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

Percentage Accurate: 98.0% → 98.0%

Time: 10.0s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. fma-define N/A

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

   4. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(\frac{z - t}{z - a}\right), \color{blue}{y}, x\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(z - a\right)\right), y, x\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(z - a\right)\right), y, x\right) \]

   7. --lowering--.f64 98.7%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(z, a\right)\right), y, x\right) \]

4. Applied egg-rr 98.7%

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

Alternative 2: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+93}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+93)
   (+ y x)
   (if (<= z -2e-22)
     (* (- z t) (/ y (- z a)))
     (if (<= z 8.6e+51) (+ x (/ y (/ a t))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+93) {
		tmp = y + x;
	} else if (z <= -2e-22) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 8.6e+51) {
		tmp = x + (y / (a / t));
	} 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 (z <= (-1.65d+93)) then
        tmp = y + x
    else if (z <= (-2d-22)) then
        tmp = (z - t) * (y / (z - a))
    else if (z <= 8.6d+51) then
        tmp = x + (y / (a / t))
    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 (z <= -1.65e+93) {
		tmp = y + x;
	} else if (z <= -2e-22) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 8.6e+51) {
		tmp = x + (y / (a / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e+93:
		tmp = y + x
	elif z <= -2e-22:
		tmp = (z - t) * (y / (z - a))
	elif z <= 8.6e+51:
		tmp = x + (y / (a / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e+93)
		tmp = Float64(y + x);
	elseif (z <= -2e-22)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (z <= 8.6e+51)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e+93)
		tmp = y + x;
	elseif (z <= -2e-22)
		tmp = (z - t) * (y / (z - a));
	elseif (z <= 8.6e+51)
		tmp = x + (y / (a / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e+93], N[(y + x), $MachinePrecision], If[LessEqual[z, -2e-22], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+51], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000004e93 or 8.5999999999999994e51 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 82.4%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 82.4%

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

   if -1.65000000000000004e93 < z < -2.0000000000000001e-22

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. fma-define N/A

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

      4. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\frac{z - t}{z - a}\right), \color{blue}{y}, x\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(z - a\right)\right), y, x\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(z - a\right)\right), y, x\right) \]

      7. --lowering--.f64 99.9%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(z, a\right)\right), y, x\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z - t\right), \color{blue}{\left(\frac{y}{z - a}\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{\color{blue}{y}}{z - a}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, \color{blue}{\left(z - a\right)}\right)\right) \]

      8. --lowering--.f64 74.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 74.9%

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

   if -2.0000000000000001e-22 < z < 8.5999999999999994e51

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 76.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 76.7%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \frac{1}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{y}\right)}\right)\right) \]

      4. /-lowering-/.f64 77.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right)\right) \]

   7. Applied egg-rr 77.4%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{a} \cdot \color{blue}{y}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{a}{t}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{a}{t}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{t}\right)}\right)\right) \]

      6. /-lowering-/.f64 77.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   9. Applied egg-rr 77.7%

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

Alternative 3: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+43}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e+43)
   (+ x (* y (/ z (- z a))))
   (if (<= z 4e-12) (+ x (* y (/ (- t z) a))) (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+43) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 4e-12) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y * ((z - 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 <= (-3.6d+43)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 4d-12) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + (y * ((z - 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 <= -3.6e+43) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 4e-12) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e+43:
		tmp = x + (y * (z / (z - a)))
	elif z <= 4e-12:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e+43)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 4e-12)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.6e+43)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 4e-12)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e+43], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-12], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6000000000000001e43

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{z - a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\left(z - a\right)}\right)\right)\right) \]

      2. --lowering--.f64 87.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(z, \color{blue}{a}\right)\right)\right)\right) \]

   5. Simplified 87.2%

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

   if -3.6000000000000001e43 < z < 3.99999999999999992e-12

   1. Initial program 97.3%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - t}{a}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z - t}{a}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(z - t\right), \color{blue}{a}\right)\right)\right) \]

      7. --lowering--.f64 80.4%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), a\right)\right)\right) \]

   5. Simplified 80.4%

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

   if 3.99999999999999992e-12 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \color{blue}{z}\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 93.3%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+43}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+25)
   (+ x (* y (/ z (- z a))))
   (if (<= z 2e-13) (+ x (/ y (/ a t))) (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+25) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 2e-13) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * ((z - 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 <= (-2.7d+25)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 2d-13) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y * ((z - 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 <= -2.7e+25) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 2e-13) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+25:
		tmp = x + (y * (z / (z - a)))
	elif z <= 2e-13:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+25)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 2e-13)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e+25)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 2e-13)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+25], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-13], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7e25

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{z - a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\left(z - a\right)}\right)\right)\right) \]

      2. --lowering--.f64 87.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(z, \color{blue}{a}\right)\right)\right)\right) \]

   5. Simplified 87.8%

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

   if -2.7e25 < z < 2.0000000000000001e-13

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 77.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 77.1%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \frac{1}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{y}\right)}\right)\right) \]

      4. /-lowering-/.f64 77.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right)\right) \]

   7. Applied egg-rr 77.9%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{a} \cdot \color{blue}{y}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{a}{t}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{a}{t}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{t}\right)}\right)\right) \]

      6. /-lowering-/.f64 77.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   9. Applied egg-rr 77.9%

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

   if 2.0000000000000001e-13 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \color{blue}{z}\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 93.3%

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

Alternative 5: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+205}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- z a)))))
   (if (<= t -2.6e+106)
     t_1
     (if (<= t 7.5e+205) (+ x (* y (/ z (- z a)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (z - a));
	double tmp;
	if (t <= -2.6e+106) {
		tmp = t_1;
	} else if (t <= 7.5e+205) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (y / (z - a))
    if (t <= (-2.6d+106)) then
        tmp = t_1
    else if (t <= 7.5d+205) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (z - a));
	double tmp;
	if (t <= -2.6e+106) {
		tmp = t_1;
	} else if (t <= 7.5e+205) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / (z - a))
	tmp = 0
	if t <= -2.6e+106:
		tmp = t_1
	elif t <= 7.5e+205:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(z - a)))
	tmp = 0.0
	if (t <= -2.6e+106)
		tmp = t_1;
	elseif (t <= 7.5e+205)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / (z - a));
	tmp = 0.0;
	if (t <= -2.6e+106)
		tmp = t_1;
	elseif (t <= 7.5e+205)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+106], t$95$1, If[LessEqual[t, 7.5e+205], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6000000000000002e106 or 7.5000000000000003e205 < t

   1. Initial program 96.9%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. fma-define N/A

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

      4. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\frac{z - t}{z - a}\right), \color{blue}{y}, x\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(z - a\right)\right), y, x\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(z - a\right)\right), y, x\right) \]

      7. --lowering--.f64 96.9%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(z, a\right)\right), y, x\right) \]

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z - t\right), \color{blue}{\left(\frac{y}{z - a}\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{\color{blue}{y}}{z - a}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, \color{blue}{\left(z - a\right)}\right)\right) \]

      8. --lowering--.f64 77.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 77.2%

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

   if -2.6000000000000002e106 < t < 7.5000000000000003e205

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{z - a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\left(z - a\right)}\right)\right)\right) \]

      2. --lowering--.f64 85.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(z, \color{blue}{a}\right)\right)\right)\right) \]

   5. Simplified 85.4%

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

Alternative 6: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+77}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+77) (+ y x) (if (<= z 4.5e+52) (+ x (/ y (/ a t))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+77) {
		tmp = y + x;
	} else if (z <= 4.5e+52) {
		tmp = x + (y / (a / t));
	} 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 (z <= (-9d+77)) then
        tmp = y + x
    else if (z <= 4.5d+52) then
        tmp = x + (y / (a / t))
    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 (z <= -9e+77) {
		tmp = y + x;
	} else if (z <= 4.5e+52) {
		tmp = x + (y / (a / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+77:
		tmp = y + x
	elif z <= 4.5e+52:
		tmp = x + (y / (a / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+77)
		tmp = Float64(y + x);
	elseif (z <= 4.5e+52)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9e+77)
		tmp = y + x;
	elseif (z <= 4.5e+52)
		tmp = x + (y / (a / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+77], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.5e+52], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000049e77 or 4.5e52 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 81.8%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 81.8%

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

   if -9.00000000000000049e77 < z < 4.5e52

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 73.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 73.4%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \frac{1}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{y}\right)}\right)\right) \]

      4. /-lowering-/.f64 74.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right)\right) \]

   7. Applied egg-rr 74.1%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{a} \cdot \color{blue}{y}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{a}{t}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{a}{t}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{t}\right)}\right)\right) \]

      6. /-lowering-/.f64 74.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   9. Applied egg-rr 74.3%

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

Alternative 7: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+79}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+79) (+ y x) (if (<= z 3.6e-14) (+ x (/ t (/ a y))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+79) {
		tmp = y + x;
	} else if (z <= 3.6e-14) {
		tmp = x + (t / (a / y));
	} 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 (z <= (-7.5d+79)) then
        tmp = y + x
    else if (z <= 3.6d-14) then
        tmp = x + (t / (a / y))
    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 (z <= -7.5e+79) {
		tmp = y + x;
	} else if (z <= 3.6e-14) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+79:
		tmp = y + x
	elif z <= 3.6e-14:
		tmp = x + (t / (a / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+79)
		tmp = Float64(y + x);
	elseif (z <= 3.6e-14)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+79)
		tmp = y + x;
	elseif (z <= 3.6e-14)
		tmp = x + (t / (a / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+79], N[(y + x), $MachinePrecision], If[LessEqual[z, 3.6e-14], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999967e79 or 3.5999999999999998e-14 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 80.8%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 80.8%

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

   if -7.49999999999999967e79 < z < 3.5999999999999998e-14

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 73.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 73.6%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \frac{1}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{y}\right)}\right)\right) \]

      4. /-lowering-/.f64 74.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right)\right) \]

   7. Applied egg-rr 74.3%

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

Alternative 8: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+81}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+81) (+ y x) (if (<= z 1.04e+52) (+ x (* y (/ t a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+81) {
		tmp = y + x;
	} else if (z <= 1.04e+52) {
		tmp = x + (y * (t / 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 (z <= (-1.1d+81)) then
        tmp = y + x
    else if (z <= 1.04d+52) then
        tmp = x + (y * (t / 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 (z <= -1.1e+81) {
		tmp = y + x;
	} else if (z <= 1.04e+52) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+81:
		tmp = y + x
	elif z <= 1.04e+52:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+81)
		tmp = Float64(y + x);
	elseif (z <= 1.04e+52)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+81)
		tmp = y + x;
	elseif (z <= 1.04e+52)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+81], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.04e+52], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999993e81 or 1.04e52 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 81.8%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 81.8%

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

   if -1.09999999999999993e81 < z < 1.04e52

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 73.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 73.6%

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

Alternative 9: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+78}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-14}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+78) (+ y x) (if (<= z 2.45e-14) (+ x (* t (/ y a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+78) {
		tmp = y + x;
	} else if (z <= 2.45e-14) {
		tmp = x + (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 (z <= (-1d+78)) then
        tmp = y + x
    else if (z <= 2.45d-14) then
        tmp = x + (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 (z <= -1e+78) {
		tmp = y + x;
	} else if (z <= 2.45e-14) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+78:
		tmp = y + x
	elif z <= 2.45e-14:
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+78)
		tmp = Float64(y + x);
	elseif (z <= 2.45e-14)
		tmp = Float64(x + 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 (z <= -1e+78)
		tmp = y + x;
	elseif (z <= 2.45e-14)
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+78], N[(y + x), $MachinePrecision], If[LessEqual[z, 2.45e-14], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000001e78 or 2.44999999999999997e-14 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 80.8%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 80.8%

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

   if -1.00000000000000001e78 < z < 2.44999999999999997e-14

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 73.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 73.6%

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

Alternative 10: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+21}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.4e+21) (+ y x) (if (<= z 1.95e-13) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.4e+21) {
		tmp = y + x;
	} else if (z <= 1.95e-13) {
		tmp = x;
	} 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 (z <= (-8.4d+21)) then
        tmp = y + x
    else if (z <= 1.95d-13) then
        tmp = x
    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 (z <= -8.4e+21) {
		tmp = y + x;
	} else if (z <= 1.95e-13) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.4e+21:
		tmp = y + x
	elif z <= 1.95e-13:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.4e+21)
		tmp = Float64(y + x);
	elseif (z <= 1.95e-13)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.4e+21)
		tmp = y + x;
	elseif (z <= 1.95e-13)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.4e+21], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.95e-13], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4e21 or 1.95000000000000002e-13 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 76.4%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 76.4%

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

   if -8.4e21 < z < 1.95000000000000002e-13

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.6%

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

Alternative 11: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

3. Final simplification 98.6%

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

Alternative 12: 51.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+245}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= z -2.4e+245) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+245) {
		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 (z <= (-2.4d+245)) 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 (z <= -2.4e+245) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+245:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+245)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+245)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+245], y, x]

Derivation

1. Split input into 2 regimes

2. if z < -2.3999999999999998e245

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 78.8%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 78.8%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   7. Step-by-step derivation

   8. Simplified 54.6%

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

   if -2.3999999999999998e245 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 53.5%

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

Alternative 13: 51.2% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

3. Taylor expanded in x around inf

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

5. Simplified 51.7%

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

Developer Target 1: 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 2024138 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

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