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

Percentage Accurate: 93.2% → 99.5%

Time: 10.8s

Alternatives: 11

Speedup: 1.0×

• 25.9% 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: 93.2% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+258} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+164}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (or (<= t_1 -5e+258) (not (<= t_1 2e+164)))
     (+ x (* y (/ (- z t) a)))
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -5e+258) || !(t_1 <= 2e+164)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * y
    if ((t_1 <= (-5d+258)) .or. (.not. (t_1 <= 2d+164))) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = x + (t_1 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -5e+258) || !(t_1 <= 2e+164)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	tmp = 0
	if (t_1 <= -5e+258) or not (t_1 <= 2e+164):
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * y)
	tmp = 0.0
	if ((t_1 <= -5e+258) || !(t_1 <= 2e+164))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * y;
	tmp = 0.0;
	if ((t_1 <= -5e+258) || ~((t_1 <= 2e+164)))
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+258], N[Not[LessEqual[t$95$1, 2e+164]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -5e258 or 2e164 < (*.f64 y (-.f64 z t))

   1. Initial program 79.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -5e258 < (*.f64 y (-.f64 z t)) < 2e164

   1. Initial program 99.4%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -5 \cdot 10^{+258} \lor \neg \left(\left(z - t\right) \cdot y \leq 2 \cdot 10^{+164}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+25} \lor \neg \left(z \leq 8.5 \cdot 10^{-11}\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+25) (not (<= z 8.5e-11)))
   (+ x (/ z (/ a y)))
   (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+25) || !(z <= 8.5e-11)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2d+25)) .or. (.not. (z <= 8.5d-11))) then
        tmp = x + (z / (a / y))
    else
        tmp = x - (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+25) || !(z <= 8.5e-11)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+25) or not (z <= 8.5e-11):
		tmp = x + (z / (a / y))
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+25) || !(z <= 8.5e-11))
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e+25) || ~((z <= 8.5e-11)))
		tmp = x + (z / (a / y));
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e+25], N[Not[LessEqual[z, 8.5e-11]], $MachinePrecision]], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000018e25 or 8.50000000000000037e-11 < z

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. associate-/l* 90.9%

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

      3. fma-define 90.9%

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

   3. Simplified 90.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 90.9%

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

      2. associate-*r/ 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-/l* 98.8%

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

   6. Applied egg-rr 98.8%

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

      1. clear-num 98.7%

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

      2. un-div-inv 98.9%

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

      3. sub-neg 98.9%

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

      4. add-sqr-sqrt 47.6%

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

      5. sqrt-unprod 79.2%

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

      6. sqr-neg 79.2%

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

      7. sqrt-unprod 41.9%

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

      8. add-sqr-sqrt 84.2%

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

   8. Applied egg-rr 84.2%

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

   9. Taylor expanded in z around inf 86.2%

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

   if -2.00000000000000018e25 < z < 8.50000000000000037e-11

   1. Initial program 94.7%

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

      1. +-commutative 94.7%

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

      2. associate-/l* 95.2%

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

      3. fma-define 95.2%

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

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 95.2%

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

      2. associate-*r/ 94.7%

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

      3. *-commutative 94.7%

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

      4. associate-/l* 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in z around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. associate-*r/ 90.8%

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

      3. distribute-lft-neg-in 90.8%

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

      4. cancel-sign-sub-inv 90.8%

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

   9. Simplified 90.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+25} \lor \neg \left(z \leq 8.5 \cdot 10^{-11}\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+120}:\\ \;\;\;\;\frac{t \cdot y}{-a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+181}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e+120)
   (/ (* t y) (- a))
   (if (<= t 6.2e+181) (+ x (/ z (/ a y))) (* (/ t a) (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+120) {
		tmp = (t * y) / -a;
	} else if (t <= 6.2e+181) {
		tmp = x + (z / (a / y));
	} 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 <= (-4.4d+120)) then
        tmp = (t * y) / -a
    else if (t <= 6.2d+181) then
        tmp = x + (z / (a / y))
    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 <= -4.4e+120) {
		tmp = (t * y) / -a;
	} else if (t <= 6.2e+181) {
		tmp = x + (z / (a / y));
	} else {
		tmp = (t / a) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e+120:
		tmp = (t * y) / -a
	elif t <= 6.2e+181:
		tmp = x + (z / (a / y))
	else:
		tmp = (t / a) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e+120)
		tmp = Float64(Float64(t * y) / Float64(-a));
	elseif (t <= 6.2e+181)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(Float64(t / a) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.4e+120)
		tmp = (t * y) / -a;
	elseif (t <= 6.2e+181)
		tmp = x + (z / (a / y));
	else
		tmp = (t / a) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e+120], N[(N[(t * y), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[t, 6.2e+181], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4000000000000003e120

   1. Initial program 91.7%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

      3. *-commutative 85.2%

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

      4. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in x around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-/l* 56.0%

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

      3. associate-*r* 56.0%

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

      4. neg-mul-1 56.0%

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

      5. *-commutative 56.0%

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

   10. Simplified 56.0%

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

       1. associate-*l/ 64.1%

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

       2. distribute-rgt-neg-out 64.1%

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

       3. distribute-neg-frac 64.1%

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

       4. distribute-neg-frac2 64.1%

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

       5. *-commutative 64.1%

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

   12. Applied egg-rr 64.1%

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

   if -4.4000000000000003e120 < t < 6.19999999999999978e181

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-/l* 94.9%

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

      3. fma-define 94.9%

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

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 94.9%

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

      2. associate-*r/ 92.6%

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

      3. *-commutative 92.6%

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

      4. associate-/l* 97.3%

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

   6. Applied egg-rr 97.3%

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

      1. clear-num 97.2%

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

      2. un-div-inv 97.3%

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

      3. sub-neg 97.3%

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

      4. add-sqr-sqrt 43.8%

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

      5. sqrt-unprod 84.1%

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

      6. sqr-neg 84.1%

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

      7. sqrt-unprod 41.5%

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

      8. add-sqr-sqrt 79.0%

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

   8. Applied egg-rr 79.0%

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

   9. Taylor expanded in z around inf 82.7%

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

   if 6.19999999999999978e181 < t

   1. Initial program 81.9%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. unsub-neg 81.9%

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

      3. *-commutative 81.9%

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

      4. associate-/l* 91.0%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in x around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 82.1%

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

      3. associate-*r* 82.1%

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

      4. neg-mul-1 82.1%

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

      5. *-commutative 82.1%

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

   10. Simplified 82.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+120}:\\ \;\;\;\;\frac{t \cdot y}{-a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+181}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+119}:\\ \;\;\;\;\frac{t \cdot y}{-a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+181}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.2e+119)
   (/ (* t y) (- a))
   (if (<= t 1.4e+181) (+ x (* z (/ y a))) (* (/ t a) (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e+119) {
		tmp = (t * y) / -a;
	} else if (t <= 1.4e+181) {
		tmp = x + (z * (y / a));
	} 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 <= (-2.2d+119)) then
        tmp = (t * y) / -a
    else if (t <= 1.4d+181) then
        tmp = x + (z * (y / a))
    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 <= -2.2e+119) {
		tmp = (t * y) / -a;
	} else if (t <= 1.4e+181) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (t / a) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.2e+119:
		tmp = (t * y) / -a
	elif t <= 1.4e+181:
		tmp = x + (z * (y / a))
	else:
		tmp = (t / a) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.2e+119)
		tmp = Float64(Float64(t * y) / Float64(-a));
	elseif (t <= 1.4e+181)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(Float64(t / a) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.2e+119)
		tmp = (t * y) / -a;
	elseif (t <= 1.4e+181)
		tmp = x + (z * (y / a));
	else
		tmp = (t / a) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.2e+119], N[(N[(t * y), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[t, 1.4e+181], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2000000000000001e119

   1. Initial program 91.7%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

      3. *-commutative 85.2%

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

      4. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in x around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-/l* 56.0%

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

      3. associate-*r* 56.0%

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

      4. neg-mul-1 56.0%

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

      5. *-commutative 56.0%

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

   10. Simplified 56.0%

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

       1. associate-*l/ 64.1%

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

       2. distribute-rgt-neg-out 64.1%

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

       3. distribute-neg-frac 64.1%

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

       4. distribute-neg-frac2 64.1%

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

       5. *-commutative 64.1%

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

   12. Applied egg-rr 64.1%

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

   if -2.2000000000000001e119 < t < 1.39999999999999992e181

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-/l* 94.9%

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

      3. fma-define 94.9%

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

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 94.9%

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

      2. associate-*r/ 92.6%

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

      3. *-commutative 92.6%

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

      4. associate-/l* 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in z around inf 82.7%

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

   if 1.39999999999999992e181 < t

   1. Initial program 81.9%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. unsub-neg 81.9%

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

      3. *-commutative 81.9%

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

      4. associate-/l* 91.0%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in x around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 82.1%

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

      3. associate-*r* 82.1%

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

      4. neg-mul-1 82.1%

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

      5. *-commutative 82.1%

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

   10. Simplified 82.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+119}:\\ \;\;\;\;\frac{t \cdot y}{-a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+181}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{t \cdot y}{-a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+181}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e+119)
   (/ (* t y) (- a))
   (if (<= t 6e+181) (+ x (* y (/ z a))) (* (/ t a) (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+119) {
		tmp = (t * y) / -a;
	} else if (t <= 6e+181) {
		tmp = x + (y * (z / a));
	} 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 <= (-1.8d+119)) then
        tmp = (t * y) / -a
    else if (t <= 6d+181) then
        tmp = x + (y * (z / a))
    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 <= -1.8e+119) {
		tmp = (t * y) / -a;
	} else if (t <= 6e+181) {
		tmp = x + (y * (z / a));
	} else {
		tmp = (t / a) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e+119:
		tmp = (t * y) / -a
	elif t <= 6e+181:
		tmp = x + (y * (z / a))
	else:
		tmp = (t / a) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e+119)
		tmp = Float64(Float64(t * y) / Float64(-a));
	elseif (t <= 6e+181)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(Float64(t / a) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.8e+119)
		tmp = (t * y) / -a;
	elseif (t <= 6e+181)
		tmp = x + (y * (z / a));
	else
		tmp = (t / a) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e+119], N[(N[(t * y), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[t, 6e+181], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.80000000000000001e119

   1. Initial program 91.7%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

      3. *-commutative 85.2%

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

      4. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in x around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-/l* 56.0%

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

      3. associate-*r* 56.0%

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

      4. neg-mul-1 56.0%

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

      5. *-commutative 56.0%

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

   10. Simplified 56.0%

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

       1. associate-*l/ 64.1%

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

       2. distribute-rgt-neg-out 64.1%

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

       3. distribute-neg-frac 64.1%

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

       4. distribute-neg-frac2 64.1%

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

       5. *-commutative 64.1%

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

   12. Applied egg-rr 64.1%

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

   if -1.80000000000000001e119 < t < 6.00000000000000024e181

   1. Initial program 92.6%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

   if 6.00000000000000024e181 < t

   1. Initial program 81.9%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. unsub-neg 81.9%

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

      3. *-commutative 81.9%

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

      4. associate-/l* 91.0%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in x around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 82.1%

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

      3. associate-*r* 82.1%

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

      4. neg-mul-1 82.1%

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

      5. *-commutative 82.1%

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

   10. Simplified 82.1%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{t \cdot y}{-a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+181}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+119}:\\ \;\;\;\;\frac{t \cdot y}{-a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+152}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+119)
   (/ (* t y) (- a))
   (if (<= t 3.4e+152) (+ x (/ (* z y) a)) (* (/ t a) (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+119) {
		tmp = (t * y) / -a;
	} else if (t <= 3.4e+152) {
		tmp = x + ((z * y) / a);
	} 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 <= (-7.2d+119)) then
        tmp = (t * y) / -a
    else if (t <= 3.4d+152) then
        tmp = x + ((z * y) / a)
    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 <= -7.2e+119) {
		tmp = (t * y) / -a;
	} else if (t <= 3.4e+152) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = (t / a) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.2e+119:
		tmp = (t * y) / -a
	elif t <= 3.4e+152:
		tmp = x + ((z * y) / a)
	else:
		tmp = (t / a) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+119)
		tmp = Float64(Float64(t * y) / Float64(-a));
	elseif (t <= 3.4e+152)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	else
		tmp = Float64(Float64(t / a) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.2e+119)
		tmp = (t * y) / -a;
	elseif (t <= 3.4e+152)
		tmp = x + ((z * y) / a);
	else
		tmp = (t / a) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+119], N[(N[(t * y), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[t, 3.4e+152], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.20000000000000003e119

   1. Initial program 91.7%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

      3. *-commutative 85.2%

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

      4. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in x around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-/l* 56.0%

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

      3. associate-*r* 56.0%

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

      4. neg-mul-1 56.0%

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

      5. *-commutative 56.0%

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

   10. Simplified 56.0%

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

       1. associate-*l/ 64.1%

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

       2. distribute-rgt-neg-out 64.1%

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

       3. distribute-neg-frac 64.1%

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

       4. distribute-neg-frac2 64.1%

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

       5. *-commutative 64.1%

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

   12. Applied egg-rr 64.1%

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

   if -7.20000000000000003e119 < t < 3.4000000000000002e152

   1. Initial program 93.3%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in z around inf 77.9%

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

   if 3.4000000000000002e152 < t

   1. Initial program 80.8%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

      3. *-commutative 77.7%

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

      4. associate-/l* 84.6%

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

   7. Simplified 84.6%

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

   8. Taylor expanded in x around 0 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-/l* 71.7%

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

      3. associate-*r* 71.7%

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

      4. neg-mul-1 71.7%

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

      5. *-commutative 71.7%

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

   10. Simplified 71.7%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+119}:\\ \;\;\;\;\frac{t \cdot y}{-a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+152}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+29} \lor \neg \left(y \leq 1.15 \cdot 10^{+110}\right):\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3e+29) (not (<= y 1.15e+110))) (* (/ t a) (- y)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e+29) || !(y <= 1.15e+110)) {
		tmp = (t / a) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3d+29)) .or. (.not. (y <= 1.15d+110))) then
        tmp = (t / a) * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e+29) || !(y <= 1.15e+110)) {
		tmp = (t / a) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3e+29) or not (y <= 1.15e+110):
		tmp = (t / a) * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3e+29) || !(y <= 1.15e+110))
		tmp = Float64(Float64(t / a) * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3e+29) || ~((y <= 1.15e+110)))
		tmp = (t / a) * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3e+29], N[Not[LessEqual[y, 1.15e+110]], $MachinePrecision]], N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.9999999999999999e29 or 1.15e110 < y

   1. Initial program 81.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. *-commutative 54.4%

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

      4. associate-/l* 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in x around 0 40.8%

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

      1. *-commutative 40.8%

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

      2. associate-/l* 47.8%

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

      3. associate-*r* 47.8%

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

      4. neg-mul-1 47.8%

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

      5. *-commutative 47.8%

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

   10. Simplified 47.8%

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

   if -2.9999999999999999e29 < y < 1.15e110

   1. Initial program 98.8%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in x around inf 52.3%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+29} \lor \neg \left(y \leq 1.15 \cdot 10^{+110}\right):\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+120}:\\ \;\;\;\;\frac{t \cdot y}{-a}\\ \mathbf{elif}\;t \leq 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e+120) (/ (* t y) (- a)) (if (<= t 1e-37) x (* (/ t a) (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+120) {
		tmp = (t * y) / -a;
	} else if (t <= 1e-37) {
		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 <= (-1.8d+120)) then
        tmp = (t * y) / -a
    else if (t <= 1d-37) 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 <= -1.8e+120) {
		tmp = (t * y) / -a;
	} else if (t <= 1e-37) {
		tmp = x;
	} else {
		tmp = (t / a) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e+120:
		tmp = (t * y) / -a
	elif t <= 1e-37:
		tmp = x
	else:
		tmp = (t / a) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e+120)
		tmp = Float64(Float64(t * y) / Float64(-a));
	elseif (t <= 1e-37)
		tmp = x;
	else
		tmp = Float64(Float64(t / a) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.8e+120)
		tmp = (t * y) / -a;
	elseif (t <= 1e-37)
		tmp = x;
	else
		tmp = (t / a) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e+120], N[(N[(t * y), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[t, 1e-37], x, N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.80000000000000008e120

   1. Initial program 91.7%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

      3. *-commutative 85.2%

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

      4. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in x around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-/l* 56.0%

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

      3. associate-*r* 56.0%

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

      4. neg-mul-1 56.0%

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

      5. *-commutative 56.0%

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

   10. Simplified 56.0%

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

       1. associate-*l/ 64.1%

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

       2. distribute-rgt-neg-out 64.1%

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

       3. distribute-neg-frac 64.1%

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

       4. distribute-neg-frac2 64.1%

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

       5. *-commutative 64.1%

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

   12. Applied egg-rr 64.1%

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

   if -1.80000000000000008e120 < t < 1.00000000000000007e-37

   1. Initial program 93.0%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in x around inf 45.8%

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

   if 1.00000000000000007e-37 < t

   1. Initial program 88.2%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. unsub-neg 75.2%

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

      3. *-commutative 75.2%

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

      4. associate-/l* 75.4%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in x around 0 53.7%

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

      1. *-commutative 53.7%

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

      2. associate-/l* 55.4%

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

      3. associate-*r* 55.4%

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

      4. neg-mul-1 55.4%

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

      5. *-commutative 55.4%

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

   10. Simplified 55.4%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+120}:\\ \;\;\;\;\frac{t \cdot y}{-a}\\ \mathbf{elif}\;t \leq 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

   1. +-commutative 91.5%

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

   2. associate-/l* 93.3%

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

   3. fma-define 93.3%

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

3. Simplified 93.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. fma-undefine 93.3%

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

   2. associate-*r/ 91.5%

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

   3. *-commutative 91.5%

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

   4. associate-/l* 96.9%

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

6. Applied egg-rr 96.9%

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

Alternative 10: 93.1% 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 91.5%

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

   1. associate-/l* 93.3%

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

3. Simplified 93.3%

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

Alternative 11: 38.9% 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 91.5%

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

   1. associate-/l* 93.3%

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

3. Simplified 93.3%

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

5. Taylor expanded in x around inf 37.2%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024151 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t)))))))

  (+ x (/ (* y (- z t)) a)))