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

Percentage Accurate: 99.9% → 99.7%

Time: 6.9s

Alternatives: 12

Speedup: N/A×

• 27.0% 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: 99.7% 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 99.6%

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

   1. associate--l+ 99.6%

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

3. Simplified 99.6%

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

   1. clear-num 99.0%

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

   2. associate-/r/ 99.4%

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

   3. *-commutative 99.4%

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

   4. associate-/r* 99.8%

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

   5. metadata-eval 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 48.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+40}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1e-53)
   (* 0.5 (/ x t))
   (if (<= (+ x y) 5e+40) (/ -0.5 (/ t z)) (/ 0.5 (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-53) {
		tmp = 0.5 * (x / t);
	} else if ((x + y) <= 5e+40) {
		tmp = -0.5 / (t / z);
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-1d-53)) then
        tmp = 0.5d0 * (x / t)
    else if ((x + y) <= 5d+40) then
        tmp = (-0.5d0) / (t / z)
    else
        tmp = 0.5d0 / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-53) {
		tmp = 0.5 * (x / t);
	} else if ((x + y) <= 5e+40) {
		tmp = -0.5 / (t / z);
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1e-53:
		tmp = 0.5 * (x / t)
	elif (x + y) <= 5e+40:
		tmp = -0.5 / (t / z)
	else:
		tmp = 0.5 / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1e-53)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (Float64(x + y) <= 5e+40)
		tmp = Float64(-0.5 / Float64(t / z));
	else
		tmp = Float64(0.5 / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1e-53)
		tmp = 0.5 * (x / t);
	elseif ((x + y) <= 5e+40)
		tmp = -0.5 / (t / z);
	else
		tmp = 0.5 / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-53], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 5e+40], N[(-0.5 / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.00000000000000003e-53

   1. Initial program 99.1%

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

      1. associate--l+ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 36.4%

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

   if -1.00000000000000003e-53 < (+.f64 x y) < 5.00000000000000003e40

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 98.3%

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

      2. associate-/r/ 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/r* 99.9%

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

      5. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 98.3%

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

   7. Applied egg-rr 98.3%

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

   8. Taylor expanded in z around inf 75.7%

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

      1. associate-*r/ 77.1%

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

      2. associate-/l* 76.8%

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

   10. Simplified 76.8%

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

   if 5.00000000000000003e40 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-/r* 99.8%

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

      5. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in y around inf 43.8%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+40}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]

Alternative 3: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+40}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1e-53)
   (* 0.5 (/ x t))
   (if (<= (+ x y) 5e+40) (/ -0.5 (/ t z)) (/ y (* t 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-53) {
		tmp = 0.5 * (x / t);
	} else if ((x + y) <= 5e+40) {
		tmp = -0.5 / (t / 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 ((x + y) <= (-1d-53)) then
        tmp = 0.5d0 * (x / t)
    else if ((x + y) <= 5d+40) then
        tmp = (-0.5d0) / (t / 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 ((x + y) <= -1e-53) {
		tmp = 0.5 * (x / t);
	} else if ((x + y) <= 5e+40) {
		tmp = -0.5 / (t / z);
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1e-53:
		tmp = 0.5 * (x / t)
	elif (x + y) <= 5e+40:
		tmp = -0.5 / (t / z)
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1e-53)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (Float64(x + y) <= 5e+40)
		tmp = Float64(-0.5 / Float64(t / z));
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1e-53)
		tmp = 0.5 * (x / t);
	elseif ((x + y) <= 5e+40)
		tmp = -0.5 / (t / z);
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-53], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 5e+40], N[(-0.5 / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.00000000000000003e-53

   1. Initial program 99.1%

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

      1. associate--l+ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 36.4%

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

   if -1.00000000000000003e-53 < (+.f64 x y) < 5.00000000000000003e40

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 98.3%

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

      2. associate-/r/ 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/r* 99.9%

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

      5. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 98.3%

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

   7. Applied egg-rr 98.3%

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

   8. Taylor expanded in z around inf 75.7%

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

      1. associate-*r/ 77.1%

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

      2. associate-/l* 76.8%

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

   10. Simplified 76.8%

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

   if 5.00000000000000003e40 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 43.9%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+40}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]

Alternative 4: 49.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+40}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1e-53)
   (* 0.5 (/ x t))
   (if (<= (+ x y) 5e+40) (/ z (/ t -0.5)) (/ y (* t 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-53) {
		tmp = 0.5 * (x / t);
	} else if ((x + y) <= 5e+40) {
		tmp = z / (t / -0.5);
	} 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 ((x + y) <= (-1d-53)) then
        tmp = 0.5d0 * (x / t)
    else if ((x + y) <= 5d+40) then
        tmp = z / (t / (-0.5d0))
    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 ((x + y) <= -1e-53) {
		tmp = 0.5 * (x / t);
	} else if ((x + y) <= 5e+40) {
		tmp = z / (t / -0.5);
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1e-53:
		tmp = 0.5 * (x / t)
	elif (x + y) <= 5e+40:
		tmp = z / (t / -0.5)
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1e-53)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (Float64(x + y) <= 5e+40)
		tmp = Float64(z / Float64(t / -0.5));
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1e-53)
		tmp = 0.5 * (x / t);
	elseif ((x + y) <= 5e+40)
		tmp = z / (t / -0.5);
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-53], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 5e+40], N[(z / N[(t / -0.5), $MachinePrecision]), $MachinePrecision], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.00000000000000003e-53

   1. Initial program 99.1%

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

      1. associate--l+ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 36.4%

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

   if -1.00000000000000003e-53 < (+.f64 x y) < 5.00000000000000003e40

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 98.3%

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

      2. associate-/r/ 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/r* 99.9%

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

      5. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 75.7%

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

      1. associate-*r/ 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-/l* 77.1%

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

   8. Simplified 77.1%

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

   if 5.00000000000000003e40 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 43.9%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+40}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]

Alternative 5: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+32} \lor \neg \left(z \leq 9.5 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e+32) (not (<= z 9.5e-23)))
   (* (/ 0.5 t) (- y z))
   (* (/ 0.5 t) (+ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+32) || !(z <= 9.5e-23)) {
		tmp = (0.5 / t) * (y - z);
	} else {
		tmp = (0.5 / t) * (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.1d+32)) .or. (.not. (z <= 9.5d-23))) then
        tmp = (0.5d0 / t) * (y - z)
    else
        tmp = (0.5d0 / t) * (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+32) || !(z <= 9.5e-23)) {
		tmp = (0.5 / t) * (y - z);
	} else {
		tmp = (0.5 / t) * (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e+32) or not (z <= 9.5e-23):
		tmp = (0.5 / t) * (y - z)
	else:
		tmp = (0.5 / t) * (x + y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e+32) || !(z <= 9.5e-23))
		tmp = Float64(Float64(0.5 / t) * Float64(y - z));
	else
		tmp = Float64(Float64(0.5 / t) * Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.1e+32) || ~((z <= 9.5e-23)))
		tmp = (0.5 / t) * (y - z);
	else
		tmp = (0.5 / t) * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e+32], N[Not[LessEqual[z, 9.5e-23]], $MachinePrecision]], N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / t), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999993e32 or 9.50000000000000058e-23 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 87.2%

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

      1. associate-*r/ 87.9%

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

      2. associate-*l/ 87.8%

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

      3. *-commutative 87.8%

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

   6. Simplified 87.8%

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

   if -3.09999999999999993e32 < z < 9.50000000000000058e-23

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 99.1%

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

      3. *-commutative 99.1%

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

      4. associate-/r* 99.8%

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

      5. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around 0 94.7%

      \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(x + y\right)} \]
   7. Step-by-step derivation

      1. +-commutative 94.1%

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

   8. Simplified 94.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+32} \lor \neg \left(z \leq 9.5 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x + y\right)\\ \end{array} \]

Alternative 6: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1e-53) (* 0.5 (/ x t)) (* (/ 0.5 t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-53) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = (0.5 / t) * (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-1d-53)) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = (0.5d0 / t) * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-53) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = (0.5 / t) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1e-53:
		tmp = 0.5 * (x / t)
	else:
		tmp = (0.5 / t) * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1e-53)
		tmp = Float64(0.5 * Float64(x / t));
	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 ((x + y) <= -1e-53)
		tmp = 0.5 * (x / t);
	else
		tmp = (0.5 / t) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-53], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000003e-53

   1. Initial program 99.1%

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

      1. associate--l+ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 36.4%

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

   if -1.00000000000000003e-53 < (+.f64 x y)

   1. Initial program 99.9%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 73.8%

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

      1. associate-*r/ 74.3%

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

      2. associate-*l/ 74.2%

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

      3. *-commutative 74.2%

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

   6. Simplified 74.2%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \]

Alternative 7: 68.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-130) (/ (- x z) (* t 2.0)) (* (/ 0.5 t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-130) {
		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 ((x + y) <= (-5d-130)) 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 ((x + y) <= -5e-130) {
		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 (x + y) <= -5e-130:
		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 (Float64(x + y) <= -5e-130)
		tmp = Float64(Float64(x - z) / Float64(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 ((x + y) <= -5e-130)
		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[N[(x + y), $MachinePrecision], -5e-130], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.9999999999999996e-130

   1. Initial program 99.1%

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

      1. associate--l+ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 60.7%

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

   if -4.9999999999999996e-130 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 73.8%

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

      1. associate-*r/ 74.3%

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

      2. associate-*l/ 74.2%

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

      3. *-commutative 74.2%

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

   6. Simplified 74.2%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \]

Alternative 8: 68.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-130) (/ (- x z) (* t 2.0)) (/ (- y z) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-130) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-5d-130)) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (y - z) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-130) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -5e-130:
		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 (Float64(x + y) <= -5e-130)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -5e-130)
		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[N[(x + y), $MachinePrecision], -5e-130], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.9999999999999996e-130

   1. Initial program 99.1%

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

      1. associate--l+ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 60.7%

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

   if -4.9999999999999996e-130 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 74.3%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \]

Alternative 9: 55.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+33} \lor \neg \left(z \leq 2.45 \cdot 10^{-24}\right):\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.2e+33) (not (<= z 2.45e-24)))
   (* -0.5 (/ z t))
   (* 0.5 (/ x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.2e+33) || !(z <= 2.45e-24)) {
		tmp = -0.5 * (z / t);
	} else {
		tmp = 0.5 * (x / 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 ((z <= (-1.2d+33)) .or. (.not. (z <= 2.45d-24))) then
        tmp = (-0.5d0) * (z / t)
    else
        tmp = 0.5d0 * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.2e+33) || !(z <= 2.45e-24)) {
		tmp = -0.5 * (z / t);
	} else {
		tmp = 0.5 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.2e+33) or not (z <= 2.45e-24):
		tmp = -0.5 * (z / t)
	else:
		tmp = 0.5 * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.2e+33) || !(z <= 2.45e-24))
		tmp = Float64(-0.5 * Float64(z / t));
	else
		tmp = Float64(0.5 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.2e+33) || ~((z <= 2.45e-24)))
		tmp = -0.5 * (z / t);
	else
		tmp = 0.5 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.2e+33], N[Not[LessEqual[z, 2.45e-24]], $MachinePrecision]], N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e33 or 2.45e-24 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 70.6%

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

      1. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -1.2e33 < z < 2.45e-24

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 49.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+33} \lor \neg \left(z \leq 2.45 \cdot 10^{-24}\right):\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 10: 55.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-21}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e+32)
   (/ -0.5 (/ t z))
   (if (<= z 3.7e-21) (* 0.5 (/ x t)) (* -0.5 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+32) {
		tmp = -0.5 / (t / z);
	} else if (z <= 3.7e-21) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = -0.5 * (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 (z <= (-5.5d+32)) then
        tmp = (-0.5d0) / (t / z)
    else if (z <= 3.7d-21) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = (-0.5d0) * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+32) {
		tmp = -0.5 / (t / z);
	} else if (z <= 3.7e-21) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = -0.5 * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e+32:
		tmp = -0.5 / (t / z)
	elif z <= 3.7e-21:
		tmp = 0.5 * (x / t)
	else:
		tmp = -0.5 * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e+32)
		tmp = Float64(-0.5 / Float64(t / z));
	elseif (z <= 3.7e-21)
		tmp = Float64(0.5 * Float64(x / t));
	else
		tmp = Float64(-0.5 * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.5e+32)
		tmp = -0.5 / (t / z);
	elseif (z <= 3.7e-21)
		tmp = 0.5 * (x / t);
	else
		tmp = -0.5 * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e+32], N[(-0.5 / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-21], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999984e32

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/r* 99.7%

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

      5. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.6%

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

   7. Applied egg-rr 99.6%

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

   8. Taylor expanded in z around inf 78.5%

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

      1. associate-*r/ 80.1%

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

      2. associate-/l* 79.7%

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

   10. Simplified 79.7%

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

   if -5.49999999999999984e32 < z < 3.7000000000000002e-21

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 49.9%

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

   if 3.7000000000000002e-21 < z

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 65.1%

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

      1. *-commutative 65.1%

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

   6. Simplified 65.1%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-21}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \]

Alternative 11: 37.1% 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 99.6%

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

   1. associate--l+ 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in x around inf 36.0%

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

5. Final simplification 36.0%

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

Alternative 12: 4.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 0.0)

C

double code(double x, double y, double z, double t) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.0;
}

Python

def code(x, y, z, t):
	return 0.0

Julia

function code(x, y, z, t)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_] := 0.0

Derivation

1. Initial program 99.6%

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

   1. associate--l+ 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in z around 0 67.8%

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

   1. +-commutative 67.8%

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

6. Simplified 67.8%

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

   1. +-commutative 67.8%

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

   2. *-commutative 67.8%

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

   3. count-2 67.8%

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

   4. flip-+ 0.0%

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

   5. +-inverses 0.0%

      \[\leadsto \frac{x + y}{\frac{t \cdot t - t \cdot t}{\color{blue}{0}}} \]

   6. +-inverses 0.0%

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

   7. associate-/r/ 0.0%

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

   8. +-inverses 0.0%

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

   9. +-inverses 0.0%

      \[\leadsto \frac{x + y}{0} \cdot \color{blue}{0} \]

8. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{\frac{x + y}{0} \cdot 0} \]
9. Step-by-step derivation

   1. mul0-rgt 4.5%

      \[\leadsto \color{blue}{0} \]

10. Simplified 4.5%

    \[\leadsto \color{blue}{0} \]

11. Final simplification 4.5%

    \[\leadsto 0 \]

Reproduce

herbie shell --seed 2023297 
(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)))