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

Percentage Accurate: 99.9% → 99.9%

Time: 6.5s

Alternatives: 10

Speedup: 1.0×

• 26.7% 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: 46.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{-19}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-88} \lor \neg \left(x \leq -1.85 \cdot 10^{-292}\right) \land \left(x \leq 2.2 \cdot 10^{-144} \lor \neg \left(x \leq 7.5 \cdot 10^{-98}\right)\right):\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.3e-19)
   (* 0.5 (/ x t))
   (if (or (<= x -3.7e-88)
           (and (not (<= x -1.85e-292))
                (or (<= x 2.2e-144) (not (<= x 7.5e-98)))))
     (* y (/ 0.5 t))
     (* z (/ -0.5 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.3e-19) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -3.7e-88) || (!(x <= -1.85e-292) && ((x <= 2.2e-144) || !(x <= 7.5e-98)))) {
		tmp = y * (0.5 / t);
	} else {
		tmp = 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 <= (-6.3d-19)) then
        tmp = 0.5d0 * (x / t)
    else if ((x <= (-3.7d-88)) .or. (.not. (x <= (-1.85d-292))) .and. (x <= 2.2d-144) .or. (.not. (x <= 7.5d-98))) then
        tmp = y * (0.5d0 / t)
    else
        tmp = 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 <= -6.3e-19) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -3.7e-88) || (!(x <= -1.85e-292) && ((x <= 2.2e-144) || !(x <= 7.5e-98)))) {
		tmp = y * (0.5 / t);
	} else {
		tmp = z * (-0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.3e-19:
		tmp = 0.5 * (x / t)
	elif (x <= -3.7e-88) or (not (x <= -1.85e-292) and ((x <= 2.2e-144) or not (x <= 7.5e-98))):
		tmp = y * (0.5 / t)
	else:
		tmp = z * (-0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.3e-19)
		tmp = Float64(0.5 * Float64(x / t));
	elseif ((x <= -3.7e-88) || (!(x <= -1.85e-292) && ((x <= 2.2e-144) || !(x <= 7.5e-98))))
		tmp = Float64(y * Float64(0.5 / t));
	else
		tmp = Float64(z * Float64(-0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.3e-19)
		tmp = 0.5 * (x / t);
	elseif ((x <= -3.7e-88) || (~((x <= -1.85e-292)) && ((x <= 2.2e-144) || ~((x <= 7.5e-98)))))
		tmp = y * (0.5 / t);
	else
		tmp = z * (-0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.3e-19], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.7e-88], And[N[Not[LessEqual[x, -1.85e-292]], $MachinePrecision], Or[LessEqual[x, 2.2e-144], N[Not[LessEqual[x, 7.5e-98]], $MachinePrecision]]]], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.30000000000000018e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.0%

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

   if -6.30000000000000018e-19 < x < -3.6999999999999997e-88 or -1.84999999999999998e-292 < x < 2.20000000000000006e-144 or 7.5000000000000006e-98 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.2%

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

      1. div-sub 97.0%

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

      2. distribute-lft-out 97.0%

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

      3. div-sub 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around inf 45.3%

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

      1. associate-*r/ 45.3%

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

      2. associate-*l/ 45.2%

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

      3. *-commutative 45.2%

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

   7. Simplified 45.2%

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

   if -3.6999999999999997e-88 < x < -1.84999999999999998e-292 or 2.20000000000000006e-144 < x < 7.5000000000000006e-98

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 57.3%

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

      1. associate-*r/ 57.3%

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

      2. associate-/l* 56.5%

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

   4. Simplified 56.5%

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

      1. associate-/r/ 57.1%

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

   6. Applied egg-rr 57.1%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{-19}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-88} \lor \neg \left(x \leq -1.85 \cdot 10^{-292}\right) \land \left(x \leq 2.2 \cdot 10^{-144} \lor \neg \left(x \leq 7.5 \cdot 10^{-98}\right)\right):\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \]

Alternative 3: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-20}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-88} \lor \neg \left(x \leq -2.1 \cdot 10^{-287}\right) \land \left(x \leq 1.8 \cdot 10^{-147} \lor \neg \left(x \leq 7 \cdot 10^{-101}\right)\right):\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.9e-20)
   (* 0.5 (/ x t))
   (if (or (<= x -3.7e-88)
           (and (not (<= x -2.1e-287))
                (or (<= x 1.8e-147) (not (<= x 7e-101)))))
     (* y (/ 0.5 t))
     (* -0.5 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e-20) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -3.7e-88) || (!(x <= -2.1e-287) && ((x <= 1.8e-147) || !(x <= 7e-101)))) {
		tmp = y * (0.5 / 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 (x <= (-2.9d-20)) then
        tmp = 0.5d0 * (x / t)
    else if ((x <= (-3.7d-88)) .or. (.not. (x <= (-2.1d-287))) .and. (x <= 1.8d-147) .or. (.not. (x <= 7d-101))) then
        tmp = y * (0.5d0 / 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 (x <= -2.9e-20) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -3.7e-88) || (!(x <= -2.1e-287) && ((x <= 1.8e-147) || !(x <= 7e-101)))) {
		tmp = y * (0.5 / t);
	} else {
		tmp = -0.5 * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.9e-20:
		tmp = 0.5 * (x / t)
	elif (x <= -3.7e-88) or (not (x <= -2.1e-287) and ((x <= 1.8e-147) or not (x <= 7e-101))):
		tmp = y * (0.5 / t)
	else:
		tmp = -0.5 * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.9e-20)
		tmp = Float64(0.5 * Float64(x / t));
	elseif ((x <= -3.7e-88) || (!(x <= -2.1e-287) && ((x <= 1.8e-147) || !(x <= 7e-101))))
		tmp = Float64(y * Float64(0.5 / 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 (x <= -2.9e-20)
		tmp = 0.5 * (x / t);
	elseif ((x <= -3.7e-88) || (~((x <= -2.1e-287)) && ((x <= 1.8e-147) || ~((x <= 7e-101)))))
		tmp = y * (0.5 / t);
	else
		tmp = -0.5 * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.9e-20], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.7e-88], And[N[Not[LessEqual[x, -2.1e-287]], $MachinePrecision], Or[LessEqual[x, 1.8e-147], N[Not[LessEqual[x, 7e-101]], $MachinePrecision]]]], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9e-20

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.0%

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

   if -2.9e-20 < x < -3.6999999999999997e-88 or -2.0999999999999999e-287 < x < 1.80000000000000006e-147 or 6.99999999999999989e-101 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.2%

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

      1. div-sub 97.0%

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

      2. distribute-lft-out 97.0%

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

      3. div-sub 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around inf 45.0%

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

      1. associate-*r/ 45.0%

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

      2. associate-*l/ 44.8%

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

      3. *-commutative 44.8%

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

   7. Simplified 44.8%

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

   if -3.6999999999999997e-88 < x < -2.0999999999999999e-287 or 1.80000000000000006e-147 < x < 6.99999999999999989e-101

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 56.5%

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

      1. *-commutative 56.5%

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

   4. Simplified 56.5%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-20}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-88} \lor \neg \left(x \leq -2.1 \cdot 10^{-287}\right) \land \left(x \leq 1.8 \cdot 10^{-147} \lor \neg \left(x \leq 7 \cdot 10^{-101}\right)\right):\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \]

Alternative 4: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-19}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-87} \lor \neg \left(x \leq -1.06 \cdot 10^{-281}\right) \land \left(x \leq 10^{-143} \lor \neg \left(x \leq 2.3 \cdot 10^{-104}\right)\right):\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.4e-19)
   (* 0.5 (/ x t))
   (if (or (<= x -1.55e-87)
           (and (not (<= x -1.06e-281))
                (or (<= x 1e-143) (not (<= x 2.3e-104)))))
     (/ (* y 0.5) t)
     (* -0.5 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e-19) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -1.55e-87) || (!(x <= -1.06e-281) && ((x <= 1e-143) || !(x <= 2.3e-104)))) {
		tmp = (y * 0.5) / 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 (x <= (-1.4d-19)) then
        tmp = 0.5d0 * (x / t)
    else if ((x <= (-1.55d-87)) .or. (.not. (x <= (-1.06d-281))) .and. (x <= 1d-143) .or. (.not. (x <= 2.3d-104))) then
        tmp = (y * 0.5d0) / 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 (x <= -1.4e-19) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -1.55e-87) || (!(x <= -1.06e-281) && ((x <= 1e-143) || !(x <= 2.3e-104)))) {
		tmp = (y * 0.5) / t;
	} else {
		tmp = -0.5 * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.4e-19:
		tmp = 0.5 * (x / t)
	elif (x <= -1.55e-87) or (not (x <= -1.06e-281) and ((x <= 1e-143) or not (x <= 2.3e-104))):
		tmp = (y * 0.5) / t
	else:
		tmp = -0.5 * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.4e-19)
		tmp = Float64(0.5 * Float64(x / t));
	elseif ((x <= -1.55e-87) || (!(x <= -1.06e-281) && ((x <= 1e-143) || !(x <= 2.3e-104))))
		tmp = Float64(Float64(y * 0.5) / 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 (x <= -1.4e-19)
		tmp = 0.5 * (x / t);
	elseif ((x <= -1.55e-87) || (~((x <= -1.06e-281)) && ((x <= 1e-143) || ~((x <= 2.3e-104)))))
		tmp = (y * 0.5) / t;
	else
		tmp = -0.5 * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.4e-19], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.55e-87], And[N[Not[LessEqual[x, -1.06e-281]], $MachinePrecision], Or[LessEqual[x, 1e-143], N[Not[LessEqual[x, 2.3e-104]], $MachinePrecision]]]], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.40000000000000001e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.0%

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

   if -1.40000000000000001e-19 < x < -1.54999999999999999e-87 or -1.06e-281 < x < 9.9999999999999995e-144 or 2.2999999999999999e-104 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 45.8%

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

      1. associate-*r/ 45.8%

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

   4. Simplified 45.8%

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

   if -1.54999999999999999e-87 < x < -1.06e-281 or 9.9999999999999995e-144 < x < 2.2999999999999999e-104

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 58.5%

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

      1. *-commutative 58.5%

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

   4. Simplified 58.5%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-19}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-87} \lor \neg \left(x \leq -1.06 \cdot 10^{-281}\right) \land \left(x \leq 10^{-143} \lor \neg \left(x \leq 2.3 \cdot 10^{-104}\right)\right):\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot 0.5}{t}\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{-21}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-289}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-141} \lor \neg \left(x \leq 1.75 \cdot 10^{-99}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* y 0.5) t)))
   (if (<= x -1.02e-21)
     (* 0.5 (/ x t))
     (if (<= x -9.6e-88)
       t_1
       (if (<= x -4.4e-289)
         (/ (* z -0.5) t)
         (if (or (<= x 1.4e-141) (not (<= x 1.75e-99)))
           t_1
           (* -0.5 (/ z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 0.5) / t;
	double tmp;
	if (x <= -1.02e-21) {
		tmp = 0.5 * (x / t);
	} else if (x <= -9.6e-88) {
		tmp = t_1;
	} else if (x <= -4.4e-289) {
		tmp = (z * -0.5) / t;
	} else if ((x <= 1.4e-141) || !(x <= 1.75e-99)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y * 0.5d0) / t
    if (x <= (-1.02d-21)) then
        tmp = 0.5d0 * (x / t)
    else if (x <= (-9.6d-88)) then
        tmp = t_1
    else if (x <= (-4.4d-289)) then
        tmp = (z * (-0.5d0)) / t
    else if ((x <= 1.4d-141) .or. (.not. (x <= 1.75d-99))) then
        tmp = t_1
    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 t_1 = (y * 0.5) / t;
	double tmp;
	if (x <= -1.02e-21) {
		tmp = 0.5 * (x / t);
	} else if (x <= -9.6e-88) {
		tmp = t_1;
	} else if (x <= -4.4e-289) {
		tmp = (z * -0.5) / t;
	} else if ((x <= 1.4e-141) || !(x <= 1.75e-99)) {
		tmp = t_1;
	} else {
		tmp = -0.5 * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 0.5) / t
	tmp = 0
	if x <= -1.02e-21:
		tmp = 0.5 * (x / t)
	elif x <= -9.6e-88:
		tmp = t_1
	elif x <= -4.4e-289:
		tmp = (z * -0.5) / t
	elif (x <= 1.4e-141) or not (x <= 1.75e-99):
		tmp = t_1
	else:
		tmp = -0.5 * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 0.5) / t)
	tmp = 0.0
	if (x <= -1.02e-21)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (x <= -9.6e-88)
		tmp = t_1;
	elseif (x <= -4.4e-289)
		tmp = Float64(Float64(z * -0.5) / t);
	elseif ((x <= 1.4e-141) || !(x <= 1.75e-99))
		tmp = t_1;
	else
		tmp = Float64(-0.5 * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 0.5) / t;
	tmp = 0.0;
	if (x <= -1.02e-21)
		tmp = 0.5 * (x / t);
	elseif (x <= -9.6e-88)
		tmp = t_1;
	elseif (x <= -4.4e-289)
		tmp = (z * -0.5) / t;
	elseif ((x <= 1.4e-141) || ~((x <= 1.75e-99)))
		tmp = t_1;
	else
		tmp = -0.5 * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[x, -1.02e-21], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.6e-88], t$95$1, If[LessEqual[x, -4.4e-289], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[x, 1.4e-141], N[Not[LessEqual[x, 1.75e-99]], $MachinePrecision]], t$95$1, N[(-0.5 * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.02000000000000004e-21

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.0%

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

   if -1.02000000000000004e-21 < x < -9.5999999999999998e-88 or -4.4e-289 < x < 1.40000000000000006e-141 or 1.7499999999999999e-99 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 45.0%

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

      1. associate-*r/ 45.0%

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

   4. Simplified 45.0%

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

   if -9.5999999999999998e-88 < x < -4.4e-289

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 54.0%

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

      1. *-commutative 54.0%

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

   4. Simplified 54.0%

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

      1. associate-*l/ 54.1%

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

   6. Applied egg-rr 54.1%

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

   if 1.40000000000000006e-141 < x < 1.7499999999999999e-99

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 80.4%

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

      1. *-commutative 80.4%

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

   4. Simplified 80.4%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-21}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-88}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-289}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-141} \lor \neg \left(x \leq 1.75 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x - z}{t}\\ \mathbf{if}\;y \leq 1.62 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ (- x z) t))))
   (if (<= y 1.62e+86)
     t_1
     (if (<= y 1.25e+121)
       (* y (/ 0.5 t))
       (if (<= y 7e+145) t_1 (/ (* y 0.5) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * ((x - z) / t);
	double tmp;
	if (y <= 1.62e+86) {
		tmp = t_1;
	} else if (y <= 1.25e+121) {
		tmp = y * (0.5 / t);
	} else if (y <= 7e+145) {
		tmp = t_1;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * ((x - z) / t)
    if (y <= 1.62d+86) then
        tmp = t_1
    else if (y <= 1.25d+121) then
        tmp = y * (0.5d0 / t)
    else if (y <= 7d+145) then
        tmp = t_1
    else
        tmp = (y * 0.5d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * ((x - z) / t);
	double tmp;
	if (y <= 1.62e+86) {
		tmp = t_1;
	} else if (y <= 1.25e+121) {
		tmp = y * (0.5 / t);
	} else if (y <= 7e+145) {
		tmp = t_1;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.5 * ((x - z) / t)
	tmp = 0
	if y <= 1.62e+86:
		tmp = t_1
	elif y <= 1.25e+121:
		tmp = y * (0.5 / t)
	elif y <= 7e+145:
		tmp = t_1
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.5 * Float64(Float64(x - z) / t))
	tmp = 0.0
	if (y <= 1.62e+86)
		tmp = t_1;
	elseif (y <= 1.25e+121)
		tmp = Float64(y * Float64(0.5 / t));
	elseif (y <= 7e+145)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.5 * ((x - z) / t);
	tmp = 0.0;
	if (y <= 1.62e+86)
		tmp = t_1;
	elseif (y <= 1.25e+121)
		tmp = y * (0.5 / t);
	elseif (y <= 7e+145)
		tmp = t_1;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.62e+86], t$95$1, If[LessEqual[y, 1.25e+121], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+145], t$95$1, N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.6200000000000001e86 or 1.25000000000000002e121 < y < 7.0000000000000002e145

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.0%

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

   if 1.6200000000000001e86 < y < 1.25000000000000002e121

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 83.3%

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

      1. div-sub 83.3%

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

      2. distribute-lft-out 83.3%

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

      3. div-sub 83.3%

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

   4. Simplified 83.3%

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

   5. Taylor expanded in y around inf 83.7%

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

      1. associate-*r/ 83.7%

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

      2. associate-*l/ 83.7%

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

      3. *-commutative 83.7%

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

   7. Simplified 83.7%

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

   if 7.0000000000000002e145 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.8%

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

      1. associate-*r/ 78.8%

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

   4. Simplified 78.8%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.62 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+145}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]

Alternative 7: 78.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{+84}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1e+84) (* 0.5 (/ (- x z) t)) (* (+ x y) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1e+84) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (x + y) * (0.5 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1d+84) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = (x + y) * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1e+84) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (x + y) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1e+84:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = (x + y) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1e+84)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1e+84)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = (x + y) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1e+84], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.00000000000000006e84

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.7%

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

   if 1.00000000000000006e84 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. associate-*l/ 85.8%

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

      3. *-commutative 85.8%

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

      4. +-commutative 85.8%

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

   4. Simplified 85.8%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{+84}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 8: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-27}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2e-27) (* 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 <= -2e-27) {
		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 <= (-2d-27)) 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 <= -2e-27) {
		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 <= -2e-27:
		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 <= -2e-27)
		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 <= -2e-27)
		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, -2e-27], 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 < -2.0000000000000001e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.9%

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

   if -2.0000000000000001e-27 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.9%

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

      1. associate-*r/ 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r/ 78.7%

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

   4. Simplified 78.7%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-27}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 9: 46.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-19}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.45e-19) (* 0.5 (/ x t)) (* y (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.45e-19) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.45d-19)) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = y * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.45e-19) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.45e-19:
		tmp = 0.5 * (x / t)
	else:
		tmp = y * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.45e-19)
		tmp = Float64(0.5 * Float64(x / t));
	else
		tmp = Float64(y * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.45e-19)
		tmp = 0.5 * (x / t);
	else
		tmp = y * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.45e-19], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.44999999999999996e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.0%

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

   if -2.44999999999999996e-19 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.4%

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

      1. div-sub 97.9%

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

      2. distribute-lft-out 97.9%

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

      3. div-sub 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in y around inf 46.1%

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

      1. associate-*r/ 46.1%

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

      2. associate-*l/ 45.9%

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

      3. *-commutative 45.9%

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

   7. Simplified 45.9%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-19}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 10: 37.9% 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. Taylor expanded in x around inf 37.8%

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

3. Final simplification 37.8%

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

Reproduce

herbie shell --seed 2023336 
(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)))