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

Percentage Accurate: 92.9% → 97.3%

Time: 9.8s

Alternatives: 10

Speedup: 1.0×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 2: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a} \cdot \left(-y\right)\\ t_2 := \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.46 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z a) (- y))) (t_2 (/ (* y t) a)))
   (if (<= a -3.7e-75)
     x
     (if (<= a -1.46e-265)
       t_2
       (if (<= a 6.4e-287)
         t_1
         (if (<= a 5.4e-217) t_2 (if (<= a 5.6e-64) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / a) * -y;
	double t_2 = (y * t) / a;
	double tmp;
	if (a <= -3.7e-75) {
		tmp = x;
	} else if (a <= -1.46e-265) {
		tmp = t_2;
	} else if (a <= 6.4e-287) {
		tmp = t_1;
	} else if (a <= 5.4e-217) {
		tmp = t_2;
	} else if (a <= 5.6e-64) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z / a) * -y
    t_2 = (y * t) / a
    if (a <= (-3.7d-75)) then
        tmp = x
    else if (a <= (-1.46d-265)) then
        tmp = t_2
    else if (a <= 6.4d-287) then
        tmp = t_1
    else if (a <= 5.4d-217) then
        tmp = t_2
    else if (a <= 5.6d-64) 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 a) {
	double t_1 = (z / a) * -y;
	double t_2 = (y * t) / a;
	double tmp;
	if (a <= -3.7e-75) {
		tmp = x;
	} else if (a <= -1.46e-265) {
		tmp = t_2;
	} else if (a <= 6.4e-287) {
		tmp = t_1;
	} else if (a <= 5.4e-217) {
		tmp = t_2;
	} else if (a <= 5.6e-64) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / a) * -y
	t_2 = (y * t) / a
	tmp = 0
	if a <= -3.7e-75:
		tmp = x
	elif a <= -1.46e-265:
		tmp = t_2
	elif a <= 6.4e-287:
		tmp = t_1
	elif a <= 5.4e-217:
		tmp = t_2
	elif a <= 5.6e-64:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / a) * Float64(-y))
	t_2 = Float64(Float64(y * t) / a)
	tmp = 0.0
	if (a <= -3.7e-75)
		tmp = x;
	elseif (a <= -1.46e-265)
		tmp = t_2;
	elseif (a <= 6.4e-287)
		tmp = t_1;
	elseif (a <= 5.4e-217)
		tmp = t_2;
	elseif (a <= 5.6e-64)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / a) * -y;
	t_2 = (y * t) / a;
	tmp = 0.0;
	if (a <= -3.7e-75)
		tmp = x;
	elseif (a <= -1.46e-265)
		tmp = t_2;
	elseif (a <= 6.4e-287)
		tmp = t_1;
	elseif (a <= 5.4e-217)
		tmp = t_2;
	elseif (a <= 5.6e-64)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -3.7e-75], x, If[LessEqual[a, -1.46e-265], t$95$2, If[LessEqual[a, 6.4e-287], t$95$1, If[LessEqual[a, 5.4e-217], t$95$2, If[LessEqual[a, 5.6e-64], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.70000000000000024e-75 or 5.60000000000000008e-64 < a

   1. Initial program 88.1%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 59.6%

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

   if -3.70000000000000024e-75 < a < -1.46000000000000005e-265 or 6.40000000000000037e-287 < a < 5.40000000000000032e-217

   1. Initial program 99.9%

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

      1. associate-*r/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in t around inf 67.8%

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

   if -1.46000000000000005e-265 < a < 6.40000000000000037e-287 or 5.40000000000000032e-217 < a < 5.60000000000000008e-64

   1. Initial program 97.7%

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

      1. associate-*r/ 85.2%

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

   3. Simplified 85.2%

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

      1. associate-*r/ 97.7%

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

      2. clear-num 97.7%

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

      3. associate-/r* 91.3%

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

   5. Applied egg-rr 91.3%

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

   6. Taylor expanded in z around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. associate-*r/ 63.1%

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

      3. distribute-rgt-neg-in 63.1%

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

   8. Simplified 63.1%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.46 \cdot 10^{-265}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-287}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-217}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 50.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(-z\right)\\ t_2 := \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-276}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- z))) (t_2 (/ (* y t) a)))
   (if (<= a -8.2e-77)
     x
     (if (<= a -2.8e-276)
       t_2
       (if (<= a 3.3e-283)
         t_1
         (if (<= a 4.8e-217) t_2 (if (<= a 3.1e-64) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -z;
	double t_2 = (y * t) / a;
	double tmp;
	if (a <= -8.2e-77) {
		tmp = x;
	} else if (a <= -2.8e-276) {
		tmp = t_2;
	} else if (a <= 3.3e-283) {
		tmp = t_1;
	} else if (a <= 4.8e-217) {
		tmp = t_2;
	} else if (a <= 3.1e-64) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / a) * -z
    t_2 = (y * t) / a
    if (a <= (-8.2d-77)) then
        tmp = x
    else if (a <= (-2.8d-276)) then
        tmp = t_2
    else if (a <= 3.3d-283) then
        tmp = t_1
    else if (a <= 4.8d-217) then
        tmp = t_2
    else if (a <= 3.1d-64) 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 a) {
	double t_1 = (y / a) * -z;
	double t_2 = (y * t) / a;
	double tmp;
	if (a <= -8.2e-77) {
		tmp = x;
	} else if (a <= -2.8e-276) {
		tmp = t_2;
	} else if (a <= 3.3e-283) {
		tmp = t_1;
	} else if (a <= 4.8e-217) {
		tmp = t_2;
	} else if (a <= 3.1e-64) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * -z
	t_2 = (y * t) / a
	tmp = 0
	if a <= -8.2e-77:
		tmp = x
	elif a <= -2.8e-276:
		tmp = t_2
	elif a <= 3.3e-283:
		tmp = t_1
	elif a <= 4.8e-217:
		tmp = t_2
	elif a <= 3.1e-64:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(-z))
	t_2 = Float64(Float64(y * t) / a)
	tmp = 0.0
	if (a <= -8.2e-77)
		tmp = x;
	elseif (a <= -2.8e-276)
		tmp = t_2;
	elseif (a <= 3.3e-283)
		tmp = t_1;
	elseif (a <= 4.8e-217)
		tmp = t_2;
	elseif (a <= 3.1e-64)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * -z;
	t_2 = (y * t) / a;
	tmp = 0.0;
	if (a <= -8.2e-77)
		tmp = x;
	elseif (a <= -2.8e-276)
		tmp = t_2;
	elseif (a <= 3.3e-283)
		tmp = t_1;
	elseif (a <= 4.8e-217)
		tmp = t_2;
	elseif (a <= 3.1e-64)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -8.2e-77], x, If[LessEqual[a, -2.8e-276], t$95$2, If[LessEqual[a, 3.3e-283], t$95$1, If[LessEqual[a, 4.8e-217], t$95$2, If[LessEqual[a, 3.1e-64], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.19999999999999925e-77 or 3.10000000000000025e-64 < a

   1. Initial program 88.1%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 59.6%

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

   if -8.19999999999999925e-77 < a < -2.79999999999999986e-276 or 3.30000000000000019e-283 < a < 4.7999999999999997e-217

   1. Initial program 99.9%

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

      1. associate-*r/ 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around inf 66.3%

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

   if -2.79999999999999986e-276 < a < 3.30000000000000019e-283 or 4.7999999999999997e-217 < a < 3.10000000000000025e-64

   1. Initial program 97.5%

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

      1. associate-*r/ 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in z around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. associate-*l/ 66.4%

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

      3. *-commutative 66.4%

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

      4. distribute-rgt-neg-in 66.4%

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

      5. distribute-frac-neg 66.4%

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

   6. Simplified 66.4%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-276}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-283}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+204}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+29} \lor \neg \left(z \leq 1.6 \cdot 10^{+57}\right) \land z \leq 2.2 \cdot 10^{+224}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+204)
   (* (/ z a) (- y))
   (if (or (<= z 2.7e+29) (and (not (<= z 1.6e+57)) (<= z 2.2e+224)))
     (+ x (* (/ y a) t))
     (* (/ y a) (- z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+204) {
		tmp = (z / a) * -y;
	} else if ((z <= 2.7e+29) || (!(z <= 1.6e+57) && (z <= 2.2e+224))) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = (y / a) * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.1d+204)) then
        tmp = (z / a) * -y
    else if ((z <= 2.7d+29) .or. (.not. (z <= 1.6d+57)) .and. (z <= 2.2d+224)) then
        tmp = x + ((y / a) * t)
    else
        tmp = (y / a) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+204) {
		tmp = (z / a) * -y;
	} else if ((z <= 2.7e+29) || (!(z <= 1.6e+57) && (z <= 2.2e+224))) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = (y / a) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+204:
		tmp = (z / a) * -y
	elif (z <= 2.7e+29) or (not (z <= 1.6e+57) and (z <= 2.2e+224)):
		tmp = x + ((y / a) * t)
	else:
		tmp = (y / a) * -z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+204)
		tmp = Float64(Float64(z / a) * Float64(-y));
	elseif ((z <= 2.7e+29) || (!(z <= 1.6e+57) && (z <= 2.2e+224)))
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(Float64(y / a) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+204)
		tmp = (z / a) * -y;
	elseif ((z <= 2.7e+29) || (~((z <= 1.6e+57)) && (z <= 2.2e+224)))
		tmp = x + ((y / a) * t);
	else
		tmp = (y / a) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+204], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], If[Or[LessEqual[z, 2.7e+29], And[N[Not[LessEqual[z, 1.6e+57]], $MachinePrecision], LessEqual[z, 2.2e+224]]], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000006e204

   1. Initial program 84.0%

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

      1. associate-*r/ 88.7%

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

   3. Simplified 88.7%

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

      1. associate-*r/ 84.0%

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

      2. clear-num 84.2%

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

      3. associate-/r* 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in z around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. associate-*r/ 83.3%

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

      3. distribute-rgt-neg-in 83.3%

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

   8. Simplified 83.3%

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

   if -1.10000000000000006e204 < z < 2.7e29 or 1.60000000000000015e57 < z < 2.2e224

   1. Initial program 93.3%

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

      1. associate-*r/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 80.1%

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

      1. sub-neg 80.1%

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

      2. mul-1-neg 80.1%

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

      3. remove-double-neg 80.1%

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

      4. +-commutative 80.1%

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

      5. associate-*l/ 83.5%

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

      6. *-commutative 83.5%

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

   6. Simplified 83.5%

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

   if 2.7e29 < z < 1.60000000000000015e57 or 2.2e224 < z

   1. Initial program 86.1%

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

      1. associate-*r/ 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in z around inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-*l/ 81.4%

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

      3. *-commutative 81.4%

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

      4. distribute-rgt-neg-in 81.4%

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

      5. distribute-frac-neg 81.4%

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

   6. Simplified 81.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+204}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+29} \lor \neg \left(z \leq 1.6 \cdot 10^{+57}\right) \land z \leq 2.2 \cdot 10^{+224}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 48:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e-73)
   (+ x (/ t (/ a y)))
   (if (<= t 48.0) (- x (* y (/ z a))) (+ x (* (/ y a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e-73) {
		tmp = x + (t / (a / y));
	} else if (t <= 48.0) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.7d-73)) then
        tmp = x + (t / (a / y))
    else if (t <= 48.0d0) then
        tmp = x - (y * (z / a))
    else
        tmp = x + ((y / a) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e-73) {
		tmp = x + (t / (a / y));
	} else if (t <= 48.0) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e-73:
		tmp = x + (t / (a / y))
	elif t <= 48.0:
		tmp = x - (y * (z / a))
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e-73)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (t <= 48.0)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e-73)
		tmp = x + (t / (a / y));
	elseif (t <= 48.0)
		tmp = x - (y * (z / a));
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e-73], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 48.0], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.69999999999999994e-73

   1. Initial program 92.7%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 85.5%

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

      1. sub-neg 85.5%

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

      2. mul-1-neg 85.5%

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

      3. remove-double-neg 85.5%

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

      4. +-commutative 85.5%

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

      5. associate-*l/ 89.8%

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

      6. *-commutative 89.8%

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

   6. Simplified 89.8%

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

      1. clear-num 52.7%

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

      2. un-div-inv 52.7%

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

   8. Applied egg-rr 89.9%

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

   if -2.69999999999999994e-73 < t < 48

   1. Initial program 92.7%

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

      1. associate-*r/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around inf 87.3%

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

   if 48 < t

   1. Initial program 90.3%

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

      1. associate-*r/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in z around 0 81.9%

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

      1. sub-neg 81.9%

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

      2. mul-1-neg 81.9%

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

      3. remove-double-neg 81.9%

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

      4. +-commutative 81.9%

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

      5. associate-*l/ 89.6%

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

      6. *-commutative 89.6%

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

   6. Simplified 89.6%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 48:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 6: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 51:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.2e-76)
   (+ x (/ t (/ a y)))
   (if (<= t 51.0) (- x (/ y (/ a z))) (+ x (* (/ y a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.2e-76) {
		tmp = x + (t / (a / y));
	} else if (t <= 51.0) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.2d-76)) then
        tmp = x + (t / (a / y))
    else if (t <= 51.0d0) then
        tmp = x - (y / (a / z))
    else
        tmp = x + ((y / a) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.2e-76) {
		tmp = x + (t / (a / y));
	} else if (t <= 51.0) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.2e-76:
		tmp = x + (t / (a / y))
	elif t <= 51.0:
		tmp = x - (y / (a / z))
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.2e-76)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (t <= 51.0)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.2e-76)
		tmp = x + (t / (a / y));
	elseif (t <= 51.0)
		tmp = x - (y / (a / z));
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.2e-76], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 51.0], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.1999999999999998e-76

   1. Initial program 92.7%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 85.5%

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

      1. sub-neg 85.5%

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

      2. mul-1-neg 85.5%

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

      3. remove-double-neg 85.5%

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

      4. +-commutative 85.5%

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

      5. associate-*l/ 89.8%

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

      6. *-commutative 89.8%

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

   6. Simplified 89.8%

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

      1. clear-num 52.7%

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

      2. un-div-inv 52.7%

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

   8. Applied egg-rr 89.9%

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

   if -3.1999999999999998e-76 < t < 51

   1. Initial program 92.7%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around inf 87.3%

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

   if 51 < t

   1. Initial program 90.3%

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

      1. associate-*r/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in z around 0 81.9%

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

      1. sub-neg 81.9%

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

      2. mul-1-neg 81.9%

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

      3. remove-double-neg 81.9%

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

      4. +-commutative 81.9%

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

      5. associate-*l/ 89.6%

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

      6. *-commutative 89.6%

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

   6. Simplified 89.6%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 51:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 7: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+36} \lor \neg \left(t \leq 1.55 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+36) (not (<= t 1.55e+134))) (* (/ y a) t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+36) || !(t <= 1.55e+134)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.4d+36)) .or. (.not. (t <= 1.55d+134))) then
        tmp = (y / a) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+36) || !(t <= 1.55e+134)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+36) or not (t <= 1.55e+134):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+36) || !(t <= 1.55e+134))
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e+36) || ~((t <= 1.55e+134)))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+36], N[Not[LessEqual[t, 1.55e+134]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999992e36 or 1.54999999999999991e134 < t

   1. Initial program 91.8%

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

      1. associate-*r/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around inf 58.7%

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

      1. associate-*l/ 63.4%

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

      2. *-commutative 63.4%

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

   6. Simplified 63.4%

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

   if -2.39999999999999992e36 < t < 1.54999999999999991e134

   1. Initial program 92.3%

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

      1. associate-*r/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around inf 50.5%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+36} \lor \neg \left(t \leq 1.55 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+31) (/ t (/ a y)) (if (<= t 1.9e+132) x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+31) {
		tmp = t / (a / y);
	} else if (t <= 1.9e+132) {
		tmp = x;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.2d+31)) then
        tmp = t / (a / y)
    else if (t <= 1.9d+132) then
        tmp = x
    else
        tmp = (y / a) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+31) {
		tmp = t / (a / y);
	} else if (t <= 1.9e+132) {
		tmp = x;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.2e+31:
		tmp = t / (a / y)
	elif t <= 1.9e+132:
		tmp = x
	else:
		tmp = (y / a) * t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+31)
		tmp = Float64(t / Float64(a / y));
	elseif (t <= 1.9e+132)
		tmp = x;
	else
		tmp = Float64(Float64(y / a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.2e+31)
		tmp = t / (a / y);
	elseif (t <= 1.9e+132)
		tmp = x;
	else
		tmp = (y / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+31], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+132], x, N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.19999999999999992e31

   1. Initial program 92.2%

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

      1. associate-*r/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in t around inf 55.2%

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

      1. associate-*l/ 59.0%

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

      2. *-commutative 59.0%

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

   6. Simplified 59.0%

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

      1. clear-num 59.1%

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

      2. un-div-inv 59.1%

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

   8. Applied egg-rr 59.1%

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

   if -7.19999999999999992e31 < t < 1.90000000000000003e132

   1. Initial program 92.3%

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

      1. associate-*r/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around inf 50.5%

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

   if 1.90000000000000003e132 < t

   1. Initial program 91.4%

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

      1. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in t around inf 62.7%

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

      1. associate-*l/ 68.2%

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

      2. *-commutative 68.2%

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

   6. Simplified 68.2%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \]

Alternative 9: 93.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

   1. associate-*r/ 94.9%

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

3. Simplified 94.9%

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

4. Final simplification 94.9%

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

Alternative 10: 39.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

   1. associate-*r/ 94.9%

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

3. Simplified 94.9%

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

4. Taylor expanded in x around inf 43.0%

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

5. Final simplification 43.0%

   \[\leadsto x \]

Developer target: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{t_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (- x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (- x (/ (* y (- z t)) a))
       (- x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x - (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x - ((y * (z - t)) / a)
    else
        tmp = x - (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x - (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x - ((y * (z - t)) / a)
	else:
		tmp = x - (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x - Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x - Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x - Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x - (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x - ((y * (z - t)) / a);
	else
		tmp = x - (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x - N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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