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

Percentage Accurate: 93.1% → 97.2%

Time: 13.2s

Alternatives: 13

Speedup: 1.0×

• 25.1% 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

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

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 92.2%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

   1. *-commutative 97.3%

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

   2. clear-num 97.0%

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

   3. un-div-inv 97.5%

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

5. Applied egg-rr 97.5%

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

6. Final simplification 97.5%

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

Alternative 2: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-y}{a}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y) a))))
   (if (<= z -4e+133)
     t_1
     (if (<= z -7.5e-202)
       x
       (if (<= z 1.85e-273) (* y (/ t a)) (if (<= z 6e+69) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / a);
	double tmp;
	if (z <= -4e+133) {
		tmp = t_1;
	} else if (z <= -7.5e-202) {
		tmp = x;
	} else if (z <= 1.85e-273) {
		tmp = y * (t / a);
	} else if (z <= 6e+69) {
		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 = z * (-y / a)
    if (z <= (-4d+133)) then
        tmp = t_1
    else if (z <= (-7.5d-202)) then
        tmp = x
    else if (z <= 1.85d-273) then
        tmp = y * (t / a)
    else if (z <= 6d+69) 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 = z * (-y / a);
	double tmp;
	if (z <= -4e+133) {
		tmp = t_1;
	} else if (z <= -7.5e-202) {
		tmp = x;
	} else if (z <= 1.85e-273) {
		tmp = y * (t / a);
	} else if (z <= 6e+69) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (-y / a)
	tmp = 0
	if z <= -4e+133:
		tmp = t_1
	elif z <= -7.5e-202:
		tmp = x
	elif z <= 1.85e-273:
		tmp = y * (t / a)
	elif z <= 6e+69:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-y) / a))
	tmp = 0.0
	if (z <= -4e+133)
		tmp = t_1;
	elseif (z <= -7.5e-202)
		tmp = x;
	elseif (z <= 1.85e-273)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 6e+69)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-y / a);
	tmp = 0.0;
	if (z <= -4e+133)
		tmp = t_1;
	elseif (z <= -7.5e-202)
		tmp = x;
	elseif (z <= 1.85e-273)
		tmp = y * (t / a);
	elseif (z <= 6e+69)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+133], t$95$1, If[LessEqual[z, -7.5e-202], x, If[LessEqual[z, 1.85e-273], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+69], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000001e133 or 5.99999999999999967e69 < z

   1. Initial program 92.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. associate-*l/ 62.1%

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

      3. *-commutative 62.1%

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

   6. Simplified 62.1%

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

   if -4.0000000000000001e133 < z < -7.50000000000000005e-202 or 1.8500000000000002e-273 < z < 5.99999999999999967e69

   1. Initial program 92.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in x around inf 56.2%

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

   if -7.50000000000000005e-202 < z < 1.8500000000000002e-273

   1. Initial program 90.9%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in t around inf 57.2%

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

      1. associate-/l* 59.4%

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

      2. associate-/r/ 61.5%

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

   6. Applied egg-rr 61.5%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+133}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \end{array} \]

Alternative 3: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+135}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+135)
   (* (/ z a) (- y))
   (if (<= z -9.2e-198)
     x
     (if (<= z 1.6e-273)
       (* y (/ t a))
       (if (<= z 2.9e+67) x (* z (/ (- y) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+135) {
		tmp = (z / a) * -y;
	} else if (z <= -9.2e-198) {
		tmp = x;
	} else if (z <= 1.6e-273) {
		tmp = y * (t / a);
	} else if (z <= 2.9e+67) {
		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 (z <= (-2.8d+135)) then
        tmp = (z / a) * -y
    else if (z <= (-9.2d-198)) then
        tmp = x
    else if (z <= 1.6d-273) then
        tmp = y * (t / a)
    else if (z <= 2.9d+67) 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 (z <= -2.8e+135) {
		tmp = (z / a) * -y;
	} else if (z <= -9.2e-198) {
		tmp = x;
	} else if (z <= 1.6e-273) {
		tmp = y * (t / a);
	} else if (z <= 2.9e+67) {
		tmp = x;
	} else {
		tmp = z * (-y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+135:
		tmp = (z / a) * -y
	elif z <= -9.2e-198:
		tmp = x
	elif z <= 1.6e-273:
		tmp = y * (t / a)
	elif z <= 2.9e+67:
		tmp = x
	else:
		tmp = z * (-y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+135)
		tmp = Float64(Float64(z / a) * Float64(-y));
	elseif (z <= -9.2e-198)
		tmp = x;
	elseif (z <= 1.6e-273)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 2.9e+67)
		tmp = x;
	else
		tmp = Float64(z * Float64(Float64(-y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e+135)
		tmp = (z / a) * -y;
	elseif (z <= -9.2e-198)
		tmp = x;
	elseif (z <= 1.6e-273)
		tmp = y * (t / a);
	elseif (z <= 2.9e+67)
		tmp = x;
	else
		tmp = z * (-y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+135], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, -9.2e-198], x, If[LessEqual[z, 1.6e-273], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+67], x, N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.80000000000000002e135

   1. Initial program 94.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 56.6%

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

      1. mul-1-neg 56.6%

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

      2. *-commutative 56.6%

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

      3. associate-/l* 59.7%

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

      4. associate-/r/ 62.6%

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

   6. Simplified 62.6%

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

   if -2.80000000000000002e135 < z < -9.20000000000000053e-198 or 1.59999999999999995e-273 < z < 2.90000000000000023e67

   1. Initial program 92.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in x around inf 56.2%

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

   if -9.20000000000000053e-198 < z < 1.59999999999999995e-273

   1. Initial program 90.9%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in t around inf 57.2%

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

      1. associate-/l* 59.4%

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

      2. associate-/r/ 61.5%

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

   6. Applied egg-rr 61.5%

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

   if 2.90000000000000023e67 < z

   1. Initial program 91.4%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. associate-*l/ 62.9%

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

      3. *-commutative 62.9%

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

   6. Simplified 62.9%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+135}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \end{array} \]

Alternative 4: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -520:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+143}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+198}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+209}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -520.0)
   (* t (/ y a))
   (if (<= t 1.9e+143)
     x
     (if (<= t 7.2e+198) (/ y (/ a t)) (if (<= t 2.4e+209) x (/ t (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -520.0) {
		tmp = t * (y / a);
	} else if (t <= 1.9e+143) {
		tmp = x;
	} else if (t <= 7.2e+198) {
		tmp = y / (a / t);
	} else if (t <= 2.4e+209) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-520.0d0)) then
        tmp = t * (y / a)
    else if (t <= 1.9d+143) then
        tmp = x
    else if (t <= 7.2d+198) then
        tmp = y / (a / t)
    else if (t <= 2.4d+209) then
        tmp = x
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -520.0) {
		tmp = t * (y / a);
	} else if (t <= 1.9e+143) {
		tmp = x;
	} else if (t <= 7.2e+198) {
		tmp = y / (a / t);
	} else if (t <= 2.4e+209) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -520.0:
		tmp = t * (y / a)
	elif t <= 1.9e+143:
		tmp = x
	elif t <= 7.2e+198:
		tmp = y / (a / t)
	elif t <= 2.4e+209:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -520.0)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 1.9e+143)
		tmp = x;
	elseif (t <= 7.2e+198)
		tmp = Float64(y / Float64(a / t));
	elseif (t <= 2.4e+209)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -520.0)
		tmp = t * (y / a);
	elseif (t <= 1.9e+143)
		tmp = x;
	elseif (t <= 7.2e+198)
		tmp = y / (a / t);
	elseif (t <= 2.4e+209)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -520.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+143], x, If[LessEqual[t, 7.2e+198], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+209], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -520

   1. Initial program 91.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around inf 55.3%

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

      1. associate-*r/ 59.8%

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

   6. Simplified 59.8%

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

   if -520 < t < 1.9e143 or 7.2000000000000004e198 < t < 2.39999999999999996e209

   1. Initial program 95.3%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around inf 54.8%

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

   if 1.9e143 < t < 7.2000000000000004e198

   1. Initial program 87.1%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in t around inf 47.8%

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

      1. associate-*r/ 54.0%

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

   6. Simplified 54.0%

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

      1. associate-*r/ 47.8%

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

      2. *-commutative 47.8%

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

      3. associate-/l* 59.5%

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

   8. Applied egg-rr 59.5%

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

   if 2.39999999999999996e209 < t

   1. Initial program 75.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 69.8%

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

      1. associate-/l* 76.2%

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

   6. Simplified 76.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -520:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+143}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+198}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+209}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 68.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-22} \lor \neg \left(y \leq 3.2 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.9e-22) (not (<= y 3.2e-77))) (* (/ y a) (- t z)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e-22) || !(y <= 3.2e-77)) {
		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 ((y <= (-2.9d-22)) .or. (.not. (y <= 3.2d-77))) 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 ((y <= -2.9e-22) || !(y <= 3.2e-77)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.9e-22) or not (y <= 3.2e-77):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.9e-22) || !(y <= 3.2e-77))
		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 ((y <= -2.9e-22) || ~((y <= 3.2e-77)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.9e-22], N[Not[LessEqual[y, 3.2e-77]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000002e-22 or 3.2e-77 < y

   1. Initial program 86.8%

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

      1. *-commutative 97.2%

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

      2. clear-num 97.1%

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

      3. un-div-inv 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in x around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-*l/ 74.9%

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

      3. distribute-rgt-out-- 63.1%

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

      4. sub-neg 63.1%

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

      5. +-commutative 63.1%

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

      6. distribute-neg-in 63.1%

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

      7. remove-double-neg 63.1%

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

      8. sub-neg 63.1%

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

      9. distribute-rgt-out-- 74.9%

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

   8. Simplified 74.9%

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

   if -2.9000000000000002e-22 < y < 3.2e-77

   1. Initial program 98.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 67.2%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-22} \lor \neg \left(y \leq 3.2 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+134} \lor \neg \left(z \leq 8.2 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.6e+134) (not (<= z 8.2e+68)))
   (* (/ y a) (- t z))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e+134) || !(z <= 8.2e+68)) {
		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 ((z <= (-6.6d+134)) .or. (.not. (z <= 8.2d+68))) 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 ((z <= -6.6e+134) || !(z <= 8.2e+68)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.6e+134) or not (z <= 8.2e+68):
		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 ((z <= -6.6e+134) || !(z <= 8.2e+68))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	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 <= -6.6e+134) || ~((z <= 8.2e+68)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.6e+134], N[Not[LessEqual[z, 8.2e+68]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e134 or 8.1999999999999998e68 < z

   1. Initial program 92.5%

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

      1. *-commutative 97.2%

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

      2. clear-num 96.5%

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

      3. un-div-inv 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in x around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-*l/ 74.5%

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

      3. distribute-rgt-out-- 61.4%

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

      4. sub-neg 61.4%

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

      5. +-commutative 61.4%

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

      6. distribute-neg-in 61.4%

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

      7. remove-double-neg 61.4%

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

      8. sub-neg 61.4%

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

      9. distribute-rgt-out-- 74.5%

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

   8. Simplified 74.5%

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

   if -6.6e134 < z < 8.1999999999999998e68

   1. Initial program 92.1%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 83.6%

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

      1. cancel-sign-sub-inv 83.6%

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

      2. metadata-eval 83.6%

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

      3. *-lft-identity 83.6%

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

      4. +-commutative 83.6%

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

      5. associate-*r/ 87.9%

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

   6. Simplified 87.9%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+134} \lor \neg \left(z \leq 8.2 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+134} \lor \neg \left(z \leq 3.8 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e+134) (not (<= z 3.8e+71)))
   (* (/ y a) (- t z))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+134) || !(z <= 3.8e+71)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.1d+134)) .or. (.not. (z <= 3.8d+71))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+134) || !(z <= 3.8e+71)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e+134) or not (z <= 3.8e+71):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e+134) || !(z <= 3.8e+71))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e+134) || ~((z <= 3.8e+71)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e+134], N[Not[LessEqual[z, 3.8e+71]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1000000000000001e134 or 3.8000000000000001e71 < z

   1. Initial program 92.5%

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

      1. *-commutative 97.2%

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

      2. clear-num 96.5%

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

      3. un-div-inv 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in x around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-*l/ 74.5%

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

      3. distribute-rgt-out-- 61.4%

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

      4. sub-neg 61.4%

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

      5. +-commutative 61.4%

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

      6. distribute-neg-in 61.4%

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

      7. remove-double-neg 61.4%

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

      8. sub-neg 61.4%

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

      9. distribute-rgt-out-- 74.5%

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

   8. Simplified 74.5%

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

   if -2.1000000000000001e134 < z < 3.8000000000000001e71

   1. Initial program 92.1%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 83.6%

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

      1. cancel-sign-sub-inv 83.6%

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

      2. metadata-eval 83.6%

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

      3. *-lft-identity 83.6%

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

      4. +-commutative 83.6%

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

      5. associate-*r/ 87.9%

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

   6. Simplified 87.9%

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

      1. associate-*r/ 83.6%

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

      2. associate-/l* 88.5%

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

   8. Applied egg-rr 88.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+134} \lor \neg \left(z \leq 3.8 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-16} \lor \neg \left(t \leq 6.1 \cdot 10^{+72}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e-16) (not (<= t 6.1e+72)))
   (+ x (/ t (/ a y)))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e-16) || !(t <= 6.1e+72)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4d-16)) .or. (.not. (t <= 6.1d+72))) then
        tmp = x + (t / (a / y))
    else
        tmp = x - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e-16) || !(t <= 6.1e+72)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e-16) or not (t <= 6.1e+72):
		tmp = x + (t / (a / y))
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e-16) || !(t <= 6.1e+72))
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4e-16) || ~((t <= 6.1e+72)))
		tmp = x + (t / (a / y));
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e-16], N[Not[LessEqual[t, 6.1e+72]], $MachinePrecision]], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9999999999999999e-16 or 6.09999999999999991e72 < t

   1. Initial program 87.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in z around 0 78.2%

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

      1. cancel-sign-sub-inv 78.2%

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

      2. metadata-eval 78.2%

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

      3. *-lft-identity 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-*r/ 88.1%

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

   6. Simplified 88.1%

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

      1. associate-*r/ 78.2%

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

      2. associate-/l* 88.1%

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

   8. Applied egg-rr 88.1%

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

   if -3.9999999999999999e-16 < t < 6.09999999999999991e72

   1. Initial program 96.1%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around inf 84.1%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-16} \lor \neg \left(t \leq 6.1 \cdot 10^{+72}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+133} \lor \neg \left(z \leq 4.6 \cdot 10^{+22}\right):\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.6e+133) (not (<= z 4.6e+22)))
   (- x (/ (* z y) a))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e+133) || !(z <= 4.6e+22)) {
		tmp = x - ((z * y) / a);
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.6d+133)) .or. (.not. (z <= 4.6d+22))) then
        tmp = x - ((z * y) / a)
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e+133) || !(z <= 4.6e+22)) {
		tmp = x - ((z * y) / a);
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.6e+133) or not (z <= 4.6e+22):
		tmp = x - ((z * y) / a)
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.6e+133) || !(z <= 4.6e+22))
		tmp = Float64(x - Float64(Float64(z * y) / a));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.6e+133) || ~((z <= 4.6e+22)))
		tmp = x - ((z * y) / a);
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.6e+133], N[Not[LessEqual[z, 4.6e+22]], $MachinePrecision]], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.59999999999999989e133 or 4.6000000000000004e22 < z

   1. Initial program 93.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 82.7%

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

   if -8.59999999999999989e133 < z < 4.6000000000000004e22

   1. Initial program 91.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around 0 83.9%

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

      1. cancel-sign-sub-inv 83.9%

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

      2. metadata-eval 83.9%

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

      3. *-lft-identity 83.9%

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

      4. +-commutative 83.9%

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

      5. associate-*r/ 88.4%

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

   6. Simplified 88.4%

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

      1. associate-*r/ 83.9%

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

      2. associate-/l* 89.0%

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

   8. Applied egg-rr 89.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+133} \lor \neg \left(z \leq 4.6 \cdot 10^{+22}\right):\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -170 \lor \neg \left(t \leq 2.4 \cdot 10^{+141}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -170.0) (not (<= t 2.4e+141))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -170.0) || !(t <= 2.4e+141)) {
		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 ((t <= (-170.0d0)) .or. (.not. (t <= 2.4d+141))) 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 ((t <= -170.0) || !(t <= 2.4e+141)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -170.0) or not (t <= 2.4e+141):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -170.0) || !(t <= 2.4e+141))
		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 ((t <= -170.0) || ~((t <= 2.4e+141)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -170.0], N[Not[LessEqual[t, 2.4e+141]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -170 or 2.39999999999999997e141 < t

   1. Initial program 86.9%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in t around inf 54.8%

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

      1. associate-*r/ 59.8%

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

   6. Simplified 59.8%

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

   if -170 < t < 2.39999999999999997e141

   1. Initial program 95.8%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 53.6%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -170 \lor \neg \left(t \leq 2.4 \cdot 10^{+141}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1950:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1950.0) (* t (/ y a)) (if (<= t 1.1e+146) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1950.0) {
		tmp = t * (y / a);
	} else if (t <= 1.1e+146) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1950.0d0)) then
        tmp = t * (y / a)
    else if (t <= 1.1d+146) then
        tmp = x
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1950.0) {
		tmp = t * (y / a);
	} else if (t <= 1.1e+146) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1950.0:
		tmp = t * (y / a)
	elif t <= 1.1e+146:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1950.0)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 1.1e+146)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1950.0)
		tmp = t * (y / a);
	elseif (t <= 1.1e+146)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1950.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+146], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1950

   1. Initial program 91.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around inf 55.3%

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

      1. associate-*r/ 59.8%

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

   6. Simplified 59.8%

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

   if -1950 < t < 1.0999999999999999e146

   1. Initial program 95.8%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 53.6%

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

   if 1.0999999999999999e146 < t

   1. Initial program 79.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around inf 54.1%

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

      1. associate-/l* 59.7%

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

   6. Simplified 59.7%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1950:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 12: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 13: 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 92.2%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in x around inf 44.1%

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

5. Final simplification 44.1%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(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)))