Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B

Percentage Accurate: 99.9% → 99.9%

Time: 11.9s

Alternatives: 14

Speedup: 1.0×

• 26.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

Alternative 2: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.5}{\frac{t}{y - z}}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-34}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 0.5 (/ t (- y z)))))
   (if (<= z -3.5e+38) t_1 (if (<= z 3.9e-34) (* (+ x y) (/ 0.5 t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.5 / (t / (y - z));
	double tmp;
	if (z <= -3.5e+38) {
		tmp = t_1;
	} else if (z <= 3.9e-34) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 / (t / (y - z))
    if (z <= (-3.5d+38)) then
        tmp = t_1
    else if (z <= 3.9d-34) then
        tmp = (x + y) * (0.5d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.5 / (t / (y - z));
	double tmp;
	if (z <= -3.5e+38) {
		tmp = t_1;
	} else if (z <= 3.9e-34) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.5 / (t / (y - z))
	tmp = 0
	if z <= -3.5e+38:
		tmp = t_1
	elif z <= 3.9e-34:
		tmp = (x + y) * (0.5 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.5 / Float64(t / Float64(y - z)))
	tmp = 0.0
	if (z <= -3.5e+38)
		tmp = t_1;
	elseif (z <= 3.9e-34)
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.5 / (t / (y - z));
	tmp = 0.0;
	if (z <= -3.5e+38)
		tmp = t_1;
	elseif (z <= 3.9e-34)
		tmp = (x + y) * (0.5 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.5 / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+38], t$95$1, If[LessEqual[z, 3.9e-34], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000002e38 or 3.89999999999999991e-34 < z

   1. Initial program 100.0%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{t \cdot 2}{\left(x + y\right) - z}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{1}{\frac{2 \cdot t}{\color{blue}{\left(x + y\right)} - z}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{1}{2 \cdot \color{blue}{\frac{t}{\left(x + y\right) - z}}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{t}{\left(x + y\right) - z}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{t}{\left(x + y\right) - z}\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\color{blue}{t}}{\left(x + y\right) - z}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\left(x + y\right) - z\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\left(x + y\right), \color{blue}{z}\right)\right)\right) \]

      9. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right)\right)\right) \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{t}{\left(x + y\right) - z}}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{t}{y - z}\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(y - z\right)}\right)\right) \]

      2. --lowering--.f64 85.6%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 85.6%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{t}{y - z}}} \]

   if -3.50000000000000002e38 < z < 3.89999999999999991e-34

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(x + y\right)}{\color{blue}{t}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\frac{1}{2}}{t} \cdot \color{blue}{\left(x + y\right)} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\frac{1}{2} \cdot 1}{t} \cdot \left(x + y\right) \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{1}{t}\right) \cdot \left(\color{blue}{x} + y\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{t}\right), \color{blue}{\left(x + y\right)}\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2} \cdot 1}{t}\right), \left(\color{blue}{x} + y\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{t}\right), \left(x + y\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \left(\color{blue}{x} + y\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \left(y + \color{blue}{x}\right)\right) \]

      10. +-lowering-+.f64 92.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 92.3%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-34}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+164}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z -0.5) t)))
   (if (<= z -3.5e+97) t_1 (if (<= z 1.45e+164) (* (+ x y) (/ 0.5 t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (z <= -3.5e+97) {
		tmp = t_1;
	} else if (z <= 1.45e+164) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * (-0.5d0)) / t
    if (z <= (-3.5d+97)) then
        tmp = t_1
    else if (z <= 1.45d+164) then
        tmp = (x + y) * (0.5d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (z <= -3.5e+97) {
		tmp = t_1;
	} else if (z <= 1.45e+164) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * -0.5) / t
	tmp = 0
	if z <= -3.5e+97:
		tmp = t_1
	elif z <= 1.45e+164:
		tmp = (x + y) * (0.5 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * -0.5) / t)
	tmp = 0.0
	if (z <= -3.5e+97)
		tmp = t_1;
	elseif (z <= 1.45e+164)
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * -0.5) / t;
	tmp = 0.0;
	if (z <= -3.5e+97)
		tmp = t_1;
	elseif (z <= 1.45e+164)
		tmp = (x + y) * (0.5 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -3.5e+97], t$95$1, If[LessEqual[z, 1.45e+164], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000001e97 or 1.4499999999999999e164 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{2} \cdot z}{\color{blue}{t}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot -1\right) \cdot z}{t} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(-1 \cdot z\right)}{t} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)}{t} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)\right), \color{blue}{t}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(-1 \cdot z\right)\right), t\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{1}{2} \cdot -1\right) \cdot z\right), t\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot z\right), t\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \frac{-1}{2}\right), t\right) \]

      10. *-lowering-*.f64 78.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), t\right) \]

   5. Simplified 78.0%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

   if -3.5000000000000001e97 < z < 1.4499999999999999e164

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(x + y\right)}{\color{blue}{t}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\frac{1}{2}}{t} \cdot \color{blue}{\left(x + y\right)} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\frac{1}{2} \cdot 1}{t} \cdot \left(x + y\right) \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{1}{t}\right) \cdot \left(\color{blue}{x} + y\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{t}\right), \color{blue}{\left(x + y\right)}\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2} \cdot 1}{t}\right), \left(\color{blue}{x} + y\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{t}\right), \left(x + y\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \left(\color{blue}{x} + y\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \left(y + \color{blue}{x}\right)\right) \]

      10. +-lowering-+.f64 81.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 81.9%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+164}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-263}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+60}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e-263)
   (/ (* x 0.5) t)
   (if (<= y 1.8e+60) (/ (* z -0.5) t) (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-263) {
		tmp = (x * 0.5) / t;
	} else if (y <= 1.8e+60) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.5d-263)) then
        tmp = (x * 0.5d0) / t
    else if (y <= 1.8d+60) then
        tmp = (z * (-0.5d0)) / t
    else
        tmp = (y * 0.5d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-263) {
		tmp = (x * 0.5) / t;
	} else if (y <= 1.8e+60) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e-263:
		tmp = (x * 0.5) / t
	elif y <= 1.8e+60:
		tmp = (z * -0.5) / t
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e-263)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (y <= 1.8e+60)
		tmp = Float64(Float64(z * -0.5) / t);
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.5e-263)
		tmp = (x * 0.5) / t;
	elseif (y <= 1.8e+60)
		tmp = (z * -0.5) / t;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e-263], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 1.8e+60], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000044e-263

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x}{t} \cdot \color{blue}{\frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{x \cdot \frac{1}{2}}{\color{blue}{t}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 38.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 38.8%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]

   if -7.50000000000000044e-263 < y < 1.79999999999999984e60

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{2} \cdot z}{\color{blue}{t}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot -1\right) \cdot z}{t} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(-1 \cdot z\right)}{t} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)}{t} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)\right), \color{blue}{t}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(-1 \cdot z\right)\right), t\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{1}{2} \cdot -1\right) \cdot z\right), t\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot z\right), t\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \frac{-1}{2}\right), t\right) \]

      10. *-lowering-*.f64 57.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), t\right) \]

   5. Simplified 57.3%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

   if 1.79999999999999984e60 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{y}{t} \cdot \color{blue}{\frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{y \cdot \frac{1}{2}}{\color{blue}{t}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot y\right), t\right) \]

      5. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, y\right), t\right) \]

   5. Simplified 74.8%

      \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-263}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+60}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-264}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e-264)
   (/ (* x 0.5) t)
   (if (<= y 1.35e+60) (* z (/ -0.5 t)) (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-264) {
		tmp = (x * 0.5) / t;
	} else if (y <= 1.35e+60) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3d-264)) then
        tmp = (x * 0.5d0) / t
    else if (y <= 1.35d+60) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = (y * 0.5d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-264) {
		tmp = (x * 0.5) / t;
	} else if (y <= 1.35e+60) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e-264:
		tmp = (x * 0.5) / t
	elif y <= 1.35e+60:
		tmp = z * (-0.5 / t)
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e-264)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (y <= 1.35e+60)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3e-264)
		tmp = (x * 0.5) / t;
	elseif (y <= 1.35e+60)
		tmp = z * (-0.5 / t);
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e-264], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 1.35e+60], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e-264

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x}{t} \cdot \color{blue}{\frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{x \cdot \frac{1}{2}}{\color{blue}{t}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 38.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 38.8%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]

   if -3e-264 < y < 1.35e60

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{2} \cdot z}{\color{blue}{t}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot -1\right) \cdot z}{t} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(-1 \cdot z\right)}{t} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)}{t} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)\right), \color{blue}{t}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(-1 \cdot z\right)\right), t\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{1}{2} \cdot -1\right) \cdot z\right), t\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot z\right), t\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \frac{-1}{2}\right), t\right) \]

      10. *-lowering-*.f64 57.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), t\right) \]

   5. Simplified 57.3%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto z \cdot \color{blue}{\frac{\frac{-1}{2}}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{-1}{2}}{t} \cdot \color{blue}{z} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{2}}{t}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, t\right), z\right) \]

   7. Applied egg-rr 57.2%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

   if 1.35e60 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{y}{t} \cdot \color{blue}{\frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{y \cdot \frac{1}{2}}{\color{blue}{t}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot y\right), t\right) \]

      5. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, y\right), t\right) \]

   5. Simplified 74.8%

      \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-264}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-263}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-263)
   (/ (* x 0.5) t)
   (if (<= y 5.5e+59) (* z (/ -0.5 t)) (/ 0.5 (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-263) {
		tmp = (x * 0.5) / t;
	} else if (y <= 5.5e+59) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.6d-263)) then
        tmp = (x * 0.5d0) / t
    else if (y <= 5.5d+59) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = 0.5d0 / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-263) {
		tmp = (x * 0.5) / t;
	} else if (y <= 5.5e+59) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e-263:
		tmp = (x * 0.5) / t
	elif y <= 5.5e+59:
		tmp = z * (-0.5 / t)
	else:
		tmp = 0.5 / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-263)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (y <= 5.5e+59)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(0.5 / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.6e-263)
		tmp = (x * 0.5) / t;
	elseif (y <= 5.5e+59)
		tmp = z * (-0.5 / t);
	else
		tmp = 0.5 / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-263], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 5.5e+59], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6e-263

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x}{t} \cdot \color{blue}{\frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{x \cdot \frac{1}{2}}{\color{blue}{t}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 38.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 38.8%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]

   if -1.6e-263 < y < 5.4999999999999999e59

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{2} \cdot z}{\color{blue}{t}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot -1\right) \cdot z}{t} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(-1 \cdot z\right)}{t} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)}{t} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)\right), \color{blue}{t}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(-1 \cdot z\right)\right), t\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{1}{2} \cdot -1\right) \cdot z\right), t\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot z\right), t\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \frac{-1}{2}\right), t\right) \]

      10. *-lowering-*.f64 57.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), t\right) \]

   5. Simplified 57.3%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto z \cdot \color{blue}{\frac{\frac{-1}{2}}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{-1}{2}}{t} \cdot \color{blue}{z} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{2}}{t}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, t\right), z\right) \]

   7. Applied egg-rr 57.2%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

   if 5.4999999999999999e59 < y

   1. Initial program 100.0%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{t \cdot 2}{\left(x + y\right) - z}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{1}{\frac{2 \cdot t}{\color{blue}{\left(x + y\right)} - z}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{1}{2 \cdot \color{blue}{\frac{t}{\left(x + y\right) - z}}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{t}{\left(x + y\right) - z}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{t}{\left(x + y\right) - z}\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\color{blue}{t}}{\left(x + y\right) - z}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\left(x + y\right) - z\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\left(x + y\right), \color{blue}{z}\right)\right)\right) \]

      9. +-lowering-+.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{t}{\left(x + y\right) - z}}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{t}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 74.6%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Simplified 74.6%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{t}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-263}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e-262)
   (* x (/ 0.5 t))
   (if (<= y 4.8e+59) (* z (/ -0.5 t)) (/ 0.5 (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-262) {
		tmp = x * (0.5 / t);
	} else if (y <= 4.8e+59) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.5d-262)) then
        tmp = x * (0.5d0 / t)
    else if (y <= 4.8d+59) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = 0.5d0 / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-262) {
		tmp = x * (0.5 / t);
	} else if (y <= 4.8e+59) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e-262:
		tmp = x * (0.5 / t)
	elif y <= 4.8e+59:
		tmp = z * (-0.5 / t)
	else:
		tmp = 0.5 / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e-262)
		tmp = Float64(x * Float64(0.5 / t));
	elseif (y <= 4.8e+59)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(0.5 / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.5e-262)
		tmp = x * (0.5 / t);
	elseif (y <= 4.8e+59)
		tmp = z * (-0.5 / t);
	else
		tmp = 0.5 / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e-262], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+59], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000003e-262

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x}{t} \cdot \color{blue}{\frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{x \cdot \frac{1}{2}}{\color{blue}{t}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 38.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 38.8%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot \frac{1}{2}}{t} \]

      2. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{2}}{t}} \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{\frac{1}{2}}{t}\right)}\right) \]

      4. /-lowering-/.f64 38.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right) \]

   7. Applied egg-rr 38.7%

      \[\leadsto \color{blue}{x \cdot \frac{0.5}{t}} \]

   if -6.5000000000000003e-262 < y < 4.8000000000000004e59

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{2} \cdot z}{\color{blue}{t}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot -1\right) \cdot z}{t} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(-1 \cdot z\right)}{t} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)}{t} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)\right), \color{blue}{t}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(-1 \cdot z\right)\right), t\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{1}{2} \cdot -1\right) \cdot z\right), t\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot z\right), t\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \frac{-1}{2}\right), t\right) \]

      10. *-lowering-*.f64 57.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), t\right) \]

   5. Simplified 57.3%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto z \cdot \color{blue}{\frac{\frac{-1}{2}}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{-1}{2}}{t} \cdot \color{blue}{z} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{2}}{t}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, t\right), z\right) \]

   7. Applied egg-rr 57.2%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

   if 4.8000000000000004e59 < y

   1. Initial program 100.0%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{t \cdot 2}{\left(x + y\right) - z}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{1}{\frac{2 \cdot t}{\color{blue}{\left(x + y\right)} - z}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{1}{2 \cdot \color{blue}{\frac{t}{\left(x + y\right) - z}}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{t}{\left(x + y\right) - z}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{t}{\left(x + y\right) - z}\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\color{blue}{t}}{\left(x + y\right) - z}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\left(x + y\right) - z\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\left(x + y\right), \color{blue}{z}\right)\right)\right) \]

      9. +-lowering-+.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{t}{\left(x + y\right) - z}}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{t}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 74.6%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Simplified 74.6%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{t}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-0.5}{\frac{t}{z}}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ -0.5 (/ t z))))
   (if (<= z -6.2e+24) t_1 (if (<= z 2.35e-42) (* x (/ 0.5 t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 / (t / z);
	double tmp;
	if (z <= -6.2e+24) {
		tmp = t_1;
	} else if (z <= 2.35e-42) {
		tmp = x * (0.5 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-0.5d0) / (t / z)
    if (z <= (-6.2d+24)) then
        tmp = t_1
    else if (z <= 2.35d-42) then
        tmp = x * (0.5d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.5 / (t / z);
	double tmp;
	if (z <= -6.2e+24) {
		tmp = t_1;
	} else if (z <= 2.35e-42) {
		tmp = x * (0.5 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 / (t / z)
	tmp = 0
	if z <= -6.2e+24:
		tmp = t_1
	elif z <= 2.35e-42:
		tmp = x * (0.5 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.5 / Float64(t / z))
	tmp = 0.0
	if (z <= -6.2e+24)
		tmp = t_1;
	elseif (z <= 2.35e-42)
		tmp = Float64(x * Float64(0.5 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 / (t / z);
	tmp = 0.0;
	if (z <= -6.2e+24)
		tmp = t_1;
	elseif (z <= 2.35e-42)
		tmp = x * (0.5 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.5 / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+24], t$95$1, If[LessEqual[z, 2.35e-42], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000022e24 or 2.35e-42 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{2} \cdot z}{\color{blue}{t}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot -1\right) \cdot z}{t} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(-1 \cdot z\right)}{t} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)}{t} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)\right), \color{blue}{t}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(-1 \cdot z\right)\right), t\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{1}{2} \cdot -1\right) \cdot z\right), t\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot z\right), t\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \frac{-1}{2}\right), t\right) \]

      10. *-lowering-*.f64 61.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), t\right) \]

   5. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto z \cdot \color{blue}{\frac{\frac{-1}{2}}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{-1}{2}}{t} \cdot \color{blue}{z} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{2}}{t}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 61.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, t\right), z\right) \]

   7. Applied egg-rr 61.1%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]
   8. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \frac{\frac{-1}{2} \cdot z}{\color{blue}{t}} \]

      2. associate-/l* N/A

         \[\leadsto \frac{-1}{2} \cdot \color{blue}{\frac{z}{t}} \]

      3. clear-num N/A

         \[\leadsto \frac{-1}{2} \cdot \frac{1}{\color{blue}{\frac{t}{z}}} \]

      4. un-div-inv N/A

         \[\leadsto \frac{\frac{-1}{2}}{\color{blue}{\frac{t}{z}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\frac{-1}{2}, \color{blue}{\left(\frac{t}{z}\right)}\right) \]

      6. /-lowering-/.f64 61.2%

         \[\leadsto \mathsf{/.f64}\left(\frac{-1}{2}, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 61.2%

      \[\leadsto \color{blue}{\frac{-0.5}{\frac{t}{z}}} \]

   if -6.20000000000000022e24 < z < 2.35e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x}{t} \cdot \color{blue}{\frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{x \cdot \frac{1}{2}}{\color{blue}{t}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 53.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot \frac{1}{2}}{t} \]

      2. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{2}}{t}} \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{\frac{1}{2}}{t}\right)}\right) \]

      4. /-lowering-/.f64 53.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right) \]

   7. Applied egg-rr 53.4%

      \[\leadsto \color{blue}{x \cdot \frac{0.5}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 55.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-0.5}{t}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ -0.5 t))))
   (if (<= z -5.5e+24) t_1 (if (<= z 1.35e-40) (* x (/ 0.5 t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (-0.5 / t);
	double tmp;
	if (z <= -5.5e+24) {
		tmp = t_1;
	} else if (z <= 1.35e-40) {
		tmp = x * (0.5 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((-0.5d0) / t)
    if (z <= (-5.5d+24)) then
        tmp = t_1
    else if (z <= 1.35d-40) then
        tmp = x * (0.5d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (-0.5 / t);
	double tmp;
	if (z <= -5.5e+24) {
		tmp = t_1;
	} else if (z <= 1.35e-40) {
		tmp = x * (0.5 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (-0.5 / t)
	tmp = 0
	if z <= -5.5e+24:
		tmp = t_1
	elif z <= 1.35e-40:
		tmp = x * (0.5 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-0.5 / t))
	tmp = 0.0
	if (z <= -5.5e+24)
		tmp = t_1;
	elseif (z <= 1.35e-40)
		tmp = Float64(x * Float64(0.5 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (-0.5 / t);
	tmp = 0.0;
	if (z <= -5.5e+24)
		tmp = t_1;
	elseif (z <= 1.35e-40)
		tmp = x * (0.5 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+24], t$95$1, If[LessEqual[z, 1.35e-40], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000002e24 or 1.35e-40 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{-1}{2} \cdot z}{\color{blue}{t}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot -1\right) \cdot z}{t} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(-1 \cdot z\right)}{t} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)}{t} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)\right), \color{blue}{t}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(-1 \cdot z\right)\right), t\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{1}{2} \cdot -1\right) \cdot z\right), t\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot z\right), t\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \frac{-1}{2}\right), t\right) \]

      10. *-lowering-*.f64 61.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), t\right) \]

   5. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto z \cdot \color{blue}{\frac{\frac{-1}{2}}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{-1}{2}}{t} \cdot \color{blue}{z} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{2}}{t}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 61.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{2}, t\right), z\right) \]

   7. Applied egg-rr 61.1%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

   if -5.5000000000000002e24 < z < 1.35e-40

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x}{t} \cdot \color{blue}{\frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{x \cdot \frac{1}{2}}{\color{blue}{t}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 53.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot \frac{1}{2}}{t} \]

      2. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{2}}{t}} \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{\frac{1}{2}}{t}\right)}\right) \]

      4. /-lowering-/.f64 53.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right) \]

   7. Applied egg-rr 53.4%

      \[\leadsto \color{blue}{x \cdot \frac{0.5}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-21}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.3e-21) (/ (- x z) (* t 2.0)) (/ (- y z) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3e-21) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.3d-21)) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (y - z) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3e-21) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.3e-21:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y - z) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.3e-21)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.3e-21)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y - z) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.3e-21], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.30000000000000009e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x - z\right)}, \mathsf{*.f64}\left(t, 2\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 80.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(\color{blue}{t}, 2\right)\right) \]

   5. Simplified 80.6%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if -3.30000000000000009e-21 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(y - z\right)}, \mathsf{*.f64}\left(t, 2\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{*.f64}\left(\color{blue}{t}, 2\right)\right) \]

   5. Simplified 80.4%

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

Alternative 11: 77.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.4e-18) (/ (- x z) (* t 2.0)) (* (- y z) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e-18) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.4d-18)) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (y - z) * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e-18) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.4e-18:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.4e-18)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.4e-18)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.4e-18], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.40000000000000006e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x - z\right)}, \mathsf{*.f64}\left(t, 2\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 80.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(\color{blue}{t}, 2\right)\right) \]

   5. Simplified 80.6%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if -1.40000000000000006e-18 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(y - z\right)}, \mathsf{*.f64}\left(t, 2\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{*.f64}\left(\color{blue}{t}, 2\right)\right) \]

   5. Simplified 80.4%

      \[\leadsto \frac{\color{blue}{y - z}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \left(y - z\right) \cdot \color{blue}{\frac{1}{t \cdot 2}} \]

      2. metadata-eval N/A

         \[\leadsto \left(y - z\right) \cdot \frac{1}{t \cdot \frac{1}{\color{blue}{\frac{1}{2}}}} \]

      3. div-inv N/A

         \[\leadsto \left(y - z\right) \cdot \frac{1}{\frac{t}{\color{blue}{\frac{1}{2}}}} \]

      4. clear-num N/A

         \[\leadsto \left(y - z\right) \cdot \frac{\frac{1}{2}}{\color{blue}{t}} \]

      5. *-commutative N/A

         \[\leadsto \frac{\frac{1}{2}}{t} \cdot \color{blue}{\left(y - z\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{t}\right), \color{blue}{\left(y - z\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \left(\color{blue}{y} - z\right)\right) \]

      8. --lowering--.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 80.1%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+111}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.5e+111) (* (+ x y) (/ 0.5 t)) (* (- y z) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e+111) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-8.5d+111)) then
        tmp = (x + y) * (0.5d0 / t)
    else
        tmp = (y - z) * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e+111) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.5e+111:
		tmp = (x + y) * (0.5 / t)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.5e+111)
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	else
		tmp = Float64(Float64(y - z) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.5e+111)
		tmp = (x + y) * (0.5 / t);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.5e+111], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999983e111

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(x + y\right)}{\color{blue}{t}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\frac{1}{2}}{t} \cdot \color{blue}{\left(x + y\right)} \]

      3. metadata-eval N/A

         \[\leadsto \frac{\frac{1}{2} \cdot 1}{t} \cdot \left(x + y\right) \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{1}{t}\right) \cdot \left(\color{blue}{x} + y\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{t}\right), \color{blue}{\left(x + y\right)}\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2} \cdot 1}{t}\right), \left(\color{blue}{x} + y\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{t}\right), \left(x + y\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \left(\color{blue}{x} + y\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \left(y + \color{blue}{x}\right)\right) \]

      10. +-lowering-+.f64 82.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y + x\right)} \]

   if -8.49999999999999983e111 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(y - z\right)}, \mathsf{*.f64}\left(t, 2\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 78.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{*.f64}\left(\color{blue}{t}, 2\right)\right) \]

   5. Simplified 78.9%

      \[\leadsto \frac{\color{blue}{y - z}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \left(y - z\right) \cdot \color{blue}{\frac{1}{t \cdot 2}} \]

      2. metadata-eval N/A

         \[\leadsto \left(y - z\right) \cdot \frac{1}{t \cdot \frac{1}{\color{blue}{\frac{1}{2}}}} \]

      3. div-inv N/A

         \[\leadsto \left(y - z\right) \cdot \frac{1}{\frac{t}{\color{blue}{\frac{1}{2}}}} \]

      4. clear-num N/A

         \[\leadsto \left(y - z\right) \cdot \frac{\frac{1}{2}}{\color{blue}{t}} \]

      5. *-commutative N/A

         \[\leadsto \frac{\frac{1}{2}}{t} \cdot \color{blue}{\left(y - z\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{t}\right), \color{blue}{\left(y - z\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \left(\color{blue}{y} - z\right)\right) \]

      8. --lowering--.f64 78.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 78.7%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+111}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{0.5}{\frac{t}{\left(x + y\right) - z}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ 0.5 (/ t (- (+ x y) z))))

C

double code(double x, double y, double z, double t) {
	return 0.5 / (t / ((x + y) - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 0.5d0 / (t / ((x + y) - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.5 / (t / ((x + y) - z));
}

Python

def code(x, y, z, t):
	return 0.5 / (t / ((x + y) - z))

Julia

function code(x, y, z, t)
	return Float64(0.5 / Float64(t / Float64(Float64(x + y) - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.5 / (t / ((x + y) - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(0.5 / N[(t / N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{t \cdot 2}{\left(x + y\right) - z}}} \]

   2. *-commutative N/A

      \[\leadsto \frac{1}{\frac{2 \cdot t}{\color{blue}{\left(x + y\right)} - z}} \]

   3. associate-/l* N/A

      \[\leadsto \frac{1}{2 \cdot \color{blue}{\frac{t}{\left(x + y\right) - z}}} \]

   4. associate-/r* N/A

      \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{t}{\left(x + y\right) - z}}} \]

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

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{t}{\left(x + y\right) - z}\right)}\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\color{blue}{t}}{\left(x + y\right) - z}\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\left(x + y\right) - z\right)}\right)\right) \]

   8. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\left(x + y\right), \color{blue}{z}\right)\right)\right) \]

   9. +-lowering-+.f64 99.4%

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right)\right)\right) \]

4. Applied egg-rr 99.4%

   \[\leadsto \color{blue}{\frac{0.5}{\frac{t}{\left(x + y\right) - z}}} \]
5. Add Preprocessing

Alternative 14: 37.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{0.5}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (/ 0.5 t)))

C

double code(double x, double y, double z, double t) {
	return x * (0.5 / t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * (0.5d0 / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (0.5 / t);
}

Python

def code(x, y, z, t):
	return x * (0.5 / t)

Julia

function code(x, y, z, t)
	return Float64(x * Float64(0.5 / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (0.5 / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{x}{t} \cdot \color{blue}{\frac{1}{2}} \]

   2. associate-*l/ N/A

      \[\leadsto \frac{x \cdot \frac{1}{2}}{\color{blue}{t}} \]

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

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

   5. *-lowering-*.f64 35.1%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

5. Simplified 35.1%

   \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{x \cdot \frac{1}{2}}{t} \]

   2. associate-/l* N/A

      \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{2}}{t}} \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{\frac{1}{2}}{t}\right)}\right) \]

   4. /-lowering-/.f64 35.0%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{t}\right)\right) \]

7. Applied egg-rr 35.0%

   \[\leadsto \color{blue}{x \cdot \frac{0.5}{t}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024158 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))