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

Percentage Accurate: 92.7% → 97.5%

Time: 9.2s

Alternatives: 11

Speedup: 1.0×

• 25.0% 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: 92.7% 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: 97.5% 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 93.6%

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

3. Taylor expanded in z around 0 88.1%

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

   1. +-commutative 88.1%

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

   2. *-commutative 88.1%

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

   3. associate-*r/ 87.3%

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

   4. mul-1-neg 87.3%

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

   5. associate-/l* 90.1%

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

   6. distribute-lft-neg-in 90.1%

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

   7. distribute-rgt-in 97.6%

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

   8. sub-neg 97.6%

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

5. Simplified 97.6%

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

   1. *-commutative 97.6%

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

   2. clear-num 97.6%

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

   3. un-div-inv 98.0%

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

7. Applied egg-rr 98.0%

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

Alternative 2: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3900000000 \lor \neg \left(x \leq 3.2 \cdot 10^{+53}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3900000000.0) (not (<= x 3.2e+53)))
   (* x (- 1.0 (/ y t)))
   (+ x (/ (* z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3900000000.0) || !(x <= 3.2e+53)) {
		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 <= (-3900000000.0d0)) .or. (.not. (x <= 3.2d+53))) 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 <= -3900000000.0) || !(x <= 3.2e+53)) {
		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 <= -3900000000.0) or not (x <= 3.2e+53):
		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 <= -3900000000.0) || !(x <= 3.2e+53))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3900000000.0) || ~((x <= 3.2e+53)))
		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, -3900000000.0], N[Not[LessEqual[x, 3.2e+53]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9e9 or 3.2e53 < x

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 96.8%

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

      1. mul-1-neg 96.8%

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

      2. unsub-neg 96.8%

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

   5. Simplified 96.8%

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

   if -3.9e9 < x < 3.2e53

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0 89.5%

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

      1. +-commutative 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*r/ 88.1%

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

      4. mul-1-neg 88.1%

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

      5. associate-/l* 88.5%

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

      6. distribute-lft-neg-in 88.5%

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

      7. distribute-rgt-in 95.5%

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

      8. sub-neg 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in z around inf 79.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3900000000 \lor \neg \left(x \leq 3.2 \cdot 10^{+53}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -450000000 \lor \neg \left(x \leq 2.4 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -450000000.0) (not (<= x 2.4e+103)))
   (* x (- 1.0 (/ y t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -450000000.0) || !(x <= 2.4e+103)) {
		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 <= (-450000000.0d0)) .or. (.not. (x <= 2.4d+103))) 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 <= -450000000.0) || !(x <= 2.4e+103)) {
		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 <= -450000000.0) or not (x <= 2.4e+103):
		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 <= -450000000.0) || !(x <= 2.4e+103))
		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 <= -450000000.0) || ~((x <= 2.4e+103)))
		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, -450000000.0], N[Not[LessEqual[x, 2.4e+103]], $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 < -4.5e8 or 2.3999999999999998e103 < x

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf 97.5%

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

      1. mul-1-neg 97.5%

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

      2. unsub-neg 97.5%

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

   5. Simplified 97.5%

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

   if -4.5e8 < x < 2.3999999999999998e103

   1. Initial program 93.0%

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

   3. Taylor expanded in z around inf 78.9%

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

      1. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -450000000 \lor \neg \left(x \leq 2.4 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-72} \lor \neg \left(x \leq 2.15 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.7e-72) (not (<= x 2.15e+55)))
   (* x (- 1.0 (/ y t)))
   (* (- z x) (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e-72) || !(x <= 2.15e+55)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (z - 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) :: tmp
    if ((x <= (-1.7d-72)) .or. (.not. (x <= 2.15d+55))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (z - x) * (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 <= -1.7e-72) || !(x <= 2.15e+55)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (z - x) * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.7e-72) or not (x <= 2.15e+55):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (z - x) * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.7e-72) || !(x <= 2.15e+55))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(z - x) * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.7e-72) || ~((x <= 2.15e+55)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (z - x) * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.7e-72], N[Not[LessEqual[x, 2.15e+55]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6999999999999999e-72 or 2.1499999999999999e55 < x

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 92.8%

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

      1. mul-1-neg 92.8%

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

      2. unsub-neg 92.8%

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

   5. Simplified 92.8%

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

   if -1.6999999999999999e-72 < x < 2.1499999999999999e55

   1. Initial program 93.3%

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

   3. Taylor expanded in y around -inf 68.6%

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

   4. Taylor expanded in z around 0 66.9%

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

      1. +-commutative 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r/ 90.0%

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

      4. mul-1-neg 90.0%

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

      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 95.7%

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

      8. sub-neg 95.7%

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

   6. Simplified 71.6%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-72} \lor \neg \left(x \leq 2.15 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{-102} \lor \neg \left(x \leq 2.5 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.9e-102) (not (<= x 2.5e-21)))
   (* x (- 1.0 (/ y t)))
   (/ (* z y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.9e-102) || !(x <= 2.5e-21)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (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 <= (-5.9d-102)) .or. (.not. (x <= 2.5d-21))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (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 <= -5.9e-102) || !(x <= 2.5e-21)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.9e-102) or not (x <= 2.5e-21):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.9e-102) || !(x <= 2.5e-21))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.9e-102) || ~((x <= 2.5e-21)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.9e-102], N[Not[LessEqual[x, 2.5e-21]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9000000000000003e-102 or 2.49999999999999986e-21 < 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 87.0%

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

      1. mul-1-neg 87.0%

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

      2. unsub-neg 87.0%

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

   5. Simplified 87.0%

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

   if -5.9000000000000003e-102 < x < 2.49999999999999986e-21

   1. Initial program 94.5%

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

   3. Taylor expanded in y around -inf 71.7%

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

   4. Taylor expanded in z around inf 64.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{-102} \lor \neg \left(x \leq 2.5 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+49} \lor \neg \left(x \leq 2.2 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.2e+49) (not (<= x 2.2e+51))) (/ (* x y) y) (* z (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.2e+49) || !(x <= 2.2e+51)) {
		tmp = (x * y) / y;
	} else {
		tmp = 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 <= (-4.2d+49)) .or. (.not. (x <= 2.2d+51))) then
        tmp = (x * y) / y
    else
        tmp = 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 <= -4.2e+49) || !(x <= 2.2e+51)) {
		tmp = (x * y) / y;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.2e+49) or not (x <= 2.2e+51):
		tmp = (x * y) / y
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.2e+49) || !(x <= 2.2e+51))
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.2e+49) || ~((x <= 2.2e+51)))
		tmp = (x * y) / y;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.2e+49], N[Not[LessEqual[x, 2.2e+51]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.20000000000000022e49 or 2.19999999999999992e51 < x

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 69.8%

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

      1. associate--l+ 69.8%

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

      2. div-sub 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in y around 0 29.1%

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

      1. *-commutative 29.1%

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

      2. associate-*l/ 61.2%

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

   8. Applied egg-rr 61.2%

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

   if -4.20000000000000022e49 < x < 2.19999999999999992e51

   1. Initial program 93.6%

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

   3. Taylor expanded in y around -inf 67.7%

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

   4. Taylor expanded in z around 0 63.3%

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

      1. +-commutative 89.2%

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

      2. *-commutative 89.2%

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

      3. associate-*r/ 87.8%

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

      4. mul-1-neg 87.8%

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

      5. associate-/l* 88.2%

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

      6. distribute-lft-neg-in 88.2%

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

      7. distribute-rgt-in 95.7%

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

      8. sub-neg 95.7%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in z around inf 55.0%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+49} \lor \neg \left(x \leq 2.2 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-21} \lor \neg \left(y \leq 8.8 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.25e-21) (not (<= y 8.8e+24))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e-21) || !(y <= 8.8e+24)) {
		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 <= (-1.25d-21)) .or. (.not. (y <= 8.8d+24))) 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 <= -1.25e-21) || !(y <= 8.8e+24)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.25e-21) or not (y <= 8.8e+24):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.25e-21) || !(y <= 8.8e+24))
		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 <= -1.25e-21) || ~((y <= 8.8e+24)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.25e-21], N[Not[LessEqual[y, 8.8e+24]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999993e-21 or 8.80000000000000007e24 < y

   1. Initial program 88.1%

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

   3. Taylor expanded in y around inf 95.1%

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

      1. associate--l+ 95.1%

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

      2. div-sub 96.0%

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

   5. Simplified 96.0%

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

   6. Taylor expanded in x around 0 50.3%

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

   if -1.24999999999999993e-21 < y < 8.80000000000000007e24

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 59.0%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-21} \lor \neg \left(y \leq 8.8 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -880000000:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -880000000.0)
   (* x (/ y (- t)))
   (if (<= x 2.8e+52) (* z (/ y t)) (/ (* x y) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -880000000.0) {
		tmp = x * (y / -t);
	} else if (x <= 2.8e+52) {
		tmp = z * (y / t);
	} else {
		tmp = (x * y) / 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 <= (-880000000.0d0)) then
        tmp = x * (y / -t)
    else if (x <= 2.8d+52) then
        tmp = z * (y / t)
    else
        tmp = (x * y) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -880000000.0) {
		tmp = x * (y / -t);
	} else if (x <= 2.8e+52) {
		tmp = z * (y / t);
	} else {
		tmp = (x * y) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -880000000.0:
		tmp = x * (y / -t)
	elif x <= 2.8e+52:
		tmp = z * (y / t)
	else:
		tmp = (x * y) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -880000000.0)
		tmp = Float64(x * Float64(y / Float64(-t)));
	elseif (x <= 2.8e+52)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = Float64(Float64(x * y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -880000000.0)
		tmp = x * (y / -t);
	elseif (x <= 2.8e+52)
		tmp = z * (y / t);
	else
		tmp = (x * y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -880000000.0], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+52], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.8e8

   1. Initial program 94.8%

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

   3. Taylor expanded in y around -inf 57.6%

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

   4. Taylor expanded in z around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. associate-/l* 58.9%

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

      3. distribute-rgt-neg-in 58.9%

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

      4. mul-1-neg 58.9%

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

      5. associate-*r/ 58.9%

         \[\leadsto x \cdot \color{blue}{\frac{-1 \cdot y}{t}} \]

      6. mul-1-neg 58.9%

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

   6. Simplified 58.9%

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

   if -8.8e8 < x < 2.8e52

   1. Initial program 93.4%

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

   3. Taylor expanded in y around -inf 67.2%

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

   4. Taylor expanded in z around 0 63.4%

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

      1. +-commutative 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*r/ 88.1%

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

      4. mul-1-neg 88.1%

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

      5. associate-/l* 88.5%

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

      6. distribute-lft-neg-in 88.5%

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

      7. distribute-rgt-in 95.5%

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

      8. sub-neg 95.5%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in z around inf 56.2%

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

   if 2.8e52 < x

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf 63.3%

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

      1. associate--l+ 63.3%

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

      2. div-sub 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around 0 36.4%

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

      1. *-commutative 36.4%

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

      2. associate-*l/ 68.8%

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

   8. Applied egg-rr 68.8%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -880000000:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+95}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.8e-44) x (if (<= t 1.85e+95) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.8e-44) {
		tmp = x;
	} else if (t <= 1.85e+95) {
		tmp = z * (y / 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 (t <= (-2.8d-44)) then
        tmp = x
    else if (t <= 1.85d+95) then
        tmp = z * (y / 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 (t <= -2.8e-44) {
		tmp = x;
	} else if (t <= 1.85e+95) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.8e-44:
		tmp = x
	elif t <= 1.85e+95:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.8e-44)
		tmp = x;
	elseif (t <= 1.85e+95)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.8e-44)
		tmp = x;
	elseif (t <= 1.85e+95)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.8e-44], x, If[LessEqual[t, 1.85e+95], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e-44 or 1.8500000000000001e95 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in y around 0 64.6%

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

   if -2.8e-44 < t < 1.8500000000000001e95

   1. Initial program 97.2%

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

   3. Taylor expanded in y around -inf 82.6%

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

   4. Taylor expanded in z around 0 74.1%

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

      1. +-commutative 88.6%

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

      2. *-commutative 88.6%

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

      3. associate-*r/ 83.9%

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

      4. mul-1-neg 83.9%

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

      5. associate-/l* 82.9%

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

      6. distribute-lft-neg-in 82.9%

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

      7. distribute-rgt-in 96.5%

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

      8. sub-neg 96.5%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in z around inf 48.6%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+95}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.4% 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 93.6%

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

3. Taylor expanded in z around 0 88.1%

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

   1. +-commutative 88.1%

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

   2. *-commutative 88.1%

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

   3. associate-*r/ 87.3%

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

   4. mul-1-neg 87.3%

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

   5. associate-/l* 90.1%

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

   6. distribute-lft-neg-in 90.1%

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

   7. distribute-rgt-in 97.6%

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

   8. sub-neg 97.6%

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

5. Simplified 97.6%

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

6. Final simplification 97.6%

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

Alternative 11: 38.7% 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 93.6%

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

3. Taylor expanded in y around 0 38.1%

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

Developer Target 1: 90.6% 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 2024185 
(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)))