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

Percentage Accurate: 98.1% → 98.1%

Time: 8.8s

Alternatives: 13

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: 98.1% 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: 98.1% 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 99.2%

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

2. Final simplification 99.2%

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

Alternative 2: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{z - a}\\ t_2 := x - y \cdot \frac{t - z}{z}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-176}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- z a))))) (t_2 (- x (* y (/ (- t z) z)))))
   (if (<= z -4.4e+187)
     t_2
     (if (<= z -1.06e-17)
       t_1
       (if (<= z 2.75e-176)
         (+ x (* y (/ t a)))
         (if (<= z 6.8e-57)
           t_1
           (if (<= z 1.8e+61) (+ x (* t (/ y a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (z - a)));
	double t_2 = x - (y * ((t - z) / z));
	double tmp;
	if (z <= -4.4e+187) {
		tmp = t_2;
	} else if (z <= -1.06e-17) {
		tmp = t_1;
	} else if (z <= 2.75e-176) {
		tmp = x + (y * (t / a));
	} else if (z <= 6.8e-57) {
		tmp = t_1;
	} else if (z <= 1.8e+61) {
		tmp = x + (t * (y / 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 = x + (z * (y / (z - a)))
    t_2 = x - (y * ((t - z) / z))
    if (z <= (-4.4d+187)) then
        tmp = t_2
    else if (z <= (-1.06d-17)) then
        tmp = t_1
    else if (z <= 2.75d-176) then
        tmp = x + (y * (t / a))
    else if (z <= 6.8d-57) then
        tmp = t_1
    else if (z <= 1.8d+61) then
        tmp = x + (t * (y / 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 = x + (z * (y / (z - a)));
	double t_2 = x - (y * ((t - z) / z));
	double tmp;
	if (z <= -4.4e+187) {
		tmp = t_2;
	} else if (z <= -1.06e-17) {
		tmp = t_1;
	} else if (z <= 2.75e-176) {
		tmp = x + (y * (t / a));
	} else if (z <= 6.8e-57) {
		tmp = t_1;
	} else if (z <= 1.8e+61) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (z - a)))
	t_2 = x - (y * ((t - z) / z))
	tmp = 0
	if z <= -4.4e+187:
		tmp = t_2
	elif z <= -1.06e-17:
		tmp = t_1
	elif z <= 2.75e-176:
		tmp = x + (y * (t / a))
	elif z <= 6.8e-57:
		tmp = t_1
	elif z <= 1.8e+61:
		tmp = x + (t * (y / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(z - a))))
	t_2 = Float64(x - Float64(y * Float64(Float64(t - z) / z)))
	tmp = 0.0
	if (z <= -4.4e+187)
		tmp = t_2;
	elseif (z <= -1.06e-17)
		tmp = t_1;
	elseif (z <= 2.75e-176)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 6.8e-57)
		tmp = t_1;
	elseif (z <= 1.8e+61)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (z - a)));
	t_2 = x - (y * ((t - z) / z));
	tmp = 0.0;
	if (z <= -4.4e+187)
		tmp = t_2;
	elseif (z <= -1.06e-17)
		tmp = t_1;
	elseif (z <= 2.75e-176)
		tmp = x + (y * (t / a));
	elseif (z <= 6.8e-57)
		tmp = t_1;
	elseif (z <= 1.8e+61)
		tmp = x + (t * (y / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+187], t$95$2, If[LessEqual[z, -1.06e-17], t$95$1, If[LessEqual[z, 2.75e-176], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-57], t$95$1, If[LessEqual[z, 1.8e+61], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.3999999999999997e187 or 1.80000000000000005e61 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 91.1%

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

   if -4.3999999999999997e187 < z < -1.06000000000000006e-17 or 2.75e-176 < z < 6.80000000000000032e-57

   1. Initial program 98.6%

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

   2. Taylor expanded in t around 0 79.9%

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

      1. associate-/l* 85.4%

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

      2. associate-/r/ 86.8%

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

   4. Applied egg-rr 86.8%

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

   if -1.06000000000000006e-17 < z < 2.75e-176

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. associate-/l* 87.0%

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

      3. associate-/r/ 87.1%

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

   4. Simplified 87.1%

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

   if 6.80000000000000032e-57 < z < 1.80000000000000005e61

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 73.5%

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

      1. +-commutative 73.5%

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

      2. associate-/l* 82.1%

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

      3. associate-/r/ 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in t around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-*l/ 82.3%

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

      3. *-commutative 82.3%

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

   7. Simplified 82.3%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+187}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-17}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-176}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-57}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \]

Alternative 3: 58.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+113}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t z))))
   (if (<= y -8e+133)
     t_1
     (if (<= y -1.05e+67)
       (+ x y)
       (if (<= y -3.9e+65)
         t_1
         (if (<= y -3.6e-241) x (if (<= y 2.85e+113) (+ x y) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (y <= -8e+133) {
		tmp = t_1;
	} else if (y <= -1.05e+67) {
		tmp = x + y;
	} else if (y <= -3.9e+65) {
		tmp = t_1;
	} else if (y <= -3.6e-241) {
		tmp = x;
	} else if (y <= 2.85e+113) {
		tmp = x + y;
	} 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 = (y / a) * (t - z)
    if (y <= (-8d+133)) then
        tmp = t_1
    else if (y <= (-1.05d+67)) then
        tmp = x + y
    else if (y <= (-3.9d+65)) then
        tmp = t_1
    else if (y <= (-3.6d-241)) then
        tmp = x
    else if (y <= 2.85d+113) then
        tmp = x + y
    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 = (y / a) * (t - z);
	double tmp;
	if (y <= -8e+133) {
		tmp = t_1;
	} else if (y <= -1.05e+67) {
		tmp = x + y;
	} else if (y <= -3.9e+65) {
		tmp = t_1;
	} else if (y <= -3.6e-241) {
		tmp = x;
	} else if (y <= 2.85e+113) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (t - z)
	tmp = 0
	if y <= -8e+133:
		tmp = t_1
	elif y <= -1.05e+67:
		tmp = x + y
	elif y <= -3.9e+65:
		tmp = t_1
	elif y <= -3.6e-241:
		tmp = x
	elif y <= 2.85e+113:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(t - z))
	tmp = 0.0
	if (y <= -8e+133)
		tmp = t_1;
	elseif (y <= -1.05e+67)
		tmp = Float64(x + y);
	elseif (y <= -3.9e+65)
		tmp = t_1;
	elseif (y <= -3.6e-241)
		tmp = x;
	elseif (y <= 2.85e+113)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * (t - z);
	tmp = 0.0;
	if (y <= -8e+133)
		tmp = t_1;
	elseif (y <= -1.05e+67)
		tmp = x + y;
	elseif (y <= -3.9e+65)
		tmp = t_1;
	elseif (y <= -3.6e-241)
		tmp = x;
	elseif (y <= 2.85e+113)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+133], t$95$1, If[LessEqual[y, -1.05e+67], N[(x + y), $MachinePrecision], If[LessEqual[y, -3.9e+65], t$95$1, If[LessEqual[y, -3.6e-241], x, If[LessEqual[y, 2.85e+113], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.0000000000000002e133 or -1.0500000000000001e67 < y < -3.8999999999999998e65 or 2.8499999999999999e113 < y

   1. Initial program 97.5%

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

   2. Taylor expanded in a around inf 55.1%

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

      1. mul-1-neg 55.1%

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

      2. unsub-neg 55.1%

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

      3. associate-/l* 62.2%

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

      4. associate-/r/ 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in x around 0 47.8%

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

      1. mul-1-neg 47.8%

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

      2. associate-*l/ 56.8%

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

      3. sub-neg 56.8%

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

      4. distribute-lft-out 50.9%

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

      5. associate-*l/ 50.3%

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

      6. +-commutative 50.3%

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

      7. *-commutative 50.3%

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

      8. distribute-lft-neg-in 50.3%

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

      9. associate-*r/ 46.2%

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

      10. mul-1-neg 46.2%

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

      11. distribute-neg-in 46.2%

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

      12. mul-1-neg 46.2%

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

      13. associate-*r/ 50.3%

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

      14. remove-double-neg 50.3%

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

      15. sub-neg 50.3%

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

      16. associate-*l/ 50.9%

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

      17. *-commutative 50.9%

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

      18. distribute-rgt-out-- 56.8%

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

   7. Simplified 56.8%

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

   if -8.0000000000000002e133 < y < -1.0500000000000001e67 or -3.5999999999999999e-241 < y < 2.8499999999999999e113

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.8%

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

      1. +-commutative 81.8%

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

   4. Simplified 81.8%

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

   if -3.8999999999999998e65 < y < -3.5999999999999999e-241

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 75.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+133}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+113}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 4: 79.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-176}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-56}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+40}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (- 1.0 (/ a z))))))
   (if (<= z -3.8e-20)
     t_1
     (if (<= z 2.75e-176)
       (+ x (* y (/ t a)))
       (if (<= z 6.5e-56)
         (+ x (* z (/ y (- z a))))
         (if (<= z 6.2e+40) (+ x (* t (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (1.0 - (a / z)));
	double tmp;
	if (z <= -3.8e-20) {
		tmp = t_1;
	} else if (z <= 2.75e-176) {
		tmp = x + (y * (t / a));
	} else if (z <= 6.5e-56) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 6.2e+40) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (1.0d0 - (a / z)))
    if (z <= (-3.8d-20)) then
        tmp = t_1
    else if (z <= 2.75d-176) then
        tmp = x + (y * (t / a))
    else if (z <= 6.5d-56) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= 6.2d+40) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (1.0 - (a / z)));
	double tmp;
	if (z <= -3.8e-20) {
		tmp = t_1;
	} else if (z <= 2.75e-176) {
		tmp = x + (y * (t / a));
	} else if (z <= 6.5e-56) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 6.2e+40) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (1.0 - (a / z)))
	tmp = 0
	if z <= -3.8e-20:
		tmp = t_1
	elif z <= 2.75e-176:
		tmp = x + (y * (t / a))
	elif z <= 6.5e-56:
		tmp = x + (z * (y / (z - a)))
	elif z <= 6.2e+40:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))))
	tmp = 0.0
	if (z <= -3.8e-20)
		tmp = t_1;
	elseif (z <= 2.75e-176)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 6.5e-56)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= 6.2e+40)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (1.0 - (a / z)));
	tmp = 0.0;
	if (z <= -3.8e-20)
		tmp = t_1;
	elseif (z <= 2.75e-176)
		tmp = x + (y * (t / a));
	elseif (z <= 6.5e-56)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= 6.2e+40)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-20], t$95$1, If[LessEqual[z, 2.75e-176], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-56], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+40], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7999999999999998e-20 or 6.1999999999999995e40 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 70.3%

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

      1. +-commutative 70.3%

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

      2. associate-/l* 89.8%

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

      3. div-sub 89.8%

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

      4. *-inverses 89.8%

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

   4. Simplified 89.8%

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

   if -3.7999999999999998e-20 < z < 2.75e-176

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. associate-/l* 87.0%

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

      3. associate-/r/ 87.1%

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

   4. Simplified 87.1%

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

   if 2.75e-176 < z < 6.4999999999999997e-56

   1. Initial program 96.6%

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

   2. Taylor expanded in t around 0 85.0%

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

      1. associate-/l* 81.7%

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

      2. associate-/r/ 88.4%

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

   4. Applied egg-rr 88.4%

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

   if 6.4999999999999997e-56 < z < 6.1999999999999995e40

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-/l* 84.4%

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

      3. associate-/r/ 84.4%

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

   4. Simplified 84.4%

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

   5. Taylor expanded in t around 0 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-*l/ 84.6%

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

      3. *-commutative 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-176}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-56}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+40}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]

Alternative 5: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-18} \lor \neg \left(z \leq 1.8 \cdot 10^{+61}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.05e-18) (not (<= z 1.8e+61)))
   (- x (* y (/ (- t z) z)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e-18) || !(z <= 1.8e+61)) {
		tmp = x - (y * ((t - z) / z));
	} 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 <= (-1.05d-18)) .or. (.not. (z <= 1.8d+61))) then
        tmp = x - (y * ((t - z) / z))
    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 <= -1.05e-18) || !(z <= 1.8e+61)) {
		tmp = x - (y * ((t - z) / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.05e-18) or not (z <= 1.8e+61):
		tmp = x - (y * ((t - z) / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.05e-18) || !(z <= 1.8e+61))
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / z)));
	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 <= -1.05e-18) || ~((z <= 1.8e+61)))
		tmp = x - (y * ((t - z) / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.05e-18], N[Not[LessEqual[z, 1.8e+61]], $MachinePrecision]], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-18 or 1.80000000000000005e61 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 85.7%

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

   if -1.05e-18 < z < 1.80000000000000005e61

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. associate-/l* 83.3%

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

      3. associate-/r/ 83.3%

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

   4. Simplified 83.3%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-18} \lor \neg \left(z \leq 1.8 \cdot 10^{+61}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 6: 82.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-20} \lor \neg \left(z \leq 3.2 \cdot 10^{-29}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e-20) (not (<= z 3.2e-29)))
   (+ x (/ y (- 1.0 (/ a z))))
   (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e-20) || !(z <= 3.2e-29)) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x + ((y / a) * (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) :: tmp
    if ((z <= (-1.65d-20)) .or. (.not. (z <= 3.2d-29))) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else
        tmp = x + ((y / a) * (t - z))
    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 <= -1.65e-20) || !(z <= 3.2e-29)) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e-20) or not (z <= 3.2e-29):
		tmp = x + (y / (1.0 - (a / z)))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e-20) || !(z <= 3.2e-29))
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e-20) || ~((z <= 3.2e-29)))
		tmp = x + (y / (1.0 - (a / z)));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e-20], N[Not[LessEqual[z, 3.2e-29]], $MachinePrecision]], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e-20 or 3.2e-29 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-/l* 88.6%

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

      3. div-sub 88.6%

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

      4. *-inverses 88.6%

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

   4. Simplified 88.6%

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

   if -1.65e-20 < z < 3.2e-29

   1. Initial program 98.3%

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

   2. Taylor expanded in a around inf 87.4%

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

      1. mul-1-neg 87.4%

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

      2. unsub-neg 87.4%

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

      3. associate-/l* 88.8%

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

      4. associate-/r/ 90.4%

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

   4. Simplified 90.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-20} \lor \neg \left(z \leq 3.2 \cdot 10^{-29}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 7: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-13} \lor \neg \left(t \leq 5 \cdot 10^{+62}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.2e-13) (not (<= t 5e+62)))
   (- x (* t (/ y (- z a))))
   (+ x (/ y (- 1.0 (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.2e-13) || !(t <= 5e+62)) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y / (1.0 - (a / 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) :: tmp
    if ((t <= (-9.2d-13)) .or. (.not. (t <= 5d+62))) then
        tmp = x - (t * (y / (z - a)))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    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 <= -9.2e-13) || !(t <= 5e+62)) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.2e-13) or not (t <= 5e+62):
		tmp = x - (t * (y / (z - a)))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.2e-13) || !(t <= 5e+62))
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.2e-13) || ~((t <= 5e+62)))
		tmp = x - (t * (y / (z - a)));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.2e-13], N[Not[LessEqual[t, 5e+62]], $MachinePrecision]], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.19999999999999917e-13 or 5.00000000000000029e62 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 91.8%

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

      1. neg-mul-1 91.8%

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

      2. distribute-neg-frac 91.8%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in x around 0 85.5%

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

      1. mul-1-neg 85.5%

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

      2. *-commutative 85.5%

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

      3. sub-neg 85.5%

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

      4. associate-/l* 91.8%

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

      5. associate-/r/ 91.0%

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

   7. Simplified 91.0%

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

   if -9.19999999999999917e-13 < t < 5.00000000000000029e62

   1. Initial program 98.7%

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

   2. Taylor expanded in t around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 92.1%

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

      3. div-sub 92.1%

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

      4. *-inverses 92.1%

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

   4. Simplified 92.1%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{a}{z}} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-13} \lor \neg \left(t \leq 5 \cdot 10^{+62}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]

Alternative 8: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.7e-14)
   (- x (* y (/ t (- z a))))
   (if (<= t 8e+62) (+ x (/ y (- 1.0 (/ a z)))) (- x (* t (/ y (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.7e-14) {
		tmp = x - (y * (t / (z - a)));
	} else if (t <= 8e+62) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x - (t * (y / (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 <= (-4.7d-14)) then
        tmp = x - (y * (t / (z - a)))
    else if (t <= 8d+62) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else
        tmp = x - (t * (y / (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 <= -4.7e-14) {
		tmp = x - (y * (t / (z - a)));
	} else if (t <= 8e+62) {
		tmp = x + (y / (1.0 - (a / z)));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.7e-14:
		tmp = x - (y * (t / (z - a)))
	elif t <= 8e+62:
		tmp = x + (y / (1.0 - (a / z)))
	else:
		tmp = x - (t * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.7e-14)
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	elseif (t <= 8e+62)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.7e-14)
		tmp = x - (y * (t / (z - a)));
	elseif (t <= 8e+62)
		tmp = x + (y / (1.0 - (a / z)));
	else
		tmp = x - (t * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.7e-14], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+62], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7000000000000002e-14

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 95.2%

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

      1. neg-mul-1 95.2%

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

      2. distribute-neg-frac 95.2%

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

   4. Simplified 95.2%

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

   if -4.7000000000000002e-14 < t < 8.00000000000000028e62

   1. Initial program 98.7%

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

   2. Taylor expanded in t around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 92.1%

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

      3. div-sub 92.1%

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

      4. *-inverses 92.1%

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

   4. Simplified 92.1%

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

   if 8.00000000000000028e62 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 87.1%

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

      1. neg-mul-1 87.1%

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

      2. distribute-neg-frac 87.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in x around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. *-commutative 78.6%

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

      3. sub-neg 78.6%

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

      4. associate-/l* 87.0%

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

      5. associate-/r/ 87.1%

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

   7. Simplified 87.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 9: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+81} \lor \neg \left(z \leq 1.7 \cdot 10^{+62}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e+81) (not (<= z 1.7e+62))) (+ x y) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e+81) || !(z <= 1.7e+62)) {
		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 <= (-2.7d+81)) .or. (.not. (z <= 1.7d+62))) 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 <= -2.7e+81) || !(z <= 1.7e+62)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e+81) or not (z <= 1.7e+62):
		tmp = x + y
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e+81) || !(z <= 1.7e+62))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e+81) || ~((z <= 1.7e+62)))
		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, -2.7e+81], N[Not[LessEqual[z, 1.7e+62]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e81 or 1.70000000000000007e62 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.2%

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

      1. +-commutative 81.2%

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

   4. Simplified 81.2%

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

   if -2.6999999999999999e81 < z < 1.70000000000000007e62

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 78.1%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+81} \lor \neg \left(z \leq 1.7 \cdot 10^{+62}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 10: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+80} \lor \neg \left(z \leq 2.6 \cdot 10^{+61}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e+80) (not (<= z 2.6e+61))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+80) || !(z <= 2.6e+61)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.5d+80)) .or. (.not. (z <= 2.6d+61))) then
        tmp = x + y
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+80) || !(z <= 2.6e+61)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.5e+80) or not (z <= 2.6e+61):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.5e+80) || !(z <= 2.6e+61))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.5e+80) || ~((z <= 2.6e+61)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.5e+80], N[Not[LessEqual[z, 2.6e+61]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000007e80 or 2.59999999999999973e61 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.2%

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

      1. +-commutative 81.2%

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

   4. Simplified 81.2%

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

   if -8.50000000000000007e80 < z < 2.59999999999999973e61

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 78.1%

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

      1. +-commutative 78.1%

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

      2. associate-/l* 80.8%

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

      3. associate-/r/ 81.5%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in t around 0 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-*l/ 80.8%

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

      3. *-commutative 80.8%

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

   7. Simplified 80.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+80} \lor \neg \left(z \leq 2.6 \cdot 10^{+61}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 11: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+82} \lor \neg \left(z \leq 3.2 \cdot 10^{+62}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.7e+82) (not (<= z 3.2e+62))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.7e+82) || !(z <= 3.2e+62)) {
		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 <= (-4.7d+82)) .or. (.not. (z <= 3.2d+62))) 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 <= -4.7e+82) || !(z <= 3.2e+62)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.7e+82) or not (z <= 3.2e+62):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.7e+82) || !(z <= 3.2e+62))
		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 <= -4.7e+82) || ~((z <= 3.2e+62)))
		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, -4.7e+82], N[Not[LessEqual[z, 3.2e+62]], $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 < -4.7e82 or 3.19999999999999984e62 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.2%

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

      1. +-commutative 81.2%

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

   4. Simplified 81.2%

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

   if -4.7e82 < z < 3.19999999999999984e62

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 78.1%

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

      1. +-commutative 78.1%

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

      2. associate-/l* 80.8%

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

      3. associate-/r/ 81.5%

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

   4. Simplified 81.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+82} \lor \neg \left(z \leq 3.2 \cdot 10^{+62}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 12: 63.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{+152}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+135}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.95e+152) x (if (<= a 7e+135) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.95e+152) {
		tmp = x;
	} else if (a <= 7e+135) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.95d+152)) then
        tmp = x
    else if (a <= 7d+135) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.95e+152) {
		tmp = x;
	} else if (a <= 7e+135) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.95e+152:
		tmp = x
	elif a <= 7e+135:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.95e+152)
		tmp = x;
	elseif (a <= 7e+135)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.95e+152)
		tmp = x;
	elseif (a <= 7e+135)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.95e+152], x, If[LessEqual[a, 7e+135], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.9500000000000001e152 or 7.0000000000000005e135 < a

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf 64.4%

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

   if -2.9500000000000001e152 < a < 7.0000000000000005e135

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 69.1%

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

      1. +-commutative 69.1%

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

   4. Simplified 69.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{+152}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+135}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 49.7% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

2. Taylor expanded in x around inf 53.5%

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

3. Final simplification 53.5%

   \[\leadsto x \]

Developer target: 98.2% 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 2023332 
(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)))))