y) (- a t)))
         (if (or (<= t 2.1e+78) (and (not (<= t 1.9e+152)) (<= t 1.2e+173)))
           t_1
           (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (a - t)));
	double tmp;
	if (t <= -1.9e+108) {
		tmp = x + y;
	} else if (t <= -2e-87) {
		tmp = t_1;
	} else if (t <= -7.8e-253) {
		tmp = x + ((z * y) / (a - t));
	} else if ((t <= 2.1e+78) || (!(t <= 1.9e+152) && (t <= 1.2e+173))) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / (a - t)))
    if (t <= (-1.9d+108)) then
        tmp = x + y
    else if (t <= (-2d-87)) then
        tmp = t_1
    else if (t <= (-7.8d-253)) then
        tmp = x + ((z * y) / (a - t))
    else if ((t <= 2.1d+78) .or. (.not. (t <= 1.9d+152)) .and. (t <= 1.2d+173)) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (a - t)));
	double tmp;
	if (t <= -1.9e+108) {
		tmp = x + y;
	} else if (t <= -2e-87) {
		tmp = t_1;
	} else if (t <= -7.8e-253) {
		tmp = x + ((z * y) / (a - t));
	} else if ((t <= 2.1e+78) || (!(t <= 1.9e+152) && (t <= 1.2e+173))) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (a - t)))
	tmp = 0
	if t <= -1.9e+108:
		tmp = x + y
	elif t <= -2e-87:
		tmp = t_1
	elif t <= -7.8e-253:
		tmp = x + ((z * y) / (a - t))
	elif (t <= 2.1e+78) or (not (t <= 1.9e+152) and (t <= 1.2e+173)):
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(a - t))))
	tmp = 0.0
	if (t <= -1.9e+108)
		tmp = Float64(x + y);
	elseif (t <= -2e-87)
		tmp = t_1;
	elseif (t <= -7.8e-253)
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	elseif ((t <= 2.1e+78) || (!(t <= 1.9e+152) && (t <= 1.2e+173)))
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (a - t)));
	tmp = 0.0;
	if (t <= -1.9e+108)
		tmp = x + y;
	elseif (t <= -2e-87)
		tmp = t_1;
	elseif (t <= -7.8e-253)
		tmp = x + ((z * y) / (a - t));
	elseif ((t <= 2.1e+78) || (~((t <= 1.9e+152)) && (t <= 1.2e+173)))
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+108], N[(x + y), $MachinePrecision], If[LessEqual[t, -2e-87], t$95$1, If[LessEqual[t, -7.8e-253], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.1e+78], And[N[Not[LessEqual[t, 1.9e+152]], $MachinePrecision], LessEqual[t, 1.2e+173]]], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.90000000000000004e108 or 2.1000000000000001e78 < t < 1.9e152 or 1.2e173 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 86.2%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 86.2%

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

   5. Simplified 86.2%

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

   if -1.90000000000000004e108 < t < -2.00000000000000004e-87 or -7.7999999999999998e-253 < t < 2.1000000000000001e78 or 1.9e152 < t < 1.2e173

   1. Initial program 97.7%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

   if -2.00000000000000004e-87 < t < -7.7999999999999998e-253

   1. Initial program 84.5%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.7%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-253}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+78} \lor \neg \left(t \leq 1.9 \cdot 10^{+152}\right) \land t \leq 1.2 \cdot 10^{+173}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-253}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+152}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + a \cdot \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- a t))))))
   (if (<= t -1.05e+101)
     (+ x y)
     (if (<= t -2e-87)
       t_1
       (if (<= t -5e-253)
         (+ x (/ (* z y) (- a t)))
         (if (<= t 5.3e+79)
           t_1
           (if (<= t 1.15e+152)
             (+ x y)
             (if (<= t 1.25e+175) t_1 (+ y (+ x (* a (/ y t))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (a - t)));
	double tmp;
	if (t <= -1.05e+101) {
		tmp = x + y;
	} else if (t <= -2e-87) {
		tmp = t_1;
	} else if (t <= -5e-253) {
		tmp = x + ((z * y) / (a - t));
	} else if (t <= 5.3e+79) {
		tmp = t_1;
	} else if (t <= 1.15e+152) {
		tmp = x + y;
	} else if (t <= 1.25e+175) {
		tmp = t_1;
	} else {
		tmp = y + (x + (a * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / (a - t)))
    if (t <= (-1.05d+101)) then
        tmp = x + y
    else if (t <= (-2d-87)) then
        tmp = t_1
    else if (t <= (-5d-253)) then
        tmp = x + ((z * y) / (a - t))
    else if (t <= 5.3d+79) then
        tmp = t_1
    else if (t <= 1.15d+152) then
        tmp = x + y
    else if (t <= 1.25d+175) then
        tmp = t_1
    else
        tmp = y + (x + (a * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (a - t)));
	double tmp;
	if (t <= -1.05e+101) {
		tmp = x + y;
	} else if (t <= -2e-87) {
		tmp = t_1;
	} else if (t <= -5e-253) {
		tmp = x + ((z * y) / (a - t));
	} else if (t <= 5.3e+79) {
		tmp = t_1;
	} else if (t <= 1.15e+152) {
		tmp = x + y;
	} else if (t <= 1.25e+175) {
		tmp = t_1;
	} else {
		tmp = y + (x + (a * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (a - t)))
	tmp = 0
	if t <= -1.05e+101:
		tmp = x + y
	elif t <= -2e-87:
		tmp = t_1
	elif t <= -5e-253:
		tmp = x + ((z * y) / (a - t))
	elif t <= 5.3e+79:
		tmp = t_1
	elif t <= 1.15e+152:
		tmp = x + y
	elif t <= 1.25e+175:
		tmp = t_1
	else:
		tmp = y + (x + (a * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(a - t))))
	tmp = 0.0
	if (t <= -1.05e+101)
		tmp = Float64(x + y);
	elseif (t <= -2e-87)
		tmp = t_1;
	elseif (t <= -5e-253)
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	elseif (t <= 5.3e+79)
		tmp = t_1;
	elseif (t <= 1.15e+152)
		tmp = Float64(x + y);
	elseif (t <= 1.25e+175)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(x + Float64(a * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (a - t)));
	tmp = 0.0;
	if (t <= -1.05e+101)
		tmp = x + y;
	elseif (t <= -2e-87)
		tmp = t_1;
	elseif (t <= -5e-253)
		tmp = x + ((z * y) / (a - t));
	elseif (t <= 5.3e+79)
		tmp = t_1;
	elseif (t <= 1.15e+152)
		tmp = x + y;
	elseif (t <= 1.25e+175)
		tmp = t_1;
	else
		tmp = y + (x + (a * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+101], N[(x + y), $MachinePrecision], If[LessEqual[t, -2e-87], t$95$1, If[LessEqual[t, -5e-253], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e+79], t$95$1, If[LessEqual[t, 1.15e+152], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.25e+175], t$95$1, N[(y + N[(x + N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.05e101 or 5.29999999999999978e79 < t < 1.14999999999999993e152

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 79.5%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 79.5%

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

   5. Simplified 79.5%

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

   if -1.05e101 < t < -2.00000000000000004e-87 or -4.99999999999999971e-253 < t < 5.29999999999999978e79 or 1.14999999999999993e152 < t < 1.25e175

   1. Initial program 97.7%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

   if -2.00000000000000004e-87 < t < -4.99999999999999971e-253

   1. Initial program 84.5%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.7%

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

   if 1.25e175 < t

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 66.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   4. Step-by-step derivation

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

         \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

      3. *-commutative 66.8%

         \[\leadsto x - \frac{\color{blue}{y \cdot t}}{a - t} \]

      4. associate-/l* 97.2%

         \[\leadsto x - \color{blue}{y \cdot \frac{t}{a - t}} \]

   5. Simplified 97.2%

      \[\leadsto \color{blue}{x - y \cdot \frac{t}{a - t}} \]

   6. Taylor expanded in t around inf 88.5%

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

      1. cancel-sign-sub-inv 88.5%

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

      2. +-commutative 88.5%

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

      3. associate-/l* 97.1%

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

      4. metadata-eval 97.1%

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

      5. *-commutative 97.1%

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

      6. *-rgt-identity 97.1%

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

   8. Simplified 97.1%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-253}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+152}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+175}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + a \cdot \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-65}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+88} \lor \neg \left(t \leq 1.18 \cdot 10^{+154}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y (* y (/ z t))))))
   (if (<= t -1.85e+30)
     t_1
     (if (<= t -5.5e-65)
       (+ x (* y (/ z (- a t))))
       (if (<= t 1.05e-80)
         (+ x (/ (* z y) (- a t)))
         (if (or (<= t 6.5e+88) (not (<= t 1.18e+154)))
           (+ x (* y (/ t (- t a))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - (y * (z / t)));
	double tmp;
	if (t <= -1.85e+30) {
		tmp = t_1;
	} else if (t <= -5.5e-65) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= 1.05e-80) {
		tmp = x + ((z * y) / (a - t));
	} else if ((t <= 6.5e+88) || !(t <= 1.18e+154)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y - (y * (z / t)))
    if (t <= (-1.85d+30)) then
        tmp = t_1
    else if (t <= (-5.5d-65)) then
        tmp = x + (y * (z / (a - t)))
    else if (t <= 1.05d-80) then
        tmp = x + ((z * y) / (a - t))
    else if ((t <= 6.5d+88) .or. (.not. (t <= 1.18d+154))) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - (y * (z / t)));
	double tmp;
	if (t <= -1.85e+30) {
		tmp = t_1;
	} else if (t <= -5.5e-65) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= 1.05e-80) {
		tmp = x + ((z * y) / (a - t));
	} else if ((t <= 6.5e+88) || !(t <= 1.18e+154)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - (y * (z / t)))
	tmp = 0
	if t <= -1.85e+30:
		tmp = t_1
	elif t <= -5.5e-65:
		tmp = x + (y * (z / (a - t)))
	elif t <= 1.05e-80:
		tmp = x + ((z * y) / (a - t))
	elif (t <= 6.5e+88) or not (t <= 1.18e+154):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - Float64(y * Float64(z / t))))
	tmp = 0.0
	if (t <= -1.85e+30)
		tmp = t_1;
	elseif (t <= -5.5e-65)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	elseif (t <= 1.05e-80)
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	elseif ((t <= 6.5e+88) || !(t <= 1.18e+154))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y - (y * (z / t)));
	tmp = 0.0;
	if (t <= -1.85e+30)
		tmp = t_1;
	elseif (t <= -5.5e-65)
		tmp = x + (y * (z / (a - t)));
	elseif (t <= 1.05e-80)
		tmp = x + ((z * y) / (a - t));
	elseif ((t <= 6.5e+88) || ~((t <= 1.18e+154)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.85e+30], t$95$1, If[LessEqual[t, -5.5e-65], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-80], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 6.5e+88], N[Not[LessEqual[t, 1.18e+154]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.85000000000000008e30 or 6.5000000000000002e88 < t < 1.18000000000000004e154

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 63.9%

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

      1. +-commutative 63.9%

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

      2. associate-*r/ 63.9%

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

      3. mul-1-neg 63.9%

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

      4. *-commutative 63.9%

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

      5. distribute-rgt-neg-out 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in z around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. associate-/l* 92.3%

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

   8. Simplified 92.3%

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

   if -1.85000000000000008e30 < t < -5.4999999999999999e-65

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 69.7%

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

      1. associate-/l* 79.6%

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

   5. Simplified 79.6%

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

   if -5.4999999999999999e-65 < t < 1.05000000000000001e-80

   1. Initial program 91.6%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.4%

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

   if 1.05000000000000001e-80 < t < 6.5000000000000002e88 or 1.18000000000000004e154 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 70.3%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   4. Step-by-step derivation

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

         \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

      3. *-commutative 70.3%

         \[\leadsto x - \frac{\color{blue}{y \cdot t}}{a - t} \]

      4. associate-/l* 85.9%

         \[\leadsto x - \color{blue}{y \cdot \frac{t}{a - t}} \]

   5. Simplified 85.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+30}:\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-65}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+88} \lor \neg \left(t \leq 1.18 \cdot 10^{+154}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+106} \lor \neg \left(t \leq 8 \cdot 10^{+79}\right) \land \left(t \leq 1.2 \cdot 10^{+152} \lor \neg \left(t \leq 2.9 \cdot 10^{+183}\right)\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.8e+106)
         (and (not (<= t 8e+79)) (or (<= t 1.2e+152) (not (<= t 2.9e+183)))))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e+106) || (!(t <= 8e+79) && ((t <= 1.2e+152) || !(t <= 2.9e+183)))) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.8d+106)) .or. (.not. (t <= 8d+79)) .and. (t <= 1.2d+152) .or. (.not. (t <= 2.9d+183))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e+106) || (!(t <= 8e+79) && ((t <= 1.2e+152) || !(t <= 2.9e+183)))) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.8e+106) or (not (t <= 8e+79) and ((t <= 1.2e+152) or not (t <= 2.9e+183))):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.8e+106) || (!(t <= 8e+79) && ((t <= 1.2e+152) || !(t <= 2.9e+183))))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.8e+106) || (~((t <= 8e+79)) && ((t <= 1.2e+152) || ~((t <= 2.9e+183)))))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.8e+106], And[N[Not[LessEqual[t, 8e+79]], $MachinePrecision], Or[LessEqual[t, 1.2e+152], N[Not[LessEqual[t, 2.9e+183]], $MachinePrecision]]]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.8000000000000004e106 or 7.99999999999999974e79 < t < 1.2e152 or 2.9000000000000001e183 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 86.9%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 86.9%

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

   5. Simplified 86.9%

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

   if -5.8000000000000004e106 < t < 7.99999999999999974e79 or 1.2e152 < t < 2.9000000000000001e183

   1. Initial program 94.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 84.3%

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

   5. Simplified 84.3%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+106} \lor \neg \left(t \leq 8 \cdot 10^{+79}\right) \land \left(t \leq 1.2 \cdot 10^{+152} \lor \neg \left(t \leq 2.9 \cdot 10^{+183}\right)\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-69}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-100}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y (* y (/ z t))))))
   (if (<= t -4.4e+30)
     t_1
     (if (<= t -1e-69)
       (+ x (* y (/ z (- a t))))
       (if (<= t 2.15e-100) (+ x (/ (* z y) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - (y * (z / t)));
	double tmp;
	if (t <= -4.4e+30) {
		tmp = t_1;
	} else if (t <= -1e-69) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= 2.15e-100) {
		tmp = x + ((z * y) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y - (y * (z / t)))
    if (t <= (-4.4d+30)) then
        tmp = t_1
    else if (t <= (-1d-69)) then
        tmp = x + (y * (z / (a - t)))
    else if (t <= 2.15d-100) then
        tmp = x + ((z * y) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - (y * (z / t)));
	double tmp;
	if (t <= -4.4e+30) {
		tmp = t_1;
	} else if (t <= -1e-69) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= 2.15e-100) {
		tmp = x + ((z * y) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - (y * (z / t)))
	tmp = 0
	if t <= -4.4e+30:
		tmp = t_1
	elif t <= -1e-69:
		tmp = x + (y * (z / (a - t)))
	elif t <= 2.15e-100:
		tmp = x + ((z * y) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - Float64(y * Float64(z / t))))
	tmp = 0.0
	if (t <= -4.4e+30)
		tmp = t_1;
	elseif (t <= -1e-69)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	elseif (t <= 2.15e-100)
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y - (y * (z / t)));
	tmp = 0.0;
	if (t <= -4.4e+30)
		tmp = t_1;
	elseif (t <= -1e-69)
		tmp = x + (y * (z / (a - t)));
	elseif (t <= 2.15e-100)
		tmp = x + ((z * y) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+30], t$95$1, If[LessEqual[t, -1e-69], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e-100], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4e30 or 2.14999999999999999e-100 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 64.0%

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

      1. +-commutative 64.0%

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

      2. associate-*r/ 64.0%

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

      3. mul-1-neg 64.0%

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

      4. *-commutative 64.0%

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

      5. distribute-rgt-neg-out 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in z around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. unsub-neg 77.1%

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

      3. associate-/l* 86.0%

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

   8. Simplified 86.0%

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

   if -4.4e30 < t < -9.9999999999999996e-70

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 69.7%

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

      1. associate-/l* 79.6%

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

   5. Simplified 79.6%

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

   if -9.9999999999999996e-70 < t < 2.14999999999999999e-100

   1. Initial program 91.2%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 95.1%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+30}:\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-69}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-100}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{z \cdot y}{t}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.4e+102)
   (+ x y)
   (if (<= t -6.8e-5)
     (- x (/ (* z y) t))
     (if (<= t 8.2e-81) (+ x (/ z (/ a y))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.4e+102) {
		tmp = x + y;
	} else if (t <= -6.8e-5) {
		tmp = x - ((z * y) / t);
	} else if (t <= 8.2e-81) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.4d+102)) then
        tmp = x + y
    else if (t <= (-6.8d-5)) then
        tmp = x - ((z * y) / t)
    else if (t <= 8.2d-81) then
        tmp = x + (z / (a / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.4e+102) {
		tmp = x + y;
	} else if (t <= -6.8e-5) {
		tmp = x - ((z * y) / t);
	} else if (t <= 8.2e-81) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.4e+102:
		tmp = x + y
	elif t <= -6.8e-5:
		tmp = x - ((z * y) / t)
	elif t <= 8.2e-81:
		tmp = x + (z / (a / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.4e+102)
		tmp = Float64(x + y);
	elseif (t <= -6.8e-5)
		tmp = Float64(x - Float64(Float64(z * y) / t));
	elseif (t <= 8.2e-81)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.4e+102)
		tmp = x + y;
	elseif (t <= -6.8e-5)
		tmp = x - ((z * y) / t);
	elseif (t <= 8.2e-81)
		tmp = x + (z / (a / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.4e+102], N[(x + y), $MachinePrecision], If[LessEqual[t, -6.8e-5], N[(x - N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-81], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4000000000000002e102 or 8.19999999999999968e-81 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.7%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 77.7%

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

   5. Simplified 77.7%

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

   if -5.4000000000000002e102 < t < -6.7999999999999999e-5

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.9%

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

      1. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in a around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

      3. associate-/l* 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in x around 0 77.6%

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

   if -6.7999999999999999e-5 < t < 8.19999999999999968e-81

   1. Initial program 92.4%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.7%

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

      1. associate-/l* 88.4%

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

   5. Simplified 88.4%

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

      1. associate-*r/ 91.7%

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

      2. clear-num 91.7%

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

   7. Applied egg-rr 91.7%

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

   8. Taylor expanded in a around inf 76.0%

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

      1. *-commutative 76.0%

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

      2. associate-*r/ 79.3%

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

   10. Simplified 79.3%

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

   11. Taylor expanded in z around 0 76.0%

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

       1. associate-/l* 76.8%

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

       2. *-commutative 76.8%

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

       3. associate-/r/ 79.3%

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

   13. Simplified 79.3%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{z \cdot y}{t}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+103}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -0.0065:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e+103)
   (+ x y)
   (if (<= t -0.0065)
     (- x (* y (/ z t)))
     (if (<= t 8.8e-71) (+ x (/ z (/ a y))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+103) {
		tmp = x + y;
	} else if (t <= -0.0065) {
		tmp = x - (y * (z / t));
	} else if (t <= 8.8e-71) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3d+103)) then
        tmp = x + y
    else if (t <= (-0.0065d0)) then
        tmp = x - (y * (z / t))
    else if (t <= 8.8d-71) then
        tmp = x + (z / (a / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+103) {
		tmp = x + y;
	} else if (t <= -0.0065) {
		tmp = x - (y * (z / t));
	} else if (t <= 8.8e-71) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3e+103:
		tmp = x + y
	elif t <= -0.0065:
		tmp = x - (y * (z / t))
	elif t <= 8.8e-71:
		tmp = x + (z / (a / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e+103)
		tmp = Float64(x + y);
	elseif (t <= -0.0065)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 8.8e-71)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3e+103)
		tmp = x + y;
	elseif (t <= -0.0065)
		tmp = x - (y * (z / t));
	elseif (t <= 8.8e-71)
		tmp = x + (z / (a / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e+103], N[(x + y), $MachinePrecision], If[LessEqual[t, -0.0065], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-71], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3e103 or 8.7999999999999999e-71 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 79.0%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 79.0%

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

   5. Simplified 79.0%

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

   if -3e103 < t < -0.0064999999999999997

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.9%

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

      1. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in a around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

      3. associate-/l* 77.5%

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

   8. Simplified 77.5%

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

   if -0.0064999999999999997 < t < 8.7999999999999999e-71

   1. Initial program 92.6%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.0%

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

      1. associate-/l* 87.8%

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

   5. Simplified 87.8%

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

      1. associate-*r/ 91.0%

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

      2. clear-num 91.0%

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

   7. Applied egg-rr 91.0%

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

   8. Taylor expanded in a around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-*r/ 78.8%

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

   10. Simplified 78.8%

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

   11. Taylor expanded in z around 0 75.6%

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

       1. associate-/l* 76.3%

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

       2. *-commutative 76.3%

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

       3. associate-/r/ 78.8%

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

   13. Simplified 78.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+103}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -0.0065:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-24} \lor \neg \left(t \leq 6 \cdot 10^{-87}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e-24) (not (<= t 6e-87))) (+ x y) (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e-24) || !(t <= 6e-87)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.45d-24)) .or. (.not. (t <= 6d-87))) then
        tmp = x + y
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e-24) || !(t <= 6e-87)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e-24) or not (t <= 6e-87):
		tmp = x + y
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e-24) || !(t <= 6e-87))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.45e-24) || ~((t <= 6e-87)))
		tmp = x + y;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e-24], N[Not[LessEqual[t, 6e-87]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4499999999999999e-24 or 6.00000000000000033e-87 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 74.8%

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

   5. Simplified 74.8%

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

   if -1.4499999999999999e-24 < t < 6.00000000000000033e-87

   1. Initial program 92.1%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 92.1%

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

      1. associate-/l* 88.7%

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

   5. Simplified 88.7%

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

      1. associate-*r/ 92.1%

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

      2. clear-num 92.2%

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

   7. Applied egg-rr 92.2%

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

   8. Taylor expanded in a around inf 76.6%

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

      1. *-commutative 76.6%

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

      2. associate-*r/ 80.0%

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

   10. Simplified 80.0%

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

   11. Taylor expanded in z around 0 76.6%

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

       1. associate-/l* 77.4%

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

       2. *-commutative 77.4%

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

       3. associate-/r/ 80.1%

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

   13. Simplified 80.1%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-24} \lor \neg \left(t \leq 6 \cdot 10^{-87}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-28} \lor \neg \left(t \leq 8.5 \cdot 10^{-89}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e-28) (not (<= t 8.5e-89))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e-28) || !(t <= 8.5e-89)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.5d-28)) .or. (.not. (t <= 8.5d-89))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e-28) || !(t <= 8.5e-89)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e-28) or not (t <= 8.5e-89):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e-28) || !(t <= 8.5e-89))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e-28) || ~((t <= 8.5e-89)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e-28], N[Not[LessEqual[t, 8.5e-89]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5000000000000001e-28 or 8.49999999999999937e-89 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 74.8%

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

   5. Simplified 74.8%

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

   if -2.5000000000000001e-28 < t < 8.49999999999999937e-89

   1. Initial program 92.1%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 92.1%

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

      1. associate-/l* 88.7%

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

   5. Simplified 88.7%

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

      1. associate-*r/ 92.1%

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

      2. clear-num 92.2%

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

   7. Applied egg-rr 92.2%

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

   8. Taylor expanded in a around inf 76.6%

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

      1. *-commutative 76.6%

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

      2. associate-*r/ 80.0%

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

   10. Simplified 80.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-28} \lor \neg \left(t \leq 8.5 \cdot 10^{-89}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+30} \lor \neg \left(t \leq 3.2 \cdot 10^{-165}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e+30) (not (<= t 3.2e-165))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+30) || !(t <= 3.2e-165)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.2d+30)) .or. (.not. (t <= 3.2d-165))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+30) || !(t <= 3.2e-165)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e+30) or not (t <= 3.2e-165):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e+30) || !(t <= 3.2e-165))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e+30) || ~((t <= 3.2e-165)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e+30], N[Not[LessEqual[t, 3.2e-165]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e30 or 3.20000000000000013e-165 < t

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.3%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -1.2e30 < t < 3.20000000000000013e-165

   1. Initial program 92.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 51.4%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+30} \lor \neg \left(t \leq 3.2 \cdot 10^{-165}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+193}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+193) (* z (/ y (- t))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+193) {
		tmp = z * (y / -t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d+193)) then
        tmp = z * (y / -t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+193) {
		tmp = z * (y / -t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+193:
		tmp = z * (y / -t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+193)
		tmp = Float64(z * Float64(y / Float64(-t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+193)
		tmp = z * (y / -t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+193], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000013e193

   1. Initial program 93.6%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.3%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in a around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

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

      3. associate-/l* 55.2%

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

   8. Simplified 55.2%

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

   9. Taylor expanded in x around 0 45.9%

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

       1. mul-1-neg 45.9%

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

       2. associate-*r/ 48.8%

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

       3. distribute-rgt-neg-out 48.8%

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

       4. distribute-neg-frac 48.8%

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

   11. Simplified 48.8%

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

   12. Taylor expanded in y around 0 45.9%

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

       1. mul-1-neg 45.9%

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

       2. distribute-neg-frac2 45.9%

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

       3. *-commutative 45.9%

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

       4. associate-*r/ 51.9%

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

   14. Simplified 51.9%

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

   if -2.00000000000000013e193 < z

   1. Initial program 97.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.6%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 65.6%

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

   5. Simplified 65.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+193}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

   1. associate-*r/ 84.2%

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

3. Simplified 84.2%

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

   1. *-commutative 84.2%

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

   2. associate-/l* 97.2%

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

6. Applied egg-rr 97.2%

   \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]
7. Add Preprocessing

Alternative 14: 50.8% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

   \[x + y \cdot \frac{z - t}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 46.3%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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