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

Percentage Accurate: 93.1% → 97.2%

Time: 9.8s

Alternatives: 14

Speedup: 1.0×

• 24.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 93.1% 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: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - t) / (a / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. associate-*l/ 96.8%

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

3. Simplified 96.8%

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

   1. *-commutative 96.8%

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

   2. clear-num 96.8%

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

   3. un-div-inv 97.1%

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

5. Applied egg-rr 97.1%

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

6. Final simplification 97.1%

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

Alternative 2: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-126}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y) a))))
   (if (<= y -2.1e+49)
     t_1
     (if (<= y 2.9e-161)
       x
       (if (<= y 1.3e-126)
         (/ (* z y) a)
         (if (<= y 2e-89)
           x
           (if (<= y 2.25e+51)
             t_1
             (if (<= y 2.8e+134)
               (* y (/ z a))
               (if (<= y 7e+225) t_1 (* z (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (y <= -2.1e+49) {
		tmp = t_1;
	} else if (y <= 2.9e-161) {
		tmp = x;
	} else if (y <= 1.3e-126) {
		tmp = (z * y) / a;
	} else if (y <= 2e-89) {
		tmp = x;
	} else if (y <= 2.25e+51) {
		tmp = t_1;
	} else if (y <= 2.8e+134) {
		tmp = y * (z / a);
	} else if (y <= 7e+225) {
		tmp = t_1;
	} else {
		tmp = z * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = t * (-y / a)
    if (y <= (-2.1d+49)) then
        tmp = t_1
    else if (y <= 2.9d-161) then
        tmp = x
    else if (y <= 1.3d-126) then
        tmp = (z * y) / a
    else if (y <= 2d-89) then
        tmp = x
    else if (y <= 2.25d+51) then
        tmp = t_1
    else if (y <= 2.8d+134) then
        tmp = y * (z / a)
    else if (y <= 7d+225) then
        tmp = t_1
    else
        tmp = z * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (y <= -2.1e+49) {
		tmp = t_1;
	} else if (y <= 2.9e-161) {
		tmp = x;
	} else if (y <= 1.3e-126) {
		tmp = (z * y) / a;
	} else if (y <= 2e-89) {
		tmp = x;
	} else if (y <= 2.25e+51) {
		tmp = t_1;
	} else if (y <= 2.8e+134) {
		tmp = y * (z / a);
	} else if (y <= 7e+225) {
		tmp = t_1;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-y / a)
	tmp = 0
	if y <= -2.1e+49:
		tmp = t_1
	elif y <= 2.9e-161:
		tmp = x
	elif y <= 1.3e-126:
		tmp = (z * y) / a
	elif y <= 2e-89:
		tmp = x
	elif y <= 2.25e+51:
		tmp = t_1
	elif y <= 2.8e+134:
		tmp = y * (z / a)
	elif y <= 7e+225:
		tmp = t_1
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (y <= -2.1e+49)
		tmp = t_1;
	elseif (y <= 2.9e-161)
		tmp = x;
	elseif (y <= 1.3e-126)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= 2e-89)
		tmp = x;
	elseif (y <= 2.25e+51)
		tmp = t_1;
	elseif (y <= 2.8e+134)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= 7e+225)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-y / a);
	tmp = 0.0;
	if (y <= -2.1e+49)
		tmp = t_1;
	elseif (y <= 2.9e-161)
		tmp = x;
	elseif (y <= 1.3e-126)
		tmp = (z * y) / a;
	elseif (y <= 2e-89)
		tmp = x;
	elseif (y <= 2.25e+51)
		tmp = t_1;
	elseif (y <= 2.8e+134)
		tmp = y * (z / a);
	elseif (y <= 7e+225)
		tmp = t_1;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+49], t$95$1, If[LessEqual[y, 2.9e-161], x, If[LessEqual[y, 1.3e-126], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2e-89], x, If[LessEqual[y, 2.25e+51], t$95$1, If[LessEqual[y, 2.8e+134], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+225], t$95$1, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.10000000000000011e49 or 2.00000000000000008e-89 < y < 2.25e51 or 2.7999999999999999e134 < y < 7.0000000000000006e225

   1. Initial program 89.6%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around 0 66.4%

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

      1. mul-1-neg 66.4%

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

      2. associate-*l/ 70.8%

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

      3. distribute-rgt-neg-out 70.8%

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

      4. +-commutative 70.8%

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

      5. *-commutative 70.8%

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

      6. distribute-lft-neg-out 70.8%

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

      7. unsub-neg 70.8%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in x around 0 52.5%

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

      1. associate-*r/ 52.5%

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

      2. *-commutative 52.5%

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

      3. neg-mul-1 52.5%

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

      4. distribute-rgt-neg-out 52.5%

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

      5. associate-*r/ 56.8%

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

   9. Simplified 56.8%

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

   if -2.10000000000000011e49 < y < 2.9e-161 or 1.3e-126 < y < 2.00000000000000008e-89

   1. Initial program 99.0%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 70.8%

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

   if 2.9e-161 < y < 1.3e-126

   1. Initial program 99.6%

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

      1. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in y around inf 44.3%

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

   5. Taylor expanded in z around inf 72.9%

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

   6. Taylor expanded in z around 0 85.8%

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

   if 2.25e51 < y < 2.7999999999999999e134

   1. Initial program 87.5%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around inf 70.8%

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

   5. Taylor expanded in z around inf 55.2%

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

   if 7.0000000000000006e225 < y

   1. Initial program 91.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 75.5%

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

   5. Taylor expanded in z around inf 63.5%

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

   6. Taylor expanded in z around 0 61.0%

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

      1. associate-*l/ 68.8%

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

   8. Simplified 68.8%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-126}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+225}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3: 49.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot \frac{t}{a}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y) (/ t a))))
   (if (<= y -1.8e+49)
     (* t (/ (- y) a))
     (if (<= y 2.9e-161)
       x
       (if (<= y 9.5e-127)
         (/ (* z y) a)
         (if (<= y 4.4e-89)
           x
           (if (<= y 6.4e+47)
             t_1
             (if (<= y 1.65e+134)
               (* y (/ z a))
               (if (<= y 6.5e+225) t_1 (* z (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y * (t / a);
	double tmp;
	if (y <= -1.8e+49) {
		tmp = t * (-y / a);
	} else if (y <= 2.9e-161) {
		tmp = x;
	} else if (y <= 9.5e-127) {
		tmp = (z * y) / a;
	} else if (y <= 4.4e-89) {
		tmp = x;
	} else if (y <= 6.4e+47) {
		tmp = t_1;
	} else if (y <= 1.65e+134) {
		tmp = y * (z / a);
	} else if (y <= 6.5e+225) {
		tmp = t_1;
	} else {
		tmp = z * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = -y * (t / a)
    if (y <= (-1.8d+49)) then
        tmp = t * (-y / a)
    else if (y <= 2.9d-161) then
        tmp = x
    else if (y <= 9.5d-127) then
        tmp = (z * y) / a
    else if (y <= 4.4d-89) then
        tmp = x
    else if (y <= 6.4d+47) then
        tmp = t_1
    else if (y <= 1.65d+134) then
        tmp = y * (z / a)
    else if (y <= 6.5d+225) then
        tmp = t_1
    else
        tmp = z * (y / a)
    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 * (t / a);
	double tmp;
	if (y <= -1.8e+49) {
		tmp = t * (-y / a);
	} else if (y <= 2.9e-161) {
		tmp = x;
	} else if (y <= 9.5e-127) {
		tmp = (z * y) / a;
	} else if (y <= 4.4e-89) {
		tmp = x;
	} else if (y <= 6.4e+47) {
		tmp = t_1;
	} else if (y <= 1.65e+134) {
		tmp = y * (z / a);
	} else if (y <= 6.5e+225) {
		tmp = t_1;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y * (t / a)
	tmp = 0
	if y <= -1.8e+49:
		tmp = t * (-y / a)
	elif y <= 2.9e-161:
		tmp = x
	elif y <= 9.5e-127:
		tmp = (z * y) / a
	elif y <= 4.4e-89:
		tmp = x
	elif y <= 6.4e+47:
		tmp = t_1
	elif y <= 1.65e+134:
		tmp = y * (z / a)
	elif y <= 6.5e+225:
		tmp = t_1
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) * Float64(t / a))
	tmp = 0.0
	if (y <= -1.8e+49)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (y <= 2.9e-161)
		tmp = x;
	elseif (y <= 9.5e-127)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= 4.4e-89)
		tmp = x;
	elseif (y <= 6.4e+47)
		tmp = t_1;
	elseif (y <= 1.65e+134)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= 6.5e+225)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y * (t / a);
	tmp = 0.0;
	if (y <= -1.8e+49)
		tmp = t * (-y / a);
	elseif (y <= 2.9e-161)
		tmp = x;
	elseif (y <= 9.5e-127)
		tmp = (z * y) / a;
	elseif (y <= 4.4e-89)
		tmp = x;
	elseif (y <= 6.4e+47)
		tmp = t_1;
	elseif (y <= 1.65e+134)
		tmp = y * (z / a);
	elseif (y <= 6.5e+225)
		tmp = t_1;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+49], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-161], x, If[LessEqual[y, 9.5e-127], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 4.4e-89], x, If[LessEqual[y, 6.4e+47], t$95$1, If[LessEqual[y, 1.65e+134], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+225], t$95$1, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.79999999999999998e49

   1. Initial program 88.9%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. associate-*l/ 64.7%

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

      3. distribute-rgt-neg-out 64.7%

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

      4. +-commutative 64.7%

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

      5. *-commutative 64.7%

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

      6. distribute-lft-neg-out 64.7%

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

      7. unsub-neg 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in x around 0 45.8%

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

      1. associate-*r/ 45.8%

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

      2. *-commutative 45.8%

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

      3. neg-mul-1 45.8%

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

      4. distribute-rgt-neg-out 45.8%

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

      5. associate-*r/ 53.2%

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

   9. Simplified 53.2%

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

   if -1.79999999999999998e49 < y < 2.9e-161 or 9.4999999999999997e-127 < y < 4.40000000000000024e-89

   1. Initial program 99.0%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 70.8%

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

   if 2.9e-161 < y < 9.4999999999999997e-127

   1. Initial program 99.6%

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

      1. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in y around inf 44.3%

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

   5. Taylor expanded in z around inf 72.9%

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

   6. Taylor expanded in z around 0 85.8%

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

   if 4.40000000000000024e-89 < y < 6.4e47 or 1.65e134 < y < 6.5000000000000006e225

   1. Initial program 90.8%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around inf 81.0%

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

   5. Taylor expanded in z around 0 66.9%

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

      1. neg-mul-1 66.9%

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

      2. distribute-neg-frac 66.9%

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

   7. Simplified 66.9%

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

   if 6.4e47 < y < 1.65e134

   1. Initial program 87.5%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around inf 70.8%

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

   5. Taylor expanded in z around inf 55.2%

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

   if 6.5000000000000006e225 < y

   1. Initial program 91.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 75.5%

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

   5. Taylor expanded in z around inf 63.5%

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

   6. Taylor expanded in z around 0 61.0%

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

      1. associate-*l/ 68.8%

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

   8. Simplified 68.8%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+47}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+225}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 49.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot \frac{t}{a}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y) (/ t a))))
   (if (<= y -2.7e+49)
     (/ t (/ a (- y)))
     (if (<= y 2.9e-161)
       x
       (if (<= y 9.5e-127)
         (/ (* z y) a)
         (if (<= y 2.4e-89)
           x
           (if (<= y 4.3e+44)
             t_1
             (if (<= y 3.1e+134)
               (* y (/ z a))
               (if (<= y 7e+225) t_1 (* z (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y * (t / a);
	double tmp;
	if (y <= -2.7e+49) {
		tmp = t / (a / -y);
	} else if (y <= 2.9e-161) {
		tmp = x;
	} else if (y <= 9.5e-127) {
		tmp = (z * y) / a;
	} else if (y <= 2.4e-89) {
		tmp = x;
	} else if (y <= 4.3e+44) {
		tmp = t_1;
	} else if (y <= 3.1e+134) {
		tmp = y * (z / a);
	} else if (y <= 7e+225) {
		tmp = t_1;
	} else {
		tmp = z * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = -y * (t / a)
    if (y <= (-2.7d+49)) then
        tmp = t / (a / -y)
    else if (y <= 2.9d-161) then
        tmp = x
    else if (y <= 9.5d-127) then
        tmp = (z * y) / a
    else if (y <= 2.4d-89) then
        tmp = x
    else if (y <= 4.3d+44) then
        tmp = t_1
    else if (y <= 3.1d+134) then
        tmp = y * (z / a)
    else if (y <= 7d+225) then
        tmp = t_1
    else
        tmp = z * (y / a)
    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 * (t / a);
	double tmp;
	if (y <= -2.7e+49) {
		tmp = t / (a / -y);
	} else if (y <= 2.9e-161) {
		tmp = x;
	} else if (y <= 9.5e-127) {
		tmp = (z * y) / a;
	} else if (y <= 2.4e-89) {
		tmp = x;
	} else if (y <= 4.3e+44) {
		tmp = t_1;
	} else if (y <= 3.1e+134) {
		tmp = y * (z / a);
	} else if (y <= 7e+225) {
		tmp = t_1;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y * (t / a)
	tmp = 0
	if y <= -2.7e+49:
		tmp = t / (a / -y)
	elif y <= 2.9e-161:
		tmp = x
	elif y <= 9.5e-127:
		tmp = (z * y) / a
	elif y <= 2.4e-89:
		tmp = x
	elif y <= 4.3e+44:
		tmp = t_1
	elif y <= 3.1e+134:
		tmp = y * (z / a)
	elif y <= 7e+225:
		tmp = t_1
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) * Float64(t / a))
	tmp = 0.0
	if (y <= -2.7e+49)
		tmp = Float64(t / Float64(a / Float64(-y)));
	elseif (y <= 2.9e-161)
		tmp = x;
	elseif (y <= 9.5e-127)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= 2.4e-89)
		tmp = x;
	elseif (y <= 4.3e+44)
		tmp = t_1;
	elseif (y <= 3.1e+134)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= 7e+225)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y * (t / a);
	tmp = 0.0;
	if (y <= -2.7e+49)
		tmp = t / (a / -y);
	elseif (y <= 2.9e-161)
		tmp = x;
	elseif (y <= 9.5e-127)
		tmp = (z * y) / a;
	elseif (y <= 2.4e-89)
		tmp = x;
	elseif (y <= 4.3e+44)
		tmp = t_1;
	elseif (y <= 3.1e+134)
		tmp = y * (z / a);
	elseif (y <= 7e+225)
		tmp = t_1;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+49], N[(t / N[(a / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-161], x, If[LessEqual[y, 9.5e-127], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2.4e-89], x, If[LessEqual[y, 4.3e+44], t$95$1, If[LessEqual[y, 3.1e+134], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+225], t$95$1, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.7000000000000001e49

   1. Initial program 88.9%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. associate-*l/ 64.7%

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

      3. distribute-rgt-neg-out 64.7%

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

      4. +-commutative 64.7%

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

      5. *-commutative 64.7%

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

      6. distribute-lft-neg-out 64.7%

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

      7. unsub-neg 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in x around 0 45.8%

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

      1. associate-*r/ 45.8%

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

      2. *-commutative 45.8%

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

      3. neg-mul-1 45.8%

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

      4. distribute-rgt-neg-out 45.8%

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

      5. associate-/l* 53.5%

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

   9. Simplified 53.5%

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

   if -2.7000000000000001e49 < y < 2.9e-161 or 9.4999999999999997e-127 < y < 2.40000000000000016e-89

   1. Initial program 99.0%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 70.8%

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

   if 2.9e-161 < y < 9.4999999999999997e-127

   1. Initial program 99.6%

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

      1. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in y around inf 44.3%

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

   5. Taylor expanded in z around inf 72.9%

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

   6. Taylor expanded in z around 0 85.8%

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

   if 2.40000000000000016e-89 < y < 4.29999999999999982e44 or 3.09999999999999982e134 < y < 7.0000000000000006e225

   1. Initial program 90.8%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around inf 81.0%

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

   5. Taylor expanded in z around 0 66.9%

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

      1. neg-mul-1 66.9%

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

      2. distribute-neg-frac 66.9%

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

   7. Simplified 66.9%

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

   if 4.29999999999999982e44 < y < 3.09999999999999982e134

   1. Initial program 87.5%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around inf 70.8%

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

   5. Taylor expanded in z around inf 55.2%

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

   if 7.0000000000000006e225 < y

   1. Initial program 91.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 75.5%

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

   5. Taylor expanded in z around inf 63.5%

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

   6. Taylor expanded in z around 0 61.0%

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

      1. associate-*l/ 68.8%

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

   8. Simplified 68.8%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+44}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+225}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 67.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a}\\ \mathbf{if}\;y \leq -2 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-125}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) a))))
   (if (<= y -2e-37)
     t_1
     (if (<= y -1e-115)
       x
       (if (<= y -1.3e-143)
         t_1
         (if (<= y 2.9e-161)
           x
           (if (<= y 1.25e-125) (/ (* z y) a) (if (<= y 1.5e-90) x t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / a);
	double tmp;
	if (y <= -2e-37) {
		tmp = t_1;
	} else if (y <= -1e-115) {
		tmp = x;
	} else if (y <= -1.3e-143) {
		tmp = t_1;
	} else if (y <= 2.9e-161) {
		tmp = x;
	} else if (y <= 1.25e-125) {
		tmp = (z * y) / a;
	} else if (y <= 1.5e-90) {
		tmp = x;
	} 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 * ((z - t) / a)
    if (y <= (-2d-37)) then
        tmp = t_1
    else if (y <= (-1d-115)) then
        tmp = x
    else if (y <= (-1.3d-143)) then
        tmp = t_1
    else if (y <= 2.9d-161) then
        tmp = x
    else if (y <= 1.25d-125) then
        tmp = (z * y) / a
    else if (y <= 1.5d-90) then
        tmp = x
    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 * ((z - t) / a);
	double tmp;
	if (y <= -2e-37) {
		tmp = t_1;
	} else if (y <= -1e-115) {
		tmp = x;
	} else if (y <= -1.3e-143) {
		tmp = t_1;
	} else if (y <= 2.9e-161) {
		tmp = x;
	} else if (y <= 1.25e-125) {
		tmp = (z * y) / a;
	} else if (y <= 1.5e-90) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / a)
	tmp = 0
	if y <= -2e-37:
		tmp = t_1
	elif y <= -1e-115:
		tmp = x
	elif y <= -1.3e-143:
		tmp = t_1
	elif y <= 2.9e-161:
		tmp = x
	elif y <= 1.25e-125:
		tmp = (z * y) / a
	elif y <= 1.5e-90:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / a))
	tmp = 0.0
	if (y <= -2e-37)
		tmp = t_1;
	elseif (y <= -1e-115)
		tmp = x;
	elseif (y <= -1.3e-143)
		tmp = t_1;
	elseif (y <= 2.9e-161)
		tmp = x;
	elseif (y <= 1.25e-125)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= 1.5e-90)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / a);
	tmp = 0.0;
	if (y <= -2e-37)
		tmp = t_1;
	elseif (y <= -1e-115)
		tmp = x;
	elseif (y <= -1.3e-143)
		tmp = t_1;
	elseif (y <= 2.9e-161)
		tmp = x;
	elseif (y <= 1.25e-125)
		tmp = (z * y) / a;
	elseif (y <= 1.5e-90)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e-37], t$95$1, If[LessEqual[y, -1e-115], x, If[LessEqual[y, -1.3e-143], t$95$1, If[LessEqual[y, 2.9e-161], x, If[LessEqual[y, 1.25e-125], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.5e-90], x, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000013e-37 or -1.0000000000000001e-115 < y < -1.29999999999999994e-143 or 1.5000000000000001e-90 < y

   1. Initial program 90.8%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around inf 77.7%

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

   5. Taylor expanded in z around 0 77.7%

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

      1. neg-mul-1 77.7%

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

      2. +-commutative 77.7%

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

      3. sub-neg 77.7%

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

      4. div-sub 79.5%

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

   7. Simplified 79.5%

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

   if -2.00000000000000013e-37 < y < -1.0000000000000001e-115 or -1.29999999999999994e-143 < y < 2.9e-161 or 1.24999999999999992e-125 < y < 1.5000000000000001e-90

   1. Initial program 98.7%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 78.8%

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

   if 2.9e-161 < y < 1.24999999999999992e-125

   1. Initial program 99.6%

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

      1. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in y around inf 44.3%

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

   5. Taylor expanded in z around inf 72.9%

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

   6. Taylor expanded in z around 0 85.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-143}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-125}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 6: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+49} \lor \neg \left(y \leq 4.5 \cdot 10^{-89} \lor \neg \left(y \leq 1350000000\right) \land y \leq 3.4 \cdot 10^{+134}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.6e+49)
         (not
          (or (<= y 4.5e-89) (and (not (<= y 1350000000.0)) (<= y 3.4e+134)))))
   (* y (/ (- z t) a))
   (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.6e+49) || !((y <= 4.5e-89) || (!(y <= 1350000000.0) && (y <= 3.4e+134)))) {
		tmp = y * ((z - t) / a);
	} 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 ((y <= (-3.6d+49)) .or. (.not. (y <= 4.5d-89) .or. (.not. (y <= 1350000000.0d0)) .and. (y <= 3.4d+134))) then
        tmp = y * ((z - t) / a)
    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 ((y <= -3.6e+49) || !((y <= 4.5e-89) || (!(y <= 1350000000.0) && (y <= 3.4e+134)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.6e+49) or not ((y <= 4.5e-89) or (not (y <= 1350000000.0) and (y <= 3.4e+134))):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.6e+49) || !((y <= 4.5e-89) || (!(y <= 1350000000.0) && (y <= 3.4e+134))))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	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 ((y <= -3.6e+49) || ~(((y <= 4.5e-89) || (~((y <= 1350000000.0)) && (y <= 3.4e+134)))))
		tmp = y * ((z - t) / a);
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.6e+49], N[Not[Or[LessEqual[y, 4.5e-89], And[N[Not[LessEqual[y, 1350000000.0]], $MachinePrecision], LessEqual[y, 3.4e+134]]]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999996e49 or 4.4999999999999999e-89 < y < 1.35e9 or 3.40000000000000018e134 < y

   1. Initial program 90.4%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in y around inf 82.7%

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

   5. Taylor expanded in z around 0 82.7%

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

      1. neg-mul-1 82.7%

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

      2. +-commutative 82.7%

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

      3. sub-neg 82.7%

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

      4. div-sub 85.2%

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

   7. Simplified 85.2%

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

   if -3.59999999999999996e49 < y < 4.4999999999999999e-89 or 1.35e9 < y < 3.40000000000000018e134

   1. Initial program 96.4%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in z around inf 82.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+49} \lor \neg \left(y \leq 4.5 \cdot 10^{-89} \lor \neg \left(y \leq 1350000000\right) \land y \leq 3.4 \cdot 10^{+134}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 7: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a}\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 650000 \lor \neg \left(y \leq 4.2 \cdot 10^{+134}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) a))))
   (if (<= y -2.15e+49)
     t_1
     (if (<= y 2.4e-89)
       (+ x (* z (/ y a)))
       (if (or (<= y 650000.0) (not (<= y 4.2e+134)))
         t_1
         (+ x (/ y (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / a);
	double tmp;
	if (y <= -2.15e+49) {
		tmp = t_1;
	} else if (y <= 2.4e-89) {
		tmp = x + (z * (y / a));
	} else if ((y <= 650000.0) || !(y <= 4.2e+134)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / a)
    if (y <= (-2.15d+49)) then
        tmp = t_1
    else if (y <= 2.4d-89) then
        tmp = x + (z * (y / a))
    else if ((y <= 650000.0d0) .or. (.not. (y <= 4.2d+134))) then
        tmp = t_1
    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 t_1 = y * ((z - t) / a);
	double tmp;
	if (y <= -2.15e+49) {
		tmp = t_1;
	} else if (y <= 2.4e-89) {
		tmp = x + (z * (y / a));
	} else if ((y <= 650000.0) || !(y <= 4.2e+134)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / a)
	tmp = 0
	if y <= -2.15e+49:
		tmp = t_1
	elif y <= 2.4e-89:
		tmp = x + (z * (y / a))
	elif (y <= 650000.0) or not (y <= 4.2e+134):
		tmp = t_1
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / a))
	tmp = 0.0
	if (y <= -2.15e+49)
		tmp = t_1;
	elseif (y <= 2.4e-89)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif ((y <= 650000.0) || !(y <= 4.2e+134))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / a);
	tmp = 0.0;
	if (y <= -2.15e+49)
		tmp = t_1;
	elseif (y <= 2.4e-89)
		tmp = x + (z * (y / a));
	elseif ((y <= 650000.0) || ~((y <= 4.2e+134)))
		tmp = t_1;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.15e+49], t$95$1, If[LessEqual[y, 2.4e-89], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 650000.0], N[Not[LessEqual[y, 4.2e+134]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.15e49 or 2.40000000000000016e-89 < y < 6.5e5 or 4.2000000000000002e134 < y

   1. Initial program 90.4%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in y around inf 82.7%

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

   5. Taylor expanded in z around 0 82.7%

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

      1. neg-mul-1 82.7%

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

      2. +-commutative 82.7%

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

      3. sub-neg 82.7%

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

      4. div-sub 85.2%

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

   7. Simplified 85.2%

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

   if -2.15e49 < y < 2.40000000000000016e-89

   1. Initial program 99.0%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around 0 87.6%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

   6. Simplified 86.8%

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

   if 6.5e5 < y < 4.2000000000000002e134

   1. Initial program 86.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 84.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 650000 \lor \neg \left(y \leq 4.2 \cdot 10^{+134}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 8: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 32000000 \lor \neg \left(y \leq 3.5 \cdot 10^{+134}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) a))))
   (if (<= y -2.7e+49)
     t_1
     (if (<= y 1.15e-89)
       (+ x (/ (* z y) a))
       (if (or (<= y 32000000.0) (not (<= y 3.5e+134)))
         t_1
         (+ x (/ y (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / a);
	double tmp;
	if (y <= -2.7e+49) {
		tmp = t_1;
	} else if (y <= 1.15e-89) {
		tmp = x + ((z * y) / a);
	} else if ((y <= 32000000.0) || !(y <= 3.5e+134)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / a)
    if (y <= (-2.7d+49)) then
        tmp = t_1
    else if (y <= 1.15d-89) then
        tmp = x + ((z * y) / a)
    else if ((y <= 32000000.0d0) .or. (.not. (y <= 3.5d+134))) then
        tmp = t_1
    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 t_1 = y * ((z - t) / a);
	double tmp;
	if (y <= -2.7e+49) {
		tmp = t_1;
	} else if (y <= 1.15e-89) {
		tmp = x + ((z * y) / a);
	} else if ((y <= 32000000.0) || !(y <= 3.5e+134)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / a)
	tmp = 0
	if y <= -2.7e+49:
		tmp = t_1
	elif y <= 1.15e-89:
		tmp = x + ((z * y) / a)
	elif (y <= 32000000.0) or not (y <= 3.5e+134):
		tmp = t_1
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / a))
	tmp = 0.0
	if (y <= -2.7e+49)
		tmp = t_1;
	elseif (y <= 1.15e-89)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	elseif ((y <= 32000000.0) || !(y <= 3.5e+134))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / a);
	tmp = 0.0;
	if (y <= -2.7e+49)
		tmp = t_1;
	elseif (y <= 1.15e-89)
		tmp = x + ((z * y) / a);
	elseif ((y <= 32000000.0) || ~((y <= 3.5e+134)))
		tmp = t_1;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+49], t$95$1, If[LessEqual[y, 1.15e-89], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 32000000.0], N[Not[LessEqual[y, 3.5e+134]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7000000000000001e49 or 1.15e-89 < y < 3.2e7 or 3.50000000000000003e134 < y

   1. Initial program 90.4%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in y around inf 82.7%

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

   5. Taylor expanded in z around 0 82.7%

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

      1. neg-mul-1 82.7%

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

      2. +-commutative 82.7%

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

      3. sub-neg 82.7%

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

      4. div-sub 85.2%

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

   7. Simplified 85.2%

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

   if -2.7000000000000001e49 < y < 1.15e-89

   1. Initial program 99.0%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around 0 87.6%

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

   if 3.2e7 < y < 3.50000000000000003e134

   1. Initial program 86.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 84.0%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 32000000 \lor \neg \left(y \leq 3.5 \cdot 10^{+134}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 49.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= y -3.8e+68)
     t_1
     (if (<= y 2.9e-161)
       x
       (if (<= y 9.5e-127) t_1 (if (<= y 1.55e+47) x (* z (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (y <= -3.8e+68) {
		tmp = t_1;
	} else if (y <= 2.9e-161) {
		tmp = x;
	} else if (y <= 9.5e-127) {
		tmp = t_1;
	} else if (y <= 1.55e+47) {
		tmp = x;
	} else {
		tmp = z * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (y <= (-3.8d+68)) then
        tmp = t_1
    else if (y <= 2.9d-161) then
        tmp = x
    else if (y <= 9.5d-127) then
        tmp = t_1
    else if (y <= 1.55d+47) then
        tmp = x
    else
        tmp = z * (y / a)
    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 (y <= -3.8e+68) {
		tmp = t_1;
	} else if (y <= 2.9e-161) {
		tmp = x;
	} else if (y <= 9.5e-127) {
		tmp = t_1;
	} else if (y <= 1.55e+47) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if y <= -3.8e+68:
		tmp = t_1
	elif y <= 2.9e-161:
		tmp = x
	elif y <= 9.5e-127:
		tmp = t_1
	elif y <= 1.55e+47:
		tmp = x
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (y <= -3.8e+68)
		tmp = t_1;
	elseif (y <= 2.9e-161)
		tmp = x;
	elseif (y <= 9.5e-127)
		tmp = t_1;
	elseif (y <= 1.55e+47)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (y <= -3.8e+68)
		tmp = t_1;
	elseif (y <= 2.9e-161)
		tmp = x;
	elseif (y <= 9.5e-127)
		tmp = t_1;
	elseif (y <= 1.55e+47)
		tmp = x;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+68], t$95$1, If[LessEqual[y, 2.9e-161], x, If[LessEqual[y, 9.5e-127], t$95$1, If[LessEqual[y, 1.55e+47], x, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000001e68 or 2.9e-161 < y < 9.4999999999999997e-127

   1. Initial program 89.2%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around inf 80.7%

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

   5. Taylor expanded in z around inf 51.3%

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

   if -3.8000000000000001e68 < y < 2.9e-161 or 9.4999999999999997e-127 < y < 1.55e47

   1. Initial program 98.4%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 61.8%

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

   if 1.55e47 < y

   1. Initial program 88.9%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 77.5%

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

   5. Taylor expanded in z around inf 48.6%

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

   6. Taylor expanded in z around 0 42.4%

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

      1. associate-*l/ 55.4%

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

   8. Simplified 55.4%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 49.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-125}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.28e+70)
   (* y (/ z a))
   (if (<= y 2.85e-161)
     x
     (if (<= y 1.2e-125) (/ (* z y) a) (if (<= y 7.8e+47) x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.28e+70) {
		tmp = y * (z / a);
	} else if (y <= 2.85e-161) {
		tmp = x;
	} else if (y <= 1.2e-125) {
		tmp = (z * y) / a;
	} else if (y <= 7.8e+47) {
		tmp = x;
	} else {
		tmp = z * (y / 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 (y <= (-1.28d+70)) then
        tmp = y * (z / a)
    else if (y <= 2.85d-161) then
        tmp = x
    else if (y <= 1.2d-125) then
        tmp = (z * y) / a
    else if (y <= 7.8d+47) then
        tmp = x
    else
        tmp = z * (y / 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 (y <= -1.28e+70) {
		tmp = y * (z / a);
	} else if (y <= 2.85e-161) {
		tmp = x;
	} else if (y <= 1.2e-125) {
		tmp = (z * y) / a;
	} else if (y <= 7.8e+47) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.28e+70:
		tmp = y * (z / a)
	elif y <= 2.85e-161:
		tmp = x
	elif y <= 1.2e-125:
		tmp = (z * y) / a
	elif y <= 7.8e+47:
		tmp = x
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.28e+70)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= 2.85e-161)
		tmp = x;
	elseif (y <= 1.2e-125)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= 7.8e+47)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.28e+70)
		tmp = y * (z / a);
	elseif (y <= 2.85e-161)
		tmp = x;
	elseif (y <= 1.2e-125)
		tmp = (z * y) / a;
	elseif (y <= 7.8e+47)
		tmp = x;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.28e+70], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.85e-161], x, If[LessEqual[y, 1.2e-125], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 7.8e+47], x, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.27999999999999994e70

   1. Initial program 87.9%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around inf 85.3%

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

   5. Taylor expanded in z around inf 48.5%

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

   if -1.27999999999999994e70 < y < 2.85000000000000011e-161 or 1.2000000000000001e-125 < y < 7.8000000000000005e47

   1. Initial program 98.4%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 61.8%

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

   if 2.85000000000000011e-161 < y < 1.2000000000000001e-125

   1. Initial program 99.6%

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

      1. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in y around inf 44.3%

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

   5. Taylor expanded in z around inf 72.9%

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

   6. Taylor expanded in z around 0 85.8%

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

   if 7.8000000000000005e47 < y

   1. Initial program 88.9%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 77.5%

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

   5. Taylor expanded in z around inf 48.6%

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

   6. Taylor expanded in z around 0 42.4%

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

      1. associate-*l/ 55.4%

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

   8. Simplified 55.4%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-125}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 11: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+57} \lor \neg \left(z \leq 2.2 \cdot 10^{-20}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+57) (not (<= z 2.2e-20)))
   (+ x (* z (/ y a)))
   (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+57) || !(z <= 2.2e-20)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t * (y / 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 ((z <= (-2d+57)) .or. (.not. (z <= 2.2d-20))) then
        tmp = x + (z * (y / a))
    else
        tmp = x - (t * (y / 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 ((z <= -2e+57) || !(z <= 2.2e-20)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+57) or not (z <= 2.2e-20):
		tmp = x + (z * (y / a))
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+57) || !(z <= 2.2e-20))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e+57) || ~((z <= 2.2e-20)))
		tmp = x + (z * (y / a));
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e+57], N[Not[LessEqual[z, 2.2e-20]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e57 or 2.19999999999999991e-20 < z

   1. Initial program 91.0%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 86.6%

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

      1. associate-*l/ 91.4%

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

      2. *-commutative 91.4%

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

   6. Simplified 91.4%

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

   if -2.0000000000000001e57 < z < 2.19999999999999991e-20

   1. Initial program 95.8%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 87.4%

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

      1. mul-1-neg 87.4%

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

      2. associate-*l/ 89.9%

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

      3. distribute-rgt-neg-out 89.9%

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

      4. +-commutative 89.9%

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

      5. *-commutative 89.9%

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

      6. distribute-lft-neg-out 89.9%

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

      7. unsub-neg 89.9%

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

   6. Simplified 89.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+57} \lor \neg \left(z \leq 2.2 \cdot 10^{-20}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 12: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+70} \lor \neg \left(y \leq 3.7 \cdot 10^{+48}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3e+70) (not (<= y 3.7e+48))) (* z (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e+70) || !(y <= 3.7e+48)) {
		tmp = z * (y / a);
	} 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 <= (-3d+70)) .or. (.not. (y <= 3.7d+48))) then
        tmp = z * (y / a)
    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 <= -3e+70) || !(y <= 3.7e+48)) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3e+70) or not (y <= 3.7e+48):
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3e+70) || !(y <= 3.7e+48))
		tmp = Float64(z * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3e+70) || ~((y <= 3.7e+48)))
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3e+70], N[Not[LessEqual[y, 3.7e+48]], $MachinePrecision]], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999976e70 or 3.6999999999999999e48 < y

   1. Initial program 88.5%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around inf 81.0%

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

   5. Taylor expanded in z around inf 48.6%

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

   6. Taylor expanded in z around 0 42.8%

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

      1. associate-*l/ 52.2%

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

   8. Simplified 52.2%

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

   if -2.99999999999999976e70 < y < 3.6999999999999999e48

   1. Initial program 98.4%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around inf 59.4%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+70} \lor \neg \left(y \leq 3.7 \cdot 10^{+48}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. associate-*l/ 96.8%

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

3. Simplified 96.8%

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

4. Final simplification 96.8%

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

Alternative 14: 39.2% 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 93.6%

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

   1. associate-*l/ 96.8%

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

3. Simplified 96.8%

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

4. Taylor expanded in x around inf 39.5%

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

5. Final simplification 39.5%

   \[\leadsto x \]

Developer target: 99.1% 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 2023208 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))