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

Percentage Accurate: 93.3% → 97.4%

Time: 11.7s

Alternatives: 12

Speedup: 1.0×

• 25.5% 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: 93.3% 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: 97.4% 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 90.3%

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

   1. associate-*l/ 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 2: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(-z\right)}{a}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-231}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 6:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z)) a)))
   (if (<= a -2.4e-94)
     x
     (if (<= a -1.45e-231)
       (/ (* y t) a)
       (if (<= a 1.75e-305)
         t_1
         (if (<= a 5e-42) (/ t (/ a y)) (if (<= a 6.0) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * -z) / a;
	double tmp;
	if (a <= -2.4e-94) {
		tmp = x;
	} else if (a <= -1.45e-231) {
		tmp = (y * t) / a;
	} else if (a <= 1.75e-305) {
		tmp = t_1;
	} else if (a <= 5e-42) {
		tmp = t / (a / y);
	} else if (a <= 6.0) {
		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) :: tmp
    t_1 = (y * -z) / a
    if (a <= (-2.4d-94)) then
        tmp = x
    else if (a <= (-1.45d-231)) then
        tmp = (y * t) / a
    else if (a <= 1.75d-305) then
        tmp = t_1
    else if (a <= 5d-42) then
        tmp = t / (a / y)
    else if (a <= 6.0d0) 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 * -z) / a;
	double tmp;
	if (a <= -2.4e-94) {
		tmp = x;
	} else if (a <= -1.45e-231) {
		tmp = (y * t) / a;
	} else if (a <= 1.75e-305) {
		tmp = t_1;
	} else if (a <= 5e-42) {
		tmp = t / (a / y);
	} else if (a <= 6.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * -z) / a
	tmp = 0
	if a <= -2.4e-94:
		tmp = x
	elif a <= -1.45e-231:
		tmp = (y * t) / a
	elif a <= 1.75e-305:
		tmp = t_1
	elif a <= 5e-42:
		tmp = t / (a / y)
	elif a <= 6.0:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(-z)) / a)
	tmp = 0.0
	if (a <= -2.4e-94)
		tmp = x;
	elseif (a <= -1.45e-231)
		tmp = Float64(Float64(y * t) / a);
	elseif (a <= 1.75e-305)
		tmp = t_1;
	elseif (a <= 5e-42)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= 6.0)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * -z) / a;
	tmp = 0.0;
	if (a <= -2.4e-94)
		tmp = x;
	elseif (a <= -1.45e-231)
		tmp = (y * t) / a;
	elseif (a <= 1.75e-305)
		tmp = t_1;
	elseif (a <= 5e-42)
		tmp = t / (a / y);
	elseif (a <= 6.0)
		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 * (-z)), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -2.4e-94], x, If[LessEqual[a, -1.45e-231], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 1.75e-305], t$95$1, If[LessEqual[a, 5e-42], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.0], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.4e-94 or 6 < a

   1. Initial program 83.8%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 61.0%

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

   if -2.4e-94 < a < -1.45e-231

   1. Initial program 99.9%

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

      1. associate-*r/ 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in t around inf 50.8%

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

   if -1.45e-231 < a < 1.7499999999999999e-305 or 5.00000000000000003e-42 < a < 6

   1. Initial program 99.7%

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

      1. associate-*r/ 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in z around inf 68.4%

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

      1. mul-1-neg 68.4%

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

   6. Simplified 68.4%

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

   if 1.7499999999999999e-305 < a < 5.00000000000000003e-42

   1. Initial program 99.8%

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

      1. associate-*r/ 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in t around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. associate-*r/ 63.9%

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

   6. Simplified 63.9%

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

      1. clear-num 63.9%

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

      2. div-inv 63.9%

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

   8. Applied egg-rr 63.9%

      \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-231}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-305}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 6:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+176}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- z))))
   (if (<= y -2.6e+188)
     t_1
     (if (<= y -1.75e+158)
       x
       (if (<= y -6.2e-27)
         t_1
         (if (<= y 9.8e-88) x (if (<= y 2.1e+176) (* (/ y a) t) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -z;
	double tmp;
	if (y <= -2.6e+188) {
		tmp = t_1;
	} else if (y <= -1.75e+158) {
		tmp = x;
	} else if (y <= -6.2e-27) {
		tmp = t_1;
	} else if (y <= 9.8e-88) {
		tmp = x;
	} else if (y <= 2.1e+176) {
		tmp = (y / a) * t;
	} else {
		tmp = 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 = (y / a) * -z
    if (y <= (-2.6d+188)) then
        tmp = t_1
    else if (y <= (-1.75d+158)) then
        tmp = x
    else if (y <= (-6.2d-27)) then
        tmp = t_1
    else if (y <= 9.8d-88) then
        tmp = x
    else if (y <= 2.1d+176) then
        tmp = (y / a) * t
    else
        tmp = 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 = (y / a) * -z;
	double tmp;
	if (y <= -2.6e+188) {
		tmp = t_1;
	} else if (y <= -1.75e+158) {
		tmp = x;
	} else if (y <= -6.2e-27) {
		tmp = t_1;
	} else if (y <= 9.8e-88) {
		tmp = x;
	} else if (y <= 2.1e+176) {
		tmp = (y / a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * -z
	tmp = 0
	if y <= -2.6e+188:
		tmp = t_1
	elif y <= -1.75e+158:
		tmp = x
	elif y <= -6.2e-27:
		tmp = t_1
	elif y <= 9.8e-88:
		tmp = x
	elif y <= 2.1e+176:
		tmp = (y / a) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(-z))
	tmp = 0.0
	if (y <= -2.6e+188)
		tmp = t_1;
	elseif (y <= -1.75e+158)
		tmp = x;
	elseif (y <= -6.2e-27)
		tmp = t_1;
	elseif (y <= 9.8e-88)
		tmp = x;
	elseif (y <= 2.1e+176)
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * -z;
	tmp = 0.0;
	if (y <= -2.6e+188)
		tmp = t_1;
	elseif (y <= -1.75e+158)
		tmp = x;
	elseif (y <= -6.2e-27)
		tmp = t_1;
	elseif (y <= 9.8e-88)
		tmp = x;
	elseif (y <= 2.1e+176)
		tmp = (y / a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[y, -2.6e+188], t$95$1, If[LessEqual[y, -1.75e+158], x, If[LessEqual[y, -6.2e-27], t$95$1, If[LessEqual[y, 9.8e-88], x, If[LessEqual[y, 2.1e+176], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.59999999999999987e188 or -1.7500000000000001e158 < y < -6.1999999999999997e-27 or 2.0999999999999999e176 < y

   1. Initial program 80.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. associate-*l/ 58.6%

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

      3. *-commutative 58.6%

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

      4. distribute-rgt-neg-in 58.6%

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

      5. distribute-frac-neg 58.6%

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

   6. Simplified 58.6%

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

   if -2.59999999999999987e188 < y < -1.7500000000000001e158 or -6.1999999999999997e-27 < y < 9.80000000000000055e-88

   1. Initial program 98.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in x around inf 69.4%

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

   if 9.80000000000000055e-88 < y < 2.0999999999999999e176

   1. Initial program 87.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 37.0%

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

      1. *-commutative 37.0%

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

      2. associate-*r/ 45.0%

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

   6. Simplified 45.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+188}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+176}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := \frac{y}{a} \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{\frac{-a}{z}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))) (t_2 (* (/ y a) (- z))))
   (if (<= z -5.4e+194)
     t_2
     (if (<= z -3.1e+106)
       t_1
       (if (<= z -2.9e+66) (/ y (/ (- a) z)) (if (<= z 1.45e+151) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = (y / a) * -z;
	double tmp;
	if (z <= -5.4e+194) {
		tmp = t_2;
	} else if (z <= -3.1e+106) {
		tmp = t_1;
	} else if (z <= -2.9e+66) {
		tmp = y / (-a / z);
	} else if (z <= 1.45e+151) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = x + (y / (a / t))
    t_2 = (y / a) * -z
    if (z <= (-5.4d+194)) then
        tmp = t_2
    else if (z <= (-3.1d+106)) then
        tmp = t_1
    else if (z <= (-2.9d+66)) then
        tmp = y / (-a / z)
    else if (z <= 1.45d+151) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = (y / a) * -z;
	double tmp;
	if (z <= -5.4e+194) {
		tmp = t_2;
	} else if (z <= -3.1e+106) {
		tmp = t_1;
	} else if (z <= -2.9e+66) {
		tmp = y / (-a / z);
	} else if (z <= 1.45e+151) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	t_2 = (y / a) * -z
	tmp = 0
	if z <= -5.4e+194:
		tmp = t_2
	elif z <= -3.1e+106:
		tmp = t_1
	elif z <= -2.9e+66:
		tmp = y / (-a / z)
	elif z <= 1.45e+151:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	t_2 = Float64(Float64(y / a) * Float64(-z))
	tmp = 0.0
	if (z <= -5.4e+194)
		tmp = t_2;
	elseif (z <= -3.1e+106)
		tmp = t_1;
	elseif (z <= -2.9e+66)
		tmp = Float64(y / Float64(Float64(-a) / z));
	elseif (z <= 1.45e+151)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	t_2 = (y / a) * -z;
	tmp = 0.0;
	if (z <= -5.4e+194)
		tmp = t_2;
	elseif (z <= -3.1e+106)
		tmp = t_1;
	elseif (z <= -2.9e+66)
		tmp = y / (-a / z);
	elseif (z <= 1.45e+151)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -5.4e+194], t$95$2, If[LessEqual[z, -3.1e+106], t$95$1, If[LessEqual[z, -2.9e+66], N[(y / N[((-a) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+151], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000003e194 or 1.45000000000000009e151 < z

   1. Initial program 82.7%

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

      1. associate-*r/ 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in z around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. associate-*l/ 70.9%

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

      3. *-commutative 70.9%

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

      4. distribute-rgt-neg-in 70.9%

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

      5. distribute-frac-neg 70.9%

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

   6. Simplified 70.9%

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

   if -5.4000000000000003e194 < z < -3.0999999999999999e106 or -2.89999999999999986e66 < z < 1.45000000000000009e151

   1. Initial program 93.1%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

      1. associate-*r/ 93.1%

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

      2. associate-/l* 94.7%

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

      3. div-inv 94.7%

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

      4. associate-/r* 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in z around 0 81.3%

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

      1. cancel-sign-sub-inv 81.3%

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

      2. metadata-eval 81.3%

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

      3. associate-*r/ 81.3%

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

      4. *-lft-identity 81.3%

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

      5. associate-/l* 82.0%

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

   8. Simplified 82.0%

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

   if -3.0999999999999999e106 < z < -2.89999999999999986e66

   1. Initial program 90.1%

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

      1. associate-*r/ 99.5%

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

   3. Simplified 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 90.1%

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

      3. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 70.8%

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

      1. associate-*r/ 80.2%

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

      2. associate-*r* 80.2%

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

      3. neg-mul-1 80.2%

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

      4. *-commutative 80.2%

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

   8. Simplified 80.2%

      \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(-y\right)} \]
   9. Step-by-step derivation

      1. add-sqr-sqrt 39.6%

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

      2. clear-num 39.6%

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

      3. sqrt-unprod 30.8%

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

      4. sqr-neg 30.8%

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

      5. sqrt-unprod 0.4%

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

      6. add-sqr-sqrt 0.9%

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

      7. associate-*l/ 0.9%

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

      8. *-un-lft-identity 0.9%

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

      9. frac-2neg 0.9%

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

      10. add-sqr-sqrt 0.5%

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

      11. sqrt-unprod 40.8%

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

      12. sqr-neg 40.8%

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

      13. sqrt-unprod 40.2%

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

      14. add-sqr-sqrt 80.6%

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

      15. distribute-neg-frac 80.6%

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

   10. Applied egg-rr 80.6%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+194}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+106}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{\frac{-a}{z}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+151}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{+106}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{\frac{-a}{z}}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+151}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- z))))
   (if (<= z -4.8e+198)
     t_1
     (if (<= z -3.55e+106)
       (+ x (/ y (/ a t)))
       (if (<= z -2.9e+66)
         (/ y (/ (- a) z))
         (if (<= z 1.02e+151) (+ x (* (/ y a) t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -z;
	double tmp;
	if (z <= -4.8e+198) {
		tmp = t_1;
	} else if (z <= -3.55e+106) {
		tmp = x + (y / (a / t));
	} else if (z <= -2.9e+66) {
		tmp = y / (-a / z);
	} else if (z <= 1.02e+151) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = 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 = (y / a) * -z
    if (z <= (-4.8d+198)) then
        tmp = t_1
    else if (z <= (-3.55d+106)) then
        tmp = x + (y / (a / t))
    else if (z <= (-2.9d+66)) then
        tmp = y / (-a / z)
    else if (z <= 1.02d+151) then
        tmp = x + ((y / a) * t)
    else
        tmp = 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 = (y / a) * -z;
	double tmp;
	if (z <= -4.8e+198) {
		tmp = t_1;
	} else if (z <= -3.55e+106) {
		tmp = x + (y / (a / t));
	} else if (z <= -2.9e+66) {
		tmp = y / (-a / z);
	} else if (z <= 1.02e+151) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * -z
	tmp = 0
	if z <= -4.8e+198:
		tmp = t_1
	elif z <= -3.55e+106:
		tmp = x + (y / (a / t))
	elif z <= -2.9e+66:
		tmp = y / (-a / z)
	elif z <= 1.02e+151:
		tmp = x + ((y / a) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(-z))
	tmp = 0.0
	if (z <= -4.8e+198)
		tmp = t_1;
	elseif (z <= -3.55e+106)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= -2.9e+66)
		tmp = Float64(y / Float64(Float64(-a) / z));
	elseif (z <= 1.02e+151)
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * -z;
	tmp = 0.0;
	if (z <= -4.8e+198)
		tmp = t_1;
	elseif (z <= -3.55e+106)
		tmp = x + (y / (a / t));
	elseif (z <= -2.9e+66)
		tmp = y / (-a / z);
	elseif (z <= 1.02e+151)
		tmp = x + ((y / a) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -4.8e+198], t$95$1, If[LessEqual[z, -3.55e+106], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e+66], N[(y / N[((-a) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+151], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8000000000000003e198 or 1.02000000000000002e151 < z

   1. Initial program 82.7%

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

      1. associate-*r/ 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in z around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. associate-*l/ 70.9%

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

      3. *-commutative 70.9%

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

      4. distribute-rgt-neg-in 70.9%

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

      5. distribute-frac-neg 70.9%

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

   6. Simplified 70.9%

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

   if -4.8000000000000003e198 < z < -3.55000000000000015e106

   1. Initial program 92.8%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*r/ 92.8%

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

      2. associate-/l* 99.9%

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

      3. div-inv 100.0%

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

      4. associate-/r* 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around 0 79.5%

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

      1. cancel-sign-sub-inv 79.5%

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

      2. metadata-eval 79.5%

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

      3. associate-*r/ 79.5%

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

      4. *-lft-identity 79.5%

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

      5. associate-/l* 79.6%

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

   8. Simplified 79.6%

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

   if -3.55000000000000015e106 < z < -2.89999999999999986e66

   1. Initial program 90.1%

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

      1. associate-*r/ 99.5%

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

   3. Simplified 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 90.1%

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

      3. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 70.8%

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

      1. associate-*r/ 80.2%

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

      2. associate-*r* 80.2%

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

      3. neg-mul-1 80.2%

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

      4. *-commutative 80.2%

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

   8. Simplified 80.2%

      \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(-y\right)} \]
   9. Step-by-step derivation

      1. add-sqr-sqrt 39.6%

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

      2. clear-num 39.6%

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

      3. sqrt-unprod 30.8%

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

      4. sqr-neg 30.8%

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

      5. sqrt-unprod 0.4%

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

      6. add-sqr-sqrt 0.9%

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

      7. associate-*l/ 0.9%

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

      8. *-un-lft-identity 0.9%

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

      9. frac-2neg 0.9%

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

      10. add-sqr-sqrt 0.5%

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

      11. sqrt-unprod 40.8%

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

      12. sqr-neg 40.8%

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

      13. sqrt-unprod 40.2%

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

      14. add-sqr-sqrt 80.6%

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

      15. distribute-neg-frac 80.6%

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

   10. Applied egg-rr 80.6%

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

   if -2.89999999999999986e66 < z < 1.02000000000000002e151

   1. Initial program 93.1%

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

      1. associate-*r/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around 0 81.4%

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

      1. sub-neg 81.4%

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

      2. mul-1-neg 81.4%

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

      3. remove-double-neg 81.4%

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

      4. +-commutative 81.4%

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

      5. *-commutative 81.4%

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

      6. associate-*r/ 86.6%

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

   6. Simplified 86.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+198}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{+106}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{\frac{-a}{z}}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+151}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]

Alternative 6: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+188}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-27} \lor \neg \left(y \leq 2 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.5e+188)
   (* (/ y a) (- z))
   (if (<= y -4.4e+158)
     x
     (if (or (<= y -2.4e-27) (not (<= y 2e-27))) (* (/ z a) (- y)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.5e+188) {
		tmp = (y / a) * -z;
	} else if (y <= -4.4e+158) {
		tmp = x;
	} else if ((y <= -2.4e-27) || !(y <= 2e-27)) {
		tmp = (z / a) * -y;
	} 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 (y <= (-2.5d+188)) then
        tmp = (y / a) * -z
    else if (y <= (-4.4d+158)) then
        tmp = x
    else if ((y <= (-2.4d-27)) .or. (.not. (y <= 2d-27))) then
        tmp = (z / a) * -y
    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 (y <= -2.5e+188) {
		tmp = (y / a) * -z;
	} else if (y <= -4.4e+158) {
		tmp = x;
	} else if ((y <= -2.4e-27) || !(y <= 2e-27)) {
		tmp = (z / a) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.5e+188:
		tmp = (y / a) * -z
	elif y <= -4.4e+158:
		tmp = x
	elif (y <= -2.4e-27) or not (y <= 2e-27):
		tmp = (z / a) * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.5e+188)
		tmp = Float64(Float64(y / a) * Float64(-z));
	elseif (y <= -4.4e+158)
		tmp = x;
	elseif ((y <= -2.4e-27) || !(y <= 2e-27))
		tmp = Float64(Float64(z / a) * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.5e+188)
		tmp = (y / a) * -z;
	elseif (y <= -4.4e+158)
		tmp = x;
	elseif ((y <= -2.4e-27) || ~((y <= 2e-27)))
		tmp = (z / a) * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.5e+188], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[y, -4.4e+158], x, If[Or[LessEqual[y, -2.4e-27], N[Not[LessEqual[y, 2e-27]], $MachinePrecision]], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5000000000000001e188

   1. Initial program 81.3%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. associate-*l/ 60.8%

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

      3. *-commutative 60.8%

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

      4. distribute-rgt-neg-in 60.8%

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

      5. distribute-frac-neg 60.8%

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

   6. Simplified 60.8%

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

   if -2.5000000000000001e188 < y < -4.4000000000000002e158 or -2.40000000000000002e-27 < y < 2.0000000000000001e-27

   1. Initial program 98.3%

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

      1. associate-*r/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 66.3%

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

   if -4.4000000000000002e158 < y < -2.40000000000000002e-27 or 2.0000000000000001e-27 < y

   1. Initial program 82.3%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 82.3%

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

      3. associate-/l* 98.0%

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

   5. Applied egg-rr 98.0%

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

   6. Taylor expanded in z around inf 45.8%

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

      1. associate-*r/ 52.7%

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

      2. associate-*r* 52.7%

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

      3. neg-mul-1 52.7%

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

      4. *-commutative 52.7%

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

   8. Simplified 52.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+188}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-27} \lor \neg \left(y \leq 2 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.4 \lor \neg \left(t \leq 1.9 \cdot 10^{+29}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.4) (not (<= t 1.9e+29)))
   (+ x (* (/ y a) t))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.4) || !(t <= 1.9e+29)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - (y * (z / a));
	}
	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 <= (-0.4d0)) .or. (.not. (t <= 1.9d+29))) then
        tmp = x + ((y / a) * t)
    else
        tmp = x - (y * (z / a))
    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 <= -0.4) || !(t <= 1.9e+29)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.4) or not (t <= 1.9e+29):
		tmp = x + ((y / a) * t)
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.4) || !(t <= 1.9e+29))
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(x - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.4) || ~((t <= 1.9e+29)))
		tmp = x + ((y / a) * t);
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.4], N[Not[LessEqual[t, 1.9e+29]], $MachinePrecision]], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.40000000000000002 or 1.89999999999999985e29 < t

   1. Initial program 88.2%

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

      1. associate-*r/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. sub-neg 78.8%

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

      2. mul-1-neg 78.8%

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

      3. remove-double-neg 78.8%

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

      4. +-commutative 78.8%

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

      5. *-commutative 78.8%

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

      6. associate-*r/ 86.7%

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

   6. Simplified 86.7%

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

   if -0.40000000000000002 < t < 1.89999999999999985e29

   1. Initial program 92.2%

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

      1. associate-*r/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around inf 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-/l* 95.1%

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

      3. associate-/r/ 90.9%

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

   6. Simplified 90.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.4 \lor \neg \left(t \leq 1.9 \cdot 10^{+29}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 8: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -82 \lor \neg \left(t \leq 3.1 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -82.0) (not (<= t 3.1e+31)))
   (+ x (* (/ y a) t))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -82.0) || !(t <= 3.1e+31)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - (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 ((t <= (-82.0d0)) .or. (.not. (t <= 3.1d+31))) then
        tmp = x + ((y / a) * t)
    else
        tmp = x - (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 ((t <= -82.0) || !(t <= 3.1e+31)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -82.0) or not (t <= 3.1e+31):
		tmp = x + ((y / a) * t)
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -82.0) || !(t <= 3.1e+31))
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -82.0) || ~((t <= 3.1e+31)))
		tmp = x + ((y / a) * t);
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -82.0], N[Not[LessEqual[t, 3.1e+31]], $MachinePrecision]], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -82 or 3.1000000000000002e31 < t

   1. Initial program 88.2%

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

      1. associate-*r/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. sub-neg 78.8%

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

      2. mul-1-neg 78.8%

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

      3. remove-double-neg 78.8%

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

      4. +-commutative 78.8%

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

      5. *-commutative 78.8%

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

      6. associate-*r/ 86.7%

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

   6. Simplified 86.7%

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

   if -82 < t < 3.1000000000000002e31

   1. Initial program 92.2%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around inf 91.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -82 \lor \neg \left(t \leq 3.1 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -51 \lor \neg \left(t \leq 1.5 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -51.0) (not (<= t 1.5e+31)))
   (+ x (* (/ y a) t))
   (- x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -51.0) || !(t <= 1.5e+31)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - (z / (a / y));
	}
	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 <= (-51.0d0)) .or. (.not. (t <= 1.5d+31))) then
        tmp = x + ((y / a) * t)
    else
        tmp = x - (z / (a / y))
    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 <= -51.0) || !(t <= 1.5e+31)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -51.0) or not (t <= 1.5e+31):
		tmp = x + ((y / a) * t)
	else:
		tmp = x - (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -51.0) || !(t <= 1.5e+31))
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(x - Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -51.0) || ~((t <= 1.5e+31)))
		tmp = x + ((y / a) * t);
	else
		tmp = x - (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -51.0], N[Not[LessEqual[t, 1.5e+31]], $MachinePrecision]], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -51 or 1.49999999999999995e31 < t

   1. Initial program 88.2%

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

      1. associate-*r/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. sub-neg 78.8%

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

      2. mul-1-neg 78.8%

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

      3. remove-double-neg 78.8%

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

      4. +-commutative 78.8%

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

      5. *-commutative 78.8%

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

      6. associate-*r/ 86.7%

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

   6. Simplified 86.7%

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

   if -51 < t < 1.49999999999999995e31

   1. Initial program 92.2%

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

      1. associate-*r/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around inf 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-/l* 95.1%

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

      3. associate-/r/ 90.9%

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

   6. Simplified 90.9%

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

      1. associate-/r/ 95.1%

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

   8. Applied egg-rr 95.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -51 \lor \neg \left(t \leq 1.5 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 93.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+132}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.3e+132) (+ x (* (/ y a) t)) (+ x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.3e+132) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	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 <= (-5.3d+132)) then
        tmp = x + ((y / a) * t)
    else
        tmp = x + (y * ((t - z) / a))
    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 <= -5.3e+132) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.3e+132:
		tmp = x + ((y / a) * t)
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.3e+132)
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.3e+132)
		tmp = x + ((y / a) * t);
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.3e+132], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.3e132

   1. Initial program 85.8%

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

      1. associate-*r/ 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in z around 0 81.1%

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

      1. sub-neg 81.1%

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

      2. mul-1-neg 81.1%

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

      3. remove-double-neg 81.1%

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

      4. +-commutative 81.1%

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

      5. *-commutative 81.1%

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

      6. associate-*r/ 94.4%

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

   6. Simplified 94.4%

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

   if -5.3e132 < t

   1. Initial program 91.1%

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

      1. associate-*r/ 94.2%

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

   3. Simplified 94.2%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+132}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]

Alternative 11: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e-95) x (if (<= a 2.6e-34) (* (/ y a) t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e-95) {
		tmp = x;
	} else if (a <= 2.6e-34) {
		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 (a <= (-3.4d-95)) then
        tmp = x
    else if (a <= 2.6d-34) 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 (a <= -3.4e-95) {
		tmp = x;
	} else if (a <= 2.6e-34) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e-95:
		tmp = x
	elif a <= 2.6e-34:
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e-95)
		tmp = x;
	elseif (a <= 2.6e-34)
		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 (a <= -3.4e-95)
		tmp = x;
	elseif (a <= 2.6e-34)
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e-95], x, If[LessEqual[a, 2.6e-34], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.39999999999999993e-95 or 2.5999999999999999e-34 < a

   1. Initial program 84.5%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 59.1%

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

   if -3.39999999999999993e-95 < a < 2.5999999999999999e-34

   1. Initial program 99.8%

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

      1. associate-*r/ 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in t around inf 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-*r/ 50.7%

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

   6. Simplified 50.7%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 38.9% 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 90.3%

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

   1. associate-*r/ 92.2%

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

3. Simplified 92.2%

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

4. Taylor expanded in x around inf 43.5%

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

5. Final simplification 43.5%

   \[\leadsto x \]

Developer target: 99.3% 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 2023257 
(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)))