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

Percentage Accurate: 98.2% → 98.2%

Time: 10.5s

Alternatives: 11

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: 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 98.9%

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

3. Final simplification 98.9%

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

Alternative 2: 75.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ t_2 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-174}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))) (t_2 (+ x (* y (/ t a)))))
   (if (<= a -7.6e+44)
     t_2
     (if (<= a -8.2e-24)
       t_1
       (if (<= a -1e-55)
         (* y (/ (- t) (- z a)))
         (if (<= a -5.3e-174) (+ x y) (if (<= a 2.6e-117) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -7.6e+44) {
		tmp = t_2;
	} else if (a <= -8.2e-24) {
		tmp = t_1;
	} else if (a <= -1e-55) {
		tmp = y * (-t / (z - a));
	} else if (a <= -5.3e-174) {
		tmp = x + y;
	} else if (a <= 2.6e-117) {
		tmp = t_1;
	} 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 = x + (y * (1.0d0 - (t / z)))
    t_2 = x + (y * (t / a))
    if (a <= (-7.6d+44)) then
        tmp = t_2
    else if (a <= (-8.2d-24)) then
        tmp = t_1
    else if (a <= (-1d-55)) then
        tmp = y * (-t / (z - a))
    else if (a <= (-5.3d-174)) then
        tmp = x + y
    else if (a <= 2.6d-117) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -7.6e+44) {
		tmp = t_2;
	} else if (a <= -8.2e-24) {
		tmp = t_1;
	} else if (a <= -1e-55) {
		tmp = y * (-t / (z - a));
	} else if (a <= -5.3e-174) {
		tmp = x + y;
	} else if (a <= 2.6e-117) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	t_2 = x + (y * (t / a))
	tmp = 0
	if a <= -7.6e+44:
		tmp = t_2
	elif a <= -8.2e-24:
		tmp = t_1
	elif a <= -1e-55:
		tmp = y * (-t / (z - a))
	elif a <= -5.3e-174:
		tmp = x + y
	elif a <= 2.6e-117:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	t_2 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (a <= -7.6e+44)
		tmp = t_2;
	elseif (a <= -8.2e-24)
		tmp = t_1;
	elseif (a <= -1e-55)
		tmp = Float64(y * Float64(Float64(-t) / Float64(z - a)));
	elseif (a <= -5.3e-174)
		tmp = Float64(x + y);
	elseif (a <= 2.6e-117)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	t_2 = x + (y * (t / a));
	tmp = 0.0;
	if (a <= -7.6e+44)
		tmp = t_2;
	elseif (a <= -8.2e-24)
		tmp = t_1;
	elseif (a <= -1e-55)
		tmp = y * (-t / (z - a));
	elseif (a <= -5.3e-174)
		tmp = x + y;
	elseif (a <= 2.6e-117)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.6e+44], t$95$2, If[LessEqual[a, -8.2e-24], t$95$1, If[LessEqual[a, -1e-55], N[(y * N[((-t) / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.3e-174], N[(x + y), $MachinePrecision], If[LessEqual[a, 2.6e-117], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.6000000000000004e44 or 2.59999999999999983e-117 < a

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 82.3%

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

   if -7.6000000000000004e44 < a < -8.20000000000000029e-24 or -5.2999999999999996e-174 < a < 2.59999999999999983e-117

   1. Initial program 97.7%

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

   3. Taylor expanded in a around 0 92.7%

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

      1. div-sub 92.7%

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

      2. *-inverses 92.7%

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

   5. Simplified 92.7%

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

   if -8.20000000000000029e-24 < a < -9.99999999999999995e-56

   1. Initial program 99.2%

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

   3. Taylor expanded in t around inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. mul-1-neg 99.6%

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

      3. distribute-lft-neg-out 99.6%

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

      4. *-commutative 99.6%

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

   5. Simplified 99.6%

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

      1. div-inv 99.2%

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

      2. add-sqr-sqrt 24.6%

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

      3. sqrt-unprod 25.2%

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

      4. sqr-neg 25.2%

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

      5. sqrt-unprod 0.6%

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

      6. add-sqr-sqrt 0.7%

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

      7. remove-double-neg 0.7%

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

      8. distribute-rgt-neg-out 0.7%

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

      9. cancel-sign-sub-inv 0.7%

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

      10. div-inv 0.7%

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

      11. add-sqr-sqrt 0.1%

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

      12. sqrt-unprod 74.7%

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

      13. sqr-neg 74.7%

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

      14. sqrt-unprod 73.8%

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

      15. add-sqr-sqrt 99.6%

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

   7. Applied egg-rr 99.6%

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

   8. Taylor expanded in x around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r/ 99.2%

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

      3. associate-*r* 99.2%

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

      4. neg-mul-1 99.2%

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

   10. Simplified 99.2%

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

   if -9.99999999999999995e-56 < a < -5.2999999999999996e-174

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.2%

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

      1. +-commutative 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+44}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-24}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-174}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-117}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ t_2 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-61}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-117}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))) (t_2 (+ x (* y (/ t a)))))
   (if (<= a -1.9e+42)
     t_2
     (if (<= a -9e-9)
       t_1
       (if (<= a -3.3e-61)
         (* y (/ (- t) (- z a)))
         (if (<= a -5.3e-174)
           t_1
           (if (<= a 1.9e-117) (+ x (* y (- 1.0 (/ t z)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -1.9e+42) {
		tmp = t_2;
	} else if (a <= -9e-9) {
		tmp = t_1;
	} else if (a <= -3.3e-61) {
		tmp = y * (-t / (z - a));
	} else if (a <= -5.3e-174) {
		tmp = t_1;
	} else if (a <= 1.9e-117) {
		tmp = x + (y * (1.0 - (t / z)));
	} 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 = x + (y * (z / (z - a)))
    t_2 = x + (y * (t / a))
    if (a <= (-1.9d+42)) then
        tmp = t_2
    else if (a <= (-9d-9)) then
        tmp = t_1
    else if (a <= (-3.3d-61)) then
        tmp = y * (-t / (z - a))
    else if (a <= (-5.3d-174)) then
        tmp = t_1
    else if (a <= 1.9d-117) then
        tmp = x + (y * (1.0d0 - (t / z)))
    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 = x + (y * (z / (z - a)));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -1.9e+42) {
		tmp = t_2;
	} else if (a <= -9e-9) {
		tmp = t_1;
	} else if (a <= -3.3e-61) {
		tmp = y * (-t / (z - a));
	} else if (a <= -5.3e-174) {
		tmp = t_1;
	} else if (a <= 1.9e-117) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	t_2 = x + (y * (t / a))
	tmp = 0
	if a <= -1.9e+42:
		tmp = t_2
	elif a <= -9e-9:
		tmp = t_1
	elif a <= -3.3e-61:
		tmp = y * (-t / (z - a))
	elif a <= -5.3e-174:
		tmp = t_1
	elif a <= 1.9e-117:
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	t_2 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (a <= -1.9e+42)
		tmp = t_2;
	elseif (a <= -9e-9)
		tmp = t_1;
	elseif (a <= -3.3e-61)
		tmp = Float64(y * Float64(Float64(-t) / Float64(z - a)));
	elseif (a <= -5.3e-174)
		tmp = t_1;
	elseif (a <= 1.9e-117)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	t_2 = x + (y * (t / a));
	tmp = 0.0;
	if (a <= -1.9e+42)
		tmp = t_2;
	elseif (a <= -9e-9)
		tmp = t_1;
	elseif (a <= -3.3e-61)
		tmp = y * (-t / (z - a));
	elseif (a <= -5.3e-174)
		tmp = t_1;
	elseif (a <= 1.9e-117)
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+42], t$95$2, If[LessEqual[a, -9e-9], t$95$1, If[LessEqual[a, -3.3e-61], N[(y * N[((-t) / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.3e-174], t$95$1, If[LessEqual[a, 1.9e-117], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.8999999999999999e42 or 1.89999999999999986e-117 < a

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 82.3%

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

   if -1.8999999999999999e42 < a < -8.99999999999999953e-9 or -3.29999999999999996e-61 < a < -5.2999999999999996e-174

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 98.2%

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

   if -8.99999999999999953e-9 < a < -3.29999999999999996e-61

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 99.2%

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

      1. associate-*r/ 99.2%

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

      2. mul-1-neg 99.2%

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

      3. distribute-lft-neg-out 99.2%

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

      4. *-commutative 99.2%

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

   5. Simplified 99.2%

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

      1. div-inv 99.1%

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

      2. add-sqr-sqrt 37.3%

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

      3. sqrt-unprod 25.8%

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

      4. sqr-neg 25.8%

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

      5. sqrt-unprod 0.6%

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

      6. add-sqr-sqrt 13.4%

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

      7. remove-double-neg 13.4%

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

      8. distribute-rgt-neg-out 13.4%

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

      9. cancel-sign-sub-inv 13.4%

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

      10. div-inv 13.4%

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

      11. add-sqr-sqrt 12.7%

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

      12. sqrt-unprod 62.7%

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

      13. sqr-neg 62.7%

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

      14. sqrt-unprod 61.5%

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

      15. add-sqr-sqrt 99.2%

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

   7. Applied egg-rr 99.2%

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

   8. Taylor expanded in x around 0 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*r/ 87.4%

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

      3. associate-*r* 87.4%

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

      4. neg-mul-1 87.4%

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

   10. Simplified 87.4%

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

   if -5.2999999999999996e-174 < a < 1.89999999999999986e-117

   1. Initial program 97.3%

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

   3. Taylor expanded in a around 0 94.4%

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

      1. div-sub 94.4%

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

      2. *-inverses 94.4%

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

   5. Simplified 94.4%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-61}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-174}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-117}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-117}:\\ \;\;\;\;x + \left(y - \frac{y \cdot t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))))
   (if (<= a -1.5e+44)
     t_1
     (if (<= a -5.4e-9)
       (+ x (* y (/ z (- z a))))
       (if (<= a -1e-55)
         (* y (/ (- t) (- z a)))
         (if (<= a 2.7e-117) (+ x (- y (/ (* y t) z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (a <= -1.5e+44) {
		tmp = t_1;
	} else if (a <= -5.4e-9) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= -1e-55) {
		tmp = y * (-t / (z - a));
	} else if (a <= 2.7e-117) {
		tmp = x + (y - ((y * t) / z));
	} 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 * (t / a))
    if (a <= (-1.5d+44)) then
        tmp = t_1
    else if (a <= (-5.4d-9)) then
        tmp = x + (y * (z / (z - a)))
    else if (a <= (-1d-55)) then
        tmp = y * (-t / (z - a))
    else if (a <= 2.7d-117) then
        tmp = x + (y - ((y * t) / z))
    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 * (t / a));
	double tmp;
	if (a <= -1.5e+44) {
		tmp = t_1;
	} else if (a <= -5.4e-9) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= -1e-55) {
		tmp = y * (-t / (z - a));
	} else if (a <= 2.7e-117) {
		tmp = x + (y - ((y * t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	tmp = 0
	if a <= -1.5e+44:
		tmp = t_1
	elif a <= -5.4e-9:
		tmp = x + (y * (z / (z - a)))
	elif a <= -1e-55:
		tmp = y * (-t / (z - a))
	elif a <= 2.7e-117:
		tmp = x + (y - ((y * t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (a <= -1.5e+44)
		tmp = t_1;
	elseif (a <= -5.4e-9)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (a <= -1e-55)
		tmp = Float64(y * Float64(Float64(-t) / Float64(z - a)));
	elseif (a <= 2.7e-117)
		tmp = Float64(x + Float64(y - Float64(Float64(y * t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	tmp = 0.0;
	if (a <= -1.5e+44)
		tmp = t_1;
	elseif (a <= -5.4e-9)
		tmp = x + (y * (z / (z - a)));
	elseif (a <= -1e-55)
		tmp = y * (-t / (z - a));
	elseif (a <= 2.7e-117)
		tmp = x + (y - ((y * t) / z));
	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[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+44], t$95$1, If[LessEqual[a, -5.4e-9], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-55], N[(y * N[((-t) / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-117], N[(x + N[(y - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.49999999999999993e44 or 2.70000000000000003e-117 < a

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 82.3%

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

   if -1.49999999999999993e44 < a < -5.4000000000000004e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   if -5.4000000000000004e-9 < a < -9.99999999999999995e-56

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 99.2%

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

      1. associate-*r/ 99.2%

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

      2. mul-1-neg 99.2%

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

      3. distribute-lft-neg-out 99.2%

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

      4. *-commutative 99.2%

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

   5. Simplified 99.2%

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

      1. div-inv 99.1%

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

      2. add-sqr-sqrt 37.3%

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

      3. sqrt-unprod 25.8%

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

      4. sqr-neg 25.8%

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

      5. sqrt-unprod 0.6%

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

      6. add-sqr-sqrt 13.4%

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

      7. remove-double-neg 13.4%

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

      8. distribute-rgt-neg-out 13.4%

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

      9. cancel-sign-sub-inv 13.4%

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

      10. div-inv 13.4%

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

      11. add-sqr-sqrt 12.7%

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

      12. sqrt-unprod 62.7%

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

      13. sqr-neg 62.7%

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

      14. sqrt-unprod 61.5%

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

      15. add-sqr-sqrt 99.2%

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

   7. Applied egg-rr 99.2%

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

   8. Taylor expanded in x around 0 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*r/ 87.4%

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

      3. associate-*r* 87.4%

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

      4. neg-mul-1 87.4%

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

   10. Simplified 87.4%

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

   if -9.99999999999999995e-56 < a < 2.70000000000000003e-117

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0 92.9%

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

   4. Taylor expanded in z around 0 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

   6. Simplified 94.1%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-117}:\\ \;\;\;\;x + \left(y - \frac{y \cdot t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;x + \left(y - \frac{y \cdot t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a (- z t))))))
   (if (<= a -1.15e+42)
     t_1
     (if (<= a -3.8e-8)
       (+ x (* y (/ z (- z a))))
       (if (<= a -1e-55)
         (* y (/ (- t) (- z a)))
         (if (<= a 3.2e-117) (+ x (- y (/ (* y t) z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / (z - t)));
	double tmp;
	if (a <= -1.15e+42) {
		tmp = t_1;
	} else if (a <= -3.8e-8) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= -1e-55) {
		tmp = y * (-t / (z - a));
	} else if (a <= 3.2e-117) {
		tmp = x + (y - ((y * t) / z));
	} 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 / (a / (z - t)))
    if (a <= (-1.15d+42)) then
        tmp = t_1
    else if (a <= (-3.8d-8)) then
        tmp = x + (y * (z / (z - a)))
    else if (a <= (-1d-55)) then
        tmp = y * (-t / (z - a))
    else if (a <= 3.2d-117) then
        tmp = x + (y - ((y * t) / z))
    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 / (a / (z - t)));
	double tmp;
	if (a <= -1.15e+42) {
		tmp = t_1;
	} else if (a <= -3.8e-8) {
		tmp = x + (y * (z / (z - a)));
	} else if (a <= -1e-55) {
		tmp = y * (-t / (z - a));
	} else if (a <= 3.2e-117) {
		tmp = x + (y - ((y * t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / (z - t)))
	tmp = 0
	if a <= -1.15e+42:
		tmp = t_1
	elif a <= -3.8e-8:
		tmp = x + (y * (z / (z - a)))
	elif a <= -1e-55:
		tmp = y * (-t / (z - a))
	elif a <= 3.2e-117:
		tmp = x + (y - ((y * t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -1.15e+42)
		tmp = t_1;
	elseif (a <= -3.8e-8)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (a <= -1e-55)
		tmp = Float64(y * Float64(Float64(-t) / Float64(z - a)));
	elseif (a <= 3.2e-117)
		tmp = Float64(x + Float64(y - Float64(Float64(y * t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / (z - t)));
	tmp = 0.0;
	if (a <= -1.15e+42)
		tmp = t_1;
	elseif (a <= -3.8e-8)
		tmp = x + (y * (z / (z - a)));
	elseif (a <= -1e-55)
		tmp = y * (-t / (z - a));
	elseif (a <= 3.2e-117)
		tmp = x + (y - ((y * t) / z));
	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[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+42], t$95$1, If[LessEqual[a, -3.8e-8], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-55], N[(y * N[((-t) / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-117], N[(x + N[(y - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.15e42 or 3.19999999999999995e-117 < a

   1. Initial program 99.5%

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

   3. Taylor expanded in a around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

      3. associate-/l* 84.1%

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

   5. Simplified 84.1%

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

   if -1.15e42 < a < -3.80000000000000028e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   if -3.80000000000000028e-8 < a < -9.99999999999999995e-56

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 99.2%

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

      1. associate-*r/ 99.2%

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

      2. mul-1-neg 99.2%

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

      3. distribute-lft-neg-out 99.2%

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

      4. *-commutative 99.2%

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

   5. Simplified 99.2%

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

      1. div-inv 99.1%

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

      2. add-sqr-sqrt 37.3%

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

      3. sqrt-unprod 25.8%

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

      4. sqr-neg 25.8%

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

      5. sqrt-unprod 0.6%

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

      6. add-sqr-sqrt 13.4%

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

      7. remove-double-neg 13.4%

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

      8. distribute-rgt-neg-out 13.4%

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

      9. cancel-sign-sub-inv 13.4%

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

      10. div-inv 13.4%

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

      11. add-sqr-sqrt 12.7%

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

      12. sqrt-unprod 62.7%

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

      13. sqr-neg 62.7%

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

      14. sqrt-unprod 61.5%

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

      15. add-sqr-sqrt 99.2%

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

   7. Applied egg-rr 99.2%

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

   8. Taylor expanded in x around 0 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*r/ 87.4%

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

      3. associate-*r* 87.4%

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

      4. neg-mul-1 87.4%

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

   10. Simplified 87.4%

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

   if -9.99999999999999995e-56 < a < 3.19999999999999995e-117

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0 92.9%

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

   4. Taylor expanded in z around 0 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

   6. Simplified 94.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;x + \left(y - \frac{y \cdot t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-123}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))))
   (if (<= a -3.1e+41)
     t_1
     (if (<= a -5.2e-187)
       (+ x y)
       (if (<= a 1.6e-123) (- x (/ (* y t) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (a <= -3.1e+41) {
		tmp = t_1;
	} else if (a <= -5.2e-187) {
		tmp = x + y;
	} else if (a <= 1.6e-123) {
		tmp = x - ((y * t) / z);
	} 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 * (t / a))
    if (a <= (-3.1d+41)) then
        tmp = t_1
    else if (a <= (-5.2d-187)) then
        tmp = x + y
    else if (a <= 1.6d-123) then
        tmp = x - ((y * t) / z)
    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 * (t / a));
	double tmp;
	if (a <= -3.1e+41) {
		tmp = t_1;
	} else if (a <= -5.2e-187) {
		tmp = x + y;
	} else if (a <= 1.6e-123) {
		tmp = x - ((y * t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	tmp = 0
	if a <= -3.1e+41:
		tmp = t_1
	elif a <= -5.2e-187:
		tmp = x + y
	elif a <= 1.6e-123:
		tmp = x - ((y * t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (a <= -3.1e+41)
		tmp = t_1;
	elseif (a <= -5.2e-187)
		tmp = Float64(x + y);
	elseif (a <= 1.6e-123)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	tmp = 0.0;
	if (a <= -3.1e+41)
		tmp = t_1;
	elseif (a <= -5.2e-187)
		tmp = x + y;
	elseif (a <= 1.6e-123)
		tmp = x - ((y * t) / z);
	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[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e+41], t$95$1, If[LessEqual[a, -5.2e-187], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.6e-123], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1e41 or 1.59999999999999989e-123 < a

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 82.3%

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

   if -3.1e41 < a < -5.1999999999999999e-187

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 72.9%

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

      1. +-commutative 72.9%

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

   5. Simplified 72.9%

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

   if -5.1999999999999999e-187 < a < 1.59999999999999989e-123

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf 79.1%

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

      1. associate-*r/ 79.1%

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

      2. mul-1-neg 79.1%

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

      3. distribute-lft-neg-out 79.1%

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

      4. *-commutative 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in z around inf 74.6%

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

      1. mul-1-neg 74.6%

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

      2. unsub-neg 74.6%

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

   8. Simplified 74.6%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-123}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-185} \lor \neg \left(a \leq 2.9 \cdot 10^{-174}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+174)
   x
   (if (or (<= a 2.4e-185) (not (<= a 2.9e-174))) (+ x y) (* (/ y z) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+174) {
		tmp = x;
	} else if ((a <= 2.4e-185) || !(a <= 2.9e-174)) {
		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 (a <= (-3.5d+174)) then
        tmp = x
    else if ((a <= 2.4d-185) .or. (.not. (a <= 2.9d-174))) 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 (a <= -3.5e+174) {
		tmp = x;
	} else if ((a <= 2.4e-185) || !(a <= 2.9e-174)) {
		tmp = x + y;
	} else {
		tmp = (y / z) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e+174:
		tmp = x
	elif (a <= 2.4e-185) or not (a <= 2.9e-174):
		tmp = x + y
	else:
		tmp = (y / z) * -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+174)
		tmp = x;
	elseif ((a <= 2.4e-185) || !(a <= 2.9e-174))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y / z) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.5e+174)
		tmp = x;
	elseif ((a <= 2.4e-185) || ~((a <= 2.9e-174)))
		tmp = x + y;
	else
		tmp = (y / z) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+174], x, If[Or[LessEqual[a, 2.4e-185], N[Not[LessEqual[a, 2.9e-174]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.5000000000000001e174

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 73.8%

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

   if -3.5000000000000001e174 < a < 2.4000000000000001e-185 or 2.9000000000000001e-174 < a

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 63.4%

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

      1. +-commutative 63.4%

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

   5. Simplified 63.4%

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

   if 2.4000000000000001e-185 < a < 2.9000000000000001e-174

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 99.7%

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

      1. associate-*r/ 99.7%

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

      2. mul-1-neg 99.7%

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

      3. distribute-lft-neg-out 99.7%

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

      4. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around 0 99.7%

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

       1. mul-1-neg 99.7%

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

       2. associate-*r/ 100.0%

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

       3. distribute-rgt-neg-in 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-185} \lor \neg \left(a \leq 2.9 \cdot 10^{-174}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-15} \lor \neg \left(t \leq 1.15 \cdot 10^{-59}\right):\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.2e-15) (not (<= t 1.15e-59)))
   (- x (/ (* y t) (- z a)))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e-15) || !(t <= 1.15e-59)) {
		tmp = x - ((y * t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.2d-15)) .or. (.not. (t <= 1.15d-59))) then
        tmp = x - ((y * t) / (z - a))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e-15) || !(t <= 1.15e-59)) {
		tmp = x - ((y * t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.2e-15) or not (t <= 1.15e-59):
		tmp = x - ((y * t) / (z - a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.2e-15) || !(t <= 1.15e-59))
		tmp = Float64(x - Float64(Float64(y * t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.2e-15) || ~((t <= 1.15e-59)))
		tmp = x - ((y * t) / (z - a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.2e-15], N[Not[LessEqual[t, 1.15e-59]], $MachinePrecision]], N[(x - N[(N[(y * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.19999999999999986e-15 or 1.1499999999999999e-59 < t

   1. Initial program 98.5%

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

   3. Taylor expanded in t around inf 85.0%

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

      1. associate-*r/ 85.0%

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

      2. mul-1-neg 85.0%

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

      3. distribute-lft-neg-out 85.0%

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

      4. *-commutative 85.0%

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

   5. Simplified 85.0%

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

      1. div-inv 85.0%

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

      2. add-sqr-sqrt 37.2%

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

      3. sqrt-unprod 40.4%

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

      4. sqr-neg 40.4%

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

      5. sqrt-unprod 24.2%

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

      6. add-sqr-sqrt 40.2%

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

      7. remove-double-neg 40.2%

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

      8. distribute-rgt-neg-out 40.2%

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

      9. cancel-sign-sub-inv 40.2%

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

      10. div-inv 40.2%

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

      11. add-sqr-sqrt 16.0%

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

      12. sqrt-unprod 45.2%

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

      13. sqr-neg 45.2%

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

      14. sqrt-unprod 47.7%

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

      15. add-sqr-sqrt 85.0%

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

   7. Applied egg-rr 85.0%

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

   if -2.19999999999999986e-15 < t < 1.1499999999999999e-59

   1. Initial program 99.4%

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

   3. Taylor expanded in t around 0 94.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-15} \lor \neg \left(t \leq 1.15 \cdot 10^{-59}\right):\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+112} \lor \neg \left(z \leq 2.2 \cdot 10^{+91}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.8e+112) (not (<= z 2.2e+91))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+112) || !(z <= 2.2e+91)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.8d+112)) .or. (.not. (z <= 2.2d+91))) then
        tmp = x + y
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+112) || !(z <= 2.2e+91)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.8e+112) or not (z <= 2.2e+91):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.8e+112) || !(z <= 2.2e+91))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.8e+112) || ~((z <= 2.2e+91)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.8e+112], N[Not[LessEqual[z, 2.2e+91]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000008e112 or 2.19999999999999999e91 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 82.7%

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

      1. +-commutative 82.7%

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

   5. Simplified 82.7%

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

   if -3.80000000000000008e112 < z < 2.19999999999999999e91

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 73.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+112} \lor \neg \left(z \leq 2.2 \cdot 10^{+91}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -6.2e+174) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+174) {
		tmp = x;
	} 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 (a <= (-6.2d+174)) then
        tmp = x
    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 (a <= -6.2e+174) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e+174:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+174)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e+174)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+174], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.2e174

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 73.8%

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

   if -6.2e174 < a

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 62.0%

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

      1. +-commutative 62.0%

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

   5. Simplified 62.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.2% 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 98.9%

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

3. Taylor expanded in x around inf 54.6%

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

4. Final simplification 54.6%

   \[\leadsto x \]
5. Add Preprocessing

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 2024034 
(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)))))