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

Percentage Accurate: 92.9% → 97.8%

Time: 9.7s

Alternatives: 12

Speedup: 1.0×

• 24.4% 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: 92.9% 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: 97.8% 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 90.0%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

   1. *-commutative 98.3%

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

   2. clear-num 98.3%

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

   3. un-div-inv 98.4%

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

5. Applied egg-rr 98.4%

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

6. Final simplification 98.4%

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

Alternative 2: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-155} \lor \neg \left(z \leq 3.5 \cdot 10^{+30}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.85e-155) (not (<= z 3.5e+30)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e-155) || !(z <= 3.5e+30)) {
		tmp = x + (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 <= (-1.85d-155)) .or. (.not. (z <= 3.5d+30))) then
        tmp = x + (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 <= -1.85e-155) || !(z <= 3.5e+30)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.85e-155) or not (z <= 3.5e+30):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.85e-155) || !(z <= 3.5e+30))
		tmp = Float64(x + 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 <= -1.85e-155) || ~((z <= 3.5e+30)))
		tmp = x + (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, -1.85e-155], N[Not[LessEqual[z, 3.5e+30]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e-155 or 3.50000000000000021e30 < z

   1. Initial program 87.3%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. clear-num 99.1%

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

      3. un-div-inv 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in z around inf 80.4%

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

      1. associate-*r/ 84.3%

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

   8. Simplified 84.3%

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

   if -1.85e-155 < z < 3.50000000000000021e30

   1. Initial program 94.8%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

   6. Simplified 87.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-155} \lor \neg \left(z \leq 3.5 \cdot 10^{+30}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]

Alternative 3: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-155} \lor \neg \left(z \leq 2.22 \cdot 10^{+30}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.55e-155) (not (<= z 2.22e+30)))
   (+ x (* z (/ y t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e-155) || !(z <= 2.22e+30)) {
		tmp = x + (z * (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 <= (-1.55d-155)) .or. (.not. (z <= 2.22d+30))) then
        tmp = x + (z * (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 <= -1.55e-155) || !(z <= 2.22e+30)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.55e-155) or not (z <= 2.22e+30):
		tmp = x + (z * (y / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.55e-155) || !(z <= 2.22e+30))
		tmp = Float64(x + Float64(z * 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 <= -1.55e-155) || ~((z <= 2.22e+30)))
		tmp = x + (z * (y / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.55e-155], N[Not[LessEqual[z, 2.22e+30]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e-155 or 2.22e30 < z

   1. Initial program 87.3%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around inf 80.4%

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

      1. associate-*l/ 89.3%

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

      2. *-commutative 89.3%

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

   6. Simplified 89.3%

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

   if -1.55e-155 < z < 2.22e30

   1. Initial program 94.8%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

   6. Simplified 87.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-155} \lor \neg \left(z \leq 2.22 \cdot 10^{+30}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]

Alternative 4: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-156}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.6e-156)
   (+ x (* z (/ y t)))
   (if (<= z 2.3e+30) (* x (- 1.0 (/ y t))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.6e-156) {
		tmp = x + (z * (y / t));
	} else if (z <= 2.3e+30) {
		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 (z <= (-8.6d-156)) then
        tmp = x + (z * (y / t))
    else if (z <= 2.3d+30) 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 (z <= -8.6e-156) {
		tmp = x + (z * (y / t));
	} else if (z <= 2.3e+30) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.6e-156:
		tmp = x + (z * (y / t))
	elif z <= 2.3e+30:
		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 (z <= -8.6e-156)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (z <= 2.3e+30)
		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 (z <= -8.6e-156)
		tmp = x + (z * (y / t));
	elseif (z <= 2.3e+30)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.6e-156], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+30], 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 3 regimes

2. if z < -8.59999999999999954e-156

   1. Initial program 87.4%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around inf 77.4%

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

      1. associate-*l/ 86.0%

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

      2. *-commutative 86.0%

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

   6. Simplified 86.0%

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

   if -8.59999999999999954e-156 < z < 2.3e30

   1. Initial program 94.8%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

   6. Simplified 87.3%

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

   if 2.3e30 < z

   1. Initial program 87.1%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in z around inf 84.2%

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

      1. associate-/r/ 94.9%

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

   6. Applied egg-rr 94.9%

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

      1. *-commutative 94.9%

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

      2. clear-num 94.9%

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

      3. un-div-inv 95.0%

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

   8. Applied egg-rr 95.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-156}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 5: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-158}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{+30}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e-158)
   (+ x (* z (/ y t)))
   (if (<= z 2.22e+30) (- x (/ x (/ t y))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e-158) {
		tmp = x + (z * (y / t));
	} else if (z <= 2.22e+30) {
		tmp = x - (x / (t / y));
	} 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 (z <= (-5.8d-158)) then
        tmp = x + (z * (y / t))
    else if (z <= 2.22d+30) then
        tmp = x - (x / (t / y))
    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 (z <= -5.8e-158) {
		tmp = x + (z * (y / t));
	} else if (z <= 2.22e+30) {
		tmp = x - (x / (t / y));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.8e-158:
		tmp = x + (z * (y / t))
	elif z <= 2.22e+30:
		tmp = x - (x / (t / y))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.8e-158)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (z <= 2.22e+30)
		tmp = Float64(x - Float64(x / Float64(t / y)));
	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 (z <= -5.8e-158)
		tmp = x + (z * (y / t));
	elseif (z <= 2.22e+30)
		tmp = x - (x / (t / y));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.8e-158], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.22e+30], N[(x - N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.79999999999999961e-158

   1. Initial program 87.4%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around inf 77.4%

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

      1. associate-*l/ 86.0%

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

      2. *-commutative 86.0%

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

   6. Simplified 86.0%

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

   if -5.79999999999999961e-158 < z < 2.22e30

   1. Initial program 94.8%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. associate-/l* 87.4%

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

   6. Simplified 87.4%

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

   if 2.22e30 < z

   1. Initial program 87.1%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in z around inf 84.2%

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

      1. associate-/r/ 94.9%

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

   6. Applied egg-rr 94.9%

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

      1. *-commutative 94.9%

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

      2. clear-num 94.9%

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

      3. un-div-inv 95.0%

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

   8. Applied egg-rr 95.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-158}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{+30}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 6: 50.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+47} \lor \neg \left(y \leq 5.3 \cdot 10^{-6}\right):\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.35e+47) (not (<= y 5.3e-6))) (* (- y) (/ x t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.35e+47) || !(y <= 5.3e-6)) {
		tmp = -y * (x / 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 <= (-1.35d+47)) .or. (.not. (y <= 5.3d-6))) then
        tmp = -y * (x / 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 <= -1.35e+47) || !(y <= 5.3e-6)) {
		tmp = -y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.35e+47) or not (y <= 5.3e-6):
		tmp = -y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.35e+47) || !(y <= 5.3e-6))
		tmp = Float64(Float64(-y) * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.35e+47) || ~((y <= 5.3e-6)))
		tmp = -y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.35e+47], N[Not[LessEqual[y, 5.3e-6]], $MachinePrecision]], N[((-y) * N[(x / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.34999999999999998e47 or 5.3000000000000001e-6 < y

   1. Initial program 82.9%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. unsub-neg 53.5%

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

   6. Simplified 53.5%

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

   7. Taylor expanded in y around inf 43.0%

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

      1. associate-*r/ 43.0%

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

      2. neg-mul-1 43.0%

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

   9. Simplified 43.0%

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

       1. associate-*r/ 39.7%

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

       2. distribute-rgt-neg-out 39.7%

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

       3. distribute-neg-frac 39.7%

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

       4. associate-*l/ 41.0%

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

       5. *-commutative 41.0%

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

   11. Applied egg-rr 41.0%

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

   if -1.34999999999999998e47 < y < 5.3000000000000001e-6

   1. Initial program 97.2%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 61.2%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+47} \lor \neg \left(y \leq 5.3 \cdot 10^{-6}\right):\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+47} \lor \neg \left(y \leq 1.5 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e+47) (not (<= y 1.5e-14))) (* (/ y t) (- x)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e+47) || !(y <= 1.5e-14)) {
		tmp = (y / t) * -x;
	} 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 <= (-1.4d+47)) .or. (.not. (y <= 1.5d-14))) then
        tmp = (y / t) * -x
    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 <= -1.4e+47) || !(y <= 1.5e-14)) {
		tmp = (y / t) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e+47) or not (y <= 1.5e-14):
		tmp = (y / t) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e+47) || !(y <= 1.5e-14))
		tmp = Float64(Float64(y / t) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.4e+47) || ~((y <= 1.5e-14)))
		tmp = (y / t) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.4e+47], N[Not[LessEqual[y, 1.5e-14]], $MachinePrecision]], N[(N[(y / t), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999994e47 or 1.4999999999999999e-14 < y

   1. Initial program 82.9%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. unsub-neg 53.5%

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

   6. Simplified 53.5%

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

   7. Taylor expanded in y around inf 43.0%

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

      1. associate-*r/ 43.0%

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

      2. neg-mul-1 43.0%

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

   9. Simplified 43.0%

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

   if -1.39999999999999994e47 < y < 1.4999999999999999e-14

   1. Initial program 97.2%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 61.2%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+47} \lor \neg \left(y \leq 1.5 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+47} \lor \neg \left(y \leq 7 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e+47) (not (<= y 7e-15))) (/ x (/ (- t) y)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e+47) || !(y <= 7e-15)) {
		tmp = x / (-t / y);
	} 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 <= (-1.3d+47)) .or. (.not. (y <= 7d-15))) then
        tmp = x / (-t / y)
    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 <= -1.3e+47) || !(y <= 7e-15)) {
		tmp = x / (-t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.3e+47) or not (y <= 7e-15):
		tmp = x / (-t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.3e+47) || !(y <= 7e-15))
		tmp = Float64(x / Float64(Float64(-t) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.3e+47) || ~((y <= 7e-15)))
		tmp = x / (-t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.3e+47], N[Not[LessEqual[y, 7e-15]], $MachinePrecision]], N[(x / N[((-t) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.30000000000000002e47 or 7.0000000000000001e-15 < y

   1. Initial program 82.9%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. unsub-neg 53.5%

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

   6. Simplified 53.5%

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

   7. Taylor expanded in y around inf 43.0%

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

      1. associate-*r/ 43.0%

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

      2. neg-mul-1 43.0%

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

   9. Simplified 43.0%

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

       1. frac-2neg 43.0%

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

       2. remove-double-neg 43.0%

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

       3. associate-*r/ 39.7%

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

   11. Applied egg-rr 39.7%

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

       1. associate-/l* 43.0%

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

   13. Simplified 43.0%

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

   if -1.30000000000000002e47 < y < 7.0000000000000001e-15

   1. Initial program 97.2%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 61.2%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+47} \lor \neg \left(y \leq 7 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 97.8% 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 90.0%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 10: 39.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+224}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 2.2e+224) x (* x (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e+224) {
		tmp = x;
	} 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) :: tmp
    if (y <= 2.2d+224) then
        tmp = x
    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 tmp;
	if (y <= 2.2e+224) {
		tmp = x;
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.2e+224:
		tmp = x
	else:
		tmp = x * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.2e+224)
		tmp = x;
	else
		tmp = Float64(x * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.2e+224)
		tmp = x;
	else
		tmp = x * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.2e+224], x, N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.2e224

   1. Initial program 89.6%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around 0 39.5%

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

   if 2.2e224 < y

   1. Initial program 95.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in y around inf 60.3%

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

      1. associate-*r/ 60.3%

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

      2. neg-mul-1 60.3%

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

   9. Simplified 60.3%

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

       1. *-commutative 60.3%

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

       2. associate-*l/ 55.5%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 30.3%

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

       5. sqr-neg 30.3%

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

       6. sqrt-unprod 11.7%

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

       7. add-sqr-sqrt 11.7%

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

       8. associate-*r/ 11.7%

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

       9. clear-num 11.7%

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

       10. un-div-inv 11.7%

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

   11. Applied egg-rr 11.7%

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

       1. associate-/r/ 25.3%

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

   13. Applied egg-rr 25.3%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+224}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \]

Alternative 11: 65.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{y}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ y t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (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 * (1.0d0 - (y / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (y / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (y / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(y / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (y / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.0%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Taylor expanded in x around inf 61.7%

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

   1. mul-1-neg 61.7%

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

   2. unsub-neg 61.7%

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

6. Simplified 61.7%

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

7. Final simplification 61.7%

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

Alternative 12: 39.3% 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 90.0%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Taylor expanded in y around 0 36.7%

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

5. Final simplification 36.7%

   \[\leadsto x \]

Developer target: 91.4% 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 2023308 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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