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

Percentage Accurate: 93.5% → 96.9%

Time: 10.6s

Alternatives: 11

Speedup: 1.0×

• 24.1% 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: 93.5% 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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

   1. *-commutative 96.5%

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

   2. clear-num 96.5%

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

   3. un-div-inv 96.9%

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

5. Applied egg-rr 96.9%

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

6. Final simplification 96.9%

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

Alternative 2: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+180}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{+131} \lor \neg \left(a \leq -2.1 \cdot 10^{+63}\right) \land a \leq 2.2 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e+180)
   x
   (if (or (<= a -4.9e+131) (and (not (<= a -2.1e+63)) (<= a 2.2e+106)))
     (* y (/ (- t z) a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+180) {
		tmp = x;
	} else if ((a <= -4.9e+131) || (!(a <= -2.1e+63) && (a <= 2.2e+106))) {
		tmp = y * ((t - z) / 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 (a <= (-5d+180)) then
        tmp = x
    else if ((a <= (-4.9d+131)) .or. (.not. (a <= (-2.1d+63))) .and. (a <= 2.2d+106)) then
        tmp = y * ((t - z) / 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 (a <= -5e+180) {
		tmp = x;
	} else if ((a <= -4.9e+131) || (!(a <= -2.1e+63) && (a <= 2.2e+106))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e+180:
		tmp = x
	elif (a <= -4.9e+131) or (not (a <= -2.1e+63) and (a <= 2.2e+106)):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e+180)
		tmp = x;
	elseif ((a <= -4.9e+131) || (!(a <= -2.1e+63) && (a <= 2.2e+106)))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5e+180)
		tmp = x;
	elseif ((a <= -4.9e+131) || (~((a <= -2.1e+63)) && (a <= 2.2e+106)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e+180], x, If[Or[LessEqual[a, -4.9e+131], And[N[Not[LessEqual[a, -2.1e+63]], $MachinePrecision], LessEqual[a, 2.2e+106]]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.9999999999999996e180 or -4.90000000000000032e131 < a < -2.1000000000000002e63 or 2.19999999999999992e106 < a

   1. Initial program 87.2%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in x around inf 70.0%

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

   if -4.9999999999999996e180 < a < -4.90000000000000032e131 or -2.1000000000000002e63 < a < 2.19999999999999992e106

   1. Initial program 95.6%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around inf 74.1%

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

      1. div-sub 76.5%

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

   6. Simplified 76.5%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+180}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{+131} \lor \neg \left(a \leq -2.1 \cdot 10^{+63}\right) \land a \leq 2.2 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-y}{a}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y) a))))
   (if (<= y -1.3e+51)
     t_1
     (if (<= y 1.25e-60) x (if (<= y 1.65e+58) t_1 (/ t (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / a);
	double tmp;
	if (y <= -1.3e+51) {
		tmp = t_1;
	} else if (y <= 1.25e-60) {
		tmp = x;
	} else if (y <= 1.65e+58) {
		tmp = t_1;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (-y / a)
    if (y <= (-1.3d+51)) then
        tmp = t_1
    else if (y <= 1.25d-60) then
        tmp = x
    else if (y <= 1.65d+58) then
        tmp = t_1
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / a);
	double tmp;
	if (y <= -1.3e+51) {
		tmp = t_1;
	} else if (y <= 1.25e-60) {
		tmp = x;
	} else if (y <= 1.65e+58) {
		tmp = t_1;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (-y / a)
	tmp = 0
	if y <= -1.3e+51:
		tmp = t_1
	elif y <= 1.25e-60:
		tmp = x
	elif y <= 1.65e+58:
		tmp = t_1
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-y) / a))
	tmp = 0.0
	if (y <= -1.3e+51)
		tmp = t_1;
	elseif (y <= 1.25e-60)
		tmp = x;
	elseif (y <= 1.65e+58)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-y / a);
	tmp = 0.0;
	if (y <= -1.3e+51)
		tmp = t_1;
	elseif (y <= 1.25e-60)
		tmp = x;
	elseif (y <= 1.65e+58)
		tmp = t_1;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+51], t$95$1, If[LessEqual[y, 1.25e-60], x, If[LessEqual[y, 1.65e+58], t$95$1, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3000000000000001e51 or 1.25e-60 < y < 1.64999999999999991e58

   1. Initial program 93.8%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 49.2%

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

      1. mul-1-neg 49.2%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

   6. Simplified 51.8%

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

   if -1.3000000000000001e51 < y < 1.25e-60

   1. Initial program 98.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 56.5%

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

   if 1.64999999999999991e58 < y

   1. Initial program 80.2%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t around inf 55.1%

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

      1. associate-/l* 63.1%

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

   6. Simplified 63.1%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 4: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;-\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.1e+51)
   (* z (/ (- y) a))
   (if (<= y 1.4e-59) x (if (<= y 1.12e+55) (- (/ z (/ a y))) (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+51) {
		tmp = z * (-y / a);
	} else if (y <= 1.4e-59) {
		tmp = x;
	} else if (y <= 1.12e+55) {
		tmp = -(z / (a / y));
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.1d+51)) then
        tmp = z * (-y / a)
    else if (y <= 1.4d-59) then
        tmp = x
    else if (y <= 1.12d+55) then
        tmp = -(z / (a / y))
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+51) {
		tmp = z * (-y / a);
	} else if (y <= 1.4e-59) {
		tmp = x;
	} else if (y <= 1.12e+55) {
		tmp = -(z / (a / y));
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.1e+51:
		tmp = z * (-y / a)
	elif y <= 1.4e-59:
		tmp = x
	elif y <= 1.12e+55:
		tmp = -(z / (a / y))
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.1e+51)
		tmp = Float64(z * Float64(Float64(-y) / a));
	elseif (y <= 1.4e-59)
		tmp = x;
	elseif (y <= 1.12e+55)
		tmp = Float64(-Float64(z / Float64(a / y)));
	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 (y <= -1.1e+51)
		tmp = z * (-y / a);
	elseif (y <= 1.4e-59)
		tmp = x;
	elseif (y <= 1.12e+55)
		tmp = -(z / (a / y));
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.1e+51], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-59], x, If[LessEqual[y, 1.12e+55], (-N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.09999999999999996e51

   1. Initial program 91.6%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in z around inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. associate-*l/ 52.1%

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

      3. *-commutative 52.1%

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

   6. Simplified 52.1%

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

   if -1.09999999999999996e51 < y < 1.3999999999999999e-59

   1. Initial program 98.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 56.5%

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

   if 1.3999999999999999e-59 < y < 1.12000000000000006e55

   1. Initial program 96.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

      1. *-commutative 96.8%

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

      2. clear-num 97.1%

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

      3. un-div-inv 97.0%

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

   5. Applied egg-rr 97.0%

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

   6. Taylor expanded in z around inf 51.2%

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

      1. associate-/l* 49.3%

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

      2. associate-*r/ 49.3%

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

      3. neg-mul-1 49.3%

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

      4. associate-/r/ 51.3%

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

   8. Simplified 51.3%

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

      1. neg-mul-1 51.3%

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

      2. associate-/l* 51.4%

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

      3. associate-*l/ 51.4%

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

      4. neg-mul-1 51.4%

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

   10. Applied egg-rr 51.4%

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

   if 1.12000000000000006e55 < y

   1. Initial program 80.2%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t around inf 55.1%

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

      1. associate-/l* 63.1%

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

   6. Simplified 63.1%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;-\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+186} \lor \neg \left(z \leq 3.5 \cdot 10^{+120}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e+186) (not (<= z 3.5e+120)))
   (* y (/ (- t z) a))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e+186) || !(z <= 3.5e+120)) {
		tmp = y * ((t - 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 <= (-2.7d+186)) .or. (.not. (z <= 3.5d+120))) then
        tmp = y * ((t - 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 <= -2.7e+186) || !(z <= 3.5e+120)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e+186) or not (z <= 3.5e+120):
		tmp = y * ((t - z) / a)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e+186) || !(z <= 3.5e+120))
		tmp = Float64(y * Float64(Float64(t - 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 <= -2.7e+186) || ~((z <= 3.5e+120)))
		tmp = y * ((t - z) / a);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e+186], N[Not[LessEqual[z, 3.5e+120]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e186 or 3.50000000000000007e120 < z

   1. Initial program 84.8%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 72.2%

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

      1. div-sub 78.0%

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

   6. Simplified 78.0%

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

   if -2.6999999999999999e186 < z < 3.50000000000000007e120

   1. Initial program 95.9%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

      1. *-commutative 96.8%

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

      2. clear-num 96.8%

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

      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. Taylor expanded in z around 0 79.8%

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

      1. cancel-sign-sub-inv 79.8%

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

      2. metadata-eval 79.8%

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

      3. *-lft-identity 79.8%

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

      4. +-commutative 79.8%

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

      5. associate-*r/ 80.7%

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

   8. Simplified 80.7%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+186} \lor \neg \left(z \leq 3.5 \cdot 10^{+120}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+21} \lor \neg \left(t \leq 8.5 \cdot 10^{+14}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.1e+21) (not (<= t 8.5e+14)))
   (+ x (* t (/ y a)))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.1e+21) || !(t <= 8.5e+14)) {
		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 ((t <= (-4.1d+21)) .or. (.not. (t <= 8.5d+14))) 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 ((t <= -4.1e+21) || !(t <= 8.5e+14)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.1e+21) or not (t <= 8.5e+14):
		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 ((t <= -4.1e+21) || !(t <= 8.5e+14))
		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 ((t <= -4.1e+21) || ~((t <= 8.5e+14)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.1e+21], N[Not[LessEqual[t, 8.5e+14]], $MachinePrecision]], 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 2 regimes

2. if t < -4.1e21 or 8.5e14 < t

   1. Initial program 90.7%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

      1. *-commutative 97.6%

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

      2. clear-num 97.5%

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

      3. un-div-inv 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in z around 0 82.1%

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

      1. cancel-sign-sub-inv 82.1%

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

      2. metadata-eval 82.1%

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

      3. *-lft-identity 82.1%

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

      4. +-commutative 82.1%

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

      5. associate-*r/ 86.7%

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

   8. Simplified 86.7%

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

   if -4.1e21 < t < 8.5e14

   1. Initial program 94.9%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around inf 82.7%

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

      1. associate-/l* 84.2%

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

   6. Simplified 84.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+21} \lor \neg \left(t \leq 8.5 \cdot 10^{+14}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 7: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+23}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 10^{+15}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+23)
   (- x (/ y (/ (- a) t)))
   (if (<= t 1e+15) (- x (/ y (/ a z))) (+ x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+23) {
		tmp = x - (y / (-a / t));
	} else if (t <= 1e+15) {
		tmp = x - (y / (a / z));
	} 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 (t <= (-1.25d+23)) then
        tmp = x - (y / (-a / t))
    else if (t <= 1d+15) then
        tmp = x - (y / (a / z))
    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 (t <= -1.25e+23) {
		tmp = x - (y / (-a / t));
	} else if (t <= 1e+15) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.25e+23:
		tmp = x - (y / (-a / t))
	elif t <= 1e+15:
		tmp = x - (y / (a / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+23)
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	elseif (t <= 1e+15)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	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 (t <= -1.25e+23)
		tmp = x - (y / (-a / t));
	elseif (t <= 1e+15)
		tmp = x - (y / (a / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+23], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+15], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25e23

   1. Initial program 88.5%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 86.9%

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

      1. associate-*r/ 86.9%

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

      2. neg-mul-1 86.9%

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

   6. Simplified 86.9%

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

   if -1.25e23 < t < 1e15

   1. Initial program 94.9%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around inf 82.7%

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

      1. associate-/l* 84.2%

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

   6. Simplified 84.2%

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

   if 1e15 < t

   1. Initial program 92.6%

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

      1. *-commutative 96.9%

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

      2. clear-num 96.9%

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

      3. un-div-inv 97.0%

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

   5. Applied egg-rr 97.0%

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

   6. Taylor expanded in z around 0 83.8%

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

      1. cancel-sign-sub-inv 83.8%

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

      2. metadata-eval 83.8%

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

      3. *-lft-identity 83.8%

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

      4. +-commutative 83.8%

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

      5. associate-*r/ 86.6%

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

   8. Simplified 86.6%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+23}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 10^{+15}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+114} \lor \neg \left(y \leq 26\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.35e+114) (not (<= y 26.0))) (* y (/ t a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.35e+114) || !(y <= 26.0)) {
		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 <= (-1.35d+114)) .or. (.not. (y <= 26.0d0))) 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 <= -1.35e+114) || !(y <= 26.0)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.35e+114) or not (y <= 26.0):
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.35e+114) || !(y <= 26.0))
		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 <= -1.35e+114) || ~((y <= 26.0)))
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.35e+114], N[Not[LessEqual[y, 26.0]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e114 or 26 < y

   1. Initial program 87.4%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t around inf 49.8%

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

      1. associate-*l/ 54.1%

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

   6. Simplified 54.1%

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

   if -1.35e114 < y < 26

   1. Initial program 97.3%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in x around inf 53.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+114} \lor \neg \left(y \leq 26\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1400:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.5e+51) (* t (/ y a)) (if (<= y 1400.0) x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.5e+51) {
		tmp = t * (y / a);
	} else if (y <= 1400.0) {
		tmp = x;
	} 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 <= (-1.5d+51)) then
        tmp = t * (y / a)
    else if (y <= 1400.0d0) then
        tmp = x
    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 <= -1.5e+51) {
		tmp = t * (y / a);
	} else if (y <= 1400.0) {
		tmp = x;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.5e+51:
		tmp = t * (y / a)
	elif y <= 1400.0:
		tmp = x
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.5e+51)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 1400.0)
		tmp = x;
	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 <= -1.5e+51)
		tmp = t * (y / a);
	elseif (y <= 1400.0)
		tmp = x;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.5e+51], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1400.0], x, N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5e51

   1. Initial program 91.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 45.9%

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

      1. div-inv 45.9%

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

      2. associate-*l* 48.0%

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

      3. div-inv 48.0%

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

      4. *-commutative 48.0%

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

   6. Applied egg-rr 48.0%

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

   if -1.5e51 < y < 1400

   1. Initial program 98.5%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 54.6%

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

   if 1400 < y

   1. Initial program 84.2%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 48.7%

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

      1. associate-*l/ 55.0%

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

   6. Simplified 55.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1400:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 10: 96.9% 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 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 11: 39.8% 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 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

4. Taylor expanded in x around inf 36.4%

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

5. Final simplification 36.4%

   \[\leadsto x \]

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 2023297 
(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)))