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

Percentage Accurate: 98.1% → 98.1%

Time: 12.4s

Alternatives: 15

Speedup: 1.0×

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: 98.1% 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, 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]

Derivation

1. Initial program 98.8%

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

2. Final simplification 98.8%

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

Alternative 2: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.72 \cdot 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -440000000000:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-161}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= t -1.72e+118)
     (+ x y)
     (if (<= t -7.2e+51)
       t_1
       (if (<= t -440000000000.0)
         (* y (- 1.0 (/ z t)))
         (if (<= t -5e-161)
           (+ x (* y (/ z a)))
           (if (<= t 1.5e+14) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -1.72e+118) {
		tmp = x + y;
	} else if (t <= -7.2e+51) {
		tmp = t_1;
	} else if (t <= -440000000000.0) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= -5e-161) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.5e+14) {
		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 + (z * (y / a))
    if (t <= (-1.72d+118)) then
        tmp = x + y
    else if (t <= (-7.2d+51)) then
        tmp = t_1
    else if (t <= (-440000000000.0d0)) then
        tmp = y * (1.0d0 - (z / t))
    else if (t <= (-5d-161)) then
        tmp = x + (y * (z / a))
    else if (t <= 1.5d+14) 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 + (z * (y / a));
	double tmp;
	if (t <= -1.72e+118) {
		tmp = x + y;
	} else if (t <= -7.2e+51) {
		tmp = t_1;
	} else if (t <= -440000000000.0) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= -5e-161) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.5e+14) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if t <= -1.72e+118:
		tmp = x + y
	elif t <= -7.2e+51:
		tmp = t_1
	elif t <= -440000000000.0:
		tmp = y * (1.0 - (z / t))
	elif t <= -5e-161:
		tmp = x + (y * (z / a))
	elif t <= 1.5e+14:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -1.72e+118)
		tmp = Float64(x + y);
	elseif (t <= -7.2e+51)
		tmp = t_1;
	elseif (t <= -440000000000.0)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (t <= -5e-161)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 1.5e+14)
		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 + (z * (y / a));
	tmp = 0.0;
	if (t <= -1.72e+118)
		tmp = x + y;
	elseif (t <= -7.2e+51)
		tmp = t_1;
	elseif (t <= -440000000000.0)
		tmp = y * (1.0 - (z / t));
	elseif (t <= -5e-161)
		tmp = x + (y * (z / a));
	elseif (t <= 1.5e+14)
		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[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.72e+118], N[(x + y), $MachinePrecision], If[LessEqual[t, -7.2e+51], t$95$1, If[LessEqual[t, -440000000000.0], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-161], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+14], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.71999999999999999e118 or 1.5e14 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 83.0%

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

   if -1.71999999999999999e118 < t < -7.20000000000000022e51 or -4.9999999999999999e-161 < t < 1.5e14

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 71.2%

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

      1. associate-/l* 76.3%

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

      2. associate-/r/ 78.3%

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

   4. Simplified 78.3%

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

   if -7.20000000000000022e51 < t < -4.4e11

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 99.3%

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

      1. associate-*r/ 99.3%

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

      2. neg-mul-1 99.3%

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

      3. distribute-rgt-neg-in 99.3%

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

      4. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 73.8%

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

   if -4.4e11 < t < -4.9999999999999999e-161

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 77.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.72 \cdot 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+51}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -440000000000:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-161}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -440000000000:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-162}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= t -1.75e+118)
     (+ x y)
     (if (<= t -9e+51)
       t_1
       (if (<= t -440000000000.0)
         (* y (- 1.0 (/ z t)))
         (if (<= t -1.65e-162)
           (+ x (/ y (/ a z)))
           (if (<= t 1.6e+15) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -1.75e+118) {
		tmp = x + y;
	} else if (t <= -9e+51) {
		tmp = t_1;
	} else if (t <= -440000000000.0) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= -1.65e-162) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.6e+15) {
		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 + (z * (y / a))
    if (t <= (-1.75d+118)) then
        tmp = x + y
    else if (t <= (-9d+51)) then
        tmp = t_1
    else if (t <= (-440000000000.0d0)) then
        tmp = y * (1.0d0 - (z / t))
    else if (t <= (-1.65d-162)) then
        tmp = x + (y / (a / z))
    else if (t <= 1.6d+15) 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 + (z * (y / a));
	double tmp;
	if (t <= -1.75e+118) {
		tmp = x + y;
	} else if (t <= -9e+51) {
		tmp = t_1;
	} else if (t <= -440000000000.0) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= -1.65e-162) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.6e+15) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if t <= -1.75e+118:
		tmp = x + y
	elif t <= -9e+51:
		tmp = t_1
	elif t <= -440000000000.0:
		tmp = y * (1.0 - (z / t))
	elif t <= -1.65e-162:
		tmp = x + (y / (a / z))
	elif t <= 1.6e+15:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -1.75e+118)
		tmp = Float64(x + y);
	elseif (t <= -9e+51)
		tmp = t_1;
	elseif (t <= -440000000000.0)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (t <= -1.65e-162)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.6e+15)
		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 + (z * (y / a));
	tmp = 0.0;
	if (t <= -1.75e+118)
		tmp = x + y;
	elseif (t <= -9e+51)
		tmp = t_1;
	elseif (t <= -440000000000.0)
		tmp = y * (1.0 - (z / t));
	elseif (t <= -1.65e-162)
		tmp = x + (y / (a / z));
	elseif (t <= 1.6e+15)
		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[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+118], N[(x + y), $MachinePrecision], If[LessEqual[t, -9e+51], t$95$1, If[LessEqual[t, -440000000000.0], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.65e-162], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+15], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.75000000000000008e118 or 1.6e15 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 83.0%

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

   if -1.75000000000000008e118 < t < -8.9999999999999999e51 or -1.65000000000000007e-162 < t < 1.6e15

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 71.2%

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

      1. associate-/l* 76.3%

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

      2. associate-/r/ 78.3%

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

   4. Simplified 78.3%

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

   if -8.9999999999999999e51 < t < -4.4e11

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 99.3%

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

      1. associate-*r/ 99.3%

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

      2. neg-mul-1 99.3%

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

      3. distribute-rgt-neg-in 99.3%

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

      4. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 73.8%

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

   if -4.4e11 < t < -1.65000000000000007e-162

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 71.9%

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

      1. associate-/l* 77.5%

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

   4. Simplified 77.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+51}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -440000000000:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-162}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -25500000000:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 6500000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+185)
   (+ x y)
   (if (<= t -25500000000.0)
     (- x (* y (/ z t)))
     (if (<= t 6500000000000.0) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+185) {
		tmp = x + y;
	} else if (t <= -25500000000.0) {
		tmp = x - (y * (z / t));
	} else if (t <= 6500000000000.0) {
		tmp = x + (z * (y / a));
	} 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 <= (-2.7d+185)) then
        tmp = x + y
    else if (t <= (-25500000000.0d0)) then
        tmp = x - (y * (z / t))
    else if (t <= 6500000000000.0d0) then
        tmp = x + (z * (y / a))
    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 <= -2.7e+185) {
		tmp = x + y;
	} else if (t <= -25500000000.0) {
		tmp = x - (y * (z / t));
	} else if (t <= 6500000000000.0) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+185:
		tmp = x + y
	elif t <= -25500000000.0:
		tmp = x - (y * (z / t))
	elif t <= 6500000000000.0:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+185)
		tmp = Float64(x + y);
	elseif (t <= -25500000000.0)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 6500000000000.0)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+185)
		tmp = x + y;
	elseif (t <= -25500000000.0)
		tmp = x - (y * (z / t));
	elseif (t <= 6500000000000.0)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+185], N[(x + y), $MachinePrecision], If[LessEqual[t, -25500000000.0], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6500000000000.0], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.70000000000000007e185 or 6.5e12 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 85.0%

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

   if -2.70000000000000007e185 < t < -2.55e10

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.8%

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

   3. Taylor expanded in a around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. mul-1-neg 76.7%

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

      3. distribute-rgt-neg-out 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in x around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. associate-/l* 77.0%

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

      4. sub-neg 77.0%

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

      5. associate-/l* 76.7%

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

      6. associate-*r/ 76.9%

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

   8. Simplified 76.9%

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

   if -2.55e10 < t < 6.5e12

   1. Initial program 97.6%

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

   2. Taylor expanded in t around 0 71.1%

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

      1. associate-/l* 77.0%

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

      2. associate-/r/ 77.1%

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

   4. Simplified 77.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -25500000000:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 6500000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6000000000:\\ \;\;\;\;x + \frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+185)
   (+ x y)
   (if (<= t -6000000000.0)
     (+ x (/ y (/ (- t) z)))
     (if (<= t 4.2e+15) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+185) {
		tmp = x + y;
	} else if (t <= -6000000000.0) {
		tmp = x + (y / (-t / z));
	} else if (t <= 4.2e+15) {
		tmp = x + (z * (y / a));
	} 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 <= (-2.7d+185)) then
        tmp = x + y
    else if (t <= (-6000000000.0d0)) then
        tmp = x + (y / (-t / z))
    else if (t <= 4.2d+15) then
        tmp = x + (z * (y / a))
    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 <= -2.7e+185) {
		tmp = x + y;
	} else if (t <= -6000000000.0) {
		tmp = x + (y / (-t / z));
	} else if (t <= 4.2e+15) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+185:
		tmp = x + y
	elif t <= -6000000000.0:
		tmp = x + (y / (-t / z))
	elif t <= 4.2e+15:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+185)
		tmp = Float64(x + y);
	elseif (t <= -6000000000.0)
		tmp = Float64(x + Float64(y / Float64(Float64(-t) / z)));
	elseif (t <= 4.2e+15)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+185)
		tmp = x + y;
	elseif (t <= -6000000000.0)
		tmp = x + (y / (-t / z));
	elseif (t <= 4.2e+15)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+185], N[(x + y), $MachinePrecision], If[LessEqual[t, -6000000000.0], N[(x + N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+15], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.70000000000000007e185 or 4.2e15 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 85.0%

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

   if -2.70000000000000007e185 < t < -6e9

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 77.7%

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

      1. associate-*r/ 77.7%

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

      2. neg-mul-1 77.7%

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

      3. distribute-rgt-neg-in 77.7%

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

      4. associate-/l* 82.7%

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

   4. Simplified 82.7%

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

   5. Taylor expanded in t around 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. neg-mul-1 77.0%

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

   7. Simplified 77.0%

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

   if -6e9 < t < 4.2e15

   1. Initial program 97.6%

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

   2. Taylor expanded in t around 0 71.1%

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

      1. associate-/l* 77.0%

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

      2. associate-/r/ 77.1%

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

   4. Simplified 77.1%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6000000000:\\ \;\;\;\;x + \frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+59} \lor \neg \left(z \leq 7 \cdot 10^{-66}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+59) (not (<= z 7e-66)))
   (+ x (* y (/ z (- a t))))
   (+ x (/ y (/ (- t a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+59) || !(z <= 7e-66)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y / ((t - 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 ((z <= (-2.8d+59)) .or. (.not. (z <= 7d-66))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (y / ((t - 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 ((z <= -2.8e+59) || !(z <= 7e-66)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y / ((t - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+59) or not (z <= 7e-66):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (y / ((t - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+59) || !(z <= 7e-66))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(t - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.8e+59) || ~((z <= 7e-66)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (y / ((t - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+59], N[Not[LessEqual[z, 7e-66]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(t - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999998e59 or 7.0000000000000001e-66 < z

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 90.3%

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

   if -2.7999999999999998e59 < z < 7.0000000000000001e-66

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 92.0%

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

      1. neg-mul-1 92.0%

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

      2. distribute-neg-frac 92.0%

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

   4. Simplified 92.0%

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

   5. Taylor expanded in y around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. neg-mul-1 79.3%

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

      3. distribute-rgt-neg-in 79.3%

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

      4. associate-/l* 92.0%

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

   7. Simplified 92.0%

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

      1. frac-2neg 92.0%

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

      2. remove-double-neg 92.0%

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

      3. associate-/r/ 86.5%

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

      4. sub-neg 86.5%

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

      5. distribute-neg-in 86.5%

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

      6. remove-double-neg 86.5%

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

   9. Applied egg-rr 86.5%

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

       1. associate-*l/ 79.3%

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

       2. associate-/l* 92.0%

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

       3. +-commutative 92.0%

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

       4. unsub-neg 92.0%

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

   11. Simplified 92.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+59} \lor \neg \left(z \leq 7 \cdot 10^{-66}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \end{array} \]

Alternative 7: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+59} \lor \neg \left(z \leq 4.5 \cdot 10^{-66}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+59) (not (<= z 4.5e-66)))
   (+ x (* y (/ z (- a t))))
   (- x (* y (/ t (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+59) || !(z <= 4.5e-66)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x - (y * (t / (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 ((z <= (-4d+59)) .or. (.not. (z <= 4.5d-66))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x - (y * (t / (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 ((z <= -4e+59) || !(z <= 4.5e-66)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+59) or not (z <= 4.5e-66):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x - (y * (t / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+59) || !(z <= 4.5e-66))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+59) || ~((z <= 4.5e-66)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x - (y * (t / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+59], N[Not[LessEqual[z, 4.5e-66]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999989e59 or 4.4999999999999998e-66 < z

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 90.3%

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

   if -3.99999999999999989e59 < z < 4.4999999999999998e-66

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 92.0%

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

      1. neg-mul-1 92.0%

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

      2. distribute-neg-frac 92.0%

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

   4. Simplified 92.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+59} \lor \neg \left(z \leq 4.5 \cdot 10^{-66}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \]

Alternative 8: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+121}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+185)
   (+ x y)
   (if (<= t 4e+121) (+ x (* y (/ z (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+185) {
		tmp = x + y;
	} else if (t <= 4e+121) {
		tmp = x + (y * (z / (a - 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 (t <= (-2.7d+185)) then
        tmp = x + y
    else if (t <= 4d+121) then
        tmp = x + (y * (z / (a - 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 (t <= -2.7e+185) {
		tmp = x + y;
	} else if (t <= 4e+121) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+185:
		tmp = x + y
	elif t <= 4e+121:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+185)
		tmp = Float64(x + y);
	elseif (t <= 4e+121)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+185)
		tmp = x + y;
	elseif (t <= 4e+121)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+185], N[(x + y), $MachinePrecision], If[LessEqual[t, 4e+121], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000007e185 or 4.00000000000000015e121 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 91.1%

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

   if -2.70000000000000007e185 < t < 4.00000000000000015e121

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 85.8%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+121}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+185}:\\ \;\;\;\;x + \left(y + \frac{y}{\frac{t}{a}}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+185)
   (+ x (+ y (/ y (/ t a))))
   (if (<= t 1.55e+122) (+ x (* y (/ z (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+185) {
		tmp = x + (y + (y / (t / a)));
	} else if (t <= 1.55e+122) {
		tmp = x + (y * (z / (a - 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 (t <= (-3.6d+185)) then
        tmp = x + (y + (y / (t / a)))
    else if (t <= 1.55d+122) then
        tmp = x + (y * (z / (a - 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 (t <= -3.6e+185) {
		tmp = x + (y + (y / (t / a)));
	} else if (t <= 1.55e+122) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e+185:
		tmp = x + (y + (y / (t / a)))
	elif t <= 1.55e+122:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+185)
		tmp = Float64(x + Float64(y + Float64(y / Float64(t / a))));
	elseif (t <= 1.55e+122)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e+185)
		tmp = x + (y + (y / (t / a)));
	elseif (t <= 1.55e+122)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+185], N[(x + N[(y + N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+122], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.60000000000000029e185

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 93.2%

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

      1. neg-mul-1 93.2%

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

      2. distribute-neg-frac 93.2%

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

   4. Simplified 93.2%

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

   5. Taylor expanded in t around inf 82.7%

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

      1. +-commutative 82.7%

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

      2. *-commutative 82.7%

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

      3. associate-/l* 93.2%

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

   7. Simplified 93.2%

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

   if -3.60000000000000029e185 < t < 1.54999999999999999e122

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 85.8%

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

   if 1.54999999999999999e122 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 90.6%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+185}:\\ \;\;\;\;x + \left(y + \frac{y}{\frac{t}{a}}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+209} \lor \neg \left(y \leq 6.6 \cdot 10^{+213}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.32e+209) (not (<= y 6.6e+213)))
   (* y (- 1.0 (/ z t)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.32e+209) || !(y <= 6.6e+213)) {
		tmp = y * (1.0 - (z / 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 ((y <= (-1.32d+209)) .or. (.not. (y <= 6.6d+213))) then
        tmp = y * (1.0d0 - (z / 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 ((y <= -1.32e+209) || !(y <= 6.6e+213)) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.32e+209) or not (y <= 6.6e+213):
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.32e+209) || !(y <= 6.6e+213))
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.32e+209) || ~((y <= 6.6e+213)))
		tmp = y * (1.0 - (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.32e+209], N[Not[LessEqual[y, 6.6e+213]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.32e209 or 6.6000000000000002e213 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. neg-mul-1 52.3%

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

      3. distribute-rgt-neg-in 52.3%

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

      4. associate-/l* 70.5%

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

   4. Simplified 70.5%

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

   5. Taylor expanded in y around inf 70.5%

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

   if -1.32e209 < y < 6.6000000000000002e213

   1. Initial program 98.6%

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

   2. Taylor expanded in t around inf 71.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+209} \lor \neg \left(y \leq 6.6 \cdot 10^{+213}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e+118) (+ x y) (if (<= t 2.8e+14) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+118) {
		tmp = x + y;
	} else if (t <= 2.8e+14) {
		tmp = x + (y * (z / a));
	} 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 <= (-1.8d+118)) then
        tmp = x + y
    else if (t <= 2.8d+14) then
        tmp = x + (y * (z / a))
    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 <= -1.8e+118) {
		tmp = x + y;
	} else if (t <= 2.8e+14) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e+118:
		tmp = x + y
	elif t <= 2.8e+14:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e+118)
		tmp = Float64(x + y);
	elseif (t <= 2.8e+14)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.8e+118)
		tmp = x + y;
	elseif (t <= 2.8e+14)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e+118], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.8e+14], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e118 or 2.8e14 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 83.0%

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

   if -1.8e118 < t < 2.8e14

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0 73.7%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 57.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.7 \cdot 10^{-297}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-165}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a 1.7e-297)
   (+ x y)
   (if (<= a 4.1e-165) (/ (* y (- z)) t) (if (<= a 1.1e+83) (+ x y) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1.7e-297) {
		tmp = x + y;
	} else if (a <= 4.1e-165) {
		tmp = (y * -z) / t;
	} else if (a <= 1.1e+83) {
		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 (a <= 1.7d-297) then
        tmp = x + y
    else if (a <= 4.1d-165) then
        tmp = (y * -z) / t
    else if (a <= 1.1d+83) 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 (a <= 1.7e-297) {
		tmp = x + y;
	} else if (a <= 4.1e-165) {
		tmp = (y * -z) / t;
	} else if (a <= 1.1e+83) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 1.7e-297:
		tmp = x + y
	elif a <= 4.1e-165:
		tmp = (y * -z) / t
	elif a <= 1.1e+83:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 1.7e-297)
		tmp = Float64(x + y);
	elseif (a <= 4.1e-165)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	elseif (a <= 1.1e+83)
		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 (a <= 1.7e-297)
		tmp = x + y;
	elseif (a <= 4.1e-165)
		tmp = (y * -z) / t;
	elseif (a <= 1.1e+83)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 1.7e-297], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.1e-165], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 1.1e+83], N[(x + y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.69999999999999991e-297 or 4.1000000000000002e-165 < a < 1.09999999999999999e83

   1. Initial program 99.4%

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

   2. Taylor expanded in t around inf 71.9%

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

   if 1.69999999999999991e-297 < a < 4.1000000000000002e-165

   1. Initial program 94.3%

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

   2. Taylor expanded in a around 0 90.8%

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

      1. associate-*r/ 90.8%

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

      2. neg-mul-1 90.8%

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

      3. distribute-rgt-neg-in 90.8%

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

      4. associate-/l* 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in y around inf 65.6%

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

   6. Taylor expanded in z around inf 59.5%

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

      1. mul-1-neg 59.5%

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

      2. associate-*r/ 54.9%

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

   8. Simplified 54.9%

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

   9. Taylor expanded in y around 0 59.5%

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

   if 1.09999999999999999e83 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 75.5%

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

      1. associate-/l* 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in x around inf 69.2%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.7 \cdot 10^{-297}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-165}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+83}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 60.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+266}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.5e+266) (+ x y) (* y (/ (- z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.5e+266) {
		tmp = x + y;
	} else {
		tmp = y * (-z / 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 (y <= 1.5d+266) then
        tmp = x + y
    else
        tmp = y * (-z / 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 (y <= 1.5e+266) {
		tmp = x + y;
	} else {
		tmp = y * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.5e+266:
		tmp = x + y
	else:
		tmp = y * (-z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.5e+266)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.5e+266)
		tmp = x + y;
	else
		tmp = y * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.5e+266], N[(x + y), $MachinePrecision], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.4999999999999999e266

   1. Initial program 98.8%

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

   2. Taylor expanded in t around inf 66.4%

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

   if 1.4999999999999999e266 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in a around 0 61.4%

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

      1. associate-*r/ 61.4%

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

      2. neg-mul-1 61.4%

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

      3. distribute-rgt-neg-in 61.4%

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

      4. associate-/l* 73.6%

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

   4. Simplified 73.6%

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

   5. Taylor expanded in y around inf 73.7%

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

   6. Taylor expanded in z around inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. associate-*r/ 68.0%

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

   8. Simplified 68.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+266}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 14: 60.5% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 98.8%

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

2. Taylor expanded in t around inf 63.7%

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

3. Final simplification 63.7%

   \[\leadsto x + y \]

Alternative 15: 50.7% 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 98.8%

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

2. Taylor expanded in t around 0 58.1%

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

   1. associate-/l* 61.3%

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

4. Simplified 61.3%

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

5. Taylor expanded in x around inf 51.6%

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

6. Final simplification 51.6%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.6× 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 2023274 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (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)))))