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

Percentage Accurate: 93.9% → 97.0%

Time: 7.7s

Alternatives: 9

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: 93.9% 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: 97.0% 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 93.9%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

   1. *-commutative 97.3%

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

   2. clear-num 97.3%

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

   3. un-div-inv 97.3%

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

5. Applied egg-rr 97.3%

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

6. Final simplification 97.3%

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

Alternative 2: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-z}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -0.24:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z) (/ a y))))
   (if (<= a -0.24)
     x
     (if (<= a -7.5e-224)
       t_1
       (if (<= a -1.08e-290)
         (* t (/ y a))
         (if (<= a 3e-201) t_1 (if (<= a 3.2e-71) (/ (* t y) a) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -z / (a / y);
	double tmp;
	if (a <= -0.24) {
		tmp = x;
	} else if (a <= -7.5e-224) {
		tmp = t_1;
	} else if (a <= -1.08e-290) {
		tmp = t * (y / a);
	} else if (a <= 3e-201) {
		tmp = t_1;
	} else if (a <= 3.2e-71) {
		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) :: t_1
    real(8) :: tmp
    t_1 = -z / (a / y)
    if (a <= (-0.24d0)) then
        tmp = x
    else if (a <= (-7.5d-224)) then
        tmp = t_1
    else if (a <= (-1.08d-290)) then
        tmp = t * (y / a)
    else if (a <= 3d-201) then
        tmp = t_1
    else if (a <= 3.2d-71) 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 t_1 = -z / (a / y);
	double tmp;
	if (a <= -0.24) {
		tmp = x;
	} else if (a <= -7.5e-224) {
		tmp = t_1;
	} else if (a <= -1.08e-290) {
		tmp = t * (y / a);
	} else if (a <= 3e-201) {
		tmp = t_1;
	} else if (a <= 3.2e-71) {
		tmp = (t * y) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -z / (a / y)
	tmp = 0
	if a <= -0.24:
		tmp = x
	elif a <= -7.5e-224:
		tmp = t_1
	elif a <= -1.08e-290:
		tmp = t * (y / a)
	elif a <= 3e-201:
		tmp = t_1
	elif a <= 3.2e-71:
		tmp = (t * y) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-z) / Float64(a / y))
	tmp = 0.0
	if (a <= -0.24)
		tmp = x;
	elseif (a <= -7.5e-224)
		tmp = t_1;
	elseif (a <= -1.08e-290)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= 3e-201)
		tmp = t_1;
	elseif (a <= 3.2e-71)
		tmp = Float64(Float64(t * y) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -z / (a / y);
	tmp = 0.0;
	if (a <= -0.24)
		tmp = x;
	elseif (a <= -7.5e-224)
		tmp = t_1;
	elseif (a <= -1.08e-290)
		tmp = t * (y / a);
	elseif (a <= 3e-201)
		tmp = t_1;
	elseif (a <= 3.2e-71)
		tmp = (t * y) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.24], x, If[LessEqual[a, -7.5e-224], t$95$1, If[LessEqual[a, -1.08e-290], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-201], t$95$1, If[LessEqual[a, 3.2e-71], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.23999999999999999 or 3.1999999999999999e-71 < a

   1. Initial program 89.5%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around inf 76.0%

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

      1. associate-*l/ 77.0%

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

      2. *-commutative 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in x around inf 57.4%

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

   if -0.23999999999999999 < a < -7.49999999999999978e-224 or -1.07999999999999997e-290 < a < 3.00000000000000002e-201

   1. Initial program 99.8%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 74.6%

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

      1. associate-*l/ 77.3%

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

      2. *-commutative 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in x around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-/l* 65.1%

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

   9. Simplified 65.1%

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

   if -7.49999999999999978e-224 < a < -1.07999999999999997e-290

   1. Initial program 99.9%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 91.9%

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

      1. associate-*r/ 91.9%

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

      2. associate-*l* 91.9%

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

      3. neg-mul-1 91.9%

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

      4. *-commutative 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in x around 0 83.5%

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

      1. associate-*r/ 83.6%

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

   9. Simplified 83.6%

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

   if 3.00000000000000002e-201 < a < 3.1999999999999999e-71

   1. Initial program 99.9%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around 0 73.9%

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

      1. associate-*r/ 72.4%

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

      2. associate-*l* 72.4%

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

      3. neg-mul-1 72.4%

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

      4. *-commutative 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in x around 0 53.3%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.24:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-224}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-201}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-y}{a}\\ \mathbf{if}\;a \leq -0.23:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-288}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y) a))))
   (if (<= a -0.23)
     x
     (if (<= a -2.3e-222)
       t_1
       (if (<= a -6.1e-288)
         (* t (/ y a))
         (if (<= a 5.5e-201) t_1 (if (<= a 2.8e-72) (/ (* t y) a) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / a);
	double tmp;
	if (a <= -0.23) {
		tmp = x;
	} else if (a <= -2.3e-222) {
		tmp = t_1;
	} else if (a <= -6.1e-288) {
		tmp = t * (y / a);
	} else if (a <= 5.5e-201) {
		tmp = t_1;
	} else if (a <= 2.8e-72) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * (-y / a)
    if (a <= (-0.23d0)) then
        tmp = x
    else if (a <= (-2.3d-222)) then
        tmp = t_1
    else if (a <= (-6.1d-288)) then
        tmp = t * (y / a)
    else if (a <= 5.5d-201) then
        tmp = t_1
    else if (a <= 2.8d-72) 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 t_1 = z * (-y / a);
	double tmp;
	if (a <= -0.23) {
		tmp = x;
	} else if (a <= -2.3e-222) {
		tmp = t_1;
	} else if (a <= -6.1e-288) {
		tmp = t * (y / a);
	} else if (a <= 5.5e-201) {
		tmp = t_1;
	} else if (a <= 2.8e-72) {
		tmp = (t * y) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (-y / a)
	tmp = 0
	if a <= -0.23:
		tmp = x
	elif a <= -2.3e-222:
		tmp = t_1
	elif a <= -6.1e-288:
		tmp = t * (y / a)
	elif a <= 5.5e-201:
		tmp = t_1
	elif a <= 2.8e-72:
		tmp = (t * y) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-y) / a))
	tmp = 0.0
	if (a <= -0.23)
		tmp = x;
	elseif (a <= -2.3e-222)
		tmp = t_1;
	elseif (a <= -6.1e-288)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= 5.5e-201)
		tmp = t_1;
	elseif (a <= 2.8e-72)
		tmp = Float64(Float64(t * y) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-y / a);
	tmp = 0.0;
	if (a <= -0.23)
		tmp = x;
	elseif (a <= -2.3e-222)
		tmp = t_1;
	elseif (a <= -6.1e-288)
		tmp = t * (y / a);
	elseif (a <= 5.5e-201)
		tmp = t_1;
	elseif (a <= 2.8e-72)
		tmp = (t * y) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.23], x, If[LessEqual[a, -2.3e-222], t$95$1, If[LessEqual[a, -6.1e-288], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-201], t$95$1, If[LessEqual[a, 2.8e-72], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.23000000000000001 or 2.7999999999999998e-72 < a

   1. Initial program 89.5%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around inf 76.0%

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

      1. associate-*l/ 77.0%

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

      2. *-commutative 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in x around inf 57.4%

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

   if -0.23000000000000001 < a < -2.3000000000000001e-222 or -6.09999999999999982e-288 < a < 5.50000000000000034e-201

   1. Initial program 99.8%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 74.6%

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

      1. associate-*l/ 77.3%

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

      2. *-commutative 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in x around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-*r/ 57.8%

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

      3. *-commutative 57.8%

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

      4. distribute-rgt-neg-in 57.8%

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

      5. associate-/r/ 65.1%

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

      6. remove-double-neg 65.1%

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

      7. distribute-frac-neg 65.1%

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

      8. neg-mul-1 65.1%

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

      9. neg-mul-1 65.1%

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

      10. times-frac 65.1%

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

      11. metadata-eval 65.1%

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

      12. *-commutative 65.1%

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

      13. *-rgt-identity 65.1%

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

      14. distribute-frac-neg 65.1%

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

      15. associate-/r/ 57.8%

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

      16. *-commutative 57.8%

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

   9. Simplified 57.8%

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

   10. Taylor expanded in y around 0 62.6%

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

       1. mul-1-neg 62.6%

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

       2. associate-*l/ 65.2%

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

       3. distribute-rgt-neg-out 65.2%

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

   12. Simplified 65.2%

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

   if -2.3000000000000001e-222 < a < -6.09999999999999982e-288

   1. Initial program 99.9%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 91.9%

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

      1. associate-*r/ 91.9%

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

      2. associate-*l* 91.9%

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

      3. neg-mul-1 91.9%

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

      4. *-commutative 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in x around 0 83.5%

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

      1. associate-*r/ 83.6%

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

   9. Simplified 83.6%

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

   if 5.50000000000000034e-201 < a < 2.7999999999999998e-72

   1. Initial program 99.9%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around 0 73.9%

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

      1. associate-*r/ 72.4%

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

      2. associate-*l* 72.4%

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

      3. neg-mul-1 72.4%

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

      4. *-commutative 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in x around 0 53.3%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.23:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-222}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-288}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-201}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+120} \lor \neg \left(t \leq 8 \cdot 10^{+18}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e+120) (not (<= t 8e+18)))
   (+ x (* t (/ y a)))
   (- x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+120) || !(t <= 8e+18)) {
		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 ((t <= (-2.8d+120)) .or. (.not. (t <= 8d+18))) 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 ((t <= -2.8e+120) || !(t <= 8e+18)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.8e+120) or not (t <= 8e+18):
		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 ((t <= -2.8e+120) || !(t <= 8e+18))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.8e+120) || ~((t <= 8e+18)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.8e+120], N[Not[LessEqual[t, 8e+18]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8000000000000001e120 or 8e18 < t

   1. Initial program 89.2%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. associate-*r/ 90.7%

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

      2. associate-*l* 90.7%

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

      3. neg-mul-1 90.7%

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

      4. *-commutative 90.7%

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

   6. Simplified 90.7%

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

      1. sub-neg 90.7%

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

      2. +-commutative 90.7%

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

      3. distribute-rgt-neg-out 90.7%

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

      4. remove-double-neg 90.7%

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

   8. Applied egg-rr 90.7%

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

   if -2.8000000000000001e120 < t < 8e18

   1. Initial program 96.8%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around inf 88.5%

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

      1. associate-*l/ 91.0%

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

      2. *-commutative 91.0%

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

   6. Simplified 91.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+120} \lor \neg \left(t \leq 8 \cdot 10^{+18}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+164}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+230}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+164)
   (/ (- z) (/ a y))
   (if (<= z 1.75e+230) (+ x (* t (/ y a))) (/ (* z (- y)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+164) {
		tmp = -z / (a / y);
	} else if (z <= 1.75e+230) {
		tmp = x + (t * (y / 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 (z <= (-1.95d+164)) then
        tmp = -z / (a / y)
    else if (z <= 1.75d+230) then
        tmp = x + (t * (y / 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 (z <= -1.95e+164) {
		tmp = -z / (a / y);
	} else if (z <= 1.75e+230) {
		tmp = x + (t * (y / a));
	} else {
		tmp = (z * -y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+164:
		tmp = -z / (a / y)
	elif z <= 1.75e+230:
		tmp = x + (t * (y / a))
	else:
		tmp = (z * -y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+164)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (z <= 1.75e+230)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(Float64(z * Float64(-y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e+164)
		tmp = -z / (a / y);
	elseif (z <= 1.75e+230)
		tmp = x + (t * (y / a));
	else
		tmp = (z * -y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+164], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+230], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * (-y)), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.94999999999999993e164

   1. Initial program 96.9%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around inf 93.8%

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

      1. associate-*l/ 93.6%

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

      2. *-commutative 93.6%

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

   6. Simplified 93.6%

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

   7. Taylor expanded in x around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-/l* 77.6%

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

   9. Simplified 77.6%

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

   if -1.94999999999999993e164 < z < 1.75e230

   1. Initial program 93.9%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around 0 73.6%

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

      1. associate-*r/ 78.5%

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

      2. associate-*l* 78.5%

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

      3. neg-mul-1 78.5%

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

      4. *-commutative 78.5%

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

   6. Simplified 78.5%

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

      1. sub-neg 78.5%

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

      2. +-commutative 78.5%

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

      3. distribute-rgt-neg-out 78.5%

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

      4. remove-double-neg 78.5%

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

   8. Applied egg-rr 78.5%

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

   if 1.75e230 < z

   1. Initial program 88.4%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in z around inf 88.4%

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

      1. associate-*l/ 86.1%

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

      2. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in x around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. associate-*r/ 68.4%

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

      3. *-commutative 68.4%

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

      4. distribute-rgt-neg-in 68.4%

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

      5. associate-/r/ 62.8%

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

      6. remove-double-neg 62.8%

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

      7. distribute-frac-neg 62.8%

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

      8. neg-mul-1 62.8%

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

      9. neg-mul-1 62.8%

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

      10. times-frac 62.8%

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

      11. metadata-eval 62.8%

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

      12. *-commutative 62.8%

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

      13. *-rgt-identity 62.8%

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

      14. distribute-frac-neg 62.8%

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

      15. associate-/r/ 68.4%

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

      16. *-commutative 68.4%

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

   9. Simplified 68.4%

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

       1. *-commutative 68.4%

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

       2. frac-2neg 68.4%

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

       3. remove-double-neg 68.4%

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

       4. associate-*l/ 71.0%

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

   11. Applied egg-rr 71.0%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+164}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+230}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{a}\\ \end{array} \]

Alternative 6: 51.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+119} \lor \neg \left(t \leq 2.1 \cdot 10^{+19}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.4e+119) (not (<= t 2.1e+19))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.4e+119) || !(t <= 2.1e+19)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9.4d+119)) .or. (.not. (t <= 2.1d+19))) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.4e+119) || !(t <= 2.1e+19)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.4e+119) or not (t <= 2.1e+19):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.4e+119) || !(t <= 2.1e+19))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.4e+119) || ~((t <= 2.1e+19)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.4e+119], N[Not[LessEqual[t, 2.1e+19]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -9.40000000000000016e119 or 2.1e19 < t

   1. Initial program 89.2%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. associate-*r/ 90.7%

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

      2. associate-*l* 90.7%

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

      3. neg-mul-1 90.7%

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

      4. *-commutative 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in x around 0 56.7%

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

      1. associate-*r/ 65.4%

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

   9. Simplified 65.4%

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

   if -9.40000000000000016e119 < t < 2.1e19

   1. Initial program 96.8%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around inf 88.5%

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

      1. associate-*l/ 91.0%

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

      2. *-commutative 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in x around inf 47.3%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+119} \lor \neg \left(t \leq 2.1 \cdot 10^{+19}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.3e+120) (* t (/ y a)) (if (<= t 1.35e+19) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e+120) {
		tmp = t * (y / a);
	} else if (t <= 1.35e+19) {
		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 <= (-2.3d+120)) then
        tmp = t * (y / a)
    else if (t <= 1.35d+19) 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 <= -2.3e+120) {
		tmp = t * (y / a);
	} else if (t <= 1.35e+19) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.3e+120:
		tmp = t * (y / a)
	elif t <= 1.35e+19:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.3e+120)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 1.35e+19)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.3e+120)
		tmp = t * (y / a);
	elseif (t <= 1.35e+19)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.3e+120], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+19], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.29999999999999993e120

   1. Initial program 87.5%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 78.7%

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

      1. associate-*r/ 91.0%

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

      2. associate-*l* 91.0%

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

      3. neg-mul-1 91.0%

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

      4. *-commutative 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in x around 0 61.6%

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

      1. associate-*r/ 71.3%

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

   9. Simplified 71.3%

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

   if -2.29999999999999993e120 < t < 1.35e19

   1. Initial program 96.8%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around inf 88.5%

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

      1. associate-*l/ 91.0%

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

      2. *-commutative 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in x around inf 47.3%

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

   if 1.35e19 < t

   1. Initial program 90.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 82.5%

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

      1. associate-*r/ 90.5%

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

      2. associate-*l* 90.5%

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

      3. neg-mul-1 90.5%

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

      4. *-commutative 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in x around 0 53.5%

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

      1. associate-*r/ 61.5%

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

   9. Simplified 61.5%

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

       1. associate-*r/ 53.5%

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

       2. associate-/l* 61.6%

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

   11. Applied egg-rr 61.6%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 97.0% 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 93.9%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 9: 39.3% 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 93.9%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in z around inf 71.7%

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

   1. associate-*l/ 73.8%

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

   2. *-commutative 73.8%

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

6. Simplified 73.8%

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

7. Taylor expanded in x around inf 39.7%

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

8. Final simplification 39.7%

   \[\leadsto x \]

Developer target: 99.2% 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 2023312 
(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)))