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

Percentage Accurate: 98.2% → 96.2%

Time: 13.3s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate-*r/ 87.5%

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

3. Simplified 87.5%

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

   1. *-commutative 87.5%

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

   2. associate-/l* 98.1%

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

6. Applied egg-rr 98.1%

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

Alternative 2: 77.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z}{t - a}\\ \mathbf{if}\;t \leq -1.52 \cdot 10^{+240}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 10^{-124}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ z (- t a))))))
   (if (<= t -1.52e+240)
     (+ x y)
     (if (<= t -1.8e+86)
       t_1
       (if (<= t -4.3e-10)
         (+ x y)
         (if (<= t 1e-124)
           (+ x (* z (/ y a)))
           (if (<= t 7.5e+42) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / (t - a)));
	double tmp;
	if (t <= -1.52e+240) {
		tmp = x + y;
	} else if (t <= -1.8e+86) {
		tmp = t_1;
	} else if (t <= -4.3e-10) {
		tmp = x + y;
	} else if (t <= 1e-124) {
		tmp = x + (z * (y / a));
	} else if (t <= 7.5e+42) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (z / (t - a)))
    if (t <= (-1.52d+240)) then
        tmp = x + y
    else if (t <= (-1.8d+86)) then
        tmp = t_1
    else if (t <= (-4.3d-10)) then
        tmp = x + y
    else if (t <= 1d-124) then
        tmp = x + (z * (y / a))
    else if (t <= 7.5d+42) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / (t - a)));
	double tmp;
	if (t <= -1.52e+240) {
		tmp = x + y;
	} else if (t <= -1.8e+86) {
		tmp = t_1;
	} else if (t <= -4.3e-10) {
		tmp = x + y;
	} else if (t <= 1e-124) {
		tmp = x + (z * (y / a));
	} else if (t <= 7.5e+42) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (z / (t - a)))
	tmp = 0
	if t <= -1.52e+240:
		tmp = x + y
	elif t <= -1.8e+86:
		tmp = t_1
	elif t <= -4.3e-10:
		tmp = x + y
	elif t <= 1e-124:
		tmp = x + (z * (y / a))
	elif t <= 7.5e+42:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(z / Float64(t - a))))
	tmp = 0.0
	if (t <= -1.52e+240)
		tmp = Float64(x + y);
	elseif (t <= -1.8e+86)
		tmp = t_1;
	elseif (t <= -4.3e-10)
		tmp = Float64(x + y);
	elseif (t <= 1e-124)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 7.5e+42)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (z / (t - a)));
	tmp = 0.0;
	if (t <= -1.52e+240)
		tmp = x + y;
	elseif (t <= -1.8e+86)
		tmp = t_1;
	elseif (t <= -4.3e-10)
		tmp = x + y;
	elseif (t <= 1e-124)
		tmp = x + (z * (y / a));
	elseif (t <= 7.5e+42)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.52e+240], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.8e+86], t$95$1, If[LessEqual[t, -4.3e-10], N[(x + y), $MachinePrecision], If[LessEqual[t, 1e-124], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+42], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5200000000000001e240 or -1.80000000000000003e86 < t < -4.30000000000000014e-10 or 7.50000000000000041e42 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

   5. Simplified 81.9%

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

   if -1.5200000000000001e240 < t < -1.80000000000000003e86 or 9.99999999999999933e-125 < t < 7.50000000000000041e42

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 84.9%

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

      1. associate-/l* 90.3%

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

   5. Simplified 90.3%

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

   if -4.30000000000000014e-10 < t < 9.99999999999999933e-125

   1. Initial program 93.8%

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

      1. associate-*r/ 94.9%

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

   3. Simplified 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-/l* 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in t around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-/l* 94.2%

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

   9. Simplified 94.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+240}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+86}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 10^{-124}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z}{t - a}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+83}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ z (- t a))))))
   (if (<= z -1.5e+22)
     t_1
     (if (<= z 2.2e+17)
       (+ x (* y (/ t (- t a))))
       (if (<= z 5.2e+35)
         (+ x (* y (/ (- z t) a)))
         (if (<= z 5.5e+83) (- x (* y (+ (/ z t) -1.0))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / (t - a)));
	double tmp;
	if (z <= -1.5e+22) {
		tmp = t_1;
	} else if (z <= 2.2e+17) {
		tmp = x + (y * (t / (t - a)));
	} else if (z <= 5.2e+35) {
		tmp = x + (y * ((z - t) / a));
	} else if (z <= 5.5e+83) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (z / (t - a)))
    if (z <= (-1.5d+22)) then
        tmp = t_1
    else if (z <= 2.2d+17) then
        tmp = x + (y * (t / (t - a)))
    else if (z <= 5.2d+35) then
        tmp = x + (y * ((z - t) / a))
    else if (z <= 5.5d+83) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / (t - a)));
	double tmp;
	if (z <= -1.5e+22) {
		tmp = t_1;
	} else if (z <= 2.2e+17) {
		tmp = x + (y * (t / (t - a)));
	} else if (z <= 5.2e+35) {
		tmp = x + (y * ((z - t) / a));
	} else if (z <= 5.5e+83) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (z / (t - a)))
	tmp = 0
	if z <= -1.5e+22:
		tmp = t_1
	elif z <= 2.2e+17:
		tmp = x + (y * (t / (t - a)))
	elif z <= 5.2e+35:
		tmp = x + (y * ((z - t) / a))
	elif z <= 5.5e+83:
		tmp = x - (y * ((z / t) + -1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(z / Float64(t - a))))
	tmp = 0.0
	if (z <= -1.5e+22)
		tmp = t_1;
	elseif (z <= 2.2e+17)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (z <= 5.2e+35)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (z <= 5.5e+83)
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (z / (t - a)));
	tmp = 0.0;
	if (z <= -1.5e+22)
		tmp = t_1;
	elseif (z <= 2.2e+17)
		tmp = x + (y * (t / (t - a)));
	elseif (z <= 5.2e+35)
		tmp = x + (y * ((z - t) / a));
	elseif (z <= 5.5e+83)
		tmp = x - (y * ((z / t) + -1.0));
	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[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+22], t$95$1, If[LessEqual[z, 2.2e+17], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+35], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+83], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5e22 or 5.4999999999999996e83 < z

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 89.6%

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

   5. Simplified 89.6%

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

   if -1.5e22 < z < 2.2e17

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

      3. *-commutative 83.2%

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

      4. associate-/l* 93.4%

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

   5. Simplified 93.4%

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

   if 2.2e17 < z < 5.20000000000000013e35

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if 5.20000000000000013e35 < z < 5.4999999999999996e83

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. unsub-neg 85.1%

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

      3. associate-/l* 97.2%

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

      4. div-sub 97.2%

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

      5. sub-neg 97.2%

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

      6. *-inverses 97.2%

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

      7. metadata-eval 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+83}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+36}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+48}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.8e+122)
   (+ x y)
   (if (<= t -3.5e+36)
     (- x (* z (/ y t)))
     (if (<= t 1.45e+48) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e+122) {
		tmp = x + y;
	} else if (t <= -3.5e+36) {
		tmp = x - (z * (y / t));
	} else if (t <= 1.45e+48) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.8d+122)) then
        tmp = x + y
    else if (t <= (-3.5d+36)) then
        tmp = x - (z * (y / t))
    else if (t <= 1.45d+48) then
        tmp = x + (z * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e+122) {
		tmp = x + y;
	} else if (t <= -3.5e+36) {
		tmp = x - (z * (y / t));
	} else if (t <= 1.45e+48) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.8e+122:
		tmp = x + y
	elif t <= -3.5e+36:
		tmp = x - (z * (y / t))
	elif t <= 1.45e+48:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.8e+122)
		tmp = Float64(x + y);
	elseif (t <= -3.5e+36)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= 1.45e+48)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.8e+122)
		tmp = x + y;
	elseif (t <= -3.5e+36)
		tmp = x - (z * (y / t));
	elseif (t <= 1.45e+48)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.8e+122], N[(x + y), $MachinePrecision], If[LessEqual[t, -3.5e+36], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+48], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8000000000000002e122 or 1.4499999999999999e48 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 86.4%

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

      1. +-commutative 86.4%

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

   5. Simplified 86.4%

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

   if -5.8000000000000002e122 < t < -3.4999999999999998e36

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.9%

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

      1. associate-/l* 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in a around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. associate-/l* 80.4%

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

   8. Simplified 80.4%

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

      1. *-commutative 80.4%

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

      2. associate-*l/ 74.4%

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

   10. Applied egg-rr 74.4%

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

       1. associate-/l* 80.5%

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

       2. *-commutative 80.5%

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

   12. Applied egg-rr 80.5%

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

   if -3.4999999999999998e36 < t < 1.4499999999999999e48

   1. Initial program 96.1%

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

      1. associate-*r/ 95.6%

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

   3. Simplified 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-/l* 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in t around 0 81.2%

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

      1. *-commutative 81.2%

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

      2. associate-/l* 84.8%

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

   9. Simplified 84.8%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+36}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+48}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+40}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+47}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+122)
   (+ x y)
   (if (<= t -1.95e+40)
     (- x (* y (/ z t)))
     (if (<= t 1.7e+47) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+122) {
		tmp = x + y;
	} else if (t <= -1.95e+40) {
		tmp = x - (y * (z / t));
	} else if (t <= 1.7e+47) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.8d+122)) then
        tmp = x + y
    else if (t <= (-1.95d+40)) then
        tmp = x - (y * (z / t))
    else if (t <= 1.7d+47) then
        tmp = x + (z * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+122) {
		tmp = x + y;
	} else if (t <= -1.95e+40) {
		tmp = x - (y * (z / t));
	} else if (t <= 1.7e+47) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+122:
		tmp = x + y
	elif t <= -1.95e+40:
		tmp = x - (y * (z / t))
	elif t <= 1.7e+47:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+122)
		tmp = Float64(x + y);
	elseif (t <= -1.95e+40)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 1.7e+47)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+122)
		tmp = x + y;
	elseif (t <= -1.95e+40)
		tmp = x - (y * (z / t));
	elseif (t <= 1.7e+47)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+122], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.95e+40], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+47], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7999999999999998e122 or 1.6999999999999999e47 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 86.4%

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

      1. +-commutative 86.4%

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

   5. Simplified 86.4%

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

   if -3.7999999999999998e122 < t < -1.95e40

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.9%

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

      1. associate-/l* 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in a around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. associate-/l* 80.4%

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

   8. Simplified 80.4%

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

   if -1.95e40 < t < 1.6999999999999999e47

   1. Initial program 96.1%

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

      1. associate-*r/ 95.6%

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

   3. Simplified 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-/l* 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in t around 0 81.2%

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

      1. *-commutative 81.2%

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

      2. associate-/l* 84.8%

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

   9. Simplified 84.8%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+40}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+47}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.8e-15)
   (+ x y)
   (if (<= t -5.8e-83)
     (+ x (/ (* z y) a))
     (if (<= t 3.6e+48) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e-15) {
		tmp = x + y;
	} else if (t <= -5.8e-83) {
		tmp = x + ((z * y) / a);
	} else if (t <= 3.6e+48) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.8d-15)) then
        tmp = x + y
    else if (t <= (-5.8d-83)) then
        tmp = x + ((z * y) / a)
    else if (t <= 3.6d+48) then
        tmp = x + (z * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e-15) {
		tmp = x + y;
	} else if (t <= -5.8e-83) {
		tmp = x + ((z * y) / a);
	} else if (t <= 3.6e+48) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.8e-15:
		tmp = x + y
	elif t <= -5.8e-83:
		tmp = x + ((z * y) / a)
	elif t <= 3.6e+48:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.8e-15)
		tmp = Float64(x + y);
	elseif (t <= -5.8e-83)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	elseif (t <= 3.6e+48)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.8e-15)
		tmp = x + y;
	elseif (t <= -5.8e-83)
		tmp = x + ((z * y) / a);
	elseif (t <= 3.6e+48)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.8e-15], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.8e-83], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+48], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7999999999999999e-15 or 3.59999999999999983e48 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 80.1%

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

      1. +-commutative 80.1%

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

   5. Simplified 80.1%

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

   if -4.7999999999999999e-15 < t < -5.7999999999999998e-83

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 99.9%

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

   if -5.7999999999999998e-83 < t < 3.59999999999999983e48

   1. Initial program 95.3%

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

      1. associate-*r/ 94.7%

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

   3. Simplified 94.7%

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

      1. *-commutative 94.7%

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

      2. associate-/l* 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in t around 0 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-/l* 88.1%

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

   9. Simplified 88.1%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-55} \lor \neg \left(a \leq 4 \cdot 10^{-54}\right):\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.2e-55) (not (<= a 4e-54)))
   (- x (* y (/ z (- t a))))
   (- x (* y (+ (/ z t) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.2e-55) || !(a <= 4e-54)) {
		tmp = x - (y * (z / (t - a)));
	} else {
		tmp = x - (y * ((z / t) + -1.0));
	}
	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 <= (-7.2d-55)) .or. (.not. (a <= 4d-54))) then
        tmp = x - (y * (z / (t - a)))
    else
        tmp = x - (y * ((z / t) + (-1.0d0)))
    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 <= -7.2e-55) || !(a <= 4e-54)) {
		tmp = x - (y * (z / (t - a)));
	} else {
		tmp = x - (y * ((z / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.2e-55) or not (a <= 4e-54):
		tmp = x - (y * (z / (t - a)))
	else:
		tmp = x - (y * ((z / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.2e-55) || !(a <= 4e-54))
		tmp = Float64(x - Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.2e-55) || ~((a <= 4e-54)))
		tmp = x - (y * (z / (t - a)));
	else
		tmp = x - (y * ((z / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.2e-55], N[Not[LessEqual[a, 4e-54]], $MachinePrecision]], N[(x - N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.2000000000000001e-55 or 4.0000000000000001e-54 < a

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 81.4%

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

      1. associate-/l* 85.3%

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

   5. Simplified 85.3%

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

   if -7.2000000000000001e-55 < a < 4.0000000000000001e-54

   1. Initial program 95.6%

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

   3. Taylor expanded in a around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

      3. associate-/l* 87.7%

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

      4. div-sub 87.7%

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

      5. sub-neg 87.7%

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

      6. *-inverses 87.7%

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

      7. metadata-eval 87.7%

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

   5. Simplified 87.7%

      \[\leadsto \color{blue}{x - y \cdot \left(\frac{z}{t} + -1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-55} \lor \neg \left(a \leq 4 \cdot 10^{-54}\right):\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+122} \lor \neg \left(t \leq 5 \cdot 10^{+49}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.8e+122) (not (<= t 5e+49))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e+122) || !(t <= 5e+49)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.8d+122)) .or. (.not. (t <= 5d+49))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e+122) || !(t <= 5e+49)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.8e+122) or not (t <= 5e+49):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.8e+122) || !(t <= 5e+49))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.8e+122) || ~((t <= 5e+49)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.8e+122], N[Not[LessEqual[t, 5e+49]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.8000000000000002e122 or 5.0000000000000004e49 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 86.4%

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

      1. +-commutative 86.4%

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

   5. Simplified 86.4%

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

   if -5.8000000000000002e122 < t < 5.0000000000000004e49

   1. Initial program 96.5%

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

      1. associate-*r/ 95.5%

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

   3. Simplified 95.5%

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

      1. *-commutative 95.5%

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

      2. associate-/l* 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in t around 0 78.2%

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

      1. *-commutative 78.2%

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

      2. associate-/l* 81.5%

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

   9. Simplified 81.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+122} \lor \neg \left(t \leq 5 \cdot 10^{+49}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+193}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+163}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.4e+193) x (if (<= a -7e+163) (/ y (/ a z)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e+193) {
		tmp = x;
	} else if (a <= -7e+163) {
		tmp = y / (a / z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.4d+193)) then
        tmp = x
    else if (a <= (-7d+163)) then
        tmp = y / (a / z)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e+193) {
		tmp = x;
	} else if (a <= -7e+163) {
		tmp = y / (a / z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.4e+193:
		tmp = x
	elif a <= -7e+163:
		tmp = y / (a / z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.4e+193)
		tmp = x;
	elseif (a <= -7e+163)
		tmp = Float64(y / Float64(a / z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.4e+193)
		tmp = x;
	elseif (a <= -7e+163)
		tmp = y / (a / z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.4e+193], x, If[LessEqual[a, -7e+163], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.39999999999999993e193

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.3%

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

   if -1.39999999999999993e193 < a < -7.0000000000000005e163

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. associate-/l* 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in z around inf 97.0%

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

      1. +-commutative 97.0%

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

   8. Simplified 97.0%

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

   9. Taylor expanded in y around inf 80.7%

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

   10. Taylor expanded in z around 0 66.9%

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

       1. associate-/l* 82.7%

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

   12. Simplified 82.7%

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

       1. clear-num 83.0%

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

       2. un-div-inv 83.2%

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

   14. Applied egg-rr 83.2%

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

   if -7.0000000000000005e163 < a

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 67.9%

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

      1. +-commutative 67.9%

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

   5. Simplified 67.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+193}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+163}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+193}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+163}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.4e+193) x (if (<= a -6.5e+163) (* y (/ z a)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e+193) {
		tmp = x;
	} else if (a <= -6.5e+163) {
		tmp = y * (z / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.4d+193)) then
        tmp = x
    else if (a <= (-6.5d+163)) then
        tmp = y * (z / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e+193) {
		tmp = x;
	} else if (a <= -6.5e+163) {
		tmp = y * (z / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.4e+193:
		tmp = x
	elif a <= -6.5e+163:
		tmp = y * (z / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.4e+193)
		tmp = x;
	elseif (a <= -6.5e+163)
		tmp = Float64(y * Float64(z / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.4e+193)
		tmp = x;
	elseif (a <= -6.5e+163)
		tmp = y * (z / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.4e+193], x, If[LessEqual[a, -6.5e+163], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.39999999999999993e193

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.3%

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

   if -1.39999999999999993e193 < a < -6.4999999999999998e163

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. associate-/l* 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in z around inf 97.0%

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

      1. +-commutative 97.0%

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

   8. Simplified 97.0%

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

   9. Taylor expanded in y around inf 80.7%

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

   10. Taylor expanded in z around 0 66.9%

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

       1. associate-/l* 82.7%

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

   12. Simplified 82.7%

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

   if -6.4999999999999998e163 < a

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 67.9%

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

      1. +-commutative 67.9%

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

   5. Simplified 67.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+193}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+163}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-10} \lor \neg \left(t \leq -6.6 \cdot 10^{-299}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e-10) (not (<= t -6.6e-299))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e-10) || !(t <= -6.6e-299)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.8d-10)) .or. (.not. (t <= (-6.6d-299)))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e-10) || !(t <= -6.6e-299)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.8e-10) or not (t <= -6.6e-299):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e-10) || !(t <= -6.6e-299))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.8e-10) || ~((t <= -6.6e-299)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e-10], N[Not[LessEqual[t, -6.6e-299]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e-10 or -6.6000000000000004e-299 < t

   1. Initial program 98.5%

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

   3. Taylor expanded in t around inf 70.8%

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

      1. +-commutative 70.8%

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

   5. Simplified 70.8%

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

   if -1.8e-10 < t < -6.6000000000000004e-299

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf 60.1%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-10} \lor \neg \left(t \leq -6.6 \cdot 10^{-299}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+138}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.76 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.2e+138) y (if (<= y 1.76e+137) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.2e+138) {
		tmp = y;
	} else if (y <= 1.76e+137) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.2d+138)) then
        tmp = y
    else if (y <= 1.76d+137) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.2e+138) {
		tmp = y;
	} else if (y <= 1.76e+137) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.2e+138:
		tmp = y
	elif y <= 1.76e+137:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.2e+138)
		tmp = y;
	elseif (y <= 1.76e+137)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.2e+138)
		tmp = y;
	elseif (y <= 1.76e+137)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.2e+138], y, If[LessEqual[y, 1.76e+137], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000014e138 or 1.76e137 < y

   1. Initial program 96.8%

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

      1. associate-*r/ 65.2%

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

   3. Simplified 65.2%

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

      1. *-commutative 65.2%

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

      2. associate-/l* 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in a around 0 50.1%

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

      1. associate-*r/ 50.1%

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

      2. neg-mul-1 50.1%

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

   9. Simplified 50.1%

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

   10. Taylor expanded in x around 0 28.4%

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

       1. mul-1-neg 28.4%

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

       2. *-commutative 28.4%

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

       3. associate-*r/ 50.1%

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

       4. sub-neg 50.1%

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

       5. *-commutative 50.1%

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

   12. Simplified 50.1%

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

   13. Taylor expanded in x around 0 26.8%

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

       1. mul-1-neg 26.8%

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

       2. associate-/l* 48.7%

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

       3. distribute-rgt-neg-in 48.7%

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

       4. div-sub 48.7%

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

       5. sub-neg 48.7%

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

       6. *-inverses 48.7%

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

       7. metadata-eval 48.7%

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

       8. distribute-neg-in 48.7%

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

       9. metadata-eval 48.7%

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

       10. +-commutative 48.7%

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

       11. sub-neg 48.7%

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

   15. Simplified 48.7%

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

   16. Taylor expanded in z around 0 33.7%

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

   if -4.20000000000000014e138 < y < 1.76e137

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 71.2%

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

Alternative 13: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

Alternative 14: 50.7% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

3. Taylor expanded in x around inf 56.7%

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

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024105 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

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

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