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

Percentage Accurate: 93.0% → 97.4%

Time: 10.0s

Alternatives: 10

Speedup: 1.0×

• 24.8% 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: 93.0% 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: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 2: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-123} \lor \neg \left(x \leq 1.02 \cdot 10^{-218}\right) \land \left(x \leq 4 \cdot 10^{-111} \lor \neg \left(x \leq 4 \cdot 10^{-35}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9e-123)
         (and (not (<= x 1.02e-218)) (or (<= x 4e-111) (not (<= x 4e-35)))))
   (* x (- 1.0 (/ y t)))
   (* y (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e-123) || (!(x <= 1.02e-218) && ((x <= 4e-111) || !(x <= 4e-35)))) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = 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 <= (-9d-123)) .or. (.not. (x <= 1.02d-218)) .and. (x <= 4d-111) .or. (.not. (x <= 4d-35))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = 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 <= -9e-123) || (!(x <= 1.02e-218) && ((x <= 4e-111) || !(x <= 4e-35)))) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9e-123) or (not (x <= 1.02e-218) and ((x <= 4e-111) or not (x <= 4e-35))):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9e-123) || (!(x <= 1.02e-218) && ((x <= 4e-111) || !(x <= 4e-35))))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -9e-123) || (~((x <= 1.02e-218)) && ((x <= 4e-111) || ~((x <= 4e-35)))))
		tmp = x * (1.0 - (y / t));
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9e-123], And[N[Not[LessEqual[x, 1.02e-218]], $MachinePrecision], Or[LessEqual[x, 4e-111], N[Not[LessEqual[x, 4e-35]], $MachinePrecision]]]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999986e-123 or 1.02e-218 < x < 4.00000000000000035e-111 or 4.00000000000000003e-35 < x

   1. Initial program 93.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

   7. Simplified 81.6%

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

   if -8.99999999999999986e-123 < x < 1.02e-218 or 4.00000000000000035e-111 < x < 4.00000000000000003e-35

   1. Initial program 92.3%

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

      1. associate-*l/ 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in y around inf 83.9%

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

   6. Taylor expanded in z around inf 77.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-123} \lor \neg \left(x \leq 1.02 \cdot 10^{-218}\right) \land \left(x \leq 4 \cdot 10^{-111} \lor \neg \left(x \leq 4 \cdot 10^{-35}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;x \leq -55000000000 \lor \neg \left(x \leq 9.5 \cdot 10^{+28}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))))
   (if (<= x -7.6e+114)
     t_1
     (if (<= x -9e+77)
       (+ x (* (/ y t) z))
       (if (or (<= x -55000000000.0) (not (<= x 9.5e+28)))
         t_1
         (+ x (/ y (/ t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -7.6e+114) {
		tmp = t_1;
	} else if (x <= -9e+77) {
		tmp = x + ((y / t) * z);
	} else if ((x <= -55000000000.0) || !(x <= 9.5e+28)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    if (x <= (-7.6d+114)) then
        tmp = t_1
    else if (x <= (-9d+77)) then
        tmp = x + ((y / t) * z)
    else if ((x <= (-55000000000.0d0)) .or. (.not. (x <= 9.5d+28))) then
        tmp = t_1
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -7.6e+114) {
		tmp = t_1;
	} else if (x <= -9e+77) {
		tmp = x + ((y / t) * z);
	} else if ((x <= -55000000000.0) || !(x <= 9.5e+28)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -7.6e+114:
		tmp = t_1
	elif x <= -9e+77:
		tmp = x + ((y / t) * z)
	elif (x <= -55000000000.0) or not (x <= 9.5e+28):
		tmp = t_1
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -7.6e+114)
		tmp = t_1;
	elseif (x <= -9e+77)
		tmp = Float64(x + Float64(Float64(y / t) * z));
	elseif ((x <= -55000000000.0) || !(x <= 9.5e+28))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (x <= -7.6e+114)
		tmp = t_1;
	elseif (x <= -9e+77)
		tmp = x + ((y / t) * z);
	elseif ((x <= -55000000000.0) || ~((x <= 9.5e+28)))
		tmp = t_1;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.6e+114], t$95$1, If[LessEqual[x, -9e+77], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -55000000000.0], N[Not[LessEqual[x, 9.5e+28]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.6000000000000001e114 or -9.00000000000000049e77 < x < -5.5e10 or 9.49999999999999927e28 < x

   1. Initial program 93.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 93.9%

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

      1. mul-1-neg 93.9%

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

      2. unsub-neg 93.9%

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

   7. Simplified 93.9%

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

   if -7.6000000000000001e114 < x < -9.00000000000000049e77

   1. Initial program 89.6%

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

   5. Taylor expanded in z around inf 87.1%

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

      1. associate-*l/ 97.5%

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

      2. *-commutative 97.5%

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

   7. Simplified 97.5%

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

   if -5.5e10 < x < 9.49999999999999927e28

   1. Initial program 92.8%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around inf 88.5%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;x \leq -55000000000 \lor \neg \left(x \leq 9.5 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= t -2.7e+28)
     x
     (if (<= t -8e-280)
       t_1
       (if (<= t 5.5e-191) (* (/ x t) (- y)) (if (<= t 2.2e+190) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (t <= -2.7e+28) {
		tmp = x;
	} else if (t <= -8e-280) {
		tmp = t_1;
	} else if (t <= 5.5e-191) {
		tmp = (x / t) * -y;
	} else if (t <= 2.2e+190) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (t <= (-2.7d+28)) then
        tmp = x
    else if (t <= (-8d-280)) then
        tmp = t_1
    else if (t <= 5.5d-191) then
        tmp = (x / t) * -y
    else if (t <= 2.2d+190) then
        tmp = t_1
    else
        tmp = x
    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 (t <= -2.7e+28) {
		tmp = x;
	} else if (t <= -8e-280) {
		tmp = t_1;
	} else if (t <= 5.5e-191) {
		tmp = (x / t) * -y;
	} else if (t <= 2.2e+190) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if t <= -2.7e+28:
		tmp = x
	elif t <= -8e-280:
		tmp = t_1
	elif t <= 5.5e-191:
		tmp = (x / t) * -y
	elif t <= 2.2e+190:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t <= -2.7e+28)
		tmp = x;
	elseif (t <= -8e-280)
		tmp = t_1;
	elseif (t <= 5.5e-191)
		tmp = Float64(Float64(x / t) * Float64(-y));
	elseif (t <= 2.2e+190)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (t <= -2.7e+28)
		tmp = x;
	elseif (t <= -8e-280)
		tmp = t_1;
	elseif (t <= 5.5e-191)
		tmp = (x / t) * -y;
	elseif (t <= 2.2e+190)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+28], x, If[LessEqual[t, -8e-280], t$95$1, If[LessEqual[t, 5.5e-191], N[(N[(x / t), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t, 2.2e+190], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000002e28 or 2.2e190 < t

   1. Initial program 88.3%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around 0 68.8%

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

   if -2.7000000000000002e28 < t < -7.9999999999999997e-280 or 5.5000000000000001e-191 < t < 2.2e190

   1. Initial program 94.9%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around inf 76.1%

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

   6. Taylor expanded in z around inf 58.3%

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

   if -7.9999999999999997e-280 < t < 5.5000000000000001e-191

   1. Initial program 97.1%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in x around inf 70.1%

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

      1. mul-1-neg 70.1%

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

      2. unsub-neg 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in y around inf 67.4%

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

      1. associate-*r/ 64.4%

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

      2. *-commutative 64.4%

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

      3. associate-*l/ 67.4%

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

      4. associate-*r/ 64.5%

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

      5. neg-mul-1 64.5%

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

      6. distribute-rgt-neg-in 64.5%

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

      7. distribute-neg-frac 64.5%

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

   10. Simplified 64.5%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+190}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.48 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= t -1.35e+29)
     x
     (if (<= t -1.35e-246)
       t_1
       (if (<= t 1.48e-71) (/ x (/ (- t) y)) (if (<= t 2.2e+190) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (t <= -1.35e+29) {
		tmp = x;
	} else if (t <= -1.35e-246) {
		tmp = t_1;
	} else if (t <= 1.48e-71) {
		tmp = x / (-t / y);
	} else if (t <= 2.2e+190) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (t <= (-1.35d+29)) then
        tmp = x
    else if (t <= (-1.35d-246)) then
        tmp = t_1
    else if (t <= 1.48d-71) then
        tmp = x / (-t / y)
    else if (t <= 2.2d+190) then
        tmp = t_1
    else
        tmp = x
    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 (t <= -1.35e+29) {
		tmp = x;
	} else if (t <= -1.35e-246) {
		tmp = t_1;
	} else if (t <= 1.48e-71) {
		tmp = x / (-t / y);
	} else if (t <= 2.2e+190) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if t <= -1.35e+29:
		tmp = x
	elif t <= -1.35e-246:
		tmp = t_1
	elif t <= 1.48e-71:
		tmp = x / (-t / y)
	elif t <= 2.2e+190:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t <= -1.35e+29)
		tmp = x;
	elseif (t <= -1.35e-246)
		tmp = t_1;
	elseif (t <= 1.48e-71)
		tmp = Float64(x / Float64(Float64(-t) / y));
	elseif (t <= 2.2e+190)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (t <= -1.35e+29)
		tmp = x;
	elseif (t <= -1.35e-246)
		tmp = t_1;
	elseif (t <= 1.48e-71)
		tmp = x / (-t / y);
	elseif (t <= 2.2e+190)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+29], x, If[LessEqual[t, -1.35e-246], t$95$1, If[LessEqual[t, 1.48e-71], N[(x / N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+190], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e29 or 2.2e190 < t

   1. Initial program 88.3%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around 0 68.8%

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

   if -1.35e29 < t < -1.3499999999999999e-246 or 1.4799999999999999e-71 < t < 2.2e190

   1. Initial program 94.4%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around inf 78.4%

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

   6. Taylor expanded in z around inf 61.4%

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

   if -1.3499999999999999e-246 < t < 1.4799999999999999e-71

   1. Initial program 96.9%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in y around inf 57.5%

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

      1. associate-*r/ 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*l/ 57.5%

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

      4. associate-*r/ 52.9%

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

      5. neg-mul-1 52.9%

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

      6. distribute-rgt-neg-in 52.9%

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

      7. distribute-neg-frac 52.9%

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

   10. Simplified 52.9%

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

       1. associate-*r/ 57.5%

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

       2. add-sqr-sqrt 28.0%

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

       3. sqrt-unprod 28.3%

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

       4. sqr-neg 28.3%

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

       5. sqrt-unprod 2.2%

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

       6. add-sqr-sqrt 4.6%

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

       7. *-commutative 4.6%

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

       8. associate-/l* 4.7%

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

       9. frac-2neg 4.7%

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

       10. add-sqr-sqrt 2.4%

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

       11. sqrt-unprod 28.6%

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

       12. sqr-neg 28.6%

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

       13. sqrt-unprod 29.6%

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

       14. add-sqr-sqrt 60.5%

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

   12. Applied egg-rr 60.5%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.48 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+190}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+25} \lor \neg \left(y \leq 160\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4e+25) (not (<= y 160.0)))
   (* y (/ (- z x) t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e+25) || !(y <= 160.0)) {
		tmp = y * ((z - x) / 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 ((y <= (-3.4d+25)) .or. (.not. (y <= 160.0d0))) then
        tmp = y * ((z - x) / 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 ((y <= -3.4e+25) || !(y <= 160.0)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.4e+25) or not (y <= 160.0):
		tmp = y * ((z - x) / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.4e+25) || !(y <= 160.0))
		tmp = Float64(y * Float64(Float64(z - x) / 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 ((y <= -3.4e+25) || ~((y <= 160.0)))
		tmp = y * ((z - x) / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.4e+25], N[Not[LessEqual[y, 160.0]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999984e25 or 160 < y

   1. Initial program 89.1%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around inf 86.2%

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

   6. Taylor expanded in z around 0 75.0%

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

      1. +-commutative 75.0%

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

      2. associate-*r/ 80.1%

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

      3. mul-1-neg 80.1%

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

      4. associate-*r/ 79.5%

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

      5. *-commutative 79.5%

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

      6. associate-*l/ 80.1%

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

      7. associate-*r/ 82.3%

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

      8. distribute-rgt-neg-in 82.3%

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

      9. *-rgt-identity 82.3%

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

      10. distribute-lft-out 86.2%

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

      11. distribute-lft-neg-in 86.2%

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

      12. cancel-sign-sub-inv 86.2%

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

      13. *-rgt-identity 86.2%

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

      14. div-sub 86.9%

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

   8. Simplified 86.9%

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

   if -3.39999999999999984e25 < y < 160

   1. Initial program 96.8%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in x around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

   7. Simplified 70.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+25} \lor \neg \left(y \leq 160\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+115} \lor \neg \left(x \leq 1.1 \cdot 10^{+27}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.4e+115) (not (<= x 1.1e+27)))
   (* x (- 1.0 (/ y t)))
   (+ x (* (/ y t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e+115) || !(x <= 1.1e+27)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.4d+115)) .or. (.not. (x <= 1.1d+27))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + ((y / t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e+115) || !(x <= 1.1e+27)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.4e+115) or not (x <= 1.1e+27):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.4e+115) || !(x <= 1.1e+27))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(y / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.4e+115) || ~((x <= 1.1e+27)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.4e+115], N[Not[LessEqual[x, 1.1e+27]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4000000000000001e115 or 1.0999999999999999e27 < x

   1. Initial program 93.3%

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

   5. Taylor expanded in x around inf 95.0%

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

      1. mul-1-neg 95.0%

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

      2. unsub-neg 95.0%

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

   7. Simplified 95.0%

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

   if -4.4000000000000001e115 < x < 1.0999999999999999e27

   1. Initial program 92.7%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around inf 81.8%

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

      1. associate-*l/ 86.1%

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

      2. *-commutative 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+115} \lor \neg \left(x \leq 1.1 \cdot 10^{+27}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-63} \lor \neg \left(t \leq 3.55 \cdot 10^{-72}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e-63) (not (<= t 3.55e-72)))
   (+ x (/ y (/ t z)))
   (/ (* y (- z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-63) || !(t <= 3.55e-72)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = (y * (z - x)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.2d-63)) .or. (.not. (t <= 3.55d-72))) then
        tmp = x + (y / (t / z))
    else
        tmp = (y * (z - x)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-63) || !(t <= 3.55e-72)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = (y * (z - x)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.2e-63) or not (t <= 3.55e-72):
		tmp = x + (y / (t / z))
	else:
		tmp = (y * (z - x)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.2e-63) || !(t <= 3.55e-72))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.2e-63) || ~((t <= 3.55e-72)))
		tmp = x + (y / (t / z));
	else
		tmp = (y * (z - x)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.2e-63], N[Not[LessEqual[t, 3.55e-72]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.19999999999999989e-63 or 3.5499999999999998e-72 < t

   1. Initial program 90.9%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around inf 89.5%

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

   if -3.19999999999999989e-63 < t < 3.5499999999999998e-72

   1. Initial program 96.1%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around inf 81.3%

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

   6. Taylor expanded in t around 0 87.6%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-63} \lor \neg \left(t \leq 3.55 \cdot 10^{-72}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+190}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.1e+30) x (if (<= t 2.2e+190) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e+30) {
		tmp = x;
	} else if (t <= 2.2e+190) {
		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 (t <= (-2.1d+30)) then
        tmp = x
    else if (t <= 2.2d+190) 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 (t <= -2.1e+30) {
		tmp = x;
	} else if (t <= 2.2e+190) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.1e+30:
		tmp = x
	elif t <= 2.2e+190:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.1e+30)
		tmp = x;
	elseif (t <= 2.2e+190)
		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 (t <= -2.1e+30)
		tmp = x;
	elseif (t <= 2.2e+190)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.1e+30], x, If[LessEqual[t, 2.2e+190], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e30 or 2.2e190 < t

   1. Initial program 88.3%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around 0 68.8%

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

   if -2.1e30 < t < 2.2e190

   1. Initial program 95.4%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 78.0%

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

   6. Taylor expanded in z around inf 56.4%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+190}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.1% 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 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in y around 0 35.4%

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

6. Final simplification 35.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 91.1% 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 2024034 
(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)))