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

Percentage Accurate: 99.9% → 99.9%

Time: 6.4s

Alternatives: 10

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. Final simplification 100.0%

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

Alternative 2: 47.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.2e-230)
   (* x (/ 0.5 t))
   (if (<= y 1.65e+83) (* z (/ -0.5 t)) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.2e-230) {
		tmp = x * (0.5 / t);
	} else if (y <= 1.65e+83) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 * (y / 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 <= 3.2d-230) then
        tmp = x * (0.5d0 / t)
    else if (y <= 1.65d+83) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.2e-230) {
		tmp = x * (0.5 / t);
	} else if (y <= 1.65e+83) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 3.2e-230:
		tmp = x * (0.5 / t)
	elif y <= 1.65e+83:
		tmp = z * (-0.5 / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.2e-230)
		tmp = Float64(x * Float64(0.5 / t));
	elseif (y <= 1.65e+83)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 3.2e-230)
		tmp = x * (0.5 / t);
	elseif (y <= 1.65e+83)
		tmp = z * (-0.5 / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.2e-230], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+83], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.2e-230

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 38.2%

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

      1. *-commutative 38.2%

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

      2. associate-*l/ 38.7%

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

      3. associate-*r/ 38.6%

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

   6. Simplified 38.6%

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

   if 3.2e-230 < y < 1.64999999999999992e83

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.6%

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

      8. *-commutative 99.6%

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

      9. associate-/r* 99.6%

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

      10. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 98.3%

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

   5. Taylor expanded in y around 0 87.3%

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

      1. metadata-eval 87.3%

         \[\leadsto \color{blue}{\frac{0.5}{-1}} \cdot \frac{z}{t} + 0.5 \cdot \frac{x}{t} \]

      2. times-frac 87.3%

         \[\leadsto \color{blue}{\frac{0.5 \cdot z}{-1 \cdot t}} + 0.5 \cdot \frac{x}{t} \]

      3. metadata-eval 87.3%

         \[\leadsto \frac{\color{blue}{\left(--0.5\right)} \cdot z}{-1 \cdot t} + 0.5 \cdot \frac{x}{t} \]

      4. distribute-lft-neg-in 87.3%

         \[\leadsto \frac{\color{blue}{--0.5 \cdot z}}{-1 \cdot t} + 0.5 \cdot \frac{x}{t} \]

      5. distribute-rgt-neg-in 87.3%

         \[\leadsto \frac{\color{blue}{-0.5 \cdot \left(-z\right)}}{-1 \cdot t} + 0.5 \cdot \frac{x}{t} \]

      6. times-frac 87.3%

         \[\leadsto \color{blue}{\frac{-0.5}{-1} \cdot \frac{-z}{t}} + 0.5 \cdot \frac{x}{t} \]

      7. metadata-eval 87.3%

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

      8. distribute-neg-frac 87.3%

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

      9. distribute-lft-in 87.3%

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

      10. +-commutative 87.3%

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

      11. sub-neg 87.3%

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

      12. div-sub 89.0%

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

      13. associate-*r/ 89.0%

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

      14. associate-*l/ 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in x around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. metadata-eval 59.2%

         \[\leadsto \frac{\color{blue}{\left(0.5 \cdot -1\right)} \cdot z}{t} \]

      3. associate-*r* 59.2%

         \[\leadsto \frac{\color{blue}{0.5 \cdot \left(-1 \cdot z\right)}}{t} \]

      4. neg-mul-1 59.2%

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

      5. associate-*l/ 58.9%

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

      6. distribute-rgt-neg-out 58.9%

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

      7. *-commutative 58.9%

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

      8. distribute-rgt-neg-in 58.9%

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

      9. distribute-neg-frac 58.9%

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

      10. metadata-eval 58.9%

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

   10. Simplified 58.9%

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

   if 1.64999999999999992e83 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 68.3%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 47.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+83}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.1e-231)
   (* x (/ 0.5 t))
   (if (<= y 1.8e+83) (/ z (/ t -0.5)) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.1e-231) {
		tmp = x * (0.5 / t);
	} else if (y <= 1.8e+83) {
		tmp = z / (t / -0.5);
	} else {
		tmp = 0.5 * (y / 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 <= 1.1d-231) then
        tmp = x * (0.5d0 / t)
    else if (y <= 1.8d+83) then
        tmp = z / (t / (-0.5d0))
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.1e-231) {
		tmp = x * (0.5 / t);
	} else if (y <= 1.8e+83) {
		tmp = z / (t / -0.5);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.1e-231:
		tmp = x * (0.5 / t)
	elif y <= 1.8e+83:
		tmp = z / (t / -0.5)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.1e-231)
		tmp = Float64(x * Float64(0.5 / t));
	elseif (y <= 1.8e+83)
		tmp = Float64(z / Float64(t / -0.5));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.1e-231)
		tmp = x * (0.5 / t);
	elseif (y <= 1.8e+83)
		tmp = z / (t / -0.5);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.1e-231], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+83], N[(z / N[(t / -0.5), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.10000000000000005e-231

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 38.2%

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

      1. *-commutative 38.2%

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

      2. associate-*l/ 38.7%

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

      3. associate-*r/ 38.6%

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

   6. Simplified 38.6%

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

   if 1.10000000000000005e-231 < y < 1.7999999999999999e83

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.6%

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

      8. *-commutative 99.6%

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

      9. associate-/r* 99.6%

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

      10. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. associate-/r/ 59.2%

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

   6. Simplified 59.2%

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

   if 1.7999999999999999e83 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 68.3%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+83}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 75.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.3e+106) (* 0.5 (/ (- x z) t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.3e+106) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * (y / 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 <= 1.3d+106) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.3e+106) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.3e+106:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.3e+106)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.3e+106)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.3e+106], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.3000000000000001e106

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.7%

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

   if 1.3000000000000001e106 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 72.8%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 5: 78.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+15}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.5e+15) (* 0.5 (/ (- x z) t)) (* 0.5 (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e+15) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((y - z) / 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 <= (-4.5d+15)) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = 0.5d0 * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e+15) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.5e+15:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.5e+15)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.5e+15)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.5e+15], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e15

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.0%

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

   if -4.5e15 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+15}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 6: 78.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+15}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.65e+15) (* (/ 0.5 t) (- x z)) (* 0.5 (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e+15) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = 0.5 * ((y - z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.65d+15)) then
        tmp = (0.5d0 / t) * (x - z)
    else
        tmp = 0.5d0 * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e+15) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = 0.5 * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.65e+15:
		tmp = (0.5 / t) * (x - z)
	else:
		tmp = 0.5 * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.65e+15)
		tmp = Float64(Float64(0.5 / t) * Float64(x - z));
	else
		tmp = Float64(0.5 * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.65e+15)
		tmp = (0.5 / t) * (x - z);
	else
		tmp = 0.5 * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.65e+15], N[(N[(0.5 / t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e15

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. associate-*l/ 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 97.0%

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

   5. Taylor expanded in y around 0 76.3%

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

      1. metadata-eval 76.3%

         \[\leadsto \color{blue}{\frac{0.5}{-1}} \cdot \frac{z}{t} + 0.5 \cdot \frac{x}{t} \]

      2. times-frac 76.3%

         \[\leadsto \color{blue}{\frac{0.5 \cdot z}{-1 \cdot t}} + 0.5 \cdot \frac{x}{t} \]

      3. metadata-eval 76.3%

         \[\leadsto \frac{\color{blue}{\left(--0.5\right)} \cdot z}{-1 \cdot t} + 0.5 \cdot \frac{x}{t} \]

      4. distribute-lft-neg-in 76.3%

         \[\leadsto \frac{\color{blue}{--0.5 \cdot z}}{-1 \cdot t} + 0.5 \cdot \frac{x}{t} \]

      5. distribute-rgt-neg-in 76.3%

         \[\leadsto \frac{\color{blue}{-0.5 \cdot \left(-z\right)}}{-1 \cdot t} + 0.5 \cdot \frac{x}{t} \]

      6. times-frac 76.3%

         \[\leadsto \color{blue}{\frac{-0.5}{-1} \cdot \frac{-z}{t}} + 0.5 \cdot \frac{x}{t} \]

      7. metadata-eval 76.3%

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

      8. distribute-neg-frac 76.3%

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

      9. distribute-lft-in 76.3%

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

      10. +-commutative 76.3%

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

      11. sub-neg 76.3%

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

      12. div-sub 78.0%

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

      13. associate-*r/ 79.4%

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

      14. associate-*l/ 79.2%

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

   7. Simplified 79.2%

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

   if -1.65e15 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+15}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 7: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (z - (x + y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

   4. associate-+l- 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   5. sub0-neg 100.0%

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

   6. neg-mul-1 100.0%

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

   7. associate-*l/ 99.7%

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

   8. *-commutative 99.7%

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

   9. associate-/r* 99.7%

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

   10. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 8: 46.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{-38}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 4.2e-38) (* 0.5 (/ x t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.2e-38) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / 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 <= 4.2d-38) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.2e-38) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 4.2e-38:
		tmp = 0.5 * (x / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4.2e-38)
		tmp = Float64(0.5 * Float64(x / t));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 4.2e-38)
		tmp = 0.5 * (x / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 4.2e-38], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.20000000000000026e-38

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 39.5%

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

   if 4.20000000000000026e-38 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 56.1%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{-38}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 9: 46.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 8.2e-38) (* x (/ 0.5 t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 8.2e-38) {
		tmp = x * (0.5 / t);
	} else {
		tmp = 0.5 * (y / 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 <= 8.2d-38) then
        tmp = x * (0.5d0 / t)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 8.2e-38) {
		tmp = x * (0.5 / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 8.2e-38:
		tmp = x * (0.5 / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 8.2e-38)
		tmp = Float64(x * Float64(0.5 / t));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 8.2e-38)
		tmp = x * (0.5 / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 8.2e-38], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.1999999999999996e-38

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 39.5%

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

      1. *-commutative 39.5%

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

      2. associate-*l/ 39.9%

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

      3. associate-*r/ 39.8%

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

   6. Simplified 39.8%

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

   if 8.1999999999999996e-38 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 56.1%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 10: 37.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 0.5 * (x / 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 = 0.5d0 * (x / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

   4. associate-+l- 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   5. sub0-neg 100.0%

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

   6. neg-mul-1 100.0%

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

   7. associate-*l/ 99.7%

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

   8. *-commutative 99.7%

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

   9. associate-/r* 99.7%

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

   10. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around inf 35.6%

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

5. Final simplification 35.6%

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

Reproduce

herbie shell --seed 2023238 
(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)))