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

Percentage Accurate: 98.2% → 96.7%

Time: 10.7s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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) / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := x + \frac{y}{\frac{z - a}{-t}}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0.01:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;t_1 \leq 100000000:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (+ x (/ y (/ (- z a) (- t))))))
   (if (<= t_1 -1e+18)
     t_2
     (if (<= t_1 0.01)
       (+ x (/ (- t z) (/ a y)))
       (if (<= t_1 100000000.0) (+ x (/ y (/ z (- z t)))) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = x + (y / ((z - a) / -t));
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = t_2;
	} else if (t_1 <= 0.01) {
		tmp = x + ((t - z) / (a / y));
	} else if (t_1 <= 100000000.0) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    t_2 = x + (y / ((z - a) / -t))
    if (t_1 <= (-1d+18)) then
        tmp = t_2
    else if (t_1 <= 0.01d0) then
        tmp = x + ((t - z) / (a / y))
    else if (t_1 <= 100000000.0d0) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = t_2
    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) / (z - a);
	double t_2 = x + (y / ((z - a) / -t));
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = t_2;
	} else if (t_1 <= 0.01) {
		tmp = x + ((t - z) / (a / y));
	} else if (t_1 <= 100000000.0) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	t_2 = x + (y / ((z - a) / -t))
	tmp = 0
	if t_1 <= -1e+18:
		tmp = t_2
	elif t_1 <= 0.01:
		tmp = x + ((t - z) / (a / y))
	elif t_1 <= 100000000.0:
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(-t))))
	tmp = 0.0
	if (t_1 <= -1e+18)
		tmp = t_2;
	elseif (t_1 <= 0.01)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	elseif (t_1 <= 100000000.0)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	t_2 = x + (y / ((z - a) / -t));
	tmp = 0.0;
	if (t_1 <= -1e+18)
		tmp = t_2;
	elseif (t_1 <= 0.01)
		tmp = x + ((t - z) / (a / y));
	elseif (t_1 <= 100000000.0)
		tmp = x + (y / (z / (z - t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+18], t$95$2, If[LessEqual[t$95$1, 0.01], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000000.0], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -1e18 or 1e8 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 97.1%

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

   2. Taylor expanded in t around inf 97.3%

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

      1. associate-*r/ 97.3%

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

      2. mul-1-neg 97.3%

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

      3. distribute-lft-neg-out 97.3%

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

      4. *-commutative 97.3%

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

      5. associate-/l* 98.2%

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

   4. Simplified 98.2%

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

   if -1e18 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.0100000000000000002

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

      3. associate-/l* 93.7%

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

      4. associate-/r/ 96.9%

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

   4. Simplified 96.9%

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

      1. *-commutative 96.9%

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

      2. clear-num 96.9%

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

      3. un-div-inv 97.9%

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

   6. Applied egg-rr 97.9%

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

   if 0.0100000000000000002 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e8

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 99.4%

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

   4. Simplified 99.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{-t}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.01:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 100000000:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{-t}}\\ \end{array} \]

Alternative 2: 83.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot t_1\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;t_1 \leq 0.002:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;t_1 \leq 10^{+137}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -1e+127)
     (* y t_1)
     (if (<= t_1 -1e+18)
       (+ x (/ y (/ (- z) t)))
       (if (<= t_1 0.002)
         (+ x (/ t (/ a y)))
         (if (<= t_1 2e+15)
           (+ x (/ y (/ z (- z t))))
           (if (<= t_1 1e+137) (+ x (* y (/ t a))) (- x (* t (/ y z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = y * t_1;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 0.002) {
		tmp = x + (t / (a / y));
	} else if (t_1 <= 2e+15) {
		tmp = x + (y / (z / (z - t)));
	} else if (t_1 <= 1e+137) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (t * (y / z));
	}
	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) / (z - a)
    if (t_1 <= (-1d+127)) then
        tmp = y * t_1
    else if (t_1 <= (-1d+18)) then
        tmp = x + (y / (-z / t))
    else if (t_1 <= 0.002d0) then
        tmp = x + (t / (a / y))
    else if (t_1 <= 2d+15) then
        tmp = x + (y / (z / (z - t)))
    else if (t_1 <= 1d+137) then
        tmp = x + (y * (t / a))
    else
        tmp = x - (t * (y / z))
    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) / (z - a);
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = y * t_1;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 0.002) {
		tmp = x + (t / (a / y));
	} else if (t_1 <= 2e+15) {
		tmp = x + (y / (z / (z - t)));
	} else if (t_1 <= 1e+137) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (t * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -1e+127:
		tmp = y * t_1
	elif t_1 <= -1e+18:
		tmp = x + (y / (-z / t))
	elif t_1 <= 0.002:
		tmp = x + (t / (a / y))
	elif t_1 <= 2e+15:
		tmp = x + (y / (z / (z - t)))
	elif t_1 <= 1e+137:
		tmp = x + (y * (t / a))
	else:
		tmp = x - (t * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -1e+127)
		tmp = Float64(y * t_1);
	elseif (t_1 <= -1e+18)
		tmp = Float64(x + Float64(y / Float64(Float64(-z) / t)));
	elseif (t_1 <= 0.002)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (t_1 <= 2e+15)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (t_1 <= 1e+137)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(t * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -1e+127)
		tmp = y * t_1;
	elseif (t_1 <= -1e+18)
		tmp = x + (y / (-z / t));
	elseif (t_1 <= 0.002)
		tmp = x + (t / (a / y));
	elseif (t_1 <= 2e+15)
		tmp = x + (y / (z / (z - t)));
	elseif (t_1 <= 1e+137)
		tmp = x + (y * (t / a));
	else
		tmp = x - (t * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+127], N[(y * t$95$1), $MachinePrecision], If[LessEqual[t$95$1, -1e+18], N[(x + N[(y / N[((-z) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.002], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+15], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+137], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.99999999999999955e126

   1. Initial program 99.7%

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

      1. associate-*r/ 95.0%

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

   3. Simplified 95.0%

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

      1. associate-*r/ 99.7%

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

      2. *-commutative 99.7%

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

      3. div-inv 99.5%

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

      4. associate-*l* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 95.0%

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

      1. div-sub 95.0%

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

   8. Simplified 95.0%

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

   if -9.99999999999999955e126 < (/.f64 (-.f64 z t) (-.f64 z a)) < -1e18

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-/l* 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. associate-*r/ 85.3%

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

      2. neg-mul-1 85.3%

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

   7. Simplified 85.3%

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

   if -1e18 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e-3

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 85.8%

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

      1. +-commutative 85.8%

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

      2. associate-/l* 89.1%

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

   4. Simplified 89.1%

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

   if 2e-3 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e15

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. associate-/l* 98.6%

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

   4. Simplified 98.6%

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

   if 2e15 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e137

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-/l* 56.1%

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

      3. associate-/r/ 75.1%

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

   4. Simplified 75.1%

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

   if 1e137 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 87.5%

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

   2. Taylor expanded in a around 0 87.2%

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

      1. +-commutative 87.2%

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

      2. associate-/l* 79.8%

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

      3. associate-/r/ 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in z around 0 87.2%

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

      1. associate-*r/ 87.2%

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

      2. mul-1-neg 87.2%

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

      3. distribute-rgt-neg-in 87.2%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in t around 0 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-*r/ 87.4%

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

      3. distribute-lft-neg-out 87.4%

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

      4. cancel-sign-sub-inv 87.4%

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

   10. Simplified 87.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.002:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+137}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 87.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot t_1\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;t_1 \leq 0.01:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;t_1 \leq 10^{+137}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -1e+127)
     (* y t_1)
     (if (<= t_1 -1e+18)
       (+ x (/ y (/ (- z) t)))
       (if (<= t_1 0.01)
         (+ x (* (/ y a) (- t z)))
         (if (<= t_1 2e+15)
           (+ x (/ y (/ z (- z t))))
           (if (<= t_1 1e+137) (+ x (* y (/ t a))) (- x (* t (/ y z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = y * t_1;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 0.01) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 2e+15) {
		tmp = x + (y / (z / (z - t)));
	} else if (t_1 <= 1e+137) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (t * (y / z));
	}
	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) / (z - a)
    if (t_1 <= (-1d+127)) then
        tmp = y * t_1
    else if (t_1 <= (-1d+18)) then
        tmp = x + (y / (-z / t))
    else if (t_1 <= 0.01d0) then
        tmp = x + ((y / a) * (t - z))
    else if (t_1 <= 2d+15) then
        tmp = x + (y / (z / (z - t)))
    else if (t_1 <= 1d+137) then
        tmp = x + (y * (t / a))
    else
        tmp = x - (t * (y / z))
    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) / (z - a);
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = y * t_1;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 0.01) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 2e+15) {
		tmp = x + (y / (z / (z - t)));
	} else if (t_1 <= 1e+137) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (t * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -1e+127:
		tmp = y * t_1
	elif t_1 <= -1e+18:
		tmp = x + (y / (-z / t))
	elif t_1 <= 0.01:
		tmp = x + ((y / a) * (t - z))
	elif t_1 <= 2e+15:
		tmp = x + (y / (z / (z - t)))
	elif t_1 <= 1e+137:
		tmp = x + (y * (t / a))
	else:
		tmp = x - (t * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -1e+127)
		tmp = Float64(y * t_1);
	elseif (t_1 <= -1e+18)
		tmp = Float64(x + Float64(y / Float64(Float64(-z) / t)));
	elseif (t_1 <= 0.01)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	elseif (t_1 <= 2e+15)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (t_1 <= 1e+137)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(t * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -1e+127)
		tmp = y * t_1;
	elseif (t_1 <= -1e+18)
		tmp = x + (y / (-z / t));
	elseif (t_1 <= 0.01)
		tmp = x + ((y / a) * (t - z));
	elseif (t_1 <= 2e+15)
		tmp = x + (y / (z / (z - t)));
	elseif (t_1 <= 1e+137)
		tmp = x + (y * (t / a));
	else
		tmp = x - (t * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+127], N[(y * t$95$1), $MachinePrecision], If[LessEqual[t$95$1, -1e+18], N[(x + N[(y / N[((-z) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.01], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+15], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+137], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.99999999999999955e126

   1. Initial program 99.7%

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

      1. associate-*r/ 95.0%

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

   3. Simplified 95.0%

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

      1. associate-*r/ 99.7%

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

      2. *-commutative 99.7%

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

      3. div-inv 99.5%

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

      4. associate-*l* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 95.0%

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

      1. div-sub 95.0%

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

   8. Simplified 95.0%

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

   if -9.99999999999999955e126 < (/.f64 (-.f64 z t) (-.f64 z a)) < -1e18

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-/l* 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. associate-*r/ 85.3%

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

      2. neg-mul-1 85.3%

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

   7. Simplified 85.3%

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

   if -1e18 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.0100000000000000002

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

      3. associate-/l* 93.7%

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

      4. associate-/r/ 96.9%

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

   4. Simplified 96.9%

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

   if 0.0100000000000000002 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e15

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 99.4%

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

   4. Simplified 99.4%

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

   if 2e15 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e137

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-/l* 56.1%

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

      3. associate-/r/ 75.1%

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

   4. Simplified 75.1%

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

   if 1e137 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 87.5%

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

   2. Taylor expanded in a around 0 87.2%

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

      1. +-commutative 87.2%

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

      2. associate-/l* 79.8%

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

      3. associate-/r/ 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in z around 0 87.2%

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

      1. associate-*r/ 87.2%

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

      2. mul-1-neg 87.2%

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

      3. distribute-rgt-neg-in 87.2%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in t around 0 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-*r/ 87.4%

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

      3. distribute-lft-neg-out 87.4%

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

      4. cancel-sign-sub-inv 87.4%

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

   10. Simplified 87.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.01:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+137}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \]

Alternative 4: 87.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot t_1\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;t_1 \leq 0.01:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;t_1 \leq 10^{+137}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -1e+127)
     (* y t_1)
     (if (<= t_1 -1e+18)
       (+ x (/ y (/ (- z) t)))
       (if (<= t_1 0.01)
         (+ x (/ (- t z) (/ a y)))
         (if (<= t_1 2e+15)
           (+ x (/ y (/ z (- z t))))
           (if (<= t_1 1e+137) (+ x (* y (/ t a))) (- x (* t (/ y z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = y * t_1;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 0.01) {
		tmp = x + ((t - z) / (a / y));
	} else if (t_1 <= 2e+15) {
		tmp = x + (y / (z / (z - t)));
	} else if (t_1 <= 1e+137) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (t * (y / z));
	}
	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) / (z - a)
    if (t_1 <= (-1d+127)) then
        tmp = y * t_1
    else if (t_1 <= (-1d+18)) then
        tmp = x + (y / (-z / t))
    else if (t_1 <= 0.01d0) then
        tmp = x + ((t - z) / (a / y))
    else if (t_1 <= 2d+15) then
        tmp = x + (y / (z / (z - t)))
    else if (t_1 <= 1d+137) then
        tmp = x + (y * (t / a))
    else
        tmp = x - (t * (y / z))
    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) / (z - a);
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = y * t_1;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 0.01) {
		tmp = x + ((t - z) / (a / y));
	} else if (t_1 <= 2e+15) {
		tmp = x + (y / (z / (z - t)));
	} else if (t_1 <= 1e+137) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (t * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -1e+127:
		tmp = y * t_1
	elif t_1 <= -1e+18:
		tmp = x + (y / (-z / t))
	elif t_1 <= 0.01:
		tmp = x + ((t - z) / (a / y))
	elif t_1 <= 2e+15:
		tmp = x + (y / (z / (z - t)))
	elif t_1 <= 1e+137:
		tmp = x + (y * (t / a))
	else:
		tmp = x - (t * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -1e+127)
		tmp = Float64(y * t_1);
	elseif (t_1 <= -1e+18)
		tmp = Float64(x + Float64(y / Float64(Float64(-z) / t)));
	elseif (t_1 <= 0.01)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	elseif (t_1 <= 2e+15)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (t_1 <= 1e+137)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(t * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -1e+127)
		tmp = y * t_1;
	elseif (t_1 <= -1e+18)
		tmp = x + (y / (-z / t));
	elseif (t_1 <= 0.01)
		tmp = x + ((t - z) / (a / y));
	elseif (t_1 <= 2e+15)
		tmp = x + (y / (z / (z - t)));
	elseif (t_1 <= 1e+137)
		tmp = x + (y * (t / a));
	else
		tmp = x - (t * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+127], N[(y * t$95$1), $MachinePrecision], If[LessEqual[t$95$1, -1e+18], N[(x + N[(y / N[((-z) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.01], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+15], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+137], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.99999999999999955e126

   1. Initial program 99.7%

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

      1. associate-*r/ 95.0%

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

   3. Simplified 95.0%

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

      1. associate-*r/ 99.7%

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

      2. *-commutative 99.7%

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

      3. div-inv 99.5%

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

      4. associate-*l* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 95.0%

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

      1. div-sub 95.0%

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

   8. Simplified 95.0%

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

   if -9.99999999999999955e126 < (/.f64 (-.f64 z t) (-.f64 z a)) < -1e18

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-/l* 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. associate-*r/ 85.3%

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

      2. neg-mul-1 85.3%

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

   7. Simplified 85.3%

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

   if -1e18 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.0100000000000000002

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

      3. associate-/l* 93.7%

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

      4. associate-/r/ 96.9%

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

   4. Simplified 96.9%

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

      1. *-commutative 96.9%

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

      2. clear-num 96.9%

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

      3. un-div-inv 97.9%

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

   6. Applied egg-rr 97.9%

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

   if 0.0100000000000000002 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e15

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 99.4%

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

   4. Simplified 99.4%

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

   if 2e15 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e137

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-/l* 56.1%

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

      3. associate-/r/ 75.1%

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

   4. Simplified 75.1%

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

   if 1e137 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 87.5%

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

   2. Taylor expanded in a around 0 87.2%

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

      1. +-commutative 87.2%

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

      2. associate-/l* 79.8%

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

      3. associate-/r/ 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in z around 0 87.2%

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

      1. associate-*r/ 87.2%

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

      2. mul-1-neg 87.2%

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

      3. distribute-rgt-neg-in 87.2%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in t around 0 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-*r/ 87.4%

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

      3. distribute-lft-neg-out 87.4%

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

      4. cancel-sign-sub-inv 87.4%

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

   10. Simplified 87.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 0.01:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+137}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \end{array} \]

Alternative 5: 83.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := y \cdot t_1\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t_1 \leq 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (* y t_1)))
   (if (<= t_1 -1e+127)
     t_2
     (if (<= t_1 -1e+18)
       (+ x (/ y (/ (- z) t)))
       (if (<= t_1 2e-17)
         (+ x (/ t (/ a y)))
         (if (<= t_1 1e+35) (+ x y) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = y * t_1;
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = t_2;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 2e-17) {
		tmp = x + (t / (a / y));
	} else if (t_1 <= 1e+35) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    t_2 = y * t_1
    if (t_1 <= (-1d+127)) then
        tmp = t_2
    else if (t_1 <= (-1d+18)) then
        tmp = x + (y / (-z / t))
    else if (t_1 <= 2d-17) then
        tmp = x + (t / (a / y))
    else if (t_1 <= 1d+35) then
        tmp = x + y
    else
        tmp = t_2
    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) / (z - a);
	double t_2 = y * t_1;
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = t_2;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 2e-17) {
		tmp = x + (t / (a / y));
	} else if (t_1 <= 1e+35) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	t_2 = y * t_1
	tmp = 0
	if t_1 <= -1e+127:
		tmp = t_2
	elif t_1 <= -1e+18:
		tmp = x + (y / (-z / t))
	elif t_1 <= 2e-17:
		tmp = x + (t / (a / y))
	elif t_1 <= 1e+35:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = Float64(y * t_1)
	tmp = 0.0
	if (t_1 <= -1e+127)
		tmp = t_2;
	elseif (t_1 <= -1e+18)
		tmp = Float64(x + Float64(y / Float64(Float64(-z) / t)));
	elseif (t_1 <= 2e-17)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (t_1 <= 1e+35)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	t_2 = y * t_1;
	tmp = 0.0;
	if (t_1 <= -1e+127)
		tmp = t_2;
	elseif (t_1 <= -1e+18)
		tmp = x + (y / (-z / t));
	elseif (t_1 <= 2e-17)
		tmp = x + (t / (a / y));
	elseif (t_1 <= 1e+35)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+127], t$95$2, If[LessEqual[t$95$1, -1e+18], N[(x + N[(y / N[((-z) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-17], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+35], N[(x + y), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.99999999999999955e126 or 9.9999999999999997e34 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 95.4%

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

      1. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

      1. associate-*r/ 95.4%

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

      2. *-commutative 95.4%

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

      3. div-inv 95.2%

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

      4. associate-*l* 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in y around inf 84.1%

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

      1. div-sub 84.1%

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

   8. Simplified 84.1%

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

   if -9.99999999999999955e126 < (/.f64 (-.f64 z t) (-.f64 z a)) < -1e18

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-/l* 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. associate-*r/ 85.3%

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

      2. neg-mul-1 85.3%

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

   7. Simplified 85.3%

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

   if -1e18 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2.00000000000000014e-17

   1. Initial program 97.0%

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

   2. Taylor expanded in z around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-/l* 88.7%

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

   4. Simplified 88.7%

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

   if 2.00000000000000014e-17 < (/.f64 (-.f64 z t) (-.f64 z a)) < 9.9999999999999997e34

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 94.3%

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

      1. +-commutative 94.3%

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

   4. Simplified 94.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 2 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]

Alternative 6: 83.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := y \cdot t_1\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;t_1 \leq 10^{+35}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))) (t_2 (* y t_1)))
   (if (<= t_1 -1e+127)
     t_2
     (if (<= t_1 -1e+18)
       (+ x (/ y (/ (- z) t)))
       (if (<= t_1 1e+35) (+ x (* y (/ z (- z a)))) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = y * t_1;
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = t_2;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 1e+35) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (z - t) / (z - a)
    t_2 = y * t_1
    if (t_1 <= (-1d+127)) then
        tmp = t_2
    else if (t_1 <= (-1d+18)) then
        tmp = x + (y / (-z / t))
    else if (t_1 <= 1d+35) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = t_2
    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) / (z - a);
	double t_2 = y * t_1;
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = t_2;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 1e+35) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	t_2 = y * t_1
	tmp = 0
	if t_1 <= -1e+127:
		tmp = t_2
	elif t_1 <= -1e+18:
		tmp = x + (y / (-z / t))
	elif t_1 <= 1e+35:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = Float64(y * t_1)
	tmp = 0.0
	if (t_1 <= -1e+127)
		tmp = t_2;
	elseif (t_1 <= -1e+18)
		tmp = Float64(x + Float64(y / Float64(Float64(-z) / t)));
	elseif (t_1 <= 1e+35)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	t_2 = y * t_1;
	tmp = 0.0;
	if (t_1 <= -1e+127)
		tmp = t_2;
	elseif (t_1 <= -1e+18)
		tmp = x + (y / (-z / t));
	elseif (t_1 <= 1e+35)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+127], t$95$2, If[LessEqual[t$95$1, -1e+18], N[(x + N[(y / N[((-z) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+35], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.99999999999999955e126 or 9.9999999999999997e34 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 95.4%

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

      1. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

      1. associate-*r/ 95.4%

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

      2. *-commutative 95.4%

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

      3. div-inv 95.2%

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

      4. associate-*l* 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in y around inf 84.1%

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

      1. div-sub 84.1%

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

   8. Simplified 84.1%

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

   if -9.99999999999999955e126 < (/.f64 (-.f64 z t) (-.f64 z a)) < -1e18

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-/l* 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. associate-*r/ 85.3%

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

      2. neg-mul-1 85.3%

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

   7. Simplified 85.3%

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

   if -1e18 < (/.f64 (-.f64 z t) (-.f64 z a)) < 9.9999999999999997e34

   1. Initial program 98.7%

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

   2. Taylor expanded in t around 0 90.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 10^{+35}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]

Alternative 7: 81.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot t_1\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;t_1 \leq 1.0000000005:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- z a))))
   (if (<= t_1 -1e+127)
     (* y t_1)
     (if (<= t_1 -1e+18)
       (+ x (/ y (/ (- z) t)))
       (if (<= t_1 1.0000000005)
         (+ x (* y (/ z (- z a))))
         (+ x (/ (* y (- z t)) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = y * t_1;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 1.0000000005) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((y * (z - t)) / z);
	}
	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) / (z - a)
    if (t_1 <= (-1d+127)) then
        tmp = y * t_1
    else if (t_1 <= (-1d+18)) then
        tmp = x + (y / (-z / t))
    else if (t_1 <= 1.0000000005d0) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + ((y * (z - t)) / z)
    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) / (z - a);
	double tmp;
	if (t_1 <= -1e+127) {
		tmp = y * t_1;
	} else if (t_1 <= -1e+18) {
		tmp = x + (y / (-z / t));
	} else if (t_1 <= 1.0000000005) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + ((y * (z - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (z - a)
	tmp = 0
	if t_1 <= -1e+127:
		tmp = y * t_1
	elif t_1 <= -1e+18:
		tmp = x + (y / (-z / t))
	elif t_1 <= 1.0000000005:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + ((y * (z - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -1e+127)
		tmp = Float64(y * t_1);
	elseif (t_1 <= -1e+18)
		tmp = Float64(x + Float64(y / Float64(Float64(-z) / t)));
	elseif (t_1 <= 1.0000000005)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (z - a);
	tmp = 0.0;
	if (t_1 <= -1e+127)
		tmp = y * t_1;
	elseif (t_1 <= -1e+18)
		tmp = x + (y / (-z / t));
	elseif (t_1 <= 1.0000000005)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + ((y * (z - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+127], N[(y * t$95$1), $MachinePrecision], If[LessEqual[t$95$1, -1e+18], N[(x + N[(y / N[((-z) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.0000000005], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -9.99999999999999955e126

   1. Initial program 99.7%

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

      1. associate-*r/ 95.0%

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

   3. Simplified 95.0%

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

      1. associate-*r/ 99.7%

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

      2. *-commutative 99.7%

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

      3. div-inv 99.5%

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

      4. associate-*l* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 95.0%

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

      1. div-sub 95.0%

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

   8. Simplified 95.0%

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

   if -9.99999999999999955e126 < (/.f64 (-.f64 z t) (-.f64 z a)) < -1e18

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-/l* 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. associate-*r/ 85.3%

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

      2. neg-mul-1 85.3%

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

   7. Simplified 85.3%

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

   if -1e18 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1.0000000005

   1. Initial program 98.6%

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

   2. Taylor expanded in t around 0 92.3%

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

   if 1.0000000005 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 95.2%

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

   2. Taylor expanded in a around 0 74.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq -1 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;\frac{z - t}{z - a} \leq 1.0000000005:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \end{array} \]

Alternative 8: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+81)
   (+ x y)
   (if (<= z -6.5e+42)
     (* y (- 1.0 (/ t z)))
     (if (<= z 7.8e-56) (+ x (/ (* y t) a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+81) {
		tmp = x + y;
	} else if (z <= -6.5e+42) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 7.8e-56) {
		tmp = x + ((y * t) / 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 (z <= (-1.8d+81)) then
        tmp = x + y
    else if (z <= (-6.5d+42)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 7.8d-56) then
        tmp = x + ((y * t) / 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 (z <= -1.8e+81) {
		tmp = x + y;
	} else if (z <= -6.5e+42) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 7.8e-56) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+81:
		tmp = x + y
	elif z <= -6.5e+42:
		tmp = y * (1.0 - (t / z))
	elif z <= 7.8e-56:
		tmp = x + ((y * t) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+81)
		tmp = Float64(x + y);
	elseif (z <= -6.5e+42)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 7.8e-56)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+81)
		tmp = x + y;
	elseif (z <= -6.5e+42)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 7.8e-56)
		tmp = x + ((y * t) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+81], N[(x + y), $MachinePrecision], If[LessEqual[z, -6.5e+42], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e-56], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000003e81 or 7.8e-56 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.7%

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

      1. +-commutative 80.7%

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

   4. Simplified 80.7%

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

   if -1.80000000000000003e81 < z < -6.50000000000000052e42

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 99.7%

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

      3. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 88.7%

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

   if -6.50000000000000052e42 < z < 7.8e-56

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 76.4%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+82)
   (+ x y)
   (if (<= z -7.2e+42)
     (* y (- 1.0 (/ t z)))
     (if (<= z 3.7e-53) (+ x (* y (/ t a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+82) {
		tmp = x + y;
	} else if (z <= -7.2e+42) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 3.7e-53) {
		tmp = x + (y * (t / 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 (z <= (-7.2d+82)) then
        tmp = x + y
    else if (z <= (-7.2d+42)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 3.7d-53) then
        tmp = x + (y * (t / 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 (z <= -7.2e+82) {
		tmp = x + y;
	} else if (z <= -7.2e+42) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 3.7e-53) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+82:
		tmp = x + y
	elif z <= -7.2e+42:
		tmp = y * (1.0 - (t / z))
	elif z <= 3.7e-53:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+82)
		tmp = Float64(x + y);
	elseif (z <= -7.2e+42)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 3.7e-53)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+82)
		tmp = x + y;
	elseif (z <= -7.2e+42)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 3.7e-53)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+82], N[(x + y), $MachinePrecision], If[LessEqual[z, -7.2e+42], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-53], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.20000000000000028e82 or 3.69999999999999982e-53 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.7%

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

      1. +-commutative 80.7%

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

   4. Simplified 80.7%

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

   if -7.20000000000000028e82 < z < -7.2000000000000002e42

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 99.7%

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

      3. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 88.7%

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

   if -7.2000000000000002e42 < z < 3.69999999999999982e-53

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-/l* 76.4%

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

      3. associate-/r/ 77.1%

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

   4. Simplified 77.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 76.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-63}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e+84)
   (+ x y)
   (if (<= z -1.8e-63)
     (- x (* t (/ y z)))
     (if (<= z 5.8e-48) (+ x (* y (/ t a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+84) {
		tmp = x + y;
	} else if (z <= -1.8e-63) {
		tmp = x - (t * (y / z));
	} else if (z <= 5.8e-48) {
		tmp = x + (y * (t / 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 (z <= (-3.1d+84)) then
        tmp = x + y
    else if (z <= (-1.8d-63)) then
        tmp = x - (t * (y / z))
    else if (z <= 5.8d-48) then
        tmp = x + (y * (t / 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 (z <= -3.1e+84) {
		tmp = x + y;
	} else if (z <= -1.8e-63) {
		tmp = x - (t * (y / z));
	} else if (z <= 5.8e-48) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e+84:
		tmp = x + y
	elif z <= -1.8e-63:
		tmp = x - (t * (y / z))
	elif z <= 5.8e-48:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e+84)
		tmp = Float64(x + y);
	elseif (z <= -1.8e-63)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 5.8e-48)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.1e+84)
		tmp = x + y;
	elseif (z <= -1.8e-63)
		tmp = x - (t * (y / z));
	elseif (z <= 5.8e-48)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e+84], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.8e-63], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-48], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000003e84 or 5.8000000000000006e-48 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.6%

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

      1. +-commutative 80.6%

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

   4. Simplified 80.6%

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

   if -3.10000000000000003e84 < z < -1.80000000000000004e-63

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 82.3%

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

      1. +-commutative 82.3%

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

      2. associate-/l* 82.5%

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

      3. associate-/r/ 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in z around 0 76.6%

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

      1. associate-*r/ 76.6%

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

      2. mul-1-neg 76.6%

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

      3. distribute-rgt-neg-in 76.6%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in t around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. associate-*r/ 76.9%

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

      3. distribute-lft-neg-out 76.9%

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

      4. cancel-sign-sub-inv 76.9%

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

   10. Simplified 76.9%

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

   if -1.80000000000000004e-63 < z < 5.8000000000000006e-48

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 79.4%

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

      3. associate-/r/ 80.3%

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

   4. Simplified 80.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-63}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+173} \lor \neg \left(y \leq 6.2 \cdot 10^{+147}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.7e+173) (not (<= y 6.2e+147)))
   (* y (- 1.0 (/ t z)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.7e+173) || !(y <= 6.2e+147)) {
		tmp = y * (1.0 - (t / z));
	} 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 <= (-4.7d+173)) .or. (.not. (y <= 6.2d+147))) then
        tmp = y * (1.0d0 - (t / z))
    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 <= -4.7e+173) || !(y <= 6.2e+147)) {
		tmp = y * (1.0 - (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.7e+173) or not (y <= 6.2e+147):
		tmp = y * (1.0 - (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.7e+173) || !(y <= 6.2e+147))
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.7e+173) || ~((y <= 6.2e+147)))
		tmp = y * (1.0 - (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.7e+173], N[Not[LessEqual[y, 6.2e+147]], $MachinePrecision]], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.70000000000000015e173 or 6.2000000000000001e147 < y

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0 36.9%

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

      1. +-commutative 36.9%

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

      2. associate-/l* 64.9%

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

      3. associate-/r/ 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in y around inf 63.4%

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

   if -4.70000000000000015e173 < y < 6.2000000000000001e147

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 69.3%

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

      1. +-commutative 69.3%

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

   4. Simplified 69.3%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+173} \lor \neg \left(y \leq 6.2 \cdot 10^{+147}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.2%

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

2. Final simplification 98.2%

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

Alternative 13: 62.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-38} \lor \neg \left(z \leq 1.5 \cdot 10^{+92}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e-38) (not (<= z 1.5e+92))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e-38) || !(z <= 1.5e+92)) {
		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 ((z <= (-5.5d-38)) .or. (.not. (z <= 1.5d+92))) 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 ((z <= -5.5e-38) || !(z <= 1.5e+92)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e-38) or not (z <= 1.5e+92):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e-38) || !(z <= 1.5e+92))
		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 ((z <= -5.5e-38) || ~((z <= 1.5e+92)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e-38], N[Not[LessEqual[z, 1.5e+92]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000005e-38 or 1.50000000000000007e92 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 78.5%

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

      1. +-commutative 78.5%

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

   4. Simplified 78.5%

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

   if -5.50000000000000005e-38 < z < 1.50000000000000007e92

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 56.8%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-38} \lor \neg \left(z \leq 1.5 \cdot 10^{+92}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 50.2% 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 98.2%

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

2. Taylor expanded in x around inf 53.1%

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

3. Final simplification 53.1%

   \[\leadsto x \]

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((z - a) / (z - 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 - a) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023321 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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