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

Percentage Accurate: 98.2% → 98.4%

Time: 11.1s

Alternatives: 13

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: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. clear-num 98.4%

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

   2. un-div-inv 98.7%

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

4. Applied egg-rr 98.7%

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

5. Final simplification 98.7%

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

Alternative 2: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+155} \lor \neg \left(t \leq -1.8 \cdot 10^{+61}\right) \land \left(t \leq -1.35 \cdot 10^{-85} \lor \neg \left(t \leq 4.4 \cdot 10^{+41}\right)\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.2e+155)
         (and (not (<= t -1.8e+61))
              (or (<= t -1.35e-85) (not (<= t 4.4e+41)))))
   (+ x y)
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e+155) || (!(t <= -1.8e+61) && ((t <= -1.35e-85) || !(t <= 4.4e+41)))) {
		tmp = x + y;
	} else {
		tmp = x + (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 <= (-4.2d+155)) .or. (.not. (t <= (-1.8d+61))) .and. (t <= (-1.35d-85)) .or. (.not. (t <= 4.4d+41))) then
        tmp = x + y
    else
        tmp = x + (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 <= -4.2e+155) || (!(t <= -1.8e+61) && ((t <= -1.35e-85) || !(t <= 4.4e+41)))) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.2e+155) or (not (t <= -1.8e+61) and ((t <= -1.35e-85) or not (t <= 4.4e+41))):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.2e+155) || (!(t <= -1.8e+61) && ((t <= -1.35e-85) || !(t <= 4.4e+41))))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.2e+155) || (~((t <= -1.8e+61)) && ((t <= -1.35e-85) || ~((t <= 4.4e+41)))))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.2e+155], And[N[Not[LessEqual[t, -1.8e+61]], $MachinePrecision], Or[LessEqual[t, -1.35e-85], N[Not[LessEqual[t, 4.4e+41]], $MachinePrecision]]]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.2e155 or -1.80000000000000005e61 < t < -1.3500000000000001e-85 or 4.3999999999999998e41 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.2%

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

   if -4.2e155 < t < -1.80000000000000005e61 or -1.3500000000000001e-85 < t < 4.3999999999999998e41

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 0 73.8%

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

      1. associate-/l* 74.0%

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

   5. Simplified 74.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+155} \lor \neg \left(t \leq -1.8 \cdot 10^{+61}\right) \land \left(t \leq -1.35 \cdot 10^{-85} \lor \neg \left(t \leq 4.4 \cdot 10^{+41}\right)\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-85} \lor \neg \left(t \leq 3.7 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+155)
   (+ x y)
   (if (<= t -1.12e+61)
     (+ x (* y (/ z a)))
     (if (or (<= t -1.4e-85) (not (<= t 3.7e+41)))
       (+ x y)
       (+ x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+155) {
		tmp = x + y;
	} else if (t <= -1.12e+61) {
		tmp = x + (y * (z / a));
	} else if ((t <= -1.4e-85) || !(t <= 3.7e+41)) {
		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 <= (-4.2d+155)) then
        tmp = x + y
    else if (t <= (-1.12d+61)) then
        tmp = x + (y * (z / a))
    else if ((t <= (-1.4d-85)) .or. (.not. (t <= 3.7d+41))) 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 <= -4.2e+155) {
		tmp = x + y;
	} else if (t <= -1.12e+61) {
		tmp = x + (y * (z / a));
	} else if ((t <= -1.4e-85) || !(t <= 3.7e+41)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+155:
		tmp = x + y
	elif t <= -1.12e+61:
		tmp = x + (y * (z / a))
	elif (t <= -1.4e-85) or not (t <= 3.7e+41):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+155)
		tmp = Float64(x + y);
	elseif (t <= -1.12e+61)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif ((t <= -1.4e-85) || !(t <= 3.7e+41))
		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 <= -4.2e+155)
		tmp = x + y;
	elseif (t <= -1.12e+61)
		tmp = x + (y * (z / a));
	elseif ((t <= -1.4e-85) || ~((t <= 3.7e+41)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+155], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.12e+61], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.4e-85], N[Not[LessEqual[t, 3.7e+41]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2e155 or -1.12e61 < t < -1.40000000000000008e-85 or 3.69999999999999981e41 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.2%

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

   if -4.2e155 < t < -1.12e61

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 56.0%

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

      1. associate-/l* 68.1%

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

   5. Simplified 68.1%

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

   if -1.40000000000000008e-85 < t < 3.69999999999999981e41

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-/l* 77.8%

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

   5. Applied egg-rr 77.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-85} \lor \neg \left(t \leq 3.7 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-85} \lor \neg \left(t \leq 3.4 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+155)
   (+ x y)
   (if (<= t -1.8e+61)
     (+ x (/ z (/ a y)))
     (if (or (<= t -1.4e-85) (not (<= t 3.4e+41)))
       (+ x y)
       (+ x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+155) {
		tmp = x + y;
	} else if (t <= -1.8e+61) {
		tmp = x + (z / (a / y));
	} else if ((t <= -1.4e-85) || !(t <= 3.4e+41)) {
		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 <= (-4.2d+155)) then
        tmp = x + y
    else if (t <= (-1.8d+61)) then
        tmp = x + (z / (a / y))
    else if ((t <= (-1.4d-85)) .or. (.not. (t <= 3.4d+41))) 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 <= -4.2e+155) {
		tmp = x + y;
	} else if (t <= -1.8e+61) {
		tmp = x + (z / (a / y));
	} else if ((t <= -1.4e-85) || !(t <= 3.4e+41)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+155:
		tmp = x + y
	elif t <= -1.8e+61:
		tmp = x + (z / (a / y))
	elif (t <= -1.4e-85) or not (t <= 3.4e+41):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+155)
		tmp = Float64(x + y);
	elseif (t <= -1.8e+61)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif ((t <= -1.4e-85) || !(t <= 3.4e+41))
		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 <= -4.2e+155)
		tmp = x + y;
	elseif (t <= -1.8e+61)
		tmp = x + (z / (a / y));
	elseif ((t <= -1.4e-85) || ~((t <= 3.4e+41)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+155], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.8e+61], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.4e-85], N[Not[LessEqual[t, 3.4e+41]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2e155 or -1.80000000000000005e61 < t < -1.40000000000000008e-85 or 3.39999999999999998e41 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.2%

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

   if -4.2e155 < t < -1.80000000000000005e61

   1. Initial program 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in t around 0 68.0%

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

      1. associate-/r/ 68.0%

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

   7. Applied egg-rr 68.0%

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

      1. *-commutative 68.0%

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

      2. clear-num 68.1%

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

      3. un-div-inv 68.1%

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

   9. Applied egg-rr 68.1%

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

   if -1.40000000000000008e-85 < t < 3.39999999999999998e41

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-/l* 77.8%

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

   5. Applied egg-rr 77.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-85} \lor \neg \left(t \leq 3.4 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-85} \lor \neg \left(t \leq 3.4 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+155)
   (+ x y)
   (if (<= t -3.7e+60)
     (+ x (/ z (/ a y)))
     (if (or (<= t -1.4e-85) (not (<= t 3.4e+41)))
       (+ x y)
       (+ x (/ (* y z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+155) {
		tmp = x + y;
	} else if (t <= -3.7e+60) {
		tmp = x + (z / (a / y));
	} else if ((t <= -1.4e-85) || !(t <= 3.4e+41)) {
		tmp = x + y;
	} else {
		tmp = x + ((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 <= (-4.2d+155)) then
        tmp = x + y
    else if (t <= (-3.7d+60)) then
        tmp = x + (z / (a / y))
    else if ((t <= (-1.4d-85)) .or. (.not. (t <= 3.4d+41))) then
        tmp = x + y
    else
        tmp = x + ((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 <= -4.2e+155) {
		tmp = x + y;
	} else if (t <= -3.7e+60) {
		tmp = x + (z / (a / y));
	} else if ((t <= -1.4e-85) || !(t <= 3.4e+41)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+155:
		tmp = x + y
	elif t <= -3.7e+60:
		tmp = x + (z / (a / y))
	elif (t <= -1.4e-85) or not (t <= 3.4e+41):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+155)
		tmp = Float64(x + y);
	elseif (t <= -3.7e+60)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif ((t <= -1.4e-85) || !(t <= 3.4e+41))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e+155)
		tmp = x + y;
	elseif (t <= -3.7e+60)
		tmp = x + (z / (a / y));
	elseif ((t <= -1.4e-85) || ~((t <= 3.4e+41)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+155], N[(x + y), $MachinePrecision], If[LessEqual[t, -3.7e+60], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.4e-85], N[Not[LessEqual[t, 3.4e+41]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2e155 or -3.69999999999999988e60 < t < -1.40000000000000008e-85 or 3.39999999999999998e41 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.2%

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

   if -4.2e155 < t < -3.69999999999999988e60

   1. Initial program 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in t around 0 68.0%

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

      1. associate-/r/ 68.0%

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

   7. Applied egg-rr 68.0%

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

      1. *-commutative 68.0%

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

      2. clear-num 68.1%

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

      3. un-div-inv 68.1%

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

   9. Applied egg-rr 68.1%

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

   if -1.40000000000000008e-85 < t < 3.39999999999999998e41

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 77.9%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-85} \lor \neg \left(t \leq 3.4 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-85}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e+155)
   (+ x y)
   (if (<= t -1.4e-85)
     (- x (* y (/ z t)))
     (if (<= t 3.8e+41) (+ x (/ (* y z) a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+155) {
		tmp = x + y;
	} else if (t <= -1.4e-85) {
		tmp = x - (y * (z / t));
	} else if (t <= 3.8e+41) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.5d+155)) then
        tmp = x + y
    else if (t <= (-1.4d-85)) then
        tmp = x - (y * (z / t))
    else if (t <= 3.8d+41) then
        tmp = x + ((y * z) / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+155) {
		tmp = x + y;
	} else if (t <= -1.4e-85) {
		tmp = x - (y * (z / t));
	} else if (t <= 3.8e+41) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e+155:
		tmp = x + y
	elif t <= -1.4e-85:
		tmp = x - (y * (z / t))
	elif t <= 3.8e+41:
		tmp = x + ((y * z) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e+155)
		tmp = Float64(x + y);
	elseif (t <= -1.4e-85)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 3.8e+41)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e+155)
		tmp = x + y;
	elseif (t <= -1.4e-85)
		tmp = x - (y * (z / t));
	elseif (t <= 3.8e+41)
		tmp = x + ((y * z) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e+155], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.4e-85], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+41], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.49999999999999973e155 or 3.8000000000000001e41 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 90.3%

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

   if -4.49999999999999973e155 < t < -1.40000000000000008e-85

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 79.1%

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

   6. Taylor expanded in a around 0 67.3%

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

      1. mul-1-neg 67.3%

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

      2. unsub-neg 67.3%

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

      3. associate-/l* 67.3%

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

   8. Simplified 67.3%

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

   if -1.40000000000000008e-85 < t < 3.8000000000000001e41

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 77.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-85}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-86}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+155)
   (+ x y)
   (if (<= t -6.4e-86)
     (- x (/ y (/ t z)))
     (if (<= t 3.15e+41) (+ x (/ (* y z) a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+155) {
		tmp = x + y;
	} else if (t <= -6.4e-86) {
		tmp = x - (y / (t / z));
	} else if (t <= 3.15e+41) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.2d+155)) then
        tmp = x + y
    else if (t <= (-6.4d-86)) then
        tmp = x - (y / (t / z))
    else if (t <= 3.15d+41) then
        tmp = x + ((y * z) / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+155) {
		tmp = x + y;
	} else if (t <= -6.4e-86) {
		tmp = x - (y / (t / z));
	} else if (t <= 3.15e+41) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+155:
		tmp = x + y
	elif t <= -6.4e-86:
		tmp = x - (y / (t / z))
	elif t <= 3.15e+41:
		tmp = x + ((y * z) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+155)
		tmp = Float64(x + y);
	elseif (t <= -6.4e-86)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	elseif (t <= 3.15e+41)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e+155)
		tmp = x + y;
	elseif (t <= -6.4e-86)
		tmp = x - (y / (t / z));
	elseif (t <= 3.15e+41)
		tmp = x + ((y * z) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+155], N[(x + y), $MachinePrecision], If[LessEqual[t, -6.4e-86], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.15e+41], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2e155 or 3.1499999999999999e41 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 90.3%

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

   if -4.2e155 < t < -6.40000000000000011e-86

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 79.1%

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

   6. Taylor expanded in a around 0 67.3%

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

      1. neg-mul-1 67.3%

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

      2. distribute-neg-frac2 67.3%

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

   8. Simplified 67.3%

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

   if -6.40000000000000011e-86 < t < 3.1499999999999999e41

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 77.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-86}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-158} \lor \neg \left(t \leq 2.3 \cdot 10^{-65}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5e-158) (not (<= t 2.3e-65)))
   (+ x (* y (/ t (- t a))))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e-158) || !(t <= 2.3e-65)) {
		tmp = x + (y * (t / (t - a)));
	} 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 <= (-5d-158)) .or. (.not. (t <= 2.3d-65))) then
        tmp = x + (y * (t / (t - a)))
    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 <= -5e-158) || !(t <= 2.3e-65)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5e-158) or not (t <= 2.3e-65):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5e-158) || !(t <= 2.3e-65))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	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 <= -5e-158) || ~((t <= 2.3e-65)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5e-158], N[Not[LessEqual[t, 2.3e-65]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.99999999999999972e-158 or 2.3e-65 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 69.8%

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

      1. mul-1-neg 69.8%

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

      2. associate-/l* 78.8%

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

      3. distribute-lft-neg-in 78.8%

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

   5. Simplified 78.8%

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

      1. associate-*r/ 69.8%

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

      2. frac-2neg 69.8%

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

      3. add-sqr-sqrt 36.9%

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

      4. sqrt-unprod 39.0%

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

      5. sqr-neg 39.0%

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

      6. sqrt-unprod 21.0%

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

      7. add-sqr-sqrt 46.8%

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

      8. distribute-lft-neg-out 46.8%

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

      9. *-commutative 46.8%

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

      10. add-sqr-sqrt 25.8%

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

      11. sqrt-unprod 39.3%

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

      12. sqr-neg 39.3%

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

      13. sqrt-unprod 32.8%

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

      14. add-sqr-sqrt 69.8%

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

      15. sub-neg 69.8%

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

      16. distribute-neg-in 69.8%

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

      17. add-sqr-sqrt 36.9%

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

      18. sqrt-unprod 57.2%

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

      19. sqr-neg 57.2%

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

      20. sqrt-unprod 24.0%

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

      21. add-sqr-sqrt 52.3%

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

      22. add-sqr-sqrt 28.2%

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

      23. sqrt-unprod 56.4%

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

      24. sqr-neg 56.4%

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

      25. sqrt-unprod 32.8%

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

      26. add-sqr-sqrt 69.8%

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

   7. Applied egg-rr 69.8%

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

      1. associate-/l* 81.5%

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

      2. +-commutative 81.5%

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

      3. unsub-neg 81.5%

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

   9. Simplified 81.5%

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

   if -4.99999999999999972e-158 < t < 2.3e-65

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0 84.0%

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

      1. *-commutative 84.0%

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

      2. associate-/l* 85.1%

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

   5. Applied egg-rr 85.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-158} \lor \neg \left(t \leq 2.3 \cdot 10^{-65}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+52} \lor \neg \left(z \leq 3.6 \cdot 10^{+67}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+52) (not (<= z 3.6e+67)))
   (+ x (* y (/ z (- a t))))
   (+ x (* y (/ t (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+52) || !(z <= 3.6e+67)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y * (t / (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 <= (-1.2d+52)) .or. (.not. (z <= 3.6d+67))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (y * (t / (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 <= -1.2e+52) || !(z <= 3.6e+67)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+52) or not (z <= 3.6e+67):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+52) || !(z <= 3.6e+67))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e+52) || ~((z <= 3.6e+67)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+52], N[Not[LessEqual[z, 3.6e+67]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e52 or 3.5999999999999999e67 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. associate-/l* 92.0%

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

   5. Simplified 92.0%

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

   if -1.2e52 < z < 3.5999999999999999e67

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. associate-/l* 88.0%

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

      3. distribute-lft-neg-in 88.0%

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

   5. Simplified 88.0%

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

      1. associate-*r/ 79.0%

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

      2. frac-2neg 79.0%

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

      3. add-sqr-sqrt 37.7%

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

      4. sqrt-unprod 50.3%

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

      5. sqr-neg 50.3%

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

      6. sqrt-unprod 27.7%

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

      7. add-sqr-sqrt 54.1%

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

      8. distribute-lft-neg-out 54.1%

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

      9. *-commutative 54.1%

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

      10. add-sqr-sqrt 26.4%

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

      11. sqrt-unprod 52.1%

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

      12. sqr-neg 52.1%

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

      13. sqrt-unprod 41.2%

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

      14. add-sqr-sqrt 79.0%

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

      15. sub-neg 79.0%

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

      16. distribute-neg-in 79.0%

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

      17. add-sqr-sqrt 37.7%

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

      18. sqrt-unprod 65.3%

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

      19. sqr-neg 65.3%

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

      20. sqrt-unprod 31.0%

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

      21. add-sqr-sqrt 61.1%

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

      22. add-sqr-sqrt 30.1%

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

      23. sqrt-unprod 66.6%

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

      24. sqr-neg 66.6%

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

      25. sqrt-unprod 41.3%

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

      26. add-sqr-sqrt 79.0%

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

   7. Applied egg-rr 79.0%

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

      1. associate-/l* 90.1%

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

      2. +-commutative 90.1%

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

      3. unsub-neg 90.1%

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

   9. Simplified 90.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+52} \lor \neg \left(z \leq 3.6 \cdot 10^{+67}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+67}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+52)
   (+ x (* y (/ z (- a t))))
   (if (<= z 3.9e+67) (+ x (* y (/ t (- t a)))) (- x (/ y (/ (- t a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+52) {
		tmp = x + (y * (z / (a - t)));
	} else if (z <= 3.9e+67) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x - (y / ((t - 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 (z <= (-1.2d+52)) then
        tmp = x + (y * (z / (a - t)))
    else if (z <= 3.9d+67) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x - (y / ((t - 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 (z <= -1.2e+52) {
		tmp = x + (y * (z / (a - t)));
	} else if (z <= 3.9e+67) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x - (y / ((t - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+52:
		tmp = x + (y * (z / (a - t)))
	elif z <= 3.9e+67:
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x - (y / ((t - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+52)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	elseif (z <= 3.9e+67)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(t - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+52)
		tmp = x + (y * (z / (a - t)));
	elseif (z <= 3.9e+67)
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x - (y / ((t - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+52], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+67], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e52

   1. Initial program 95.9%

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

   3. Taylor expanded in z around inf 87.3%

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

      1. associate-/l* 94.9%

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

   5. Simplified 94.9%

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

   if -1.2e52 < z < 3.90000000000000007e67

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. associate-/l* 88.0%

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

      3. distribute-lft-neg-in 88.0%

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

   5. Simplified 88.0%

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

      1. associate-*r/ 79.0%

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

      2. frac-2neg 79.0%

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

      3. add-sqr-sqrt 37.7%

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

      4. sqrt-unprod 50.3%

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

      5. sqr-neg 50.3%

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

      6. sqrt-unprod 27.7%

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

      7. add-sqr-sqrt 54.1%

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

      8. distribute-lft-neg-out 54.1%

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

      9. *-commutative 54.1%

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

      10. add-sqr-sqrt 26.4%

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

      11. sqrt-unprod 52.1%

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

      12. sqr-neg 52.1%

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

      13. sqrt-unprod 41.2%

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

      14. add-sqr-sqrt 79.0%

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

      15. sub-neg 79.0%

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

      16. distribute-neg-in 79.0%

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

      17. add-sqr-sqrt 37.7%

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

      18. sqrt-unprod 65.3%

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

      19. sqr-neg 65.3%

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

      20. sqrt-unprod 31.0%

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

      21. add-sqr-sqrt 61.1%

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

      22. add-sqr-sqrt 30.1%

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

      23. sqrt-unprod 66.6%

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

      24. sqr-neg 66.6%

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

      25. sqrt-unprod 41.3%

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

      26. add-sqr-sqrt 79.0%

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

   7. Applied egg-rr 79.0%

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

      1. associate-/l* 90.1%

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

      2. +-commutative 90.1%

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

      3. unsub-neg 90.1%

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

   9. Simplified 90.1%

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

   if 3.90000000000000007e67 < z

   1. Initial program 97.9%

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

      1. clear-num 97.9%

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

      2. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 91.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+67}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-85} \lor \neg \left(t \leq 3.2 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.9e-85) (not (<= t 3.2e+41))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.9e-85) || !(t <= 3.2e+41)) {
		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 <= (-3.9d-85)) .or. (.not. (t <= 3.2d+41))) 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 <= -3.9e-85) || !(t <= 3.2e+41)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.9e-85) or not (t <= 3.2e+41):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.9e-85) || !(t <= 3.2e+41))
		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 <= -3.9e-85) || ~((t <= 3.2e+41)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.9e-85], N[Not[LessEqual[t, 3.2e+41]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -3.89999999999999988e-85 or 3.2000000000000001e41 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 78.1%

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

   if -3.89999999999999988e-85 < t < 3.2000000000000001e41

   1. Initial program 96.6%

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

   3. Taylor expanded in t around 0 77.2%

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

   4. Taylor expanded in x around inf 49.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-85} \lor \neg \left(t \leq 3.2 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 98.4%

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

3. Final simplification 98.4%

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

Alternative 13: 50.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in t around 0 59.4%

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

4. Taylor expanded in x around inf 50.9%

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

5. Final simplification 50.9%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 99.3% 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 2024046 
(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)))))