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

Percentage Accurate: 93.4% → 97.4%

Time: 15.0s

Alternatives: 14

Speedup: 1.0×

• 25.3% 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: 93.4% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(t - z), $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/ 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. Add Preprocessing

5. Taylor expanded in y around 0 93.6%

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

   1. *-commutative 93.6%

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

   2. associate-/l* 98.0%

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

7. Simplified 98.0%

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

8. Final simplification 98.0%

   \[\leadsto x + \frac{t - z}{\frac{a}{y}} \]
9. Add Preprocessing

Alternative 2: 50.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-125}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (/ a z))))
   (if (<= a -5.1e+25)
     x
     (if (<= a -1.9e-54)
       t_1
       (if (<= a -8e-125)
         (/ t (/ a y))
         (if (<= a -3.1e-288) t_1 (if (<= a 2.55e-33) (* t (/ y a)) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / (a / z);
	double tmp;
	if (a <= -5.1e+25) {
		tmp = x;
	} else if (a <= -1.9e-54) {
		tmp = t_1;
	} else if (a <= -8e-125) {
		tmp = t / (a / y);
	} else if (a <= -3.1e-288) {
		tmp = t_1;
	} else if (a <= 2.55e-33) {
		tmp = t * (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) :: t_1
    real(8) :: tmp
    t_1 = -y / (a / z)
    if (a <= (-5.1d+25)) then
        tmp = x
    else if (a <= (-1.9d-54)) then
        tmp = t_1
    else if (a <= (-8d-125)) then
        tmp = t / (a / y)
    else if (a <= (-3.1d-288)) then
        tmp = t_1
    else if (a <= 2.55d-33) then
        tmp = t * (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 t_1 = -y / (a / z);
	double tmp;
	if (a <= -5.1e+25) {
		tmp = x;
	} else if (a <= -1.9e-54) {
		tmp = t_1;
	} else if (a <= -8e-125) {
		tmp = t / (a / y);
	} else if (a <= -3.1e-288) {
		tmp = t_1;
	} else if (a <= 2.55e-33) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / (a / z)
	tmp = 0
	if a <= -5.1e+25:
		tmp = x
	elif a <= -1.9e-54:
		tmp = t_1
	elif a <= -8e-125:
		tmp = t / (a / y)
	elif a <= -3.1e-288:
		tmp = t_1
	elif a <= 2.55e-33:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(a / z))
	tmp = 0.0
	if (a <= -5.1e+25)
		tmp = x;
	elseif (a <= -1.9e-54)
		tmp = t_1;
	elseif (a <= -8e-125)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= -3.1e-288)
		tmp = t_1;
	elseif (a <= 2.55e-33)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / (a / z);
	tmp = 0.0;
	if (a <= -5.1e+25)
		tmp = x;
	elseif (a <= -1.9e-54)
		tmp = t_1;
	elseif (a <= -8e-125)
		tmp = t / (a / y);
	elseif (a <= -3.1e-288)
		tmp = t_1;
	elseif (a <= 2.55e-33)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.1e+25], x, If[LessEqual[a, -1.9e-54], t$95$1, If[LessEqual[a, -8e-125], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.1e-288], t$95$1, If[LessEqual[a, 2.55e-33], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.1000000000000004e25 or 2.55000000000000004e-33 < a

   1. Initial program 88.9%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around inf 65.9%

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

   if -5.1000000000000004e25 < a < -1.9000000000000001e-54 or -8.0000000000000001e-125 < a < -3.09999999999999983e-288

   1. Initial program 99.8%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around inf 69.1%

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

      1. mul-1-neg 69.1%

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

      2. associate-/l* 63.5%

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

   7. Simplified 63.5%

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

   if -1.9000000000000001e-54 < a < -8.0000000000000001e-125

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 53.0%

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

      1. associate-/l* 59.1%

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

   7. Simplified 59.1%

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

   if -3.09999999999999983e-288 < a < 2.55000000000000004e-33

   1. Initial program 98.2%

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

   5. Taylor expanded in y around 0 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in t around inf 56.5%

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

      1. associate-*r/ 61.8%

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

   10. Simplified 61.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-54}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-125}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-288}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-126}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-290}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 10^{-33}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e+27)
   x
   (if (<= a -5.2e-54)
     (/ (- y) (/ a z))
     (if (<= a -1.55e-126)
       (/ t (/ a y))
       (if (<= a -8.8e-290)
         (* z (/ y (- a)))
         (if (<= a 1e-33) (* t (/ y a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+27) {
		tmp = x;
	} else if (a <= -5.2e-54) {
		tmp = -y / (a / z);
	} else if (a <= -1.55e-126) {
		tmp = t / (a / y);
	} else if (a <= -8.8e-290) {
		tmp = z * (y / -a);
	} else if (a <= 1e-33) {
		tmp = t * (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 (a <= (-2.1d+27)) then
        tmp = x
    else if (a <= (-5.2d-54)) then
        tmp = -y / (a / z)
    else if (a <= (-1.55d-126)) then
        tmp = t / (a / y)
    else if (a <= (-8.8d-290)) then
        tmp = z * (y / -a)
    else if (a <= 1d-33) then
        tmp = t * (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 (a <= -2.1e+27) {
		tmp = x;
	} else if (a <= -5.2e-54) {
		tmp = -y / (a / z);
	} else if (a <= -1.55e-126) {
		tmp = t / (a / y);
	} else if (a <= -8.8e-290) {
		tmp = z * (y / -a);
	} else if (a <= 1e-33) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e+27:
		tmp = x
	elif a <= -5.2e-54:
		tmp = -y / (a / z)
	elif a <= -1.55e-126:
		tmp = t / (a / y)
	elif a <= -8.8e-290:
		tmp = z * (y / -a)
	elif a <= 1e-33:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+27)
		tmp = x;
	elseif (a <= -5.2e-54)
		tmp = Float64(Float64(-y) / Float64(a / z));
	elseif (a <= -1.55e-126)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= -8.8e-290)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (a <= 1e-33)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e+27)
		tmp = x;
	elseif (a <= -5.2e-54)
		tmp = -y / (a / z);
	elseif (a <= -1.55e-126)
		tmp = t / (a / y);
	elseif (a <= -8.8e-290)
		tmp = z * (y / -a);
	elseif (a <= 1e-33)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+27], x, If[LessEqual[a, -5.2e-54], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.55e-126], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.8e-290], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-33], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.09999999999999995e27 or 1.0000000000000001e-33 < a

   1. Initial program 88.9%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around inf 65.9%

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

   if -2.09999999999999995e27 < a < -5.20000000000000004e-54

   1. Initial program 99.6%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in z around inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. associate-/l* 55.1%

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

   7. Simplified 55.1%

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

   if -5.20000000000000004e-54 < a < -1.5500000000000001e-126

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 53.0%

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

      1. associate-/l* 59.1%

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

   7. Simplified 59.1%

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

   if -1.5500000000000001e-126 < a < -8.8000000000000004e-290

   1. Initial program 99.9%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. associate-*l/ 74.7%

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

      3. *-commutative 74.7%

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

      4. distribute-rgt-neg-in 74.7%

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

      5. *-lft-identity 74.7%

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

      6. associate-*l/ 74.8%

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

      7. remove-double-neg 74.8%

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

      8. neg-mul-1 74.8%

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

      9. associate-*r* 74.8%

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

      10. *-commutative 74.8%

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

      11. neg-mul-1 74.8%

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

      12. *-commutative 74.8%

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

      13. distribute-neg-frac 74.8%

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

      14. metadata-eval 74.8%

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

      15. metadata-eval 74.8%

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

      16. associate-/r* 74.8%

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

      17. neg-mul-1 74.8%

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

      18. associate-*r/ 74.7%

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

      19. *-rgt-identity 74.7%

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

      20. distribute-frac-neg 74.7%

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

      21. remove-double-neg 74.7%

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

   7. Simplified 74.7%

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

   if -8.8000000000000004e-290 < a < 1.0000000000000001e-33

   1. Initial program 98.2%

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

   5. Taylor expanded in y around 0 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in t around inf 56.5%

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

      1. associate-*r/ 61.8%

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

   10. Simplified 61.8%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-126}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-290}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 10^{-33}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-53}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-124}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-289}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e+25)
   x
   (if (<= a -2.6e-53)
     (/ (- y) (/ a z))
     (if (<= a -2.1e-124)
       (/ t (/ a y))
       (if (<= a -3.7e-289)
         (/ (- z) (/ a y))
         (if (<= a 1.18e-29) (* t (/ y a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+25) {
		tmp = x;
	} else if (a <= -2.6e-53) {
		tmp = -y / (a / z);
	} else if (a <= -2.1e-124) {
		tmp = t / (a / y);
	} else if (a <= -3.7e-289) {
		tmp = -z / (a / y);
	} else if (a <= 1.18e-29) {
		tmp = t * (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 (a <= (-6d+25)) then
        tmp = x
    else if (a <= (-2.6d-53)) then
        tmp = -y / (a / z)
    else if (a <= (-2.1d-124)) then
        tmp = t / (a / y)
    else if (a <= (-3.7d-289)) then
        tmp = -z / (a / y)
    else if (a <= 1.18d-29) then
        tmp = t * (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 (a <= -6e+25) {
		tmp = x;
	} else if (a <= -2.6e-53) {
		tmp = -y / (a / z);
	} else if (a <= -2.1e-124) {
		tmp = t / (a / y);
	} else if (a <= -3.7e-289) {
		tmp = -z / (a / y);
	} else if (a <= 1.18e-29) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e+25:
		tmp = x
	elif a <= -2.6e-53:
		tmp = -y / (a / z)
	elif a <= -2.1e-124:
		tmp = t / (a / y)
	elif a <= -3.7e-289:
		tmp = -z / (a / y)
	elif a <= 1.18e-29:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e+25)
		tmp = x;
	elseif (a <= -2.6e-53)
		tmp = Float64(Float64(-y) / Float64(a / z));
	elseif (a <= -2.1e-124)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= -3.7e-289)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (a <= 1.18e-29)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e+25)
		tmp = x;
	elseif (a <= -2.6e-53)
		tmp = -y / (a / z);
	elseif (a <= -2.1e-124)
		tmp = t / (a / y);
	elseif (a <= -3.7e-289)
		tmp = -z / (a / y);
	elseif (a <= 1.18e-29)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e+25], x, If[LessEqual[a, -2.6e-53], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e-124], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.7e-289], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.18e-29], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.00000000000000011e25 or 1.17999999999999996e-29 < a

   1. Initial program 88.9%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around inf 65.9%

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

   if -6.00000000000000011e25 < a < -2.59999999999999996e-53

   1. Initial program 99.6%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in z around inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. associate-/l* 55.1%

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

   7. Simplified 55.1%

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

   if -2.59999999999999996e-53 < a < -2.1000000000000001e-124

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 53.0%

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

      1. associate-/l* 59.1%

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

   7. Simplified 59.1%

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

   if -2.1000000000000001e-124 < a < -3.69999999999999989e-289

   1. Initial program 99.9%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. associate-*l/ 74.7%

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

      3. *-commutative 74.7%

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

      4. distribute-rgt-neg-in 74.7%

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

      5. *-lft-identity 74.7%

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

      6. associate-*l/ 74.8%

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

      7. remove-double-neg 74.8%

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

      8. neg-mul-1 74.8%

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

      9. associate-*r* 74.8%

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

      10. *-commutative 74.8%

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

      11. neg-mul-1 74.8%

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

      12. *-commutative 74.8%

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

      13. distribute-neg-frac 74.8%

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

      14. metadata-eval 74.8%

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

      15. metadata-eval 74.8%

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

      16. associate-/r* 74.8%

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

      17. neg-mul-1 74.8%

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

      18. associate-*r/ 74.7%

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

      19. *-rgt-identity 74.7%

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

      20. distribute-frac-neg 74.7%

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

      21. remove-double-neg 74.7%

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

   7. Simplified 74.7%

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

      1. add-sqr-sqrt 29.6%

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

      2. sqrt-unprod 29.9%

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

      3. frac-times 18.8%

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

      4. sqr-neg 18.8%

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

      5. frac-times 29.9%

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

      6. sqrt-unprod 0.3%

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

      7. add-sqr-sqrt 8.2%

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

      8. clear-num 8.2%

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

      9. div-inv 8.2%

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

      10. frac-2neg 8.2%

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

      11. distribute-frac-neg 8.2%

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

      12. add-sqr-sqrt 8.2%

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

      13. sqrt-unprod 8.1%

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

      14. sqr-neg 8.1%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 74.7%

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

   9. Applied egg-rr 74.7%

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

   if -3.69999999999999989e-289 < a < 1.17999999999999996e-29

   1. Initial program 98.2%

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

   5. Taylor expanded in y around 0 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in t around inf 56.5%

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

      1. associate-*r/ 61.8%

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

   10. Simplified 61.8%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-53}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-124}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-289}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-54}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-288}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+27)
   x
   (if (<= a -2.55e-54)
     (/ (- y) (/ a z))
     (if (<= a -5.8e-125)
       (/ t (/ a y))
       (if (<= a -2.9e-288)
         (/ (* z (- y)) a)
         (if (<= a 7.6e-32) (* t (/ y a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+27) {
		tmp = x;
	} else if (a <= -2.55e-54) {
		tmp = -y / (a / z);
	} else if (a <= -5.8e-125) {
		tmp = t / (a / y);
	} else if (a <= -2.9e-288) {
		tmp = (z * -y) / a;
	} else if (a <= 7.6e-32) {
		tmp = t * (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 (a <= (-3.5d+27)) then
        tmp = x
    else if (a <= (-2.55d-54)) then
        tmp = -y / (a / z)
    else if (a <= (-5.8d-125)) then
        tmp = t / (a / y)
    else if (a <= (-2.9d-288)) then
        tmp = (z * -y) / a
    else if (a <= 7.6d-32) then
        tmp = t * (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 (a <= -3.5e+27) {
		tmp = x;
	} else if (a <= -2.55e-54) {
		tmp = -y / (a / z);
	} else if (a <= -5.8e-125) {
		tmp = t / (a / y);
	} else if (a <= -2.9e-288) {
		tmp = (z * -y) / a;
	} else if (a <= 7.6e-32) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e+27:
		tmp = x
	elif a <= -2.55e-54:
		tmp = -y / (a / z)
	elif a <= -5.8e-125:
		tmp = t / (a / y)
	elif a <= -2.9e-288:
		tmp = (z * -y) / a
	elif a <= 7.6e-32:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+27)
		tmp = x;
	elseif (a <= -2.55e-54)
		tmp = Float64(Float64(-y) / Float64(a / z));
	elseif (a <= -5.8e-125)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= -2.9e-288)
		tmp = Float64(Float64(z * Float64(-y)) / a);
	elseif (a <= 7.6e-32)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.5e+27)
		tmp = x;
	elseif (a <= -2.55e-54)
		tmp = -y / (a / z);
	elseif (a <= -5.8e-125)
		tmp = t / (a / y);
	elseif (a <= -2.9e-288)
		tmp = (z * -y) / a;
	elseif (a <= 7.6e-32)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+27], x, If[LessEqual[a, -2.55e-54], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.8e-125], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.9e-288], N[(N[(z * (-y)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 7.6e-32], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.5000000000000002e27 or 7.60000000000000015e-32 < a

   1. Initial program 88.9%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around inf 65.9%

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

   if -3.5000000000000002e27 < a < -2.55000000000000005e-54

   1. Initial program 99.6%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in z around inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. associate-/l* 55.1%

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

   7. Simplified 55.1%

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

   if -2.55000000000000005e-54 < a < -5.8000000000000004e-125

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 53.0%

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

      1. associate-/l* 59.1%

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

   7. Simplified 59.1%

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

   if -5.8000000000000004e-125 < a < -2.90000000000000015e-288

   1. Initial program 99.9%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. associate-*l/ 74.7%

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

      3. *-commutative 74.7%

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

      4. distribute-rgt-neg-in 74.7%

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

      5. *-lft-identity 74.7%

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

      6. associate-*l/ 74.8%

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

      7. remove-double-neg 74.8%

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

      8. neg-mul-1 74.8%

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

      9. associate-*r* 74.8%

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

      10. *-commutative 74.8%

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

      11. neg-mul-1 74.8%

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

      12. *-commutative 74.8%

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

      13. distribute-neg-frac 74.8%

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

      14. metadata-eval 74.8%

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

      15. metadata-eval 74.8%

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

      16. associate-/r* 74.8%

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

      17. neg-mul-1 74.8%

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

      18. associate-*r/ 74.7%

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

      19. *-rgt-identity 74.7%

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

      20. distribute-frac-neg 74.7%

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

      21. remove-double-neg 74.7%

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

   7. Simplified 74.7%

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

      1. *-commutative 74.7%

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

      2. frac-2neg 74.7%

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

      3. remove-double-neg 74.7%

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

      4. associate-*l/ 81.6%

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

   9. Applied egg-rr 81.6%

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

   if -2.90000000000000015e-288 < a < 7.60000000000000015e-32

   1. Initial program 98.2%

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

   5. Taylor expanded in y around 0 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in t around inf 56.5%

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

      1. associate-*r/ 61.8%

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

   10. Simplified 61.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-54}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-288}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+37} \lor \neg \left(z \leq 3.15 \cdot 10^{-71}\right):\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+37) (not (<= z 3.15e-71)))
   (- x (/ z (/ a y)))
   (- x (/ y (/ (- a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+37) || !(z <= 3.15e-71)) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x - (y / (-a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9d+37)) .or. (.not. (z <= 3.15d-71))) then
        tmp = x - (z / (a / y))
    else
        tmp = x - (y / (-a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+37) || !(z <= 3.15e-71)) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x - (y / (-a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+37) or not (z <= 3.15e-71):
		tmp = x - (z / (a / y))
	else:
		tmp = x - (y / (-a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+37) || !(z <= 3.15e-71))
		tmp = Float64(x - Float64(z / Float64(a / y)));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e+37) || ~((z <= 3.15e-71)))
		tmp = x - (z / (a / y));
	else
		tmp = x - (y / (-a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e+37], N[Not[LessEqual[z, 3.15e-71]], $MachinePrecision]], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999923e37 or 3.1500000000000002e-71 < z

   1. Initial program 90.7%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-/l* 88.1%

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

      3. associate-/r/ 85.2%

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

   7. Simplified 85.2%

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

      1. associate-/r/ 88.1%

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

   9. Applied egg-rr 88.1%

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

   if -8.99999999999999923e37 < z < 3.1500000000000002e-71

   1. Initial program 96.9%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around 0 90.1%

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

      1. associate-*r/ 90.1%

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

      2. neg-mul-1 90.1%

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

   7. Simplified 90.1%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+37} \lor \neg \left(z \leq 3.15 \cdot 10^{-71}\right):\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+25} \lor \neg \left(a \leq 2.4 \cdot 10^{-32}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.5e+25) (not (<= a 2.4e-32)))
   (+ x (/ (* t y) a))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.5e+25) || !(a <= 2.4e-32)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = (y / a) * (t - 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 ((a <= (-6.5d+25)) .or. (.not. (a <= 2.4d-32))) then
        tmp = x + ((t * y) / a)
    else
        tmp = (y / a) * (t - 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 ((a <= -6.5e+25) || !(a <= 2.4e-32)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.5e+25) or not (a <= 2.4e-32):
		tmp = x + ((t * y) / a)
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.5e+25) || !(a <= 2.4e-32))
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.5e+25) || ~((a <= 2.4e-32)))
		tmp = x + ((t * y) / a);
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.5e+25], N[Not[LessEqual[a, 2.4e-32]], $MachinePrecision]], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.50000000000000005e25 or 2.4000000000000001e-32 < a

   1. Initial program 88.9%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. neg-mul-1 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in x around 0 79.6%

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

   if -6.50000000000000005e25 < a < 2.4000000000000001e-32

   1. Initial program 99.1%

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

   5. Taylor expanded in y around 0 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in x around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. associate-*l/ 82.7%

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

      3. distribute-rgt-out-- 68.5%

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

      4. sub-neg 68.5%

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

      5. +-commutative 68.5%

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

      6. distribute-neg-in 68.5%

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

      7. remove-double-neg 68.5%

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

      8. sub-neg 68.5%

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

      9. distribute-rgt-out-- 82.7%

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

   10. Simplified 82.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+25} \lor \neg \left(a \leq 2.4 \cdot 10^{-32}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+38} \lor \neg \left(z \leq 5.6 \cdot 10^{-85}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e+38) (not (<= z 5.6e-85)))
   (- x (* y (/ z a)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+38) || !(z <= 5.6e-85)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (y * (t / 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 <= (-1.65d+38)) .or. (.not. (z <= 5.6d-85))) then
        tmp = x - (y * (z / a))
    else
        tmp = x + (y * (t / 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 <= -1.65e+38) || !(z <= 5.6e-85)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e+38) or not (z <= 5.6e-85):
		tmp = x - (y * (z / a))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e+38) || !(z <= 5.6e-85))
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e+38) || ~((z <= 5.6e-85)))
		tmp = x - (y * (z / a));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e+38], N[Not[LessEqual[z, 5.6e-85]], $MachinePrecision]], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e38 or 5.60000000000000033e-85 < z

   1. Initial program 90.9%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-/l* 88.0%

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

      3. associate-/r/ 85.2%

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

   7. Simplified 85.2%

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

   if -1.65e38 < z < 5.60000000000000033e-85

   1. Initial program 96.8%

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

   5. Taylor expanded in z around 0 89.3%

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

      1. sub-neg 89.3%

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

      2. mul-1-neg 89.3%

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

      3. remove-double-neg 89.3%

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

      4. +-commutative 89.3%

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

      5. associate-/l* 91.5%

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

      6. associate-/r/ 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+38} \lor \neg \left(z \leq 5.6 \cdot 10^{-85}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+37} \lor \neg \left(z \leq 2.7 \cdot 10^{-86}\right):\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e+37) (not (<= z 2.7e-86)))
   (- x (/ z (/ a y)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+37) || !(z <= 2.7e-86)) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x + (y * (t / 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 <= (-1.65d+37)) .or. (.not. (z <= 2.7d-86))) then
        tmp = x - (z / (a / y))
    else
        tmp = x + (y * (t / 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 <= -1.65e+37) || !(z <= 2.7e-86)) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e+37) or not (z <= 2.7e-86):
		tmp = x - (z / (a / y))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e+37) || !(z <= 2.7e-86))
		tmp = Float64(x - Float64(z / Float64(a / y)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e+37) || ~((z <= 2.7e-86)))
		tmp = x - (z / (a / y));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e+37], N[Not[LessEqual[z, 2.7e-86]], $MachinePrecision]], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e37 or 2.69999999999999992e-86 < z

   1. Initial program 90.9%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-/l* 88.0%

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

      3. associate-/r/ 85.2%

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

   7. Simplified 85.2%

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

      1. associate-/r/ 88.0%

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

   9. Applied egg-rr 88.0%

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

   if -1.65e37 < z < 2.69999999999999992e-86

   1. Initial program 96.8%

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

   5. Taylor expanded in z around 0 89.3%

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

      1. sub-neg 89.3%

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

      2. mul-1-neg 89.3%

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

      3. remove-double-neg 89.3%

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

      4. +-commutative 89.3%

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

      5. associate-/l* 91.5%

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

      6. associate-/r/ 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+37} \lor \neg \left(z \leq 2.7 \cdot 10^{-86}\right):\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.25e+98) x (if (<= a 1.5e+100) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e+98) {
		tmp = x;
	} else if (a <= 1.5e+100) {
		tmp = (y / a) * (t - z);
	} 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 <= (-1.25d+98)) then
        tmp = x
    else if (a <= 1.5d+100) then
        tmp = (y / a) * (t - z)
    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 <= -1.25e+98) {
		tmp = x;
	} else if (a <= 1.5e+100) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.25e+98:
		tmp = x
	elif a <= 1.5e+100:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.25e+98)
		tmp = x;
	elseif (a <= 1.5e+100)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.25e+98)
		tmp = x;
	elseif (a <= 1.5e+100)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.25e+98], x, If[LessEqual[a, 1.5e+100], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.25e98 or 1.49999999999999993e100 < a

   1. Initial program 85.8%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around inf 75.4%

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

   if -1.25e98 < a < 1.49999999999999993e100

   1. Initial program 98.2%

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

   5. Taylor expanded in y around 0 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-/l* 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in x around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. associate-*l/ 76.4%

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

      3. distribute-rgt-out-- 65.9%

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

      4. sub-neg 65.9%

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

      5. +-commutative 65.9%

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

      6. distribute-neg-in 65.9%

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

      7. remove-double-neg 65.9%

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

      8. sub-neg 65.9%

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

      9. distribute-rgt-out-- 76.4%

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

   10. Simplified 76.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-32}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e+25)
   (+ x (* y (/ t a)))
   (if (<= a 1.65e-32) (* (/ y a) (- t z)) (+ x (/ (* t y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+25) {
		tmp = x + (y * (t / a));
	} else if (a <= 1.65e-32) {
		tmp = (y / a) * (t - z);
	} 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 (a <= (-6d+25)) then
        tmp = x + (y * (t / a))
    else if (a <= 1.65d-32) then
        tmp = (y / a) * (t - z)
    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 (a <= -6e+25) {
		tmp = x + (y * (t / a));
	} else if (a <= 1.65e-32) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e+25:
		tmp = x + (y * (t / a))
	elif a <= 1.65e-32:
		tmp = (y / a) * (t - z)
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e+25)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (a <= 1.65e-32)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e+25)
		tmp = x + (y * (t / a));
	elseif (a <= 1.65e-32)
		tmp = (y / a) * (t - z);
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e+25], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-32], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.00000000000000011e25

   1. Initial program 85.9%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 78.2%

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

      1. sub-neg 78.2%

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

      2. mul-1-neg 78.2%

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

      3. remove-double-neg 78.2%

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

      4. +-commutative 78.2%

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

      5. associate-/l* 85.8%

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

      6. associate-/r/ 85.7%

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

   7. Simplified 85.7%

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

   if -6.00000000000000011e25 < a < 1.65000000000000013e-32

   1. Initial program 99.1%

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

   5. Taylor expanded in y around 0 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in x around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. associate-*l/ 82.7%

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

      3. distribute-rgt-out-- 68.5%

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

      4. sub-neg 68.5%

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

      5. +-commutative 68.5%

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

      6. distribute-neg-in 68.5%

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

      7. remove-double-neg 68.5%

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

      8. sub-neg 68.5%

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

      9. distribute-rgt-out-- 82.7%

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

   10. Simplified 82.7%

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

   if 1.65000000000000013e-32 < a

   1. Initial program 91.3%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around 0 79.5%

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

      1. associate-*r/ 79.5%

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

      2. neg-mul-1 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in x around 0 80.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-32}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3e-93) x (if (<= a 5.8e-28) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e-93) {
		tmp = x;
	} else if (a <= 5.8e-28) {
		tmp = t * (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 (a <= (-3d-93)) then
        tmp = x
    else if (a <= 5.8d-28) then
        tmp = t * (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 (a <= -3e-93) {
		tmp = x;
	} else if (a <= 5.8e-28) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3e-93:
		tmp = x
	elif a <= 5.8e-28:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3e-93)
		tmp = x;
	elseif (a <= 5.8e-28)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3e-93)
		tmp = x;
	elseif (a <= 5.8e-28)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3e-93], x, If[LessEqual[a, 5.8e-28], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0000000000000001e-93 or 5.80000000000000026e-28 < a

   1. Initial program 90.9%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in x around inf 59.2%

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

   if -3.0000000000000001e-93 < a < 5.80000000000000026e-28

   1. Initial program 98.9%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around 0 98.9%

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

      1. *-commutative 98.9%

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

      2. associate-/l* 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in t around inf 50.5%

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

      1. associate-*r/ 55.8%

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

   10. Simplified 55.8%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

5. Final simplification 98.0%

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

Alternative 14: 39.6% 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/ 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. Add Preprocessing

5. Taylor expanded in x around inf 43.3%

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

6. Final simplification 43.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.1% accurate, 0.5× 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 2024020 
(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)))