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

Percentage Accurate: 93.4% → 97.1%

Time: 11.6s

Alternatives: 11

Speedup: 1.0×

• 25.1% 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: 93.4% 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: 97.1% 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 92.1%

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

   1. *-commutative 92.1%

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

   2. associate-/l* 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 2: 95.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+276} \lor \neg \left(t_1 \leq \infty\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (or (<= t_1 -5e+276) (not (<= t_1 INFINITY)))
     (* y (/ (- z t) a))
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -5e+276) || !(t_1 <= ((double) INFINITY))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -5e+276) || !(t_1 <= Double.POSITIVE_INFINITY)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	tmp = 0
	if (t_1 <= -5e+276) or not (t_1 <= math.inf):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * y)
	tmp = 0.0
	if ((t_1 <= -5e+276) || !(t_1 <= Inf))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * y;
	tmp = 0.0;
	if ((t_1 <= -5e+276) || ~((t_1 <= Inf)))
		tmp = y * ((z - t) / a);
	else
		tmp = x + (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+276], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -5.00000000000000001e276 or +inf.0 < (*.f64 y (-.f64 z t))

   1. Initial program 58.3%

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

   2. Taylor expanded in x around 0 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-*l/ 89.4%

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

   4. Applied egg-rr 89.4%

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

   if -5.00000000000000001e276 < (*.f64 y (-.f64 z t)) < +inf.0

   1. Initial program 96.1%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -5 \cdot 10^{+276} \lor \neg \left(\left(z - t\right) \cdot y \leq \infty\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \]

Alternative 3: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-194} \lor \neg \left(y \leq 6 \cdot 10^{-87} \lor \neg \left(y \leq 2.4 \cdot 10^{-29}\right) \land y \leq 7.6 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9.4e-194)
         (not (or (<= y 6e-87) (and (not (<= y 2.4e-29)) (<= y 7.6e-19)))))
   (* y (/ (- z t) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9.4e-194) || !((y <= 6e-87) || (!(y <= 2.4e-29) && (y <= 7.6e-19)))) {
		tmp = y * ((z - 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 <= (-9.4d-194)) .or. (.not. (y <= 6d-87) .or. (.not. (y <= 2.4d-29)) .and. (y <= 7.6d-19))) then
        tmp = y * ((z - 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 <= -9.4e-194) || !((y <= 6e-87) || (!(y <= 2.4e-29) && (y <= 7.6e-19)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9.4e-194) or not ((y <= 6e-87) or (not (y <= 2.4e-29) and (y <= 7.6e-19))):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9.4e-194) || !((y <= 6e-87) || (!(y <= 2.4e-29) && (y <= 7.6e-19))))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -9.4e-194) || ~(((y <= 6e-87) || (~((y <= 2.4e-29)) && (y <= 7.6e-19)))))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9.4e-194], N[Not[Or[LessEqual[y, 6e-87], And[N[Not[LessEqual[y, 2.4e-29]], $MachinePrecision], LessEqual[y, 7.6e-19]]]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.4000000000000005e-194 or 6.00000000000000033e-87 < y < 2.39999999999999992e-29 or 7.6e-19 < y

   1. Initial program 89.9%

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

   2. Taylor expanded in x around 0 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-*l/ 70.8%

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

   4. Applied egg-rr 70.8%

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

   if -9.4000000000000005e-194 < y < 6.00000000000000033e-87 or 2.39999999999999992e-29 < y < 7.6e-19

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 70.8%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-194} \lor \neg \left(y \leq 6 \cdot 10^{-87} \lor \neg \left(y \leq 2.4 \cdot 10^{-29}\right) \land y \leq 7.6 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 47.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-95} \lor \neg \left(a \leq -6.5 \cdot 10^{-131}\right) \land a \leq 0.00055:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e+73)
   x
   (if (or (<= a -9.4e-95) (and (not (<= a -6.5e-131)) (<= a 0.00055)))
     (* y (/ z a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+73) {
		tmp = x;
	} else if ((a <= -9.4e-95) || (!(a <= -6.5e-131) && (a <= 0.00055))) {
		tmp = y * (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 <= (-7d+73)) then
        tmp = x
    else if ((a <= (-9.4d-95)) .or. (.not. (a <= (-6.5d-131))) .and. (a <= 0.00055d0)) then
        tmp = y * (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 <= -7e+73) {
		tmp = x;
	} else if ((a <= -9.4e-95) || (!(a <= -6.5e-131) && (a <= 0.00055))) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e+73:
		tmp = x
	elif (a <= -9.4e-95) or (not (a <= -6.5e-131) and (a <= 0.00055)):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e+73)
		tmp = x;
	elseif ((a <= -9.4e-95) || (!(a <= -6.5e-131) && (a <= 0.00055)))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e+73)
		tmp = x;
	elseif ((a <= -9.4e-95) || (~((a <= -6.5e-131)) && (a <= 0.00055)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e+73], x, If[Or[LessEqual[a, -9.4e-95], And[N[Not[LessEqual[a, -6.5e-131]], $MachinePrecision], LessEqual[a, 0.00055]]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -7.00000000000000004e73 or -9.3999999999999995e-95 < a < -6.5000000000000002e-131 or 5.50000000000000033e-4 < a

   1. Initial program 86.8%

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

   2. Taylor expanded in x around inf 57.4%

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

   if -7.00000000000000004e73 < a < -9.3999999999999995e-95 or -6.5000000000000002e-131 < a < 5.50000000000000033e-4

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 70.1%

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

      1. associate-*l/ 71.8%

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

      2. *-commutative 71.8%

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

   4. Simplified 71.8%

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

      1. clear-num 71.7%

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

      2. un-div-inv 70.9%

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

   6. Applied egg-rr 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/r/ 67.0%

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

      3. fma-def 67.0%

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

   8. Applied egg-rr 67.0%

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

   9. Taylor expanded in z around inf 58.3%

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

       1. associate-*r/ 54.6%

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

   11. Simplified 54.6%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-95} \lor \neg \left(a \leq -6.5 \cdot 10^{-131}\right) \land a \leq 0.00055:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y a))))
   (if (<= a -4.2e+73)
     x
     (if (<= a 1.65e-247)
       t_1
       (if (<= a 2.7e-159) (* y (/ (- t) a)) (if (<= a 3.9e-10) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / a);
	double tmp;
	if (a <= -4.2e+73) {
		tmp = x;
	} else if (a <= 1.65e-247) {
		tmp = t_1;
	} else if (a <= 2.7e-159) {
		tmp = y * (-t / a);
	} else if (a <= 3.9e-10) {
		tmp = t_1;
	} 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 <= (-4.2d+73)) then
        tmp = x
    else if (a <= 1.65d-247) then
        tmp = t_1
    else if (a <= 2.7d-159) then
        tmp = y * (-t / a)
    else if (a <= 3.9d-10) then
        tmp = t_1
    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 <= -4.2e+73) {
		tmp = x;
	} else if (a <= 1.65e-247) {
		tmp = t_1;
	} else if (a <= 2.7e-159) {
		tmp = y * (-t / a);
	} else if (a <= 3.9e-10) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / a)
	tmp = 0
	if a <= -4.2e+73:
		tmp = x
	elif a <= 1.65e-247:
		tmp = t_1
	elif a <= 2.7e-159:
		tmp = y * (-t / a)
	elif a <= 3.9e-10:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / a))
	tmp = 0.0
	if (a <= -4.2e+73)
		tmp = x;
	elseif (a <= 1.65e-247)
		tmp = t_1;
	elseif (a <= 2.7e-159)
		tmp = Float64(y * Float64(Float64(-t) / a));
	elseif (a <= 3.9e-10)
		tmp = t_1;
	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 <= -4.2e+73)
		tmp = x;
	elseif (a <= 1.65e-247)
		tmp = t_1;
	elseif (a <= 2.7e-159)
		tmp = y * (-t / a);
	elseif (a <= 3.9e-10)
		tmp = t_1;
	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, -4.2e+73], x, If[LessEqual[a, 1.65e-247], t$95$1, If[LessEqual[a, 2.7e-159], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-10], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.2000000000000003e73 or 3.9e-10 < a

   1. Initial program 85.8%

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

   2. Taylor expanded in x around inf 57.9%

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

   if -4.2000000000000003e73 < a < 1.64999999999999986e-247 or 2.7e-159 < a < 3.9e-10

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 83.7%

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

   3. Taylor expanded in z around inf 59.9%

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

      1. associate-*l/ 76.6%

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

      2. *-commutative 76.6%

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

   5. Simplified 61.9%

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

   if 1.64999999999999986e-247 < a < 2.7e-159

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 80.2%

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

   3. Taylor expanded in z around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. associate-*l/ 58.9%

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

      3. distribute-rgt-neg-in 58.9%

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

   5. Simplified 58.9%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-247}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-84}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-35}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e-84)
   (+ x (* z (/ y a)))
   (if (<= z 1.18e-35) (- x (* t (/ y a))) (+ x (/ z (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e-84) {
		tmp = x + (z * (y / a));
	} else if (z <= 1.18e-35) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.95d-84)) then
        tmp = x + (z * (y / a))
    else if (z <= 1.18d-35) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e-84) {
		tmp = x + (z * (y / a));
	} else if (z <= 1.18e-35) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e-84:
		tmp = x + (z * (y / a))
	elif z <= 1.18e-35:
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e-84)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (z <= 1.18e-35)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e-84)
		tmp = x + (z * (y / a));
	elseif (z <= 1.18e-35)
		tmp = x - (t * (y / a));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e-84], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.18e-35], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95000000000000011e-84

   1. Initial program 92.9%

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

   2. Taylor expanded in z around inf 80.3%

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

      1. associate-*l/ 84.7%

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

      2. *-commutative 84.7%

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

   4. Simplified 84.7%

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

   if -1.95000000000000011e-84 < z < 1.17999999999999999e-35

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-*l/ 92.0%

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

      3. unsub-neg 92.0%

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

      4. associate-*l/ 90.3%

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

      5. associate-*r/ 91.3%

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

   4. Simplified 91.3%

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

   if 1.17999999999999999e-35 < z

   1. Initial program 89.1%

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

   2. Taylor expanded in z around inf 81.6%

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

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

   4. Simplified 85.0%

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

      1. clear-num 85.0%

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

      2. un-div-inv 85.0%

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

   6. Applied egg-rr 85.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-84}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-35}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-84}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{-34}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e-84)
   (+ x (* z (/ y a)))
   (if (<= z 1e-34) (- x (* y (/ t a))) (+ x (/ z (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-84) {
		tmp = x + (z * (y / a));
	} else if (z <= 1e-34) {
		tmp = x - (y * (t / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d-84)) then
        tmp = x + (z * (y / a))
    else if (z <= 1d-34) then
        tmp = x - (y * (t / a))
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-84) {
		tmp = x + (z * (y / a));
	} else if (z <= 1e-34) {
		tmp = x - (y * (t / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e-84:
		tmp = x + (z * (y / a))
	elif z <= 1e-34:
		tmp = x - (y * (t / a))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e-84)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (z <= 1e-34)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e-84)
		tmp = x + (z * (y / a));
	elseif (z <= 1e-34)
		tmp = x - (y * (t / a));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e-84], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-34], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000001e-84

   1. Initial program 92.9%

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

   2. Taylor expanded in z around inf 80.3%

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

      1. associate-*l/ 84.7%

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

      2. *-commutative 84.7%

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

   4. Simplified 84.7%

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

   if -2.0000000000000001e-84 < z < 9.99999999999999928e-35

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-*l/ 92.0%

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

      3. unsub-neg 92.0%

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

      4. *-commutative 92.0%

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

   4. Simplified 92.0%

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

   if 9.99999999999999928e-35 < z

   1. Initial program 89.1%

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

   2. Taylor expanded in z around inf 81.6%

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

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

   4. Simplified 85.0%

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

      1. clear-num 85.0%

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

      2. un-div-inv 85.0%

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

   6. Applied egg-rr 85.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-84}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{-34}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-84}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-36}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e-84)
   (+ x (* z (/ y a)))
   (if (<= z 3.6e-36) (- x (/ t (/ a y))) (+ x (/ z (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-84) {
		tmp = x + (z * (y / a));
	} else if (z <= 3.6e-36) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d-84)) then
        tmp = x + (z * (y / a))
    else if (z <= 3.6d-36) then
        tmp = x - (t / (a / y))
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-84) {
		tmp = x + (z * (y / a));
	} else if (z <= 3.6e-36) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e-84:
		tmp = x + (z * (y / a))
	elif z <= 3.6e-36:
		tmp = x - (t / (a / y))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e-84)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (z <= 3.6e-36)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e-84)
		tmp = x + (z * (y / a));
	elseif (z <= 3.6e-36)
		tmp = x - (t / (a / y));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e-84], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-36], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000001e-84

   1. Initial program 92.9%

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

   2. Taylor expanded in z around inf 80.3%

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

      1. associate-*l/ 84.7%

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

      2. *-commutative 84.7%

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

   4. Simplified 84.7%

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

   if -2.0000000000000001e-84 < z < 3.60000000000000032e-36

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-*l/ 92.0%

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

      3. unsub-neg 92.0%

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

      4. *-commutative 92.0%

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

   4. Simplified 92.0%

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

   5. Taylor expanded in y around 0 90.3%

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

      1. associate-/l* 92.1%

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

   7. Simplified 92.1%

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

   if 3.60000000000000032e-36 < z

   1. Initial program 89.1%

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

   2. Taylor expanded in z around inf 81.6%

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

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

   4. Simplified 85.0%

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

      1. clear-num 85.0%

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

      2. un-div-inv 85.0%

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

   6. Applied egg-rr 85.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-84}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-36}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e+74) x (if (<= a 5.4e-12) (* z (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+74) {
		tmp = x;
	} else if (a <= 5.4e-12) {
		tmp = z * (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 (a <= (-2.1d+74)) then
        tmp = x
    else if (a <= 5.4d-12) then
        tmp = z * (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 (a <= -2.1e+74) {
		tmp = x;
	} else if (a <= 5.4e-12) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e+74:
		tmp = x
	elif a <= 5.4e-12:
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+74)
		tmp = x;
	elseif (a <= 5.4e-12)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e+74)
		tmp = x;
	elseif (a <= 5.4e-12)
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+74], x, If[LessEqual[a, 5.4e-12], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.0999999999999999e74 or 5.39999999999999961e-12 < a

   1. Initial program 85.8%

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

   2. Taylor expanded in x around inf 57.9%

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

   if -2.0999999999999999e74 < a < 5.39999999999999961e-12

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 83.3%

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

   3. Taylor expanded in z around inf 55.5%

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

      1. associate-*l/ 72.4%

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

      2. *-commutative 72.4%

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

   5. Simplified 58.0%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.4 \cdot 10^{+184}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 6.4e+184) (+ x (* z (/ y a))) (* t (/ (- y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 6.4e+184) {
		tmp = x + (z * (y / a));
	} else {
		tmp = 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 <= 6.4d+184) then
        tmp = x + (z * (y / a))
    else
        tmp = 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 <= 6.4e+184) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t * (-y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 6.4e+184:
		tmp = x + (z * (y / a))
	else:
		tmp = t * (-y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 6.4e+184)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(-y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 6.4e+184)
		tmp = x + (z * (y / a));
	else
		tmp = t * (-y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 6.4e+184], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.39999999999999966e184

   1. Initial program 92.9%

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

   2. Taylor expanded in z around inf 74.6%

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

      1. associate-*l/ 79.1%

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

      2. *-commutative 79.1%

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

   4. Simplified 79.1%

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

   if 6.39999999999999966e184 < t

   1. Initial program 83.6%

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

   2. Taylor expanded in z around 0 79.4%

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

      1. mul-1-neg 79.4%

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

      2. associate-*l/ 83.3%

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

      3. unsub-neg 83.3%

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

      4. *-commutative 83.3%

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

   4. Simplified 83.3%

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

   5. Taylor expanded in y around 0 79.4%

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

      1. associate-/l* 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in x around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-*r/ 74.8%

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

      3. distribute-rgt-neg-out 74.8%

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

      4. distribute-neg-frac 74.8%

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

   10. Simplified 74.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.4 \cdot 10^{+184}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \end{array} \]

Alternative 11: 39.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

2. Taylor expanded in x around inf 37.4%

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

3. Final simplification 37.4%

   \[\leadsto x \]

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 2023336 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))