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

Percentage Accurate: 93.3% → 95.4%

Time: 7.9s

Alternatives: 11

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+143}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -5e+143) (+ x (* (/ y a) (- t z))) (+ x (/ (* y (- t z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+143) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z - t) <= (-5d+143)) then
        tmp = x + ((y / a) * (t - z))
    else
        tmp = x + ((y * (t - z)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+143) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -5e+143:
		tmp = x + ((y / a) * (t - z))
	else:
		tmp = x + ((y * (t - z)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -5e+143)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -5e+143)
		tmp = x + ((y / a) * (t - z));
	else
		tmp = x + ((y * (t - z)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -5e+143], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -5.00000000000000012e143

   1. Initial program 83.7%

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

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

   if -5.00000000000000012e143 < (-.f64 z t)

   1. Initial program 99.2%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+143}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]

Alternative 2: 48.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -92 \lor \neg \left(x \leq -2.4 \cdot 10^{-29}\right) \land x \leq 2.1 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.05e+43)
   x
   (if (or (<= x -92.0) (and (not (<= x -2.4e-29)) (<= x 2.1e-99)))
     (* y (/ t a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.05e+43) {
		tmp = x;
	} else if ((x <= -92.0) || (!(x <= -2.4e-29) && (x <= 2.1e-99))) {
		tmp = y * (t / 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 (x <= (-2.05d+43)) then
        tmp = x
    else if ((x <= (-92.0d0)) .or. (.not. (x <= (-2.4d-29))) .and. (x <= 2.1d-99)) then
        tmp = y * (t / 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 (x <= -2.05e+43) {
		tmp = x;
	} else if ((x <= -92.0) || (!(x <= -2.4e-29) && (x <= 2.1e-99))) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.05e+43:
		tmp = x
	elif (x <= -92.0) or (not (x <= -2.4e-29) and (x <= 2.1e-99)):
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.05e+43)
		tmp = x;
	elseif ((x <= -92.0) || (!(x <= -2.4e-29) && (x <= 2.1e-99)))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.05e+43)
		tmp = x;
	elseif ((x <= -92.0) || (~((x <= -2.4e-29)) && (x <= 2.1e-99)))
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.05e+43], x, If[Or[LessEqual[x, -92.0], And[N[Not[LessEqual[x, -2.4e-29]], $MachinePrecision], LessEqual[x, 2.1e-99]]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.05e43 or -92 < x < -2.39999999999999992e-29 or 2.09999999999999984e-99 < x

   1. Initial program 97.4%

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

      1. associate-*r/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 73.8%

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

      1. neg-mul-1 73.8%

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

      2. distribute-neg-frac 73.8%

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

   6. Simplified 73.8%

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

   7. Taylor expanded in x around inf 59.8%

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

   if -2.05e43 < x < -92 or -2.39999999999999992e-29 < x < 2.09999999999999984e-99

   1. Initial program 93.1%

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

      1. associate-*r/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in z around 0 66.3%

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

      1. neg-mul-1 66.3%

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

      2. distribute-neg-frac 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in x around 0 54.6%

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

      1. *-commutative 54.6%

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

      2. associate-*l/ 54.8%

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

      3. *-commutative 54.8%

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

   9. Simplified 54.8%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -92 \lor \neg \left(x \leq -2.4 \cdot 10^{-29}\right) \land x \leq 2.1 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 49.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -260 \lor \neg \left(x \leq -2.1 \cdot 10^{-29}\right) \land x \leq 3.4 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.1e+54)
   x
   (if (or (<= x -260.0) (and (not (<= x -2.1e-29)) (<= x 3.4e-30)))
     (* t (/ y a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.1e+54) {
		tmp = x;
	} else if ((x <= -260.0) || (!(x <= -2.1e-29) && (x <= 3.4e-30))) {
		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 (x <= (-2.1d+54)) then
        tmp = x
    else if ((x <= (-260.0d0)) .or. (.not. (x <= (-2.1d-29))) .and. (x <= 3.4d-30)) 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 (x <= -2.1e+54) {
		tmp = x;
	} else if ((x <= -260.0) || (!(x <= -2.1e-29) && (x <= 3.4e-30))) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.1e+54:
		tmp = x
	elif (x <= -260.0) or (not (x <= -2.1e-29) and (x <= 3.4e-30)):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.1e+54)
		tmp = x;
	elseif ((x <= -260.0) || (!(x <= -2.1e-29) && (x <= 3.4e-30)))
		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 (x <= -2.1e+54)
		tmp = x;
	elseif ((x <= -260.0) || (~((x <= -2.1e-29)) && (x <= 3.4e-30)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.1e+54], x, If[Or[LessEqual[x, -260.0], And[N[Not[LessEqual[x, -2.1e-29]], $MachinePrecision], LessEqual[x, 3.4e-30]]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999986e54 or -260 < x < -2.09999999999999989e-29 or 3.4000000000000003e-30 < x

   1. Initial program 96.9%

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

      1. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around 0 77.8%

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

      1. neg-mul-1 77.8%

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

      2. distribute-neg-frac 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in x around inf 65.6%

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

   if -2.09999999999999986e54 < x < -260 or -2.09999999999999989e-29 < x < 3.4000000000000003e-30

   1. Initial program 94.4%

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

      1. associate-*r/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around 0 63.8%

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

      1. neg-mul-1 63.8%

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

      2. distribute-neg-frac 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in x around 0 50.7%

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

      1. associate-*l/ 51.9%

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

   9. Applied egg-rr 51.9%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -260 \lor \neg \left(x \leq -2.1 \cdot 10^{-29}\right) \land x \leq 3.4 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 49.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -0.25:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.1e+52)
   x
   (if (<= x -0.25)
     (/ (* t y) a)
     (if (<= x -2.25e-29) x (if (<= x 1.35e-33) (* t (/ y a)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.1e+52) {
		tmp = x;
	} else if (x <= -0.25) {
		tmp = (t * y) / a;
	} else if (x <= -2.25e-29) {
		tmp = x;
	} else if (x <= 1.35e-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 (x <= (-6.1d+52)) then
        tmp = x
    else if (x <= (-0.25d0)) then
        tmp = (t * y) / a
    else if (x <= (-2.25d-29)) then
        tmp = x
    else if (x <= 1.35d-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 (x <= -6.1e+52) {
		tmp = x;
	} else if (x <= -0.25) {
		tmp = (t * y) / a;
	} else if (x <= -2.25e-29) {
		tmp = x;
	} else if (x <= 1.35e-33) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.1e+52:
		tmp = x
	elif x <= -0.25:
		tmp = (t * y) / a
	elif x <= -2.25e-29:
		tmp = x
	elif x <= 1.35e-33:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.1e+52)
		tmp = x;
	elseif (x <= -0.25)
		tmp = Float64(Float64(t * y) / a);
	elseif (x <= -2.25e-29)
		tmp = x;
	elseif (x <= 1.35e-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 (x <= -6.1e+52)
		tmp = x;
	elseif (x <= -0.25)
		tmp = (t * y) / a;
	elseif (x <= -2.25e-29)
		tmp = x;
	elseif (x <= 1.35e-33)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.1e+52], x, If[LessEqual[x, -0.25], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[x, -2.25e-29], x, If[LessEqual[x, 1.35e-33], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.09999999999999996e52 or -0.25 < x < -2.2499999999999999e-29 or 1.35e-33 < x

   1. Initial program 96.9%

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

      1. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around 0 77.8%

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

      1. neg-mul-1 77.8%

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

      2. distribute-neg-frac 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in x around inf 65.6%

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

   if -6.09999999999999996e52 < x < -0.25

   1. Initial program 100.0%

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

      1. associate-*r/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in z around 0 73.0%

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

      1. neg-mul-1 73.0%

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

      2. distribute-neg-frac 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in x around 0 57.9%

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

   if -2.2499999999999999e-29 < x < 1.35e-33

   1. Initial program 93.5%

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

      1. associate-*r/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around 0 62.3%

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

      1. neg-mul-1 62.3%

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

      2. distribute-neg-frac 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in x around 0 49.5%

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

      1. associate-*l/ 51.8%

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

   9. Applied egg-rr 51.8%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -0.25:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+24} \lor \neg \left(z \leq 5.9 \cdot 10^{+69}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.05e+24) (not (<= z 5.9e+69)))
   (- x (* y (/ z a)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e+24) || !(z <= 5.9e+69)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.05d+24)) .or. (.not. (z <= 5.9d+69))) then
        tmp = x - (y * (z / a))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e+24) || !(z <= 5.9e+69)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.05e+24) or not (z <= 5.9e+69):
		tmp = x - (y * (z / a))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.05e+24) || !(z <= 5.9e+69))
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.05e+24) || ~((z <= 5.9e+69)))
		tmp = x - (y * (z / a));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.05e+24], N[Not[LessEqual[z, 5.9e+69]], $MachinePrecision]], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e24 or 5.90000000000000004e69 < z

   1. Initial program 94.3%

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

      1. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in z around inf 84.5%

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

   if -1.0500000000000001e24 < z < 5.90000000000000004e69

   1. Initial program 96.6%

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

      1. associate-*r/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 86.9%

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

      1. neg-mul-1 86.9%

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

      2. distribute-neg-frac 86.9%

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

   6. Simplified 86.9%

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

      1. sub-neg 86.9%

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

      2. +-commutative 86.9%

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

      3. distribute-lft-neg-in 86.9%

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

      4. *-commutative 86.9%

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

      5. frac-2neg 86.9%

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

      6. remove-double-neg 86.9%

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

      7. associate-/r/ 89.4%

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

      8. frac-2neg 89.4%

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

      9. div-inv 90.0%

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

      10. clear-num 90.0%

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

   8. Applied egg-rr 90.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+24} \lor \neg \left(z \leq 5.9 \cdot 10^{+69}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+25} \lor \neg \left(z \leq 3.35 \cdot 10^{+68}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+25) (not (<= z 3.35e+68)))
   (- x (* z (/ y a)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+25) || !(z <= 3.35e+68)) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9d+25)) .or. (.not. (z <= 3.35d+68))) then
        tmp = x - (z * (y / a))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+25) || !(z <= 3.35e+68)) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+25) or not (z <= 3.35e+68):
		tmp = x - (z * (y / a))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+25) || !(z <= 3.35e+68))
		tmp = Float64(x - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e+25) || ~((z <= 3.35e+68)))
		tmp = x - (z * (y / a));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e+25], N[Not[LessEqual[z, 3.35e+68]], $MachinePrecision]], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000006e25 or 3.3499999999999999e68 < z

   1. Initial program 94.3%

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

      1. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in z around inf 86.2%

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

      1. associate-*l/ 90.9%

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

      2. *-commutative 90.9%

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

   6. Simplified 90.9%

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

   if -9.0000000000000006e25 < z < 3.3499999999999999e68

   1. Initial program 96.6%

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

      1. associate-*r/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 86.9%

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

      1. neg-mul-1 86.9%

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

      2. distribute-neg-frac 86.9%

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

   6. Simplified 86.9%

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

      1. sub-neg 86.9%

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

      2. +-commutative 86.9%

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

      3. distribute-lft-neg-in 86.9%

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

      4. *-commutative 86.9%

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

      5. frac-2neg 86.9%

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

      6. remove-double-neg 86.9%

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

      7. associate-/r/ 89.4%

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

      8. frac-2neg 89.4%

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

      9. div-inv 90.0%

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

      10. clear-num 90.0%

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

   8. Applied egg-rr 90.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+25} \lor \neg \left(z \leq 3.35 \cdot 10^{+68}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+68}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+23)
   (- x (* z (/ y a)))
   (if (<= z 7.4e+68) (+ x (* t (/ y a))) (- x (/ z (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+23) {
		tmp = x - (z * (y / a));
	} else if (z <= 7.4e+68) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d+23)) then
        tmp = x - (z * (y / a))
    else if (z <= 7.4d+68) then
        tmp = x + (t * (y / a))
    else
        tmp = x - (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+23) {
		tmp = x - (z * (y / a));
	} else if (z <= 7.4e+68) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+23:
		tmp = x - (z * (y / a))
	elif z <= 7.4e+68:
		tmp = x + (t * (y / a))
	else:
		tmp = x - (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+23)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	elseif (z <= 7.4e+68)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+23)
		tmp = x - (z * (y / a));
	elseif (z <= 7.4e+68)
		tmp = x + (t * (y / a));
	else
		tmp = x - (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+23], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+68], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e23

   1. Initial program 93.2%

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

      1. associate-*r/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around inf 84.5%

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

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

   6. Simplified 91.2%

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

   if -4.8e23 < z < 7.39999999999999996e68

   1. Initial program 96.6%

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

      1. associate-*r/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 86.9%

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

      1. neg-mul-1 86.9%

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

      2. distribute-neg-frac 86.9%

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

   6. Simplified 86.9%

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

      1. sub-neg 86.9%

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

      2. +-commutative 86.9%

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

      3. distribute-lft-neg-in 86.9%

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

      4. *-commutative 86.9%

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

      5. frac-2neg 86.9%

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

      6. remove-double-neg 86.9%

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

      7. associate-/r/ 89.4%

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

      8. frac-2neg 89.4%

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

      9. div-inv 90.0%

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

      10. clear-num 90.0%

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

   8. Applied egg-rr 90.0%

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

   if 7.39999999999999996e68 < z

   1. Initial program 95.6%

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

      1. associate-*r/ 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in z around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-/r/ 90.5%

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

   6. Applied egg-rr 90.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+68}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 93.3% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.6%

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

   1. associate-*r/ 93.2%

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

3. Simplified 93.2%

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

4. Final simplification 93.2%

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

Alternative 9: 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 95.6%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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 10: 72.4% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

   1. associate-*r/ 93.2%

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

3. Simplified 93.2%

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

4. Taylor expanded in z around 0 70.7%

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

   1. neg-mul-1 70.7%

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

   2. distribute-neg-frac 70.7%

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

6. Simplified 70.7%

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

   1. sub-neg 70.7%

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

   2. +-commutative 70.7%

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

   3. distribute-lft-neg-in 70.7%

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

   4. *-commutative 70.7%

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

   5. frac-2neg 70.7%

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

   6. remove-double-neg 70.7%

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

   7. associate-/r/ 73.4%

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

   8. frac-2neg 73.4%

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

   9. div-inv 73.7%

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

   10. clear-num 73.8%

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

8. Applied egg-rr 73.8%

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

9. Final simplification 73.8%

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

Alternative 11: 40.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

   1. associate-*r/ 93.2%

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

3. Simplified 93.2%

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

4. Taylor expanded in z around 0 70.7%

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

   1. neg-mul-1 70.7%

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

   2. distribute-neg-frac 70.7%

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

6. Simplified 70.7%

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

7. Taylor expanded in x around inf 41.1%

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

8. Final simplification 41.1%

   \[\leadsto x \]

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 2023224 
(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)))