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

Percentage Accurate: 100.0% → 99.9%

Time: 4.4s

Alternatives: 6

Speedup: N/A×

• 26.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% 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

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

FPCore

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

C

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

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) * 0.5d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. /-rgt-identity 99.2%

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

   2. metadata-eval 99.2%

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

   3. associate-/l* 99.2%

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

   4. metadata-eval 99.2%

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

   5. metadata-eval 99.2%

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

   6. metadata-eval 99.2%

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

   7. metadata-eval 99.2%

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

   8. associate-/r/ 99.7%

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

   9. associate--l+ 99.7%

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

   10. metadata-eval 99.7%

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

   11. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 2: 47.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-5}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-308}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.3e-5)
   (* 0.5 (/ x t))
   (if (<= x 7.2e-308) (/ (* z -0.5) t) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.3e-5) {
		tmp = 0.5 * (x / t);
	} else if (x <= 7.2e-308) {
		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 (x <= (-2.3d-5)) then
        tmp = 0.5d0 * (x / t)
    else if (x <= 7.2d-308) 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 (x <= -2.3e-5) {
		tmp = 0.5 * (x / t);
	} else if (x <= 7.2e-308) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.3e-5:
		tmp = 0.5 * (x / t)
	elif x <= 7.2e-308:
		tmp = (z * -0.5) / t
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.3e-5)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (x <= 7.2e-308)
		tmp = Float64(Float64(z * -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 (x <= -2.3e-5)
		tmp = 0.5 * (x / t);
	elseif (x <= 7.2e-308)
		tmp = (z * -0.5) / t;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.3e-5], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-308], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3e-5

   1. Initial program 100.0%

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

      1. /-rgt-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-/r/ 100.0%

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

      9. associate--l+ 100.0%

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

      10. metadata-eval 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 59.1%

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

   if -2.3e-5 < x < 7.1999999999999997e-308

   1. Initial program 100.0%

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

      1. /-rgt-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-/r/ 98.7%

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

      9. associate--l+ 98.7%

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

      10. metadata-eval 98.7%

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

      11. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around inf 45.1%

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

      1. associate-*r/ 46.4%

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

      2. *-commutative 46.4%

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

   6. Simplified 46.4%

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

   if 7.1999999999999997e-308 < x

   1. Initial program 98.4%

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

      1. /-rgt-identity 98.4%

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

      2. metadata-eval 98.4%

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

      3. associate-/l* 98.4%

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

      4. metadata-eval 98.4%

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

      5. metadata-eval 98.4%

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

      6. metadata-eval 98.4%

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

      7. metadata-eval 98.4%

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

      8. associate-/r/ 100.0%

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

      9. associate--l+ 100.0%

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

      10. metadata-eval 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 39.3%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-5}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-308}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.5e+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 <= 1.5e+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 <= 1.5d+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 <= 1.5e+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 <= 1.5e+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 <= 1.5e+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 <= 1.5e+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, 1.5e+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 < 1.5e106

   1. Initial program 99.5%

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

      1. /-rgt-identity 99.5%

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

      2. metadata-eval 99.5%

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

      3. associate-/l* 99.5%

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

      4. metadata-eval 99.5%

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

      5. metadata-eval 99.5%

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

      6. metadata-eval 99.5%

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

      7. metadata-eval 99.5%

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

      8. associate-/r/ 99.6%

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

      9. associate--l+ 99.6%

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

      10. metadata-eval 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 75.1%

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

   if 1.5e106 < y

   1. Initial program 97.9%

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

      1. /-rgt-identity 97.9%

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

      2. metadata-eval 97.9%

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

      3. associate-/l* 97.9%

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

      4. metadata-eval 97.9%

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

      5. metadata-eval 97.9%

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

      6. metadata-eval 97.9%

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

      7. metadata-eval 97.9%

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

      8. associate-/r/ 100.0%

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

      9. associate--l+ 100.0%

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

      10. metadata-eval 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 74.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-85}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e-85) (* 0.5 (/ (- x z) t)) (* (- y z) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-85) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.6d-85)) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = (y - z) * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-85) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.6e-85:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e-85)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(Float64(y - z) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.6e-85)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e-85], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000011e-85

   1. Initial program 100.0%

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

      1. /-rgt-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-/r/ 100.0%

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

      9. associate--l+ 100.0%

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

      10. metadata-eval 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.3%

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

   if -2.60000000000000011e-85 < x

   1. Initial program 98.8%

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

      1. /-rgt-identity 98.8%

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

      2. metadata-eval 98.8%

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

      3. associate-/l* 98.8%

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

      4. metadata-eval 98.8%

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

      5. metadata-eval 98.8%

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

      6. metadata-eval 98.8%

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

      7. metadata-eval 98.8%

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

      8. associate-/r/ 99.5%

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

      9. associate--l+ 99.5%

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

      10. metadata-eval 99.5%

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

      11. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 74.8%

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

      1. associate-*r/ 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-*r/ 75.0%

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

   6. Simplified 75.0%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-85}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 5: 44.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-85}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.6e-85) (* 0.5 (/ x t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.6e-85) {
		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 (x <= (-3.6d-85)) 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 (x <= -3.6e-85) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.6e-85:
		tmp = 0.5 * (x / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.6e-85)
		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 (x <= -3.6e-85)
		tmp = 0.5 * (x / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.6e-85], 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 x < -3.5999999999999998e-85

   1. Initial program 100.0%

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

      1. /-rgt-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/l* 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-/r/ 100.0%

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

      9. associate--l+ 100.0%

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

      10. metadata-eval 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 51.8%

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

   if -3.5999999999999998e-85 < x

   1. Initial program 98.8%

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

      1. /-rgt-identity 98.8%

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

      2. metadata-eval 98.8%

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

      3. associate-/l* 98.8%

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

      4. metadata-eval 98.8%

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

      5. metadata-eval 98.8%

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

      6. metadata-eval 98.8%

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

      7. metadata-eval 98.8%

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

      8. associate-/r/ 99.5%

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

      9. associate--l+ 99.5%

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

      10. metadata-eval 99.5%

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

      11. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 44.4%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-85}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6: 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 99.2%

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

   1. /-rgt-identity 99.2%

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

   2. metadata-eval 99.2%

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

   3. associate-/l* 99.2%

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

   4. metadata-eval 99.2%

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

   5. metadata-eval 99.2%

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

   6. metadata-eval 99.2%

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

   7. metadata-eval 99.2%

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

   8. associate-/r/ 99.7%

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

   9. associate--l+ 99.7%

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

   10. metadata-eval 99.7%

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

   11. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around inf 38.3%

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

5. Final simplification 38.3%

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

Reproduce

herbie shell --seed 2023301 
(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)))