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

Percentage Accurate: 98.4% → 98.4%

Time: 9.1s

Alternatives: 9

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: 98.4% 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: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

Alternative 2: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-36}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+58}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e-36)
   (+ x y)
   (if (<= z 4.2e-92)
     (+ x (* t (/ y a)))
     (if (<= z 1.02e+58) (- x (* y (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e-36) {
		tmp = x + y;
	} else if (z <= 4.2e-92) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.02e+58) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.4d-36)) then
        tmp = x + y
    else if (z <= 4.2d-92) then
        tmp = x + (t * (y / a))
    else if (z <= 1.02d+58) then
        tmp = x - (y * (t / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e-36) {
		tmp = x + y;
	} else if (z <= 4.2e-92) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.02e+58) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e-36:
		tmp = x + y
	elif z <= 4.2e-92:
		tmp = x + (t * (y / a))
	elif z <= 1.02e+58:
		tmp = x - (y * (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e-36)
		tmp = Float64(x + y);
	elseif (z <= 4.2e-92)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 1.02e+58)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e-36)
		tmp = x + y;
	elseif (z <= 4.2e-92)
		tmp = x + (t * (y / a));
	elseif (z <= 1.02e+58)
		tmp = x - (y * (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e-36], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.2e-92], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+58], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4000000000000003e-36 or 1.02000000000000005e58 < 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 81.0%

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

   5. Simplified 81.0%

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

   if -3.4000000000000003e-36 < z < 4.2e-92

   1. Initial program 94.6%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 81.7%

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

   5. Simplified 81.7%

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

   if 4.2e-92 < z < 1.02000000000000005e58

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r/ N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. distribute-lft-out-- N/A

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

      9. associate-*r/ N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. --lowering--.f64 N/A

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

      13. +-commutative N/A

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

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

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

      15. distribute-rgt-out-- N/A

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

      16. associate-/l* N/A

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

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

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

      18. /-lowering-/.f64 N/A

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

   5. Simplified 62.3%

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

   6. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in y around 0

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

   11. Simplified 59.5%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-36}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+58}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-73}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-174}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e-73)
   (+ x y)
   (if (<= z 6e-226) x (if (<= z 7.2e-174) (/ (* y t) a) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-73) {
		tmp = x + y;
	} else if (z <= 6e-226) {
		tmp = x;
	} else if (z <= 7.2e-174) {
		tmp = (y * t) / a;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d-73)) then
        tmp = x + y
    else if (z <= 6d-226) then
        tmp = x
    else if (z <= 7.2d-174) then
        tmp = (y * t) / a
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-73) {
		tmp = x + y;
	} else if (z <= 6e-226) {
		tmp = x;
	} else if (z <= 7.2e-174) {
		tmp = (y * t) / a;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e-73:
		tmp = x + y
	elif z <= 6e-226:
		tmp = x
	elif z <= 7.2e-174:
		tmp = (y * t) / a
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e-73)
		tmp = Float64(x + y);
	elseif (z <= 6e-226)
		tmp = x;
	elseif (z <= 7.2e-174)
		tmp = Float64(Float64(y * t) / a);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e-73)
		tmp = x + y;
	elseif (z <= 6e-226)
		tmp = x;
	elseif (z <= 7.2e-174)
		tmp = (y * t) / a;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e-73], N[(x + y), $MachinePrecision], If[LessEqual[z, 6e-226], x, If[LessEqual[z, 7.2e-174], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999999e-73 or 7.19999999999999997e-174 < z

   1. Initial program 99.3%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 74.3%

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

   5. Simplified 74.3%

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

   if -2.4999999999999999e-73 < z < 5.9999999999999999e-226

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 56.9%

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

   if 5.9999999999999999e-226 < z < 7.19999999999999997e-174

   1. Initial program 92.1%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot t\right), a\right) \]

      3. *-lowering-*.f64 54.7%

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

   8. Simplified 54.7%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-73}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-174}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ t z)))))
   (if (<= z -1.65e-74) t_1 (if (<= z 4.2e-92) (+ x (* t (/ y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (t / z));
	double tmp;
	if (z <= -1.65e-74) {
		tmp = t_1;
	} else if (z <= 4.2e-92) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (y * (t / z))
    if (z <= (-1.65d-74)) then
        tmp = t_1
    else if (z <= 4.2d-92) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (t / z));
	double tmp;
	if (z <= -1.65e-74) {
		tmp = t_1;
	} else if (z <= 4.2e-92) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y * (t / z))
	tmp = 0
	if z <= -1.65e-74:
		tmp = t_1
	elif z <= 4.2e-92:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y * Float64(t / z)))
	tmp = 0.0
	if (z <= -1.65e-74)
		tmp = t_1;
	elseif (z <= 4.2e-92)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y * (t / z));
	tmp = 0.0;
	if (z <= -1.65e-74)
		tmp = t_1;
	elseif (z <= 4.2e-92)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e-74], t$95$1, If[LessEqual[z, 4.2e-92], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999998e-74 or 4.2e-92 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r/ N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. distribute-lft-out-- N/A

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

      9. associate-*r/ N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. --lowering--.f64 N/A

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

      13. +-commutative N/A

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

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

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

      15. distribute-rgt-out-- N/A

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

      16. associate-/l* N/A

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

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

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

      18. /-lowering-/.f64 N/A

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

   5. Simplified 80.9%

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

   6. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 84.1%

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

   8. Simplified 84.1%

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

   if -1.64999999999999998e-74 < z < 4.2e-92

   1. Initial program 95.2%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-74}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -3.3e-75) t_1 (if (<= z 3.7e-92) (+ x (* t (/ y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -3.3e-75) {
		tmp = t_1;
	} else if (z <= 3.7e-92) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-3.3d-75)) then
        tmp = t_1
    else if (z <= 3.7d-92) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -3.3e-75) {
		tmp = t_1;
	} else if (z <= 3.7e-92) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -3.3e-75:
		tmp = t_1
	elif z <= 3.7e-92:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -3.3e-75)
		tmp = t_1;
	elseif (z <= 3.7e-92)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -3.3e-75)
		tmp = t_1;
	elseif (z <= 3.7e-92)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e-75], t$95$1, If[LessEqual[z, 3.7e-92], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e-75 or 3.69999999999999977e-92 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in a around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. /-lowering-/.f64 84.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 84.0%

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

   if -3.3e-75 < z < 3.69999999999999977e-92

   1. Initial program 95.2%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 83.4%

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

   5. Simplified 83.4%

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

Alternative 6: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-34}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-34) (+ x y) (if (<= z 4.2e-92) (+ x (* t (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-34) {
		tmp = x + y;
	} else if (z <= 4.2e-92) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d-34)) then
        tmp = x + y
    else if (z <= 4.2d-92) then
        tmp = x + (t * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-34) {
		tmp = x + y;
	} else if (z <= 4.2e-92) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-34:
		tmp = x + y
	elif z <= 4.2e-92:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-34)
		tmp = Float64(x + y);
	elseif (z <= 4.2e-92)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-34)
		tmp = x + y;
	elseif (z <= 4.2e-92)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-34], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.2e-92], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000014e-34 or 4.2e-92 < 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 74.9%

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

   5. Simplified 74.9%

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

   if -5.50000000000000014e-34 < z < 4.2e-92

   1. Initial program 94.6%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 81.7%

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

   5. Simplified 81.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-34}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-73}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e-73) (+ x y) (if (<= z 1.4e-174) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e-73) {
		tmp = x + y;
	} else if (z <= 1.4e-174) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.9d-73)) then
        tmp = x + y
    else if (z <= 1.4d-174) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e-73) {
		tmp = x + y;
	} else if (z <= 1.4e-174) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e-73:
		tmp = x + y
	elif z <= 1.4e-174:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e-73)
		tmp = Float64(x + y);
	elseif (z <= 1.4e-174)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e-73)
		tmp = x + y;
	elseif (z <= 1.4e-174)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e-73], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.4e-174], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9000000000000001e-73 or 1.39999999999999999e-174 < z

   1. Initial program 99.3%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 73.9%

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

   5. Simplified 73.9%

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

   if -1.9000000000000001e-73 < z < 1.39999999999999999e-174

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 51.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-73}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-235}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.9e-197) x (if (<= x 2.9e-235) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.9e-197) {
		tmp = x;
	} else if (x <= 2.9e-235) {
		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 (x <= (-4.9d-197)) then
        tmp = x
    else if (x <= 2.9d-235) 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 (x <= -4.9e-197) {
		tmp = x;
	} else if (x <= 2.9e-235) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.9e-197:
		tmp = x
	elif x <= 2.9e-235:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.9e-197)
		tmp = x;
	elseif (x <= 2.9e-235)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.9e-197)
		tmp = x;
	elseif (x <= 2.9e-235)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.9e-197], x, If[LessEqual[x, 2.9e-235], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9000000000000002e-197 or 2.90000000000000009e-235 < x

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 60.8%

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

   if -4.9000000000000002e-197 < x < 2.90000000000000009e-235

   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 46.4%

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

   5. Simplified 46.4%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 42.3%

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

Alternative 9: 51.4% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

3. Taylor expanded in x around inf

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

5. Simplified 52.5%

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

Developer Target 1: 98.4% 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 2024152 
(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)))))