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

Percentage Accurate: 99.9% → 99.9%

Time: 7.7s

Alternatives: 9

Speedup: 1.0×

• 25.8% 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: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+144}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.5e-51)
   (/ (- x z) (* t 2.0))
   (if (<= y 1.9e+144) (/ (- y z) (* t 2.0)) (/ (+ x y) (* t 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.5e-51) {
		tmp = (x - z) / (t * 2.0);
	} else if (y <= 1.9e+144) {
		tmp = (y - z) / (t * 2.0);
	} else {
		tmp = (x + y) / (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 (y <= 7.5d-51) then
        tmp = (x - z) / (t * 2.0d0)
    else if (y <= 1.9d+144) then
        tmp = (y - z) / (t * 2.0d0)
    else
        tmp = (x + y) / (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 (y <= 7.5e-51) {
		tmp = (x - z) / (t * 2.0);
	} else if (y <= 1.9e+144) {
		tmp = (y - z) / (t * 2.0);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 7.5e-51:
		tmp = (x - z) / (t * 2.0)
	elif y <= 1.9e+144:
		tmp = (y - z) / (t * 2.0)
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.5e-51)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	elseif (y <= 1.9e+144)
		tmp = Float64(Float64(y - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 7.5e-51)
		tmp = (x - z) / (t * 2.0);
	elseif (y <= 1.9e+144)
		tmp = (y - z) / (t * 2.0);
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.5e-51], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+144], N[(N[(y - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.49999999999999976e-51

   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 75.3%

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

   5. Simplified 75.3%

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

   if 7.49999999999999976e-51 < y < 1.90000000000000013e144

   1. Initial program 99.9%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   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 75.2%

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

   5. Simplified 75.2%

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

   if 1.90000000000000013e144 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 97.3%

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

   5. Simplified 97.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+144}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+143}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7e-51)
   (/ (- x z) (* t 2.0))
   (if (<= y 3.8e+143) (/ 0.5 (/ t (- y z))) (/ (+ x y) (* t 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7e-51) {
		tmp = (x - z) / (t * 2.0);
	} else if (y <= 3.8e+143) {
		tmp = 0.5 / (t / (y - z));
	} else {
		tmp = (x + y) / (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 (y <= 7d-51) then
        tmp = (x - z) / (t * 2.0d0)
    else if (y <= 3.8d+143) then
        tmp = 0.5d0 / (t / (y - z))
    else
        tmp = (x + y) / (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 (y <= 7e-51) {
		tmp = (x - z) / (t * 2.0);
	} else if (y <= 3.8e+143) {
		tmp = 0.5 / (t / (y - z));
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 7e-51:
		tmp = (x - z) / (t * 2.0)
	elif y <= 3.8e+143:
		tmp = 0.5 / (t / (y - z))
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7e-51)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	elseif (y <= 3.8e+143)
		tmp = Float64(0.5 / Float64(t / Float64(y - z)));
	else
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 7e-51)
		tmp = (x - z) / (t * 2.0);
	elseif (y <= 3.8e+143)
		tmp = 0.5 / (t / (y - z));
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7e-51], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+143], N[(0.5 / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.9999999999999995e-51

   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 75.3%

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

   5. Simplified 75.3%

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

   if 6.9999999999999995e-51 < y < 3.8e143

   1. Initial program 99.9%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   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. associate--l+ N/A

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

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

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

      10. --lowering--.f64 99.6%

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

   4. Applied egg-rr 99.6%

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

   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 75.0%

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

   7. Simplified 75.0%

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

   if 3.8e143 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 97.3%

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

   5. Simplified 97.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+143}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{-259}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+23}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1e-259)
   (/ (* x 0.5) t)
   (if (<= y 1.32e+23) (/ (* z -0.5) t) (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1e-259) {
		tmp = (x * 0.5) / t;
	} else if (y <= 1.32e+23) {
		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 <= 1d-259) then
        tmp = (x * 0.5d0) / t
    else if (y <= 1.32d+23) 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 <= 1e-259) {
		tmp = (x * 0.5) / t;
	} else if (y <= 1.32e+23) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1e-259:
		tmp = (x * 0.5) / t
	elif y <= 1.32e+23:
		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 <= 1e-259)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (y <= 1.32e+23)
		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 <= 1e-259)
		tmp = (x * 0.5) / t;
	elseif (y <= 1.32e+23)
		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, 1e-259], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 1.32e+23], 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 < 1.0000000000000001e-259

   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 40.6%

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

   5. Simplified 40.6%

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

   if 1.0000000000000001e-259 < y < 1.3199999999999999e23

   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 46.1%

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

   5. Simplified 46.1%

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

   if 1.3199999999999999e23 < y

   1. Initial program 99.9%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   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 64.3%

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

   5. Simplified 64.3%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{-259}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+23}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{-20}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.26e-20) (/ (+ x y) (* t 2.0)) (/ 0.5 (/ t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.26e-20) {
		tmp = (x + y) / (t * 2.0);
	} else {
		tmp = 0.5 / (t / (y - z));
	}
	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 <= (-1.26d-20)) then
        tmp = (x + y) / (t * 2.0d0)
    else
        tmp = 0.5d0 / (t / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.26e-20) {
		tmp = (x + y) / (t * 2.0);
	} else {
		tmp = 0.5 / (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.26e-20:
		tmp = (x + y) / (t * 2.0)
	else:
		tmp = 0.5 / (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.26e-20)
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	else
		tmp = Float64(0.5 / Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.26e-20)
		tmp = (x + y) / (t * 2.0);
	else
		tmp = 0.5 / (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.26e-20], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.26e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 81.5%

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

   5. Simplified 81.5%

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

   if -1.26e-20 < x

   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. associate--l+ N/A

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

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

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

      10. --lowering--.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   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 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{-20}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+123}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.45e+123) (/ (* x 0.5) t) (/ 0.5 (/ t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.45e+123) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = 0.5 / (t / (y - z));
	}
	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 <= (-1.45d+123)) then
        tmp = (x * 0.5d0) / t
    else
        tmp = 0.5d0 / (t / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.45e+123) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = 0.5 / (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.45e+123:
		tmp = (x * 0.5) / t
	else:
		tmp = 0.5 / (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.45e+123)
		tmp = Float64(Float64(x * 0.5) / t);
	else
		tmp = Float64(0.5 / Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.45e+123)
		tmp = (x * 0.5) / t;
	else
		tmp = 0.5 / (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.45e+123], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(0.5 / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45000000000000005e123

   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 75.4%

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

   5. Simplified 75.4%

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

   if -1.45000000000000005e123 < x

   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. associate--l+ N/A

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

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

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

      10. --lowering--.f64 99.5%

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

   4. Applied egg-rr 99.5%

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

   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 75.2%

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

   7. Simplified 75.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+123}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 46.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.5e-54) (/ (* x 0.5) t) (/ (* y 0.5) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e-54) {
		tmp = (x * 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 (x <= (-2.5d-54)) then
        tmp = (x * 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 (x <= -2.5e-54) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.5e-54:
		tmp = (x * 0.5) / t
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.5e-54)
		tmp = Float64(Float64(x * 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 (x <= -2.5e-54)
		tmp = (x * 0.5) / t;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.5e-54], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.50000000000000008e-54

   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 53.3%

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

   5. Simplified 53.3%

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

   if -2.50000000000000008e-54 < x

   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 44.2%

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

   5. Simplified 44.2%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.6% accurate, 1.0× speedup

Math

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

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(x + Float64(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[(x + N[(y - z), $MachinePrecision]), $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. associate--l+ N/A

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

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

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

   10. --lowering--.f64 99.5%

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

4. Applied egg-rr 99.5%

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

Alternative 9: 36.8% accurate, 1.8× speedup

Math

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

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(Float64(x * 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[(N[(x * 0.5), $MachinePrecision] / t), $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 37.9%

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

5. Simplified 37.9%

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

6. Final simplification 37.9%

   \[\leadsto \frac{x \cdot 0.5}{t} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024149 
(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)))