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

Percentage Accurate: 99.9% → 99.9%

Time: 8.5s

Alternatives: 11

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: 46.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-296}:\\ \;\;\;\;\frac{\frac{x}{t}}{2}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.2e-296)
   (/ (/ x t) 2.0)
   (if (<= y 8.4e+70) (/ (* z -0.5) t) (/ (/ y t) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.2e-296) {
		tmp = (x / t) / 2.0;
	} else if (y <= 8.4e+70) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (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 <= (-7.2d-296)) then
        tmp = (x / t) / 2.0d0
    else if (y <= 8.4d+70) then
        tmp = (z * (-0.5d0)) / t
    else
        tmp = (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 <= -7.2e-296) {
		tmp = (x / t) / 2.0;
	} else if (y <= 8.4e+70) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (y / t) / 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.2e-296:
		tmp = (x / t) / 2.0
	elif y <= 8.4e+70:
		tmp = (z * -0.5) / t
	else:
		tmp = (y / t) / 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.2e-296)
		tmp = Float64(Float64(x / t) / 2.0);
	elseif (y <= 8.4e+70)
		tmp = Float64(Float64(z * -0.5) / t);
	else
		tmp = Float64(Float64(y / t) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.2e-296)
		tmp = (x / t) / 2.0;
	elseif (y <= 8.4e+70)
		tmp = (z * -0.5) / t;
	else
		tmp = (y / t) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.2e-296], N[(N[(x / t), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[y, 8.4e+70], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(N[(y / t), $MachinePrecision] / 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.19999999999999961e-296

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 35.8%

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

   7. Simplified 35.8%

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

   if -7.19999999999999961e-296 < y < 8.4000000000000003e70

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   6. 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 51.4%

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

   7. Simplified 51.4%

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

   if 8.4000000000000003e70 < y

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 77.3%

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

   7. Simplified 77.3%

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

Alternative 3: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-296}:\\ \;\;\;\;\frac{\frac{x}{t}}{2}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+69}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6e-296)
   (/ (/ x t) 2.0)
   (if (<= y 6.9e+69) (/ (* z -0.5) t) (* y (/ 0.5 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e-296) {
		tmp = (x / t) / 2.0;
	} else if (y <= 6.9e+69) {
		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 <= (-6d-296)) then
        tmp = (x / t) / 2.0d0
    else if (y <= 6.9d+69) 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 <= -6e-296) {
		tmp = (x / t) / 2.0;
	} else if (y <= 6.9e+69) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6e-296:
		tmp = (x / t) / 2.0
	elif y <= 6.9e+69:
		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 <= -6e-296)
		tmp = Float64(Float64(x / t) / 2.0);
	elseif (y <= 6.9e+69)
		tmp = Float64(Float64(z * -0.5) / t);
	else
		tmp = Float64(y * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6e-296)
		tmp = (x / t) / 2.0;
	elseif (y <= 6.9e+69)
		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, -6e-296], N[(N[(x / t), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[y, 6.9e+69], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9999999999999995e-296

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 35.8%

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

   7. Simplified 35.8%

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

   if -5.9999999999999995e-296 < y < 6.9000000000000001e69

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   6. 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 51.4%

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

   7. Simplified 51.4%

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

   if 6.9000000000000001e69 < y

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-/l/ N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

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

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

      5. associate-/r* N/A

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

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

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

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

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

      10. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \color{blue}{\left(z - y\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(z + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{z}\right)\right)\right)\right) \]

      13. associate--r+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf

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

   9. Simplified 77.1%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-296}:\\ \;\;\;\;\frac{\frac{x}{t}}{2}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+69}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+74}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8e-297)
   (* x (/ 0.5 t))
   (if (<= y 1.06e+74) (/ (* z -0.5) t) (* y (/ 0.5 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e-297) {
		tmp = x * (0.5 / t);
	} else if (y <= 1.06e+74) {
		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 <= (-3.8d-297)) then
        tmp = x * (0.5d0 / t)
    else if (y <= 1.06d+74) 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 <= -3.8e-297) {
		tmp = x * (0.5 / t);
	} else if (y <= 1.06e+74) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.8e-297:
		tmp = x * (0.5 / t)
	elif y <= 1.06e+74:
		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 <= -3.8e-297)
		tmp = Float64(x * Float64(0.5 / t));
	elseif (y <= 1.06e+74)
		tmp = Float64(Float64(z * -0.5) / t);
	else
		tmp = Float64(y * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.8e-297)
		tmp = x * (0.5 / t);
	elseif (y <= 1.06e+74)
		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, -3.8e-297], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+74], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.80000000000000005e-297

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 35.7%

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

   7. Simplified 35.7%

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

   if -3.80000000000000005e-297 < y < 1.05999999999999999e74

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   6. 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 51.4%

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

   7. Simplified 51.4%

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

   if 1.05999999999999999e74 < y

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-/l/ N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

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

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

      5. associate-/r* N/A

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

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

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

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

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

      10. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \color{blue}{\left(z - y\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(z + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{z}\right)\right)\right)\right) \]

      13. associate--r+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf

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

   9. Simplified 77.1%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+74}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{x - z}{t}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y - z}{t}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.2e-58) (/ (/ (- x z) t) 2.0) (/ (/ (- y z) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.2e-58) {
		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 (y <= 7.2d-58) 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 (y <= 7.2e-58) {
		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 y <= 7.2e-58:
		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 (y <= 7.2e-58)
		tmp = Float64(Float64(Float64(x - z) / t) / 2.0);
	else
		tmp = Float64(Float64(Float64(y - z) / t) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 7.2e-58)
		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[y, 7.2e-58], N[(N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.20000000000000019e-58

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

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

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

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

      2. --lowering--.f64 76.3%

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

   7. Simplified 76.3%

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

   if 7.20000000000000019e-58 < y

   1. Initial program 99.9%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

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

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

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

      2. --lowering--.f64 82.3%

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

   7. Simplified 82.3%

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

Alternative 6: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{\frac{x - z}{t}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 4.8e-51) (/ (/ (- x z) t) 2.0) (* (/ 0.5 t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.8e-51) {
		tmp = ((x - z) / 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 (y <= 4.8d-51) then
        tmp = ((x - z) / 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 (y <= 4.8e-51) {
		tmp = ((x - z) / t) / 2.0;
	} else {
		tmp = (0.5 / t) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 4.8e-51:
		tmp = ((x - z) / t) / 2.0
	else:
		tmp = (0.5 / t) * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4.8e-51)
		tmp = Float64(Float64(Float64(x - z) / t) / 2.0);
	else
		tmp = Float64(Float64(0.5 / t) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 4.8e-51)
		tmp = ((x - z) / t) / 2.0;
	else
		tmp = (0.5 / t) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 4.8e-51], N[(N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.8e-51

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

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

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

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

      2. --lowering--.f64 76.8%

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

   7. Simplified 76.8%

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

   if 4.8e-51 < y

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

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

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

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

      2. --lowering--.f64 85.5%

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

   7. Simplified 85.5%

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

      1. div-inv N/A

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

      2. metadata-eval N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      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 85.3%

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

   9. Applied egg-rr 85.3%

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

Alternative 7: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{-51}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 4.6e-51) (* (/ 0.5 t) (- x z)) (* (/ 0.5 t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.6e-51) {
		tmp = (0.5 / t) * (x - z);
	} 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 (y <= 4.6d-51) then
        tmp = (0.5d0 / t) * (x - z)
    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 (y <= 4.6e-51) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (0.5 / t) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 4.6e-51:
		tmp = (0.5 / t) * (x - z)
	else:
		tmp = (0.5 / t) * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4.6e-51)
		tmp = Float64(Float64(0.5 / t) * Float64(x - z));
	else
		tmp = Float64(Float64(0.5 / t) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 4.6e-51)
		tmp = (0.5 / t) * (x - z);
	else
		tmp = (0.5 / t) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 4.6e-51], N[(N[(0.5 / t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.60000000000000004e-51

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-/l/ N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

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

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

      5. associate-/r* N/A

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

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

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

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

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

      10. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \color{blue}{\left(z - y\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(z + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{z}\right)\right)\right)\right) \]

      13. associate--r+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. --lowering--.f64 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0

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

      1. --lowering--.f64 76.6%

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

   9. Simplified 76.6%

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

   if 4.60000000000000004e-51 < y

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

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

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

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

      2. --lowering--.f64 85.5%

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

   7. Simplified 85.5%

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

      1. div-inv N/A

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

      2. metadata-eval N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      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 85.3%

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

   9. Applied egg-rr 85.3%

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

Alternative 8: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+120}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.9e+120) (* (/ 0.5 t) (- x z)) (/ (/ y t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.9e+120) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (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 <= 1.9d+120) then
        tmp = (0.5d0 / t) * (x - z)
    else
        tmp = (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 <= 1.9e+120) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (y / t) / 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.9e+120:
		tmp = (0.5 / t) * (x - z)
	else:
		tmp = (y / t) / 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.9e+120)
		tmp = Float64(Float64(0.5 / t) * Float64(x - z));
	else
		tmp = Float64(Float64(y / t) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.9e+120)
		tmp = (0.5 / t) * (x - z);
	else
		tmp = (y / t) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.9e+120], N[(N[(0.5 / t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.8999999999999999e120

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-/l/ N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

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

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

      5. associate-/r* N/A

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

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

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

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

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

      10. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \color{blue}{\left(z - y\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(z + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{z}\right)\right)\right)\right) \]

      13. associate--r+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. --lowering--.f64 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0

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

      1. --lowering--.f64 76.4%

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

   9. Simplified 76.4%

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

   if 1.8999999999999999e120 < y

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 83.0%

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

   7. Simplified 83.0%

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

Alternative 9: 45.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.2e-58) (* x (/ 0.5 t)) (* y (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.2e-58) {
		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 (y <= 7.2d-58) 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 (y <= 7.2e-58) {
		tmp = x * (0.5 / t);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 7.2e-58:
		tmp = x * (0.5 / t)
	else:
		tmp = y * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.2e-58)
		tmp = Float64(x * Float64(0.5 / t));
	else
		tmp = Float64(y * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 7.2e-58)
		tmp = x * (0.5 / t);
	else
		tmp = y * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.2e-58], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.20000000000000019e-58

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 41.1%

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

   7. Simplified 41.1%

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

   if 7.20000000000000019e-58 < y

   1. Initial program 99.9%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. +-commutative N/A

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

      7. associate-+l- N/A

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

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

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

      9. --lowering--.f64 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-/l/ N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

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

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

      5. associate-/r* N/A

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

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

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

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

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

      10. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \color{blue}{\left(z - y\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(z + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{z}\right)\right)\right)\right) \]

      13. associate--r+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf

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

   9. Simplified 60.1%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.7% accurate, 1.0× speedup

Math

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

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(Float64(0.5 / 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[(N[(0.5 / t), $MachinePrecision] * N[(x + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. associate-/r* N/A

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

   2. /-lowering-/.f64 N/A

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

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

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

   4. +-commutative N/A

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

   5. associate--l+ N/A

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

   6. +-commutative N/A

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

   7. associate-+l- N/A

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

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

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

   9. --lowering--.f64 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-/l/ N/A

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

   2. clear-num N/A

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

   3. associate-/r/ N/A

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

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

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

   5. associate-/r* N/A

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

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

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

   7. metadata-eval N/A

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

   8. sub-neg N/A

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

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

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

   10. neg-sub0 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \color{blue}{\left(z - y\right)}\right)\right)\right) \]

   11. sub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(z + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right)\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(0 - \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{z}\right)\right)\right)\right) \]

   13. associate--r+ N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), \mathsf{+.f64}\left(x, \left(\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

   14. neg-sub0 N/A

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

   15. remove-double-neg N/A

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

   16. --lowering--.f64 99.7%

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

6. Applied egg-rr 99.7%

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

Alternative 11: 37.2% 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. Step-by-step derivation

   1. associate-/r* N/A

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

   2. /-lowering-/.f64 N/A

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

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

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

   4. +-commutative N/A

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

   5. associate--l+ N/A

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

   6. +-commutative N/A

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

   7. associate-+l- N/A

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

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

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

   9. --lowering--.f64 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{\frac{x - \left(z - y\right)}{t}}{2}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

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

   1. *-lft-identity N/A

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

   2. associate-*l/ N/A

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

   3. associate-*l* N/A

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

   4. *-commutative N/A

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

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

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

   6. associate-*r/ N/A

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

   7. metadata-eval N/A

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

   8. /-lowering-/.f64 36.8%

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

7. Simplified 36.8%

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

Reproduce

herbie shell --seed 2024152 
(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)))