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

Percentage Accurate: 93.1% → 97.2%

Time: 10.6s

Alternatives: 15

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. associate-*r/ 91.8%

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

3. Simplified 91.8%

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

   1. *-commutative 91.8%

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

   2. associate-*l/ 93.6%

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

   3. associate-/l* 97.1%

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

5. Applied egg-rr 97.1%

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

6. Final simplification 97.1%

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

Alternative 2: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 150000000000:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+134} \lor \neg \left(y \leq 7 \cdot 10^{+225}\right):\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.5e+49)
   (/ t (/ a y))
   (if (<= y 4.5e-89)
     x
     (if (<= y 150000000000.0)
       (/ (* t y) a)
       (if (or (<= y 3.6e+134) (not (<= y 7e+225)))
         (* z (/ (- y) a))
         (* y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.5e+49) {
		tmp = t / (a / y);
	} else if (y <= 4.5e-89) {
		tmp = x;
	} else if (y <= 150000000000.0) {
		tmp = (t * y) / a;
	} else if ((y <= 3.6e+134) || !(y <= 7e+225)) {
		tmp = z * (-y / a);
	} else {
		tmp = 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 (y <= (-2.5d+49)) then
        tmp = t / (a / y)
    else if (y <= 4.5d-89) then
        tmp = x
    else if (y <= 150000000000.0d0) then
        tmp = (t * y) / a
    else if ((y <= 3.6d+134) .or. (.not. (y <= 7d+225))) then
        tmp = z * (-y / a)
    else
        tmp = 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 (y <= -2.5e+49) {
		tmp = t / (a / y);
	} else if (y <= 4.5e-89) {
		tmp = x;
	} else if (y <= 150000000000.0) {
		tmp = (t * y) / a;
	} else if ((y <= 3.6e+134) || !(y <= 7e+225)) {
		tmp = z * (-y / a);
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.5e+49:
		tmp = t / (a / y)
	elif y <= 4.5e-89:
		tmp = x
	elif y <= 150000000000.0:
		tmp = (t * y) / a
	elif (y <= 3.6e+134) or not (y <= 7e+225):
		tmp = z * (-y / a)
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.5e+49)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 4.5e-89)
		tmp = x;
	elseif (y <= 150000000000.0)
		tmp = Float64(Float64(t * y) / a);
	elseif ((y <= 3.6e+134) || !(y <= 7e+225))
		tmp = Float64(z * Float64(Float64(-y) / a));
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.5e+49)
		tmp = t / (a / y);
	elseif (y <= 4.5e-89)
		tmp = x;
	elseif (y <= 150000000000.0)
		tmp = (t * y) / a;
	elseif ((y <= 3.6e+134) || ~((y <= 7e+225)))
		tmp = z * (-y / a);
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.5e+49], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-89], x, If[LessEqual[y, 150000000000.0], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[y, 3.6e+134], N[Not[LessEqual[y, 7e+225]], $MachinePrecision]], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.5000000000000002e49

   1. Initial program 88.9%

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

      1. associate-*r/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 45.7%

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

      1. associate-*l/ 53.2%

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

      2. *-commutative 53.2%

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

   6. Simplified 53.2%

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

      1. clear-num 53.1%

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

      2. div-inv 53.4%

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

   8. Applied egg-rr 53.4%

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

   if -2.5000000000000002e49 < y < 4.4999999999999999e-89

   1. Initial program 99.0%

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

      1. associate-*r/ 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in x around inf 67.3%

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

   if 4.4999999999999999e-89 < y < 1.5e11

   1. Initial program 99.9%

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

      1. associate-*r/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in t around inf 67.7%

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

   if 1.5e11 < y < 3.59999999999999988e134 or 7.0000000000000006e225 < y

   1. Initial program 89.1%

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

      1. associate-*r/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in z around inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. associate-*l/ 57.6%

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

      3. *-commutative 57.6%

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

      4. distribute-rgt-neg-in 57.6%

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

      5. distribute-frac-neg 57.6%

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

   6. Simplified 57.6%

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

   if 3.59999999999999988e134 < y < 7.0000000000000006e225

   1. Initial program 86.5%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. associate-*l/ 86.5%

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

      3. associate-/l* 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in t around inf 72.4%

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

      1. associate-*r/ 77.0%

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

   8. Simplified 77.0%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 150000000000:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+134} \lor \neg \left(y \leq 7 \cdot 10^{+225}\right):\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 3: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 13500000000:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+134}:\\ \;\;\;\;\frac{y}{\frac{-a}{z}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+225}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.9e+49)
   (/ t (/ a y))
   (if (<= y 9.2e-94)
     x
     (if (<= y 13500000000.0)
       (/ (* t y) a)
       (if (<= y 3.7e+134)
         (/ y (/ (- a) z))
         (if (<= y 7e+225) (* y (/ t a)) (* z (/ (- y) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.9e+49) {
		tmp = t / (a / y);
	} else if (y <= 9.2e-94) {
		tmp = x;
	} else if (y <= 13500000000.0) {
		tmp = (t * y) / a;
	} else if (y <= 3.7e+134) {
		tmp = y / (-a / z);
	} else if (y <= 7e+225) {
		tmp = y * (t / a);
	} else {
		tmp = z * (-y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.9d+49)) then
        tmp = t / (a / y)
    else if (y <= 9.2d-94) then
        tmp = x
    else if (y <= 13500000000.0d0) then
        tmp = (t * y) / a
    else if (y <= 3.7d+134) then
        tmp = y / (-a / z)
    else if (y <= 7d+225) then
        tmp = y * (t / a)
    else
        tmp = z * (-y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.9e+49) {
		tmp = t / (a / y);
	} else if (y <= 9.2e-94) {
		tmp = x;
	} else if (y <= 13500000000.0) {
		tmp = (t * y) / a;
	} else if (y <= 3.7e+134) {
		tmp = y / (-a / z);
	} else if (y <= 7e+225) {
		tmp = y * (t / a);
	} else {
		tmp = z * (-y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.9e+49:
		tmp = t / (a / y)
	elif y <= 9.2e-94:
		tmp = x
	elif y <= 13500000000.0:
		tmp = (t * y) / a
	elif y <= 3.7e+134:
		tmp = y / (-a / z)
	elif y <= 7e+225:
		tmp = y * (t / a)
	else:
		tmp = z * (-y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.9e+49)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 9.2e-94)
		tmp = x;
	elseif (y <= 13500000000.0)
		tmp = Float64(Float64(t * y) / a);
	elseif (y <= 3.7e+134)
		tmp = Float64(y / Float64(Float64(-a) / z));
	elseif (y <= 7e+225)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(z * Float64(Float64(-y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.9e+49)
		tmp = t / (a / y);
	elseif (y <= 9.2e-94)
		tmp = x;
	elseif (y <= 13500000000.0)
		tmp = (t * y) / a;
	elseif (y <= 3.7e+134)
		tmp = y / (-a / z);
	elseif (y <= 7e+225)
		tmp = y * (t / a);
	else
		tmp = z * (-y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.9e+49], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-94], x, If[LessEqual[y, 13500000000.0], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 3.7e+134], N[(y / N[((-a) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+225], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.8999999999999999e49

   1. Initial program 88.9%

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

      1. associate-*r/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 45.7%

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

      1. associate-*l/ 53.2%

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

      2. *-commutative 53.2%

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

   6. Simplified 53.2%

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

      1. clear-num 53.1%

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

      2. div-inv 53.4%

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

   8. Applied egg-rr 53.4%

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

   if -1.8999999999999999e49 < y < 9.1999999999999997e-94

   1. Initial program 99.0%

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

      1. associate-*r/ 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in x around inf 67.3%

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

   if 9.1999999999999997e-94 < y < 1.35e10

   1. Initial program 99.9%

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

      1. associate-*r/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in t around inf 67.7%

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

   if 1.35e10 < y < 3.70000000000000013e134

   1. Initial program 86.4%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 42.8%

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

      1. mul-1-neg 42.8%

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

      2. associate-*l/ 48.3%

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

      3. *-commutative 48.3%

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

      4. distribute-rgt-neg-in 48.3%

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

      5. distribute-frac-neg 48.3%

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

   6. Simplified 48.3%

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

      1. *-commutative 48.3%

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

      2. distribute-frac-neg 48.3%

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

      3. distribute-lft-neg-in 48.3%

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

      4. associate-/r/ 49.4%

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

      5. frac-2neg 49.4%

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

      6. distribute-neg-frac 49.4%

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

      7. remove-double-neg 49.4%

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

      8. distribute-neg-frac 49.4%

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

   8. Applied egg-rr 49.4%

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

   if 3.70000000000000013e134 < y < 7.0000000000000006e225

   1. Initial program 86.5%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. associate-*l/ 86.5%

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

      3. associate-/l* 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in t around inf 72.4%

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

      1. associate-*r/ 77.0%

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

   8. Simplified 77.0%

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

   if 7.0000000000000006e225 < y

   1. Initial program 92.3%

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

      1. associate-*r/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. associate-*l/ 68.4%

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

      3. *-commutative 68.4%

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

      4. distribute-rgt-neg-in 68.4%

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

      5. distribute-frac-neg 68.4%

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

   6. Simplified 68.4%

      \[\leadsto \color{blue}{z \cdot \frac{-y}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 13500000000:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+134}:\\ \;\;\;\;\frac{y}{\frac{-a}{z}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+225}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \end{array} \]

Alternative 4: 68.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-38} \lor \neg \left(y \leq -2 \cdot 10^{-75} \lor \neg \left(y \leq -1.6 \cdot 10^{-143}\right) \land y \leq 2.2 \cdot 10^{-161}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.4e-38)
         (not (or (<= y -2e-75) (and (not (<= y -1.6e-143)) (<= y 2.2e-161)))))
   (* (/ y a) (- t z))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.4e-38) || !((y <= -2e-75) || (!(y <= -1.6e-143) && (y <= 2.2e-161)))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.4d-38)) .or. (.not. (y <= (-2d-75)) .or. (.not. (y <= (-1.6d-143))) .and. (y <= 2.2d-161))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.4e-38) || !((y <= -2e-75) || (!(y <= -1.6e-143) && (y <= 2.2e-161)))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.4e-38) or not ((y <= -2e-75) or (not (y <= -1.6e-143) and (y <= 2.2e-161))):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.4e-38) || !((y <= -2e-75) || (!(y <= -1.6e-143) && (y <= 2.2e-161))))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.4e-38) || ~(((y <= -2e-75) || (~((y <= -1.6e-143)) && (y <= 2.2e-161)))))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.4e-38], N[Not[Or[LessEqual[y, -2e-75], And[N[Not[LessEqual[y, -1.6e-143]], $MachinePrecision], LessEqual[y, 2.2e-161]]]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.40000000000000015e-38 or -1.9999999999999999e-75 < y < -1.5999999999999999e-143 or 2.20000000000000002e-161 < y

   1. Initial program 91.8%

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

      1. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-*l/ 91.8%

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

      3. associate-/l* 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in x around 0 70.2%

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

      1. associate-/l* 74.4%

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

      2. div-sub 64.7%

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

      3. associate-/l* 62.9%

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

      4. associate-/l* 64.2%

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

      5. associate-*r/ 62.5%

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

      6. associate-*r/ 64.2%

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

      7. associate-*l/ 64.3%

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

      8. *-commutative 64.3%

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

      9. distribute-lft-out-- 64.3%

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

      10. neg-mul-1 64.3%

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

      11. rem-3cbrt-rft 64.2%

          \[\leadsto \left(-\color{blue}{\sqrt[3]{\frac{z \cdot y}{a}} \cdot \left(\sqrt[3]{\frac{z \cdot y}{a}} \cdot \sqrt[3]{\frac{z \cdot y}{a}}\right)}\right) - -1 \cdot \left(y \cdot \frac{t}{a}\right) \]

      12. unpow2 64.2%

          \[\leadsto \left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot \color{blue}{{\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}}\right) - -1 \cdot \left(y \cdot \frac{t}{a}\right) \]

      13. neg-mul-1 64.2%

          \[\leadsto \left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}\right) - \color{blue}{\left(-y \cdot \frac{t}{a}\right)} \]

      14. distribute-lft-neg-in 64.2%

          \[\leadsto \left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}\right) - \color{blue}{\left(-y\right) \cdot \frac{t}{a}} \]

      15. cancel-sign-sub 64.2%

          \[\leadsto \color{blue}{\left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}\right) + y \cdot \frac{t}{a}} \]

      16. distribute-lft-neg-in 64.2%

          \[\leadsto \color{blue}{\left(-\sqrt[3]{\frac{z \cdot y}{a}}\right) \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}} + y \cdot \frac{t}{a} \]

   8. Simplified 74.1%

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

   if -4.40000000000000015e-38 < y < -1.9999999999999999e-75 or -1.5999999999999999e-143 < y < 2.20000000000000002e-161

   1. Initial program 98.5%

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

      1. associate-*r/ 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in x around inf 80.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-38} \lor \neg \left(y \leq -2 \cdot 10^{-75} \lor \neg \left(y \leq -1.6 \cdot 10^{-143}\right) \land y \leq 2.2 \cdot 10^{-161}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+49} \lor \neg \left(y \leq 2.4 \cdot 10^{-91} \lor \neg \left(y \leq 1.4 \cdot 10^{+87}\right) \land y \leq 3.4 \cdot 10^{+134}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.7e+49)
         (not (or (<= y 2.4e-91) (and (not (<= y 1.4e+87)) (<= y 3.4e+134)))))
   (* t (/ y a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.7e+49) || !((y <= 2.4e-91) || (!(y <= 1.4e+87) && (y <= 3.4e+134)))) {
		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 ((y <= (-2.7d+49)) .or. (.not. (y <= 2.4d-91) .or. (.not. (y <= 1.4d+87)) .and. (y <= 3.4d+134))) 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 ((y <= -2.7e+49) || !((y <= 2.4e-91) || (!(y <= 1.4e+87) && (y <= 3.4e+134)))) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.7e+49) or not ((y <= 2.4e-91) or (not (y <= 1.4e+87) and (y <= 3.4e+134))):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.7e+49) || !((y <= 2.4e-91) || (!(y <= 1.4e+87) && (y <= 3.4e+134))))
		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 ((y <= -2.7e+49) || ~(((y <= 2.4e-91) || (~((y <= 1.4e+87)) && (y <= 3.4e+134)))))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.7e+49], N[Not[Or[LessEqual[y, 2.4e-91], And[N[Not[LessEqual[y, 1.4e+87]], $MachinePrecision], LessEqual[y, 3.4e+134]]]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000001e49 or 2.40000000000000011e-91 < y < 1.40000000000000008e87 or 3.40000000000000018e134 < y

   1. Initial program 89.7%

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

      1. associate-*r/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around inf 49.8%

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

      1. associate-*l/ 53.6%

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

      2. *-commutative 53.6%

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

   6. Simplified 53.6%

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

   if -2.7000000000000001e49 < y < 2.40000000000000011e-91 or 1.40000000000000008e87 < y < 3.40000000000000018e134

   1. Initial program 98.3%

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

      1. associate-*r/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 65.9%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+49} \lor \neg \left(y \leq 2.4 \cdot 10^{-91} \lor \neg \left(y \leq 1.4 \cdot 10^{+87}\right) \land y \leq 3.4 \cdot 10^{+134}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 49.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+87} \lor \neg \left(y \leq 3.4 \cdot 10^{+134}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.8e+49)
   (* t (/ y a))
   (if (<= y 1.2e-93)
     x
     (if (or (<= y 1.55e+87) (not (<= y 3.4e+134))) (* y (/ t a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.8e+49) {
		tmp = t * (y / a);
	} else if (y <= 1.2e-93) {
		tmp = x;
	} else if ((y <= 1.55e+87) || !(y <= 3.4e+134)) {
		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 (y <= (-1.8d+49)) then
        tmp = t * (y / a)
    else if (y <= 1.2d-93) then
        tmp = x
    else if ((y <= 1.55d+87) .or. (.not. (y <= 3.4d+134))) 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 (y <= -1.8e+49) {
		tmp = t * (y / a);
	} else if (y <= 1.2e-93) {
		tmp = x;
	} else if ((y <= 1.55e+87) || !(y <= 3.4e+134)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.8e+49:
		tmp = t * (y / a)
	elif y <= 1.2e-93:
		tmp = x
	elif (y <= 1.55e+87) or not (y <= 3.4e+134):
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.8e+49)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 1.2e-93)
		tmp = x;
	elseif ((y <= 1.55e+87) || !(y <= 3.4e+134))
		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 (y <= -1.8e+49)
		tmp = t * (y / a);
	elseif (y <= 1.2e-93)
		tmp = x;
	elseif ((y <= 1.55e+87) || ~((y <= 3.4e+134)))
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.8e+49], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-93], x, If[Or[LessEqual[y, 1.55e+87], N[Not[LessEqual[y, 3.4e+134]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999998e49

   1. Initial program 88.9%

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

      1. associate-*r/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 45.7%

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

      1. associate-*l/ 53.2%

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

      2. *-commutative 53.2%

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

   6. Simplified 53.2%

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

   if -1.79999999999999998e49 < y < 1.2000000000000001e-93 or 1.55e87 < y < 3.40000000000000018e134

   1. Initial program 98.3%

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

      1. associate-*r/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 65.9%

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

   if 1.2000000000000001e-93 < y < 1.55e87 or 3.40000000000000018e134 < y

   1. Initial program 90.3%

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

      1. associate-*r/ 97.3%

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

   3. Simplified 97.3%

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

      1. *-commutative 97.3%

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

      2. associate-*l/ 90.3%

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

      3. associate-/l* 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in t around inf 52.9%

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

      1. associate-*r/ 56.3%

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

   8. Simplified 56.3%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+87} \lor \neg \left(y \leq 3.4 \cdot 10^{+134}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 49.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+84} \lor \neg \left(y \leq 3.4 \cdot 10^{+134}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.2e+49)
   (/ t (/ a y))
   (if (<= y 4.2e-89)
     x
     (if (or (<= y 6e+84) (not (<= y 3.4e+134))) (* y (/ t a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.2e+49) {
		tmp = t / (a / y);
	} else if (y <= 4.2e-89) {
		tmp = x;
	} else if ((y <= 6e+84) || !(y <= 3.4e+134)) {
		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 (y <= (-2.2d+49)) then
        tmp = t / (a / y)
    else if (y <= 4.2d-89) then
        tmp = x
    else if ((y <= 6d+84) .or. (.not. (y <= 3.4d+134))) 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 (y <= -2.2e+49) {
		tmp = t / (a / y);
	} else if (y <= 4.2e-89) {
		tmp = x;
	} else if ((y <= 6e+84) || !(y <= 3.4e+134)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.2e+49:
		tmp = t / (a / y)
	elif y <= 4.2e-89:
		tmp = x
	elif (y <= 6e+84) or not (y <= 3.4e+134):
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.2e+49)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 4.2e-89)
		tmp = x;
	elseif ((y <= 6e+84) || !(y <= 3.4e+134))
		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 (y <= -2.2e+49)
		tmp = t / (a / y);
	elseif (y <= 4.2e-89)
		tmp = x;
	elseif ((y <= 6e+84) || ~((y <= 3.4e+134)))
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.2e+49], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-89], x, If[Or[LessEqual[y, 6e+84], N[Not[LessEqual[y, 3.4e+134]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2000000000000001e49

   1. Initial program 88.9%

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

      1. associate-*r/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 45.7%

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

      1. associate-*l/ 53.2%

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

      2. *-commutative 53.2%

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

   6. Simplified 53.2%

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

      1. clear-num 53.1%

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

      2. div-inv 53.4%

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

   8. Applied egg-rr 53.4%

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

   if -2.2000000000000001e49 < y < 4.2000000000000002e-89 or 5.99999999999999992e84 < y < 3.40000000000000018e134

   1. Initial program 98.3%

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

      1. associate-*r/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 65.9%

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

   if 4.2000000000000002e-89 < y < 5.99999999999999992e84 or 3.40000000000000018e134 < y

   1. Initial program 90.3%

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

      1. associate-*r/ 97.3%

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

   3. Simplified 97.3%

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

      1. *-commutative 97.3%

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

      2. associate-*l/ 90.3%

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

      3. associate-/l* 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in t around inf 52.9%

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

      1. associate-*r/ 56.3%

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

   8. Simplified 56.3%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+84} \lor \neg \left(y \leq 3.4 \cdot 10^{+134}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-11} \lor \neg \left(a \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.9e-11) (not (<= a 8e-99)))
   (+ x (* y (/ t a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e-11) || !(a <= 8e-99)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.9d-11)) .or. (.not. (a <= 8d-99))) then
        tmp = x + (y * (t / a))
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e-11) || !(a <= 8e-99)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.9e-11) or not (a <= 8e-99):
		tmp = x + (y * (t / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.9e-11) || !(a <= 8e-99))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.9e-11) || ~((a <= 8e-99)))
		tmp = x + (y * (t / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.9e-11], N[Not[LessEqual[a, 8e-99]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8999999999999999e-11 or 8.0000000000000002e-99 < a

   1. Initial program 90.1%

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

      1. associate-*r/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around 0 77.5%

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

      1. neg-mul-1 77.5%

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

      2. distribute-neg-frac 77.5%

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

   6. Simplified 77.5%

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

      1. sub-neg 77.5%

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

      2. distribute-lft-neg-in 77.5%

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

      3. add-sqr-sqrt 39.2%

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

      4. sqrt-unprod 56.6%

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

      5. sqr-neg 56.6%

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

      6. sqrt-unprod 25.8%

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

      7. add-sqr-sqrt 54.2%

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

      8. add-sqr-sqrt 27.9%

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

      9. sqrt-unprod 51.0%

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

      10. sqr-neg 51.0%

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

      11. sqrt-unprod 35.1%

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

      12. add-sqr-sqrt 77.5%

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

   8. Applied egg-rr 77.5%

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

   if -1.8999999999999999e-11 < a < 8.0000000000000002e-99

   1. Initial program 98.9%

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

      1. associate-*r/ 83.4%

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

   3. Simplified 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-*l/ 98.9%

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

      3. associate-/l* 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in x around 0 83.2%

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

      1. associate-/l* 81.5%

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

      2. div-sub 66.9%

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

      3. associate-/l* 69.9%

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

      4. associate-/l* 75.5%

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

      5. associate-*r/ 69.9%

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

      6. associate-*r/ 75.5%

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

      7. associate-*l/ 67.2%

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

      8. *-commutative 67.2%

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

      9. distribute-lft-out-- 67.2%

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

      10. neg-mul-1 67.2%

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

      11. rem-3cbrt-rft 67.1%

          \[\leadsto \left(-\color{blue}{\sqrt[3]{\frac{z \cdot y}{a}} \cdot \left(\sqrt[3]{\frac{z \cdot y}{a}} \cdot \sqrt[3]{\frac{z \cdot y}{a}}\right)}\right) - -1 \cdot \left(y \cdot \frac{t}{a}\right) \]

      12. unpow2 67.1%

          \[\leadsto \left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot \color{blue}{{\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}}\right) - -1 \cdot \left(y \cdot \frac{t}{a}\right) \]

      13. neg-mul-1 67.1%

          \[\leadsto \left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}\right) - \color{blue}{\left(-y \cdot \frac{t}{a}\right)} \]

      14. distribute-lft-neg-in 67.1%

          \[\leadsto \left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}\right) - \color{blue}{\left(-y\right) \cdot \frac{t}{a}} \]

      15. cancel-sign-sub 67.1%

          \[\leadsto \color{blue}{\left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}\right) + y \cdot \frac{t}{a}} \]

      16. distribute-lft-neg-in 67.1%

          \[\leadsto \color{blue}{\left(-\sqrt[3]{\frac{z \cdot y}{a}}\right) \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}} + y \cdot \frac{t}{a} \]

   8. Simplified 81.6%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-11} \lor \neg \left(a \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 9: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+57} \lor \neg \left(z \leq 3.05 \cdot 10^{-22}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.85e+57) (not (<= z 3.05e-22)))
   (- x (* y (/ z a)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.85e+57) || !(z <= 3.05e-22)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.85d+57)) .or. (.not. (z <= 3.05d-22))) then
        tmp = x - (y * (z / a))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.85e+57) || !(z <= 3.05e-22)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.85e+57) or not (z <= 3.05e-22):
		tmp = x - (y * (z / a))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.85e+57) || !(z <= 3.05e-22))
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.85e+57) || ~((z <= 3.05e-22)))
		tmp = x - (y * (z / a));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.85e+57], N[Not[LessEqual[z, 3.05e-22]], $MachinePrecision]], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8499999999999999e57 or 3.04999999999999978e-22 < z

   1. Initial program 91.0%

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

      1. associate-*r/ 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in z around inf 86.6%

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

   if -2.8499999999999999e57 < z < 3.04999999999999978e-22

   1. Initial program 95.8%

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

      1. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 87.4%

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

      1. sub-neg 87.4%

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

      2. mul-1-neg 87.4%

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

      3. remove-double-neg 87.4%

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

      4. +-commutative 87.4%

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

      5. associate-*l/ 89.8%

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

      6. *-commutative 89.8%

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

   6. Simplified 89.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+57} \lor \neg \left(z \leq 3.05 \cdot 10^{-22}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+194}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+171}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+194)
   (* (/ y a) (- t z))
   (if (<= z 1.9e+171) (+ x (* t (/ y a))) (/ (- z) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+194) {
		tmp = (y / a) * (t - z);
	} else if (z <= 1.9e+171) {
		tmp = x + (t * (y / a));
	} else {
		tmp = -z / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d+194)) then
        tmp = (y / a) * (t - z)
    else if (z <= 1.9d+171) then
        tmp = x + (t * (y / a))
    else
        tmp = -z / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+194) {
		tmp = (y / a) * (t - z);
	} else if (z <= 1.9e+171) {
		tmp = x + (t * (y / a));
	} else {
		tmp = -z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+194:
		tmp = (y / a) * (t - z)
	elif z <= 1.9e+171:
		tmp = x + (t * (y / a))
	else:
		tmp = -z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+194)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (z <= 1.9e+171)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(Float64(-z) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+194)
		tmp = (y / a) * (t - z);
	elseif (z <= 1.9e+171)
		tmp = x + (t * (y / a));
	else
		tmp = -z / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+194], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+171], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999999e194

   1. Initial program 83.6%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. *-commutative 87.8%

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

      2. associate-*l/ 83.6%

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

      3. associate-/l* 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in x around 0 70.8%

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

      1. associate-/l* 82.8%

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

      2. div-sub 74.1%

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

      3. associate-/l* 65.8%

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

      4. associate-/l* 66.1%

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

      5. associate-*r/ 65.9%

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

      6. associate-*r/ 66.1%

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

      7. associate-*l/ 70.2%

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

      8. *-commutative 70.2%

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

      9. distribute-lft-out-- 70.2%

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

      10. neg-mul-1 70.2%

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

      11. rem-3cbrt-rft 69.6%

          \[\leadsto \left(-\color{blue}{\sqrt[3]{\frac{z \cdot y}{a}} \cdot \left(\sqrt[3]{\frac{z \cdot y}{a}} \cdot \sqrt[3]{\frac{z \cdot y}{a}}\right)}\right) - -1 \cdot \left(y \cdot \frac{t}{a}\right) \]

      12. unpow2 69.6%

          \[\leadsto \left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot \color{blue}{{\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}}\right) - -1 \cdot \left(y \cdot \frac{t}{a}\right) \]

      13. neg-mul-1 69.6%

          \[\leadsto \left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}\right) - \color{blue}{\left(-y \cdot \frac{t}{a}\right)} \]

      14. distribute-lft-neg-in 69.6%

          \[\leadsto \left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}\right) - \color{blue}{\left(-y\right) \cdot \frac{t}{a}} \]

      15. cancel-sign-sub 69.6%

          \[\leadsto \color{blue}{\left(-\sqrt[3]{\frac{z \cdot y}{a}} \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}\right) + y \cdot \frac{t}{a}} \]

      16. distribute-lft-neg-in 69.6%

          \[\leadsto \color{blue}{\left(-\sqrt[3]{\frac{z \cdot y}{a}}\right) \cdot {\left(\sqrt[3]{\frac{z \cdot y}{a}}\right)}^{2}} + y \cdot \frac{t}{a} \]

   8. Simplified 83.0%

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

   if -5.4999999999999999e194 < z < 1.9000000000000001e171

   1. Initial program 95.2%

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

      1. associate-*r/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 80.6%

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

      1. sub-neg 80.6%

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

      2. mul-1-neg 80.6%

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

      3. remove-double-neg 80.6%

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

      4. +-commutative 80.6%

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

      5. associate-*l/ 82.7%

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

      6. *-commutative 82.7%

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

   6. Simplified 82.7%

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

   if 1.9000000000000001e171 < z

   1. Initial program 90.5%

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

      1. associate-*r/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. associate-*l/ 87.1%

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

      3. *-commutative 87.1%

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

      4. distribute-rgt-neg-in 87.1%

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

      5. distribute-frac-neg 87.1%

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

   6. Simplified 87.1%

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

      1. add-sqr-sqrt 46.9%

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

      2. sqrt-unprod 43.9%

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

      3. distribute-frac-neg 43.9%

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

      4. distribute-frac-neg 43.9%

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

      5. sqr-neg 43.9%

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

      6. sqrt-unprod 0.3%

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

      7. add-sqr-sqrt 0.8%

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

      8. clear-num 0.8%

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

      9. div-inv 0.8%

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

      10. frac-2neg 0.8%

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

      11. distribute-neg-frac 0.8%

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

      12. add-sqr-sqrt 0.2%

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

      13. sqrt-unprod 34.0%

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

      14. sqr-neg 34.0%

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

      15. sqrt-unprod 40.1%

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

      16. add-sqr-sqrt 87.1%

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

      17. frac-2neg 87.1%

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

   8. Applied egg-rr 87.1%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+194}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+171}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \end{array} \]

Alternative 11: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+55}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-15}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e+55)
   (- x (* y (/ z a)))
   (if (<= z 1.38e-15) (+ x (* t (/ y a))) (- x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+55) {
		tmp = x - (y * (z / a));
	} else if (z <= 1.38e-15) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.1d+55)) then
        tmp = x - (y * (z / a))
    else if (z <= 1.38d-15) then
        tmp = x + (t * (y / a))
    else
        tmp = x - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+55) {
		tmp = x - (y * (z / a));
	} else if (z <= 1.38e-15) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e+55:
		tmp = x - (y * (z / a))
	elif z <= 1.38e-15:
		tmp = x + (t * (y / a))
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e+55)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (z <= 1.38e-15)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.1e+55)
		tmp = x - (y * (z / a));
	elseif (z <= 1.38e-15)
		tmp = x + (t * (y / a));
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e+55], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.38e-15], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1000000000000001e55

   1. Initial program 88.6%

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

      1. associate-*r/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around inf 82.4%

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

   if -2.1000000000000001e55 < z < 1.3799999999999999e-15

   1. Initial program 95.8%

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

      1. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 87.4%

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

      1. sub-neg 87.4%

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

      2. mul-1-neg 87.4%

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

      3. remove-double-neg 87.4%

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

      4. +-commutative 87.4%

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

      5. associate-*l/ 89.8%

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

      6. *-commutative 89.8%

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

   6. Simplified 89.8%

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

   if 1.3799999999999999e-15 < z

   1. Initial program 92.8%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in z around inf 89.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+55}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-15}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 12: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+57}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-20}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+57)
   (- x (* y (/ z a)))
   (if (<= z 1.4e-20) (+ x (* t (/ y a))) (- x (/ (* z y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+57) {
		tmp = x - (y * (z / a));
	} else if (z <= 1.4e-20) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - ((z * y) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d+57)) then
        tmp = x - (y * (z / a))
    else if (z <= 1.4d-20) then
        tmp = x + (t * (y / a))
    else
        tmp = x - ((z * y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+57) {
		tmp = x - (y * (z / a));
	} else if (z <= 1.4e-20) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+57:
		tmp = x - (y * (z / a))
	elif z <= 1.4e-20:
		tmp = x + (t * (y / a))
	else:
		tmp = x - ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+57)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (z <= 1.4e-20)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+57)
		tmp = x - (y * (z / a));
	elseif (z <= 1.4e-20)
		tmp = x + (t * (y / a));
	else
		tmp = x - ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+57], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-20], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000001e57

   1. Initial program 88.6%

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

      1. associate-*r/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around inf 82.4%

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

   if -2.0000000000000001e57 < z < 1.4000000000000001e-20

   1. Initial program 95.8%

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

      1. associate-*r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 87.4%

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

      1. sub-neg 87.4%

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

      2. mul-1-neg 87.4%

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

      3. remove-double-neg 87.4%

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

      4. +-commutative 87.4%

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

      5. associate-*l/ 89.8%

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

      6. *-commutative 89.8%

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

   6. Simplified 89.8%

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

   if 1.4000000000000001e-20 < z

   1. Initial program 92.8%

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

      1. associate-*r/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in z around inf 89.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+57}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-20}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \]

Alternative 13: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. associate-*r/ 91.8%

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

3. Simplified 91.8%

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

4. Final simplification 91.8%

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

Alternative 14: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. associate-*l/ 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 15: 39.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. associate-*r/ 91.8%

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

3. Simplified 91.8%

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

4. Taylor expanded in x around inf 39.5%

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

5. Final simplification 39.5%

   \[\leadsto x \]

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 2023208 
(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)))