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

Percentage Accurate: 92.2% → 97.9%

Time: 9.4s

Alternatives: 11

Speedup: 1.0×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{z - x}{\frac{t}{y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

3. Taylor expanded in z around 0 85.9%

   \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot y}{t} + \frac{y \cdot z}{t}\right)} \]
4. Step-by-step derivation

   1. +-commutative 85.9%

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

   2. *-commutative 85.9%

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

   3. associate-*r/ 85.0%

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

   4. mul-1-neg 85.0%

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

   5. associate-/l* 90.5%

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

   6. distribute-lft-neg-in 90.5%

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

   7. distribute-rgt-in 97.3%

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

   8. sub-neg 97.3%

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

5. Simplified 97.3%

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

6. Taylor expanded in y around 0 90.6%

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

   1. associate-/l* 93.1%

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

   2. *-commutative 93.1%

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

   3. associate-/r/ 97.6%

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

8. Simplified 97.6%

   \[\leadsto x + \color{blue}{\frac{z - x}{\frac{t}{y}}} \]
9. Add Preprocessing

Alternative 2: 54.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= y -4.4e+60)
     t_1
     (if (<= y 5.4e-21) x (if (<= y 9e+117) t_1 (* x (/ y (- t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (y <= -4.4e+60) {
		tmp = t_1;
	} else if (y <= 5.4e-21) {
		tmp = x;
	} else if (y <= 9e+117) {
		tmp = t_1;
	} else {
		tmp = x * (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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (y <= (-4.4d+60)) then
        tmp = t_1
    else if (y <= 5.4d-21) then
        tmp = x
    else if (y <= 9d+117) then
        tmp = t_1
    else
        tmp = x * (y / -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (y <= -4.4e+60) {
		tmp = t_1;
	} else if (y <= 5.4e-21) {
		tmp = x;
	} else if (y <= 9e+117) {
		tmp = t_1;
	} else {
		tmp = x * (y / -t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if y <= -4.4e+60:
		tmp = t_1
	elif y <= 5.4e-21:
		tmp = x
	elif y <= 9e+117:
		tmp = t_1
	else:
		tmp = x * (y / -t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (y <= -4.4e+60)
		tmp = t_1;
	elseif (y <= 5.4e-21)
		tmp = x;
	elseif (y <= 9e+117)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (y <= -4.4e+60)
		tmp = t_1;
	elseif (y <= 5.4e-21)
		tmp = x;
	elseif (y <= 9e+117)
		tmp = t_1;
	else
		tmp = x * (y / -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+60], t$95$1, If[LessEqual[y, 5.4e-21], x, If[LessEqual[y, 9e+117], t$95$1, N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.39999999999999992e60 or 5.4000000000000002e-21 < y < 9e117

   1. Initial program 81.0%

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

   3. Taylor expanded in y around -inf 71.9%

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

   4. Taylor expanded in z around inf 48.3%

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

      1. associate-/l* 73.2%

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

   6. Simplified 60.8%

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

   if -4.39999999999999992e60 < y < 5.4000000000000002e-21

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 66.3%

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

   if 9e117 < y

   1. Initial program 85.8%

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

   3. Taylor expanded in x around inf 67.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 67.7%

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

      2. unsub-neg 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in y around inf 53.2%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 53.2%

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

      2. distribute-frac-neg2 53.2%

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

   8. Simplified 53.2%

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

Alternative 3: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot \frac{1}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4e+63)
   (* x (- 1.0 (/ y t)))
   (if (<= x 2.55e+51) (+ x (/ z (/ t y))) (* x (- 1.0 (* y (/ 1.0 t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e+63) {
		tmp = x * (1.0 - (y / t));
	} else if (x <= 2.55e+51) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x * (1.0 - (y * (1.0 / 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 <= (-4d+63)) then
        tmp = x * (1.0d0 - (y / t))
    else if (x <= 2.55d+51) then
        tmp = x + (z / (t / y))
    else
        tmp = x * (1.0d0 - (y * (1.0d0 / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e+63) {
		tmp = x * (1.0 - (y / t));
	} else if (x <= 2.55e+51) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x * (1.0 - (y * (1.0 / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4e+63:
		tmp = x * (1.0 - (y / t))
	elif x <= 2.55e+51:
		tmp = x + (z / (t / y))
	else:
		tmp = x * (1.0 - (y * (1.0 / t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4e+63)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif (x <= 2.55e+51)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * Float64(1.0 / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4e+63)
		tmp = x * (1.0 - (y / t));
	elseif (x <= 2.55e+51)
		tmp = x + (z / (t / y));
	else
		tmp = x * (1.0 - (y * (1.0 / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4e+63], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.55e+51], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.00000000000000023e63

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf 92.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 92.6%

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

      2. unsub-neg 92.6%

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

   5. Simplified 92.6%

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

   if -4.00000000000000023e63 < x < 2.55000000000000005e51

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 89.6%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot y}{t} + \frac{y \cdot z}{t}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 89.6%

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

      2. *-commutative 89.6%

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

      3. associate-*r/ 88.9%

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

      4. mul-1-neg 88.9%

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

      5. associate-/l* 89.4%

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

      6. distribute-lft-neg-in 89.4%

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

      7. distribute-rgt-in 95.2%

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

      8. sub-neg 95.2%

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

   5. Simplified 95.2%

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

   6. Taylor expanded in y around 0 93.9%

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

      1. associate-/l* 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-/r/ 95.8%

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

   8. Simplified 95.8%

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

   9. Taylor expanded in z around inf 87.0%

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

   if 2.55000000000000005e51 < x

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf 92.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 92.9%

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

      2. unsub-neg 92.9%

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

   5. Simplified 92.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
   6. Step-by-step derivation

      1. clear-num 93.0%

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

      2. associate-/r/ 92.9%

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

   7. Applied egg-rr 92.9%

      \[\leadsto x \cdot \left(1 - \color{blue}{\frac{1}{t} \cdot y}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot \frac{1}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+63} \lor \neg \left(x \leq 1.4 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1e+63) (not (<= x 1.4e+51)))
   (* x (- 1.0 (/ y t)))
   (+ x (/ z (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1e+63) || !(x <= 1.4e+51)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z / (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 <= (-1d+63)) .or. (.not. (x <= 1.4d+51))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (z / (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 <= -1e+63) || !(x <= 1.4e+51)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1e+63) or not (x <= 1.4e+51):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1e+63) || !(x <= 1.4e+51))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1e+63) || ~((x <= 1.4e+51)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1e+63], N[Not[LessEqual[x, 1.4e+51]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.00000000000000006e63 or 1.40000000000000002e51 < x

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf 92.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 92.7%

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

      2. unsub-neg 92.7%

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

   5. Simplified 92.7%

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

   if -1.00000000000000006e63 < x < 1.40000000000000002e51

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 89.6%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot y}{t} + \frac{y \cdot z}{t}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 89.6%

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

      2. *-commutative 89.6%

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

      3. associate-*r/ 88.9%

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

      4. mul-1-neg 88.9%

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

      5. associate-/l* 89.4%

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

      6. distribute-lft-neg-in 89.4%

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

      7. distribute-rgt-in 95.2%

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

      8. sub-neg 95.2%

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

   5. Simplified 95.2%

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

   6. Taylor expanded in y around 0 93.9%

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

      1. associate-/l* 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-/r/ 95.8%

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

   8. Simplified 95.8%

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

   9. Taylor expanded in z around inf 87.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+63} \lor \neg \left(x \leq 1.4 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+66} \lor \neg \left(x \leq 2.8 \cdot 10^{+50}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.4e+66) (not (<= x 2.8e+50)))
   (* x (- 1.0 (/ y t)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.4e+66) || !(x <= 2.8e+50)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (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 <= (-1.4d+66)) .or. (.not. (x <= 2.8d+50))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (z * (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 <= -1.4e+66) || !(x <= 2.8e+50)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.4e+66) or not (x <= 2.8e+50):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.4e+66) || !(x <= 2.8e+50))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.4e+66) || ~((x <= 2.8e+50)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.4e+66], N[Not[LessEqual[x, 2.8e+50]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e66 or 2.7999999999999998e50 < x

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf 92.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 92.7%

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

      2. unsub-neg 92.7%

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

   5. Simplified 92.7%

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

   if -1.4e66 < x < 2.7999999999999998e50

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 89.6%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot y}{t} + \frac{y \cdot z}{t}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 89.6%

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

      2. *-commutative 89.6%

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

      3. associate-*r/ 88.9%

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

      4. mul-1-neg 88.9%

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

      5. associate-/l* 89.4%

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

      6. distribute-lft-neg-in 89.4%

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

      7. distribute-rgt-in 95.2%

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

      8. sub-neg 95.2%

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

   5. Simplified 95.2%

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

   6. Taylor expanded in z around inf 86.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+66} \lor \neg \left(x \leq 2.8 \cdot 10^{+50}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+60} \lor \neg \left(x \leq 1.15 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.6e+60) (not (<= x 1.15e+51)))
   (* x (- 1.0 (/ y t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.6e+60) || !(x <= 1.15e+51)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.6d+60)) .or. (.not. (x <= 1.15d+51))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.6e+60) || !(x <= 1.15e+51)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.6e+60) or not (x <= 1.15e+51):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.6e+60) || !(x <= 1.15e+51))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.6e+60) || ~((x <= 1.15e+51)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.6e+60], N[Not[LessEqual[x, 1.15e+51]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.60000000000000034e60 or 1.15000000000000003e51 < x

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf 92.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 92.7%

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

      2. unsub-neg 92.7%

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

   5. Simplified 92.7%

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

   if -4.60000000000000034e60 < x < 1.15000000000000003e51

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. associate-/l* 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+60} \lor \neg \left(x \leq 1.15 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+154} \lor \neg \left(z \leq 5.7 \cdot 10^{+84}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.4e+154) (not (<= z 5.7e+84)))
   (* (- z x) (/ y t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.4e+154) || !(z <= 5.7e+84)) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x * (1.0 - (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 ((z <= (-5.4d+154)) .or. (.not. (z <= 5.7d+84))) then
        tmp = (z - x) * (y / t)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.4e+154) || !(z <= 5.7e+84)) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.4e+154) or not (z <= 5.7e+84):
		tmp = (z - x) * (y / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.4e+154) || !(z <= 5.7e+84))
		tmp = Float64(Float64(z - x) * Float64(y / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.4e+154) || ~((z <= 5.7e+84)))
		tmp = (z - x) * (y / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.4e+154], N[Not[LessEqual[z, 5.7e+84]], $MachinePrecision]], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.40000000000000011e154 or 5.6999999999999997e84 < z

   1. Initial program 86.1%

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

   3. Taylor expanded in y around -inf 65.0%

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

   4. Taylor expanded in z around 0 53.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{t} + \frac{y \cdot z}{t}} \]
   5. Step-by-step derivation

      1. +-commutative 74.8%

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

      2. *-commutative 74.8%

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

      3. associate-*r/ 84.0%

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

      4. mul-1-neg 84.0%

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

      5. associate-/l* 87.4%

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

      6. distribute-lft-neg-in 87.4%

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

      7. distribute-rgt-in 99.8%

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

      8. sub-neg 99.8%

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

   6. Simplified 78.7%

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

   if -5.40000000000000011e154 < z < 5.6999999999999997e84

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 82.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 82.1%

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

      2. unsub-neg 82.1%

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

   5. Simplified 82.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+154} \lor \neg \left(z \leq 5.7 \cdot 10^{+84}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+144} \lor \neg \left(z \leq 4.2 \cdot 10^{+203}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e+144) (not (<= z 4.2e+203)))
   (* y (/ z t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+144) || !(z <= 4.2e+203)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (1.0 - (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 ((z <= (-1.4d+144)) .or. (.not. (z <= 4.2d+203))) then
        tmp = y * (z / t)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+144) || !(z <= 4.2e+203)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e+144) or not (z <= 4.2e+203):
		tmp = y * (z / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e+144) || !(z <= 4.2e+203))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.4e+144) || ~((z <= 4.2e+203)))
		tmp = y * (z / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e+144], N[Not[LessEqual[z, 4.2e+203]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000003e144 or 4.19999999999999967e203 < z

   1. Initial program 85.4%

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

   3. Taylor expanded in y around -inf 66.0%

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

   4. Taylor expanded in z around inf 64.0%

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

      1. associate-/l* 90.1%

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

   6. Simplified 73.6%

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

   if -1.40000000000000003e144 < z < 4.19999999999999967e203

   1. Initial program 92.2%

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

   3. Taylor expanded in x around inf 79.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

   5. Simplified 79.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+144} \lor \neg \left(z \leq 4.2 \cdot 10^{+203}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+58} \lor \neg \left(y \leq 2.25 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.6e+58) (not (<= y 2.25e-20))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e+58) || !(y <= 2.25e-20)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	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 <= (-1.6d+58)) .or. (.not. (y <= 2.25d-20))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e+58) || !(y <= 2.25e-20)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.6e+58) or not (y <= 2.25e-20):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.6e+58) || !(y <= 2.25e-20))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.6e+58) || ~((y <= 2.25e-20)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.6e+58], N[Not[LessEqual[y, 2.25e-20]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000008e58 or 2.2500000000000001e-20 < y

   1. Initial program 83.0%

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

   3. Taylor expanded in y around -inf 75.0%

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

   4. Taylor expanded in z around inf 45.4%

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

      1. associate-/l* 66.0%

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

   6. Simplified 53.3%

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

   if -1.60000000000000008e58 < y < 2.2500000000000001e-20

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 66.3%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+58} \lor \neg \left(y \leq 2.25 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

3. Taylor expanded in z around 0 85.9%

   \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot y}{t} + \frac{y \cdot z}{t}\right)} \]
4. Step-by-step derivation

   1. +-commutative 85.9%

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

   2. *-commutative 85.9%

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

   3. associate-*r/ 85.0%

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

   4. mul-1-neg 85.0%

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

   5. associate-/l* 90.5%

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

   6. distribute-lft-neg-in 90.5%

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

   7. distribute-rgt-in 97.3%

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

   8. sub-neg 97.3%

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

5. Simplified 97.3%

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

6. Final simplification 97.3%

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

Alternative 11: 38.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

3. Taylor expanded in y around 0 40.6%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 91.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024180 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (+ (* x (/ y t)) (* (- z) (/ y t)))))

  (+ x (/ (* y (- z x)) t)))