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

Percentage Accurate: 93.3% → 95.9%

Time: 14.6s

Alternatives: 11

Speedup: 1.0×

• 24.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.8e-103) (+ x (/ (* y (- t z)) a)) (- x (/ y (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.8e-103) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 1.8d-103) then
        tmp = x + ((y * (t - z)) / a)
    else
        tmp = x - (y / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.8e-103) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.8e-103:
		tmp = x + ((y * (t - z)) / a)
	else:
		tmp = x - (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.8e-103)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.8e-103)
		tmp = x + ((y * (t - z)) / a);
	else
		tmp = x - (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.8e-103], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.7999999999999999e-103

   1. Initial program 98.7%

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

   if 1.7999999999999999e-103 < y

   1. Initial program 86.2%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 2: 49.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-y}{a}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y) a))))
   (if (<= t -1.05e+117)
     (* t (/ y a))
     (if (<= t -1.9e-154)
       x
       (if (<= t -1.9e-300)
         t_1
         (if (<= t 2.8e-111)
           x
           (if (<= t 4.6e+77) t_1 (if (<= t 1.2e+96) x (/ t (/ a y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / a);
	double tmp;
	if (t <= -1.05e+117) {
		tmp = t * (y / a);
	} else if (t <= -1.9e-154) {
		tmp = x;
	} else if (t <= -1.9e-300) {
		tmp = t_1;
	} else if (t <= 2.8e-111) {
		tmp = x;
	} else if (t <= 4.6e+77) {
		tmp = t_1;
	} else if (t <= 1.2e+96) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * (-y / a)
    if (t <= (-1.05d+117)) then
        tmp = t * (y / a)
    else if (t <= (-1.9d-154)) then
        tmp = x
    else if (t <= (-1.9d-300)) then
        tmp = t_1
    else if (t <= 2.8d-111) then
        tmp = x
    else if (t <= 4.6d+77) then
        tmp = t_1
    else if (t <= 1.2d+96) 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 t_1 = z * (-y / a);
	double tmp;
	if (t <= -1.05e+117) {
		tmp = t * (y / a);
	} else if (t <= -1.9e-154) {
		tmp = x;
	} else if (t <= -1.9e-300) {
		tmp = t_1;
	} else if (t <= 2.8e-111) {
		tmp = x;
	} else if (t <= 4.6e+77) {
		tmp = t_1;
	} else if (t <= 1.2e+96) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (-y / a)
	tmp = 0
	if t <= -1.05e+117:
		tmp = t * (y / a)
	elif t <= -1.9e-154:
		tmp = x
	elif t <= -1.9e-300:
		tmp = t_1
	elif t <= 2.8e-111:
		tmp = x
	elif t <= 4.6e+77:
		tmp = t_1
	elif t <= 1.2e+96:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-y) / a))
	tmp = 0.0
	if (t <= -1.05e+117)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= -1.9e-154)
		tmp = x;
	elseif (t <= -1.9e-300)
		tmp = t_1;
	elseif (t <= 2.8e-111)
		tmp = x;
	elseif (t <= 4.6e+77)
		tmp = t_1;
	elseif (t <= 1.2e+96)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-y / a);
	tmp = 0.0;
	if (t <= -1.05e+117)
		tmp = t * (y / a);
	elseif (t <= -1.9e-154)
		tmp = x;
	elseif (t <= -1.9e-300)
		tmp = t_1;
	elseif (t <= 2.8e-111)
		tmp = x;
	elseif (t <= 4.6e+77)
		tmp = t_1;
	elseif (t <= 1.2e+96)
		tmp = x;
	else
		tmp = t / (a / y);
	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[t, -1.05e+117], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e-154], x, If[LessEqual[t, -1.9e-300], t$95$1, If[LessEqual[t, 2.8e-111], x, If[LessEqual[t, 4.6e+77], t$95$1, If[LessEqual[t, 1.2e+96], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.0500000000000001e117

   1. Initial program 91.5%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around inf 66.5%

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

      1. associate-*l/ 56.4%

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

      2. *-commutative 56.4%

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

   6. Simplified 56.4%

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

      1. clear-num 56.4%

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

      2. un-div-inv 56.3%

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

   8. Applied egg-rr 56.3%

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

      1. associate-/r/ 70.5%

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

   10. Applied egg-rr 70.5%

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

   if -1.0500000000000001e117 < t < -1.90000000000000005e-154 or -1.90000000000000006e-300 < t < 2.79999999999999995e-111 or 4.5999999999999999e77 < t < 1.19999999999999996e96

   1. Initial program 95.1%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in x around inf 55.3%

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

   if -1.90000000000000005e-154 < t < -1.90000000000000006e-300 or 2.79999999999999995e-111 < t < 4.5999999999999999e77

   1. Initial program 98.0%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. associate-*l/ 53.3%

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

      3. *-commutative 53.3%

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

   6. Simplified 53.3%

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

   if 1.19999999999999996e96 < t

   1. Initial program 88.0%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around inf 68.9%

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

      1. associate-*l/ 71.0%

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

      2. *-commutative 71.0%

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

   6. Simplified 71.0%

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

      1. clear-num 70.8%

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

      2. un-div-inv 70.8%

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

   8. Applied egg-rr 70.8%

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

      1. associate-/r/ 72.9%

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

   10. Applied egg-rr 72.9%

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

       1. clear-num 73.0%

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

       2. associate-*l/ 73.0%

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

       3. *-un-lft-identity 73.0%

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

   12. Applied egg-rr 73.0%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 3: 49.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-z}{a}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z) a))))
   (if (<= t -1.15e+117)
     (* t (/ y a))
     (if (<= t -1.25e-155)
       x
       (if (<= t 1.2e-267)
         t_1
         (if (<= t 1.9e-113)
           x
           (if (<= t 1.2e-15) t_1 (if (<= t 4.8e+17) x (/ t (/ a y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-z / a);
	double tmp;
	if (t <= -1.15e+117) {
		tmp = t * (y / a);
	} else if (t <= -1.25e-155) {
		tmp = x;
	} else if (t <= 1.2e-267) {
		tmp = t_1;
	} else if (t <= 1.9e-113) {
		tmp = x;
	} else if (t <= 1.2e-15) {
		tmp = t_1;
	} else if (t <= 4.8e+17) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (-z / a)
    if (t <= (-1.15d+117)) then
        tmp = t * (y / a)
    else if (t <= (-1.25d-155)) then
        tmp = x
    else if (t <= 1.2d-267) then
        tmp = t_1
    else if (t <= 1.9d-113) then
        tmp = x
    else if (t <= 1.2d-15) then
        tmp = t_1
    else if (t <= 4.8d+17) 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 t_1 = y * (-z / a);
	double tmp;
	if (t <= -1.15e+117) {
		tmp = t * (y / a);
	} else if (t <= -1.25e-155) {
		tmp = x;
	} else if (t <= 1.2e-267) {
		tmp = t_1;
	} else if (t <= 1.9e-113) {
		tmp = x;
	} else if (t <= 1.2e-15) {
		tmp = t_1;
	} else if (t <= 4.8e+17) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-z / a)
	tmp = 0
	if t <= -1.15e+117:
		tmp = t * (y / a)
	elif t <= -1.25e-155:
		tmp = x
	elif t <= 1.2e-267:
		tmp = t_1
	elif t <= 1.9e-113:
		tmp = x
	elif t <= 1.2e-15:
		tmp = t_1
	elif t <= 4.8e+17:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-z) / a))
	tmp = 0.0
	if (t <= -1.15e+117)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= -1.25e-155)
		tmp = x;
	elseif (t <= 1.2e-267)
		tmp = t_1;
	elseif (t <= 1.9e-113)
		tmp = x;
	elseif (t <= 1.2e-15)
		tmp = t_1;
	elseif (t <= 4.8e+17)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-z / a);
	tmp = 0.0;
	if (t <= -1.15e+117)
		tmp = t * (y / a);
	elseif (t <= -1.25e-155)
		tmp = x;
	elseif (t <= 1.2e-267)
		tmp = t_1;
	elseif (t <= 1.9e-113)
		tmp = x;
	elseif (t <= 1.2e-15)
		tmp = t_1;
	elseif (t <= 4.8e+17)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+117], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e-155], x, If[LessEqual[t, 1.2e-267], t$95$1, If[LessEqual[t, 1.9e-113], x, If[LessEqual[t, 1.2e-15], t$95$1, If[LessEqual[t, 4.8e+17], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.14999999999999994e117

   1. Initial program 91.5%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around inf 66.5%

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

      1. associate-*l/ 56.4%

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

      2. *-commutative 56.4%

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

   6. Simplified 56.4%

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

      1. clear-num 56.4%

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

      2. un-div-inv 56.3%

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

   8. Applied egg-rr 56.3%

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

      1. associate-/r/ 70.5%

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

   10. Applied egg-rr 70.5%

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

   if -1.14999999999999994e117 < t < -1.25e-155 or 1.1999999999999999e-267 < t < 1.89999999999999992e-113 or 1.19999999999999997e-15 < t < 4.8e17

   1. Initial program 94.7%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 57.6%

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

   if -1.25e-155 < t < 1.1999999999999999e-267 or 1.89999999999999992e-113 < t < 1.19999999999999997e-15

   1. Initial program 97.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 97.0%

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

   5. Applied egg-rr 97.0%

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

   6. Taylor expanded in z around inf 55.2%

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

      1. associate-*r/ 57.3%

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

      2. mul-1-neg 57.3%

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

      3. distribute-rgt-neg-in 57.3%

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

      4. distribute-neg-frac 57.3%

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

   8. Simplified 57.3%

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

   if 4.8e17 < t

   1. Initial program 90.8%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in t around inf 59.1%

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

      1. associate-*l/ 60.7%

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

      2. *-commutative 60.7%

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

   6. Simplified 60.7%

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

      1. clear-num 60.6%

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

      2. un-div-inv 60.6%

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

   8. Applied egg-rr 60.6%

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

      1. associate-/r/ 62.2%

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

   10. Applied egg-rr 62.2%

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

       1. clear-num 62.3%

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

       2. associate-*l/ 62.3%

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

       3. *-un-lft-identity 62.3%

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

   12. Applied egg-rr 62.3%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-267}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 4: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0045:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-14} \lor \neg \left(x \leq 13500\right) \land x \leq 2.6 \cdot 10^{+177}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -0.0045)
   x
   (if (or (<= x 2.9e-14) (and (not (<= x 13500.0)) (<= x 2.6e+177)))
     (* (/ y a) (- t z))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -0.0045) {
		tmp = x;
	} else if ((x <= 2.9e-14) || (!(x <= 13500.0) && (x <= 2.6e+177))) {
		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 (x <= (-0.0045d0)) then
        tmp = x
    else if ((x <= 2.9d-14) .or. (.not. (x <= 13500.0d0)) .and. (x <= 2.6d+177)) 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 (x <= -0.0045) {
		tmp = x;
	} else if ((x <= 2.9e-14) || (!(x <= 13500.0) && (x <= 2.6e+177))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -0.0045:
		tmp = x
	elif (x <= 2.9e-14) or (not (x <= 13500.0) and (x <= 2.6e+177)):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -0.0045)
		tmp = x;
	elseif ((x <= 2.9e-14) || (!(x <= 13500.0) && (x <= 2.6e+177)))
		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 (x <= -0.0045)
		tmp = x;
	elseif ((x <= 2.9e-14) || (~((x <= 13500.0)) && (x <= 2.6e+177)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -0.0045], x, If[Or[LessEqual[x, 2.9e-14], And[N[Not[LessEqual[x, 13500.0]], $MachinePrecision], LessEqual[x, 2.6e+177]]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00449999999999999966 or 2.9000000000000003e-14 < x < 13500 or 2.59999999999999979e177 < x

   1. Initial program 92.3%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 66.8%

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

   if -0.00449999999999999966 < x < 2.9000000000000003e-14 or 13500 < x < 2.59999999999999979e177

   1. Initial program 95.1%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

      1. associate-/r/ 95.4%

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

   5. Applied egg-rr 95.4%

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

   6. Taylor expanded in y around inf 71.8%

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

      1. distribute-lft-out-- 66.5%

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

      2. associate-*r/ 67.7%

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

      3. associate-*l/ 63.9%

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

      4. associate-*r/ 65.4%

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

      5. associate-*l/ 66.4%

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

      6. distribute-lft-out-- 77.0%

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

   8. Simplified 77.0%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0045:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-14} \lor \neg \left(x \leq 13500\right) \land x \leq 2.6 \cdot 10^{+177}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-44}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+17}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t z))))
   (if (<= t -1.35e+118)
     t_1
     (if (<= t -1.8e-44)
       (+ x (* y (/ t a)))
       (if (<= t 1.95e+17) (- x (* y (/ z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (t <= -1.35e+118) {
		tmp = t_1;
	} else if (t <= -1.8e-44) {
		tmp = x + (y * (t / a));
	} else if (t <= 1.95e+17) {
		tmp = x - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / a) * (t - z)
    if (t <= (-1.35d+118)) then
        tmp = t_1
    else if (t <= (-1.8d-44)) then
        tmp = x + (y * (t / a))
    else if (t <= 1.95d+17) then
        tmp = x - (y * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (t <= -1.35e+118) {
		tmp = t_1;
	} else if (t <= -1.8e-44) {
		tmp = x + (y * (t / a));
	} else if (t <= 1.95e+17) {
		tmp = x - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (t - z)
	tmp = 0
	if t <= -1.35e+118:
		tmp = t_1
	elif t <= -1.8e-44:
		tmp = x + (y * (t / a))
	elif t <= 1.95e+17:
		tmp = x - (y * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(t - z))
	tmp = 0.0
	if (t <= -1.35e+118)
		tmp = t_1;
	elseif (t <= -1.8e-44)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t <= 1.95e+17)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * (t - z);
	tmp = 0.0;
	if (t <= -1.35e+118)
		tmp = t_1;
	elseif (t <= -1.8e-44)
		tmp = x + (y * (t / a));
	elseif (t <= 1.95e+17)
		tmp = x - (y * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+118], t$95$1, If[LessEqual[t, -1.8e-44], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+17], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e118 or 1.95e17 < t

   1. Initial program 91.1%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

      1. associate-/r/ 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in y around inf 70.9%

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

      1. distribute-lft-out-- 63.6%

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

      2. associate-*r/ 64.6%

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

      3. associate-*l/ 58.2%

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

      4. associate-*r/ 59.5%

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

      5. associate-*l/ 65.9%

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

      6. distribute-lft-out-- 81.5%

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

   8. Simplified 81.5%

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

   if -1.35e118 < t < -1.7999999999999999e-44

   1. Initial program 96.6%

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

      1. sub-neg 96.6%

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

      2. +-commutative 96.6%

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

      3. associate-*l/ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. *-commutative 99.9%

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

      11. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 85.0%

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

      1. associate-*l/ 88.3%

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

      2. *-commutative 88.3%

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

   6. Simplified 88.3%

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

   if -1.7999999999999999e-44 < t < 1.95e17

   1. Initial program 95.8%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-*l/ 90.7%

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

      3. *-commutative 90.7%

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

   6. Simplified 90.7%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+118}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-44}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+17}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 6: 78.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+107} \lor \neg \left(z \leq 5.1 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.85e+107) (not (<= z 5.1e+84)))
   (* (/ y a) (- t z))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.85e+107) || !(z <= 5.1e+84)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.85d+107)) .or. (.not. (z <= 5.1d+84))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.85e+107) || !(z <= 5.1e+84)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.85e+107) or not (z <= 5.1e+84):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.85e+107) || !(z <= 5.1e+84))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.85e+107) || ~((z <= 5.1e+84)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.85e+107], N[Not[LessEqual[z, 5.1e+84]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.84999999999999986e107 or 5.1000000000000001e84 < z

   1. Initial program 91.4%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

      1. associate-/r/ 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in y around inf 68.4%

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

      1. distribute-lft-out-- 58.3%

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

      2. associate-*r/ 61.1%

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

      3. associate-*l/ 61.2%

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

      4. associate-*r/ 61.2%

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

      5. associate-*l/ 62.1%

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

      6. distribute-lft-out-- 76.8%

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

   8. Simplified 76.8%

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

   if -2.84999999999999986e107 < z < 5.1000000000000001e84

   1. Initial program 95.6%

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

      1. sub-neg 95.6%

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

      2. +-commutative 95.6%

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

      3. associate-*l/ 97.1%

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

      4. distribute-rgt-neg-in 97.1%

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

      5. sub-neg 97.1%

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

      6. distribute-neg-in 97.1%

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

      7. remove-double-neg 97.1%

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

      8. +-commutative 97.1%

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

      9. sub-neg 97.1%

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

      10. *-commutative 97.1%

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

      11. fma-def 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around 0 83.1%

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

      1. associate-*l/ 82.5%

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

      2. *-commutative 82.5%

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

   6. Simplified 82.5%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+107} \lor \neg \left(z \leq 5.1 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 7: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+117} \lor \neg \left(t \leq 1.4 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.2e+117) (not (<= t 1.4e+16))) (* y (/ t a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e+117) || !(t <= 1.4e+16)) {
		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 ((t <= (-4.2d+117)) .or. (.not. (t <= 1.4d+16))) 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 ((t <= -4.2e+117) || !(t <= 1.4e+16)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.2e+117) or not (t <= 1.4e+16):
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.2e+117) || !(t <= 1.4e+16))
		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 ((t <= -4.2e+117) || ~((t <= 1.4e+16)))
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.2e+117], N[Not[LessEqual[t, 1.4e+16]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -4.2000000000000002e117 or 1.4e16 < t

   1. Initial program 91.1%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in t around inf 61.7%

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

      1. associate-*l/ 59.2%

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

      2. *-commutative 59.2%

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

   6. Simplified 59.2%

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

   if -4.2000000000000002e117 < t < 1.4e16

   1. Initial program 96.0%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 48.9%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+117} \lor \neg \left(t \leq 1.4 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 51.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+117} \lor \neg \left(t \leq 4.8 \cdot 10^{+17}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+117) (not (<= t 4.8e+17))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+117) || !(t <= 4.8e+17)) {
		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 <= (-2.4d+117)) .or. (.not. (t <= 4.8d+17))) 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 <= -2.4e+117) || !(t <= 4.8e+17)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+117) or not (t <= 4.8e+17):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+117) || !(t <= 4.8e+17))
		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 <= -2.4e+117) || ~((t <= 4.8e+17)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+117], N[Not[LessEqual[t, 4.8e+17]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.3999999999999999e117 or 4.8e17 < t

   1. Initial program 91.1%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in t around inf 61.7%

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

      1. associate-*l/ 59.2%

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

      2. *-commutative 59.2%

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

   6. Simplified 59.2%

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

      1. clear-num 59.1%

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

      2. un-div-inv 59.1%

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

   8. Applied egg-rr 59.1%

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

      1. associate-/r/ 65.1%

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

   10. Applied egg-rr 65.1%

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

   if -2.3999999999999999e117 < t < 4.8e17

   1. Initial program 96.0%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 48.9%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+117} \lor \neg \left(t \leq 4.8 \cdot 10^{+17}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 51.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.12e+117) (* t (/ y a)) (if (<= t 1.6e+17) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.12e+117) {
		tmp = t * (y / a);
	} else if (t <= 1.6e+17) {
		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 <= (-1.12d+117)) then
        tmp = t * (y / a)
    else if (t <= 1.6d+17) 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 <= -1.12e+117) {
		tmp = t * (y / a);
	} else if (t <= 1.6e+17) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.12e+117:
		tmp = t * (y / a)
	elif t <= 1.6e+17:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.12e+117)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 1.6e+17)
		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 <= -1.12e+117)
		tmp = t * (y / a);
	elseif (t <= 1.6e+17)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.12e+117], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+17], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.12000000000000002e117

   1. Initial program 91.5%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around inf 66.5%

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

      1. associate-*l/ 56.4%

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

      2. *-commutative 56.4%

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

   6. Simplified 56.4%

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

      1. clear-num 56.4%

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

      2. un-div-inv 56.3%

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

   8. Applied egg-rr 56.3%

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

      1. associate-/r/ 70.5%

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

   10. Applied egg-rr 70.5%

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

   if -1.12000000000000002e117 < t < 1.6e17

   1. Initial program 96.0%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 48.9%

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

   if 1.6e17 < t

   1. Initial program 90.8%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in t around inf 59.1%

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

      1. associate-*l/ 60.7%

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

      2. *-commutative 60.7%

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

   6. Simplified 60.7%

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

      1. clear-num 60.6%

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

      2. un-div-inv 60.6%

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

   8. Applied egg-rr 60.6%

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

      1. associate-/r/ 62.2%

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

   10. Applied egg-rr 62.2%

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

       1. clear-num 62.3%

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

       2. associate-*l/ 62.3%

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

       3. *-un-lft-identity 62.3%

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

   12. Applied egg-rr 62.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 97.1% 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 94.1%

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

   1. associate-/l* 93.1%

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

3. Simplified 93.1%

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

   1. associate-/r/ 96.5%

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

5. Applied egg-rr 96.5%

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

6. Final simplification 96.5%

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

Alternative 11: 40.7% 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 94.1%

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

   1. associate-/l* 93.1%

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

3. Simplified 93.1%

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

4. Taylor expanded in x around inf 36.4%

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

5. Final simplification 36.4%

   \[\leadsto x \]

Developer target: 99.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023301 
(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)))