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

Percentage Accurate: 85.7% → 98.0%

Time: 9.6s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 83.7%

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

   1. +-commutative 83.7%

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

   2. associate-/l* 98.4%

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

   3. fma-define 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 82.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-20} \lor \neg \left(t\_1 \leq 10^{+168}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 -1e-20) (not (<= t_1 1e+168)))
     (* y (/ (- z t) (- z a)))
     (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -1e-20) || !(t_1 <= 1e+168)) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (z - a)
    if ((t_1 <= (-1d-20)) .or. (.not. (t_1 <= 1d+168))) then
        tmp = y * ((z - t) / (z - a))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -1e-20) || !(t_1 <= 1e+168)) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -1e-20) or not (t_1 <= 1e+168):
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -1e-20) || !(t_1 <= 1e+168))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -1e-20) || ~((t_1 <= 1e+168)))
		tmp = y * ((z - t) / (z - a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-20], N[Not[LessEqual[t$95$1, 1e+168]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -9.99999999999999945e-21 or 9.9999999999999993e167 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 63.3%

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

   3. Taylor expanded in x around 0 58.1%

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

      1. associate-*r/ 84.8%

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

   5. Simplified 84.8%

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

   if -9.99999999999999945e-21 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 9.9999999999999993e167

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 88.0%

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

      1. associate-/l* 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -1 \cdot 10^{-20} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 10^{+168}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+26} \lor \neg \left(y \leq 6 \cdot 10^{-11}\right) \land \left(y \leq 4.3 \cdot 10^{+66} \lor \neg \left(y \leq 1.35 \cdot 10^{+130}\right)\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7e+26)
         (and (not (<= y 6e-11)) (or (<= y 4.3e+66) (not (<= y 1.35e+130)))))
   (* y (/ (- z t) (- z a)))
   (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7e+26) || (!(y <= 6e-11) && ((y <= 4.3e+66) || !(y <= 1.35e+130)))) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = y + 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 ((y <= (-7d+26)) .or. (.not. (y <= 6d-11)) .and. (y <= 4.3d+66) .or. (.not. (y <= 1.35d+130))) then
        tmp = y * ((z - t) / (z - a))
    else
        tmp = y + 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 ((y <= -7e+26) || (!(y <= 6e-11) && ((y <= 4.3e+66) || !(y <= 1.35e+130)))) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7e+26) or (not (y <= 6e-11) and ((y <= 4.3e+66) or not (y <= 1.35e+130))):
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7e+26) || (!(y <= 6e-11) && ((y <= 4.3e+66) || !(y <= 1.35e+130))))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -7e+26) || (~((y <= 6e-11)) && ((y <= 4.3e+66) || ~((y <= 1.35e+130)))))
		tmp = y * ((z - t) / (z - a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7e+26], And[N[Not[LessEqual[y, 6e-11]], $MachinePrecision], Or[LessEqual[y, 4.3e+66], N[Not[LessEqual[y, 1.35e+130]], $MachinePrecision]]]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999998e26 or 6e-11 < y < 4.30000000000000027e66 or 1.3499999999999999e130 < y

   1. Initial program 69.6%

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

   3. Taylor expanded in x around 0 57.2%

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

      1. associate-*r/ 83.1%

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

   5. Simplified 83.1%

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

   if -6.9999999999999998e26 < y < 6e-11 or 4.30000000000000027e66 < y < 1.3499999999999999e130

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 79.5%

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

      1. +-commutative 79.5%

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

   5. Simplified 79.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+26} \lor \neg \left(y \leq 6 \cdot 10^{-11}\right) \land \left(y \leq 4.3 \cdot 10^{+66} \lor \neg \left(y \leq 1.35 \cdot 10^{+130}\right)\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 0.058:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+143} \lor \neg \left(z \leq 9.5 \cdot 10^{+180}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e-41)
   (+ y x)
   (if (<= z 0.058)
     (+ x (/ y (/ a t)))
     (if (or (<= z 3.8e+143) (not (<= z 9.5e+180)))
       (+ y x)
       (- x (* y (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e-41) {
		tmp = y + x;
	} else if (z <= 0.058) {
		tmp = x + (y / (a / t));
	} else if ((z <= 3.8e+143) || !(z <= 9.5e+180)) {
		tmp = y + x;
	} else {
		tmp = x - (y * (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3d-41)) then
        tmp = y + x
    else if (z <= 0.058d0) then
        tmp = x + (y / (a / t))
    else if ((z <= 3.8d+143) .or. (.not. (z <= 9.5d+180))) then
        tmp = y + x
    else
        tmp = x - (y * (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e-41) {
		tmp = y + x;
	} else if (z <= 0.058) {
		tmp = x + (y / (a / t));
	} else if ((z <= 3.8e+143) || !(z <= 9.5e+180)) {
		tmp = y + x;
	} else {
		tmp = x - (y * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e-41:
		tmp = y + x
	elif z <= 0.058:
		tmp = x + (y / (a / t))
	elif (z <= 3.8e+143) or not (z <= 9.5e+180):
		tmp = y + x
	else:
		tmp = x - (y * (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e-41)
		tmp = Float64(y + x);
	elseif (z <= 0.058)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif ((z <= 3.8e+143) || !(z <= 9.5e+180))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(y * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e-41)
		tmp = y + x;
	elseif (z <= 0.058)
		tmp = x + (y / (a / t));
	elseif ((z <= 3.8e+143) || ~((z <= 9.5e+180)))
		tmp = y + x;
	else
		tmp = x - (y * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e-41], N[(y + x), $MachinePrecision], If[LessEqual[z, 0.058], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.8e+143], N[Not[LessEqual[z, 9.5e+180]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999989e-41 or 0.0580000000000000029 < z < 3.8e143 or 9.5000000000000003e180 < z

   1. Initial program 74.7%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -2.99999999999999989e-41 < z < 0.0580000000000000029

   1. Initial program 96.6%

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

      1. associate-/l* 96.5%

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

      2. clear-num 95.7%

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

      3. un-div-inv 95.6%

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

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in z around 0 73.0%

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

   if 3.8e143 < z < 9.5000000000000003e180

   1. Initial program 67.4%

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

      1. associate-/l* 99.7%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. associate-/r/ 99.9%

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

      2. clear-num 99.9%

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

      3. associate-*l/ 99.9%

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

      4. *-un-lft-identity 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in a around 0 67.4%

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

      1. associate-/l* 83.6%

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

   9. Simplified 83.6%

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

   10. Taylor expanded in z around 0 86.4%

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

       1. neg-mul-1 86.4%

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

       2. distribute-neg-frac 86.4%

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

   12. Simplified 86.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 0.058:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+143} \lor \neg \left(z \leq 9.5 \cdot 10^{+180}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{-z}\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+180}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+278}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- z)))))
   (if (<= t -1.85e+184)
     t_1
     (if (<= t 8e+180)
       (+ y x)
       (if (<= t 4.1e+270) t_1 (if (<= t 4.7e+278) (+ y x) (/ (* y t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -z);
	double tmp;
	if (t <= -1.85e+184) {
		tmp = t_1;
	} else if (t <= 8e+180) {
		tmp = y + x;
	} else if (t <= 4.1e+270) {
		tmp = t_1;
	} else if (t <= 4.7e+278) {
		tmp = y + x;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / -z)
    if (t <= (-1.85d+184)) then
        tmp = t_1
    else if (t <= 8d+180) then
        tmp = y + x
    else if (t <= 4.1d+270) then
        tmp = t_1
    else if (t <= 4.7d+278) then
        tmp = y + x
    else
        tmp = (y * t) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -z);
	double tmp;
	if (t <= -1.85e+184) {
		tmp = t_1;
	} else if (t <= 8e+180) {
		tmp = y + x;
	} else if (t <= 4.1e+270) {
		tmp = t_1;
	} else if (t <= 4.7e+278) {
		tmp = y + x;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / -z)
	tmp = 0
	if t <= -1.85e+184:
		tmp = t_1
	elif t <= 8e+180:
		tmp = y + x
	elif t <= 4.1e+270:
		tmp = t_1
	elif t <= 4.7e+278:
		tmp = y + x
	else:
		tmp = (y * t) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(-z)))
	tmp = 0.0
	if (t <= -1.85e+184)
		tmp = t_1;
	elseif (t <= 8e+180)
		tmp = Float64(y + x);
	elseif (t <= 4.1e+270)
		tmp = t_1;
	elseif (t <= 4.7e+278)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y * t) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / -z);
	tmp = 0.0;
	if (t <= -1.85e+184)
		tmp = t_1;
	elseif (t <= 8e+180)
		tmp = y + x;
	elseif (t <= 4.1e+270)
		tmp = t_1;
	elseif (t <= 4.7e+278)
		tmp = y + x;
	else
		tmp = (y * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.85e+184], t$95$1, If[LessEqual[t, 8e+180], N[(y + x), $MachinePrecision], If[LessEqual[t, 4.1e+270], t$95$1, If[LessEqual[t, 4.7e+278], N[(y + x), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8499999999999999e184 or 8.0000000000000001e180 < t < 4.09999999999999996e270

   1. Initial program 80.6%

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

   3. Taylor expanded in x around 0 66.9%

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

   4. Taylor expanded in t around inf 66.0%

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

      1. mul-1-neg 79.6%

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

      2. associate-/l* 92.5%

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

      3. distribute-rgt-neg-in 92.5%

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

      4. distribute-neg-frac2 92.5%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in z around inf 57.4%

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

      1. associate-*r/ 57.4%

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

      2. neg-mul-1 57.4%

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

   9. Simplified 57.4%

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

   if -1.8499999999999999e184 < t < 8.0000000000000001e180 or 4.09999999999999996e270 < t < 4.7e278

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 71.0%

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

      1. +-commutative 71.0%

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

   5. Simplified 71.0%

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

   if 4.7e278 < t

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0 73.2%

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

   4. Taylor expanded in z around 0 57.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+180}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+270}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+278}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+81}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-90}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e+81)
   (+ x (* t (/ y a)))
   (if (<= a 1.9e-90)
     (+ x (* y (- 1.0 (/ t z))))
     (if (<= a 4.2e-23) (* y (/ (- z t) (- z a))) (+ x (/ y (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+81) {
		tmp = x + (t * (y / a));
	} else if (a <= 1.9e-90) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (a <= 4.2e-23) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.6d+81)) then
        tmp = x + (t * (y / a))
    else if (a <= 1.9d-90) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (a <= 4.2d-23) then
        tmp = y * ((z - t) / (z - a))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+81) {
		tmp = x + (t * (y / a));
	} else if (a <= 1.9e-90) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (a <= 4.2e-23) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e+81:
		tmp = x + (t * (y / a))
	elif a <= 1.9e-90:
		tmp = x + (y * (1.0 - (t / z)))
	elif a <= 4.2e-23:
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e+81)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 1.9e-90)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (a <= 4.2e-23)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e+81)
		tmp = x + (t * (y / a));
	elseif (a <= 1.9e-90)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (a <= 4.2e-23)
		tmp = y * ((z - t) / (z - a));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e+81], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-90], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-23], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.60000000000000005e81

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 75.5%

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

      1. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   if -3.60000000000000005e81 < a < 1.9e-90

   1. Initial program 88.5%

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

   3. Taylor expanded in a around 0 79.7%

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

      1. associate-/l* 88.9%

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

      2. div-sub 88.9%

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

      3. *-inverses 88.9%

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

   5. Simplified 88.9%

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

   if 1.9e-90 < a < 4.2000000000000002e-23

   1. Initial program 90.8%

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

   3. Taylor expanded in x around 0 77.7%

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

      1. associate-*r/ 86.7%

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

   5. Simplified 86.7%

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

   if 4.2000000000000002e-23 < a

   1. Initial program 71.6%

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

      1. associate-/l* 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 78.0%

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

Alternative 7: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0074 \lor \neg \left(t \leq 3.2 \cdot 10^{+123}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.0074) (not (<= t 3.2e+123)))
   (+ x (* t (/ y (- a z))))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.0074) || !(t <= 3.2e+123)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-0.0074d0)) .or. (.not. (t <= 3.2d+123))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.0074) || !(t <= 3.2e+123)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.0074) or not (t <= 3.2e+123):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.0074) || !(t <= 3.2e+123))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.0074) || ~((t <= 3.2e+123)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.0074], N[Not[LessEqual[t, 3.2e+123]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0074000000000000003 or 3.20000000000000005e123 < t

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. associate-/l* 91.0%

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

      3. distribute-rgt-neg-in 91.0%

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

      4. distribute-neg-frac2 91.0%

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

   5. Simplified 91.0%

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

   if -0.0074000000000000003 < t < 3.20000000000000005e123

   1. Initial program 85.0%

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

   3. Taylor expanded in t around 0 74.7%

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

      1. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0074 \lor \neg \left(t \leq 3.2 \cdot 10^{+123}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-40} \lor \neg \left(z \leq 0.215\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e-40) (not (<= z 0.215))) (+ y x) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e-40) || !(z <= 0.215)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.1d-40)) .or. (.not. (z <= 0.215d0))) then
        tmp = y + x
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e-40) || !(z <= 0.215)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e-40) or not (z <= 0.215):
		tmp = y + x
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e-40) || !(z <= 0.215))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e-40) || ~((z <= 0.215)))
		tmp = y + x;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e-40], N[Not[LessEqual[z, 0.215]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.10000000000000018e-40 or 0.214999999999999997 < z

   1. Initial program 74.1%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -2.10000000000000018e-40 < z < 0.214999999999999997

   1. Initial program 96.6%

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

      1. associate-/l* 96.5%

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

      2. clear-num 95.7%

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

      3. un-div-inv 95.6%

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

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in z around 0 73.0%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-40} \lor \neg \left(z \leq 0.215\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-40} \lor \neg \left(z \leq 2900\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.4e-40) (not (<= z 2900.0))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e-40) || !(z <= 2900.0)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.4d-40)) .or. (.not. (z <= 2900.0d0))) then
        tmp = y + x
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e-40) || !(z <= 2900.0)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.4e-40) or not (z <= 2900.0):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.4e-40) || !(z <= 2900.0))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.4e-40) || ~((z <= 2900.0)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.4e-40], N[Not[LessEqual[z, 2900.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.39999999999999984e-40 or 2900 < z

   1. Initial program 74.1%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -3.39999999999999984e-40 < z < 2900

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-40} \lor \neg \left(z \leq 2900\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+185} \lor \neg \left(t \leq 7.8 \cdot 10^{+164}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7e+185) (not (<= t 7.8e+164))) (* y (/ (- z t) z)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+185) || !(t <= 7.8e+164)) {
		tmp = y * ((z - t) / z);
	} else {
		tmp = y + 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 <= (-7d+185)) .or. (.not. (t <= 7.8d+164))) then
        tmp = y * ((z - t) / z)
    else
        tmp = y + 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 <= -7e+185) || !(t <= 7.8e+164)) {
		tmp = y * ((z - t) / z);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7e+185) or not (t <= 7.8e+164):
		tmp = y * ((z - t) / z)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7e+185) || !(t <= 7.8e+164))
		tmp = Float64(y * Float64(Float64(z - t) / z));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7e+185) || ~((t <= 7.8e+164)))
		tmp = y * ((z - t) / z);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7e+185], N[Not[LessEqual[t, 7.8e+164]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.00000000000000046e185 or 7.79999999999999971e164 < t

   1. Initial program 78.5%

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

   3. Taylor expanded in x around 0 62.5%

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

      1. associate-*r/ 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in a around 0 53.8%

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

   if -7.00000000000000046e185 < t < 7.79999999999999971e164

   1. Initial program 85.4%

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

   3. Taylor expanded in z around inf 71.8%

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

      1. +-commutative 71.8%

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

   5. Simplified 71.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+185} \lor \neg \left(t \leq 7.8 \cdot 10^{+164}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+248} \lor \neg \left(t \leq 4.2 \cdot 10^{+227}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e+248) (not (<= t 4.2e+227))) (* t (/ y a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e+248) || !(t <= 4.2e+227)) {
		tmp = t * (y / a);
	} else {
		tmp = y + 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+248)) .or. (.not. (t <= 4.2d+227))) then
        tmp = t * (y / a)
    else
        tmp = y + 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+248) || !(t <= 4.2e+227)) {
		tmp = t * (y / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.8e+248) or not (t <= 4.2e+227):
		tmp = t * (y / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e+248) || !(t <= 4.2e+227))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.8e+248) || ~((t <= 4.2e+227)))
		tmp = t * (y / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e+248], N[Not[LessEqual[t, 4.2e+227]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.80000000000000001e248 or 4.20000000000000039e227 < t

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0 67.1%

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

   4. Taylor expanded in z around 0 56.4%

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

      1. associate-/l* 78.5%

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

   6. Simplified 63.6%

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

   if -1.80000000000000001e248 < t < 4.20000000000000039e227

   1. Initial program 83.9%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. +-commutative 66.1%

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

   5. Simplified 66.1%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+248} \lor \neg \left(t \leq 4.2 \cdot 10^{+227}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+224}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+185)
   (* y (/ t (- z)))
   (if (<= t 8.5e+224) (+ y x) (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+185) {
		tmp = y * (t / -z);
	} else if (t <= 8.5e+224) {
		tmp = y + x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.8d+185)) then
        tmp = y * (t / -z)
    else if (t <= 8.5d+224) then
        tmp = y + x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+185) {
		tmp = y * (t / -z);
	} else if (t <= 8.5e+224) {
		tmp = y + x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+185:
		tmp = y * (t / -z)
	elif t <= 8.5e+224:
		tmp = y + x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+185)
		tmp = Float64(y * Float64(t / Float64(-z)));
	elseif (t <= 8.5e+224)
		tmp = Float64(y + x);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+185)
		tmp = y * (t / -z);
	elseif (t <= 8.5e+224)
		tmp = y + x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+185], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+224], N[(y + x), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999982e185

   1. Initial program 83.1%

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

   3. Taylor expanded in x around 0 65.7%

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

   4. Taylor expanded in t around inf 65.4%

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

      1. mul-1-neg 82.7%

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

      2. associate-/l* 92.7%

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

      3. distribute-rgt-neg-in 92.7%

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

      4. distribute-neg-frac2 92.7%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in z around inf 48.7%

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

      1. associate-*r/ 48.7%

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

      2. neg-mul-1 48.7%

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

      3. distribute-lft-neg-in 48.7%

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

   9. Simplified 48.7%

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

       1. associate-/l* 55.4%

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

       2. distribute-lft-neg-out 55.4%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 7.9%

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

       5. sqr-neg 7.9%

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

       6. sqrt-unprod 8.3%

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

       7. add-sqr-sqrt 8.3%

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

       8. associate-/l* 8.2%

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

       9. div-inv 8.2%

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

       10. *-commutative 8.2%

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

       11. associate-*l* 8.3%

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

       12. add-sqr-sqrt 8.3%

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

       13. sqrt-unprod 7.9%

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

       14. sqr-neg 7.9%

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

       15. sqrt-unprod 0.0%

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

       16. add-sqr-sqrt 55.1%

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

       17. div-inv 55.1%

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

   11. Applied egg-rr 55.1%

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

   if -2.79999999999999982e185 < t < 8.50000000000000046e224

   1. Initial program 84.4%

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

   3. Taylor expanded in z around inf 68.7%

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

      1. +-commutative 68.7%

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

   5. Simplified 68.7%

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

   if 8.50000000000000046e224 < t

   1. Initial program 76.6%

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

   3. Taylor expanded in x around 0 58.5%

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

   4. Taylor expanded in z around 0 45.6%

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

      1. associate-/l* 75.4%

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

   6. Simplified 57.2%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+224}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.13 \lor \neg \left(y \leq 1.75 \cdot 10^{+140}\right):\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -0.13) (not (<= y 1.75e+140))) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -0.13) || !(y <= 1.75e+140)) {
		tmp = 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 ((y <= (-0.13d0)) .or. (.not. (y <= 1.75d+140))) then
        tmp = 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 ((y <= -0.13) || !(y <= 1.75e+140)) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -0.13) or not (y <= 1.75e+140):
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -0.13) || !(y <= 1.75e+140))
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -0.13) || ~((y <= 1.75e+140)))
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -0.13], N[Not[LessEqual[y, 1.75e+140]], $MachinePrecision]], y, x]

Derivation

1. Split input into 2 regimes

2. if y < -0.13 or 1.74999999999999995e140 < y

   1. Initial program 63.2%

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

   3. Taylor expanded in x around 0 53.0%

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

   4. Taylor expanded in z around inf 38.2%

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

   if -0.13 < y < 1.74999999999999995e140

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf 65.6%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.13 \lor \neg \left(y \leq 1.75 \cdot 10^{+140}\right):\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.7%

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

   1. associate-/l* 98.4%

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

   2. clear-num 98.1%

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

   3. un-div-inv 98.1%

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

4. Applied egg-rr 98.1%

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

Alternative 15: 60.1% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

3. Taylor expanded in z around inf 61.6%

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

   1. +-commutative 61.6%

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

5. Simplified 61.6%

   \[\leadsto \color{blue}{y + x} \]
6. Add Preprocessing

Alternative 16: 49.9% 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 83.7%

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

3. Taylor expanded in x around inf 47.1%

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

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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