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

Percentage Accurate: 93.3% → 97.5%

Time: 11.4s

Alternatives: 14

Speedup: 0.6×

• 24.5% 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: 93.3% 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: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e-60) (+ x (* y (/ (- t z) a))) (- x (/ (- z t) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e-60) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - ((z - 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 (a <= (-3.1d-60)) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x - ((z - 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 (a <= -3.1e-60) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - ((z - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e-60:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x - ((z - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e-60)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x - Float64(Float64(z - t) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.1e-60)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x - ((z - t) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e-60], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.09999999999999988e-60

   1. Initial program 88.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -3.09999999999999988e-60 < a

   1. Initial program 97.7%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in y around 0 97.7%

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

      1. associate-*l/ 98.3%

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

      2. *-commutative 98.3%

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

   7. Simplified 98.3%

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

      1. clear-num 98.2%

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

      2. un-div-inv 98.9%

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

   9. Applied egg-rr 98.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{-a}\\ \mathbf{if}\;y \leq -0.072:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2050000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+130}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a)))))
   (if (<= y -0.072)
     t_1
     (if (<= y -1e-30)
       x
       (if (<= y -1.52e-58)
         t_1
         (if (<= y -6.6e-93)
           (/ t (/ a y))
           (if (<= y 2050000000000.0)
             x
             (if (<= y 3.5e+130)
               (/ (* y t) a)
               (if (<= y 6e+150) t_1 (* t (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / -a);
	double tmp;
	if (y <= -0.072) {
		tmp = t_1;
	} else if (y <= -1e-30) {
		tmp = x;
	} else if (y <= -1.52e-58) {
		tmp = t_1;
	} else if (y <= -6.6e-93) {
		tmp = t / (a / y);
	} else if (y <= 2050000000000.0) {
		tmp = x;
	} else if (y <= 3.5e+130) {
		tmp = (y * t) / a;
	} else if (y <= 6e+150) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / -a)
    if (y <= (-0.072d0)) then
        tmp = t_1
    else if (y <= (-1d-30)) then
        tmp = x
    else if (y <= (-1.52d-58)) then
        tmp = t_1
    else if (y <= (-6.6d-93)) then
        tmp = t / (a / y)
    else if (y <= 2050000000000.0d0) then
        tmp = x
    else if (y <= 3.5d+130) then
        tmp = (y * t) / a
    else if (y <= 6d+150) then
        tmp = t_1
    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 t_1 = y * (z / -a);
	double tmp;
	if (y <= -0.072) {
		tmp = t_1;
	} else if (y <= -1e-30) {
		tmp = x;
	} else if (y <= -1.52e-58) {
		tmp = t_1;
	} else if (y <= -6.6e-93) {
		tmp = t / (a / y);
	} else if (y <= 2050000000000.0) {
		tmp = x;
	} else if (y <= 3.5e+130) {
		tmp = (y * t) / a;
	} else if (y <= 6e+150) {
		tmp = t_1;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / -a)
	tmp = 0
	if y <= -0.072:
		tmp = t_1
	elif y <= -1e-30:
		tmp = x
	elif y <= -1.52e-58:
		tmp = t_1
	elif y <= -6.6e-93:
		tmp = t / (a / y)
	elif y <= 2050000000000.0:
		tmp = x
	elif y <= 3.5e+130:
		tmp = (y * t) / a
	elif y <= 6e+150:
		tmp = t_1
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(-a)))
	tmp = 0.0
	if (y <= -0.072)
		tmp = t_1;
	elseif (y <= -1e-30)
		tmp = x;
	elseif (y <= -1.52e-58)
		tmp = t_1;
	elseif (y <= -6.6e-93)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 2050000000000.0)
		tmp = x;
	elseif (y <= 3.5e+130)
		tmp = Float64(Float64(y * t) / a);
	elseif (y <= 6e+150)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / -a);
	tmp = 0.0;
	if (y <= -0.072)
		tmp = t_1;
	elseif (y <= -1e-30)
		tmp = x;
	elseif (y <= -1.52e-58)
		tmp = t_1;
	elseif (y <= -6.6e-93)
		tmp = t / (a / y);
	elseif (y <= 2050000000000.0)
		tmp = x;
	elseif (y <= 3.5e+130)
		tmp = (y * t) / a;
	elseif (y <= 6e+150)
		tmp = t_1;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.072], t$95$1, If[LessEqual[y, -1e-30], x, If[LessEqual[y, -1.52e-58], t$95$1, If[LessEqual[y, -6.6e-93], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2050000000000.0], x, If[LessEqual[y, 3.5e+130], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 6e+150], t$95$1, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -0.0719999999999999946 or -1e-30 < y < -1.51999999999999993e-58 or 3.5000000000000001e130 < y < 6.00000000000000025e150

   1. Initial program 85.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. associate-/l* 66.4%

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

      3. distribute-rgt-neg-in 66.4%

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

      4. distribute-neg-frac2 66.4%

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

   7. Simplified 66.4%

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

   if -0.0719999999999999946 < y < -1e-30 or -6.6000000000000003e-93 < y < 2.05e12

   1. Initial program 99.8%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in x around inf 64.8%

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

   if -1.51999999999999993e-58 < y < -6.6000000000000003e-93

   1. Initial program 100.0%

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

      1. associate-/l* 76.8%

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

   3. Simplified 76.8%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in t around inf 51.4%

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

      1. associate-/l* 51.1%

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

   10. Simplified 51.1%

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

       1. clear-num 51.1%

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

       2. div-inv 51.4%

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

   12. Applied egg-rr 51.4%

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

   if 2.05e12 < y < 3.5000000000000001e130

   1. Initial program 96.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 62.0%

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

      1. *-commutative 62.0%

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

   7. Simplified 62.0%

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

   if 6.00000000000000025e150 < y

   1. Initial program 93.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 93.8%

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

      1. associate-*l/ 90.7%

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

      2. *-commutative 90.7%

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

   7. Simplified 90.7%

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

   8. Taylor expanded in t around inf 63.5%

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

      1. associate-/l* 67.1%

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

   10. Simplified 67.1%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.072:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2050000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+130}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-190} \lor \neg \left(y \leq 2.4 \cdot 10^{-164} \lor \neg \left(y \leq 6 \cdot 10^{-149}\right) \land y \leq 1.85 \cdot 10^{-78}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.3e-190)
         (not (or (<= y 2.4e-164) (and (not (<= y 6e-149)) (<= y 1.85e-78)))))
   (* y (/ (- t z) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.3e-190) || !((y <= 2.4e-164) || (!(y <= 6e-149) && (y <= 1.85e-78)))) {
		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 ((y <= (-1.3d-190)) .or. (.not. (y <= 2.4d-164) .or. (.not. (y <= 6d-149)) .and. (y <= 1.85d-78))) 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 ((y <= -1.3e-190) || !((y <= 2.4e-164) || (!(y <= 6e-149) && (y <= 1.85e-78)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.3e-190) or not ((y <= 2.4e-164) or (not (y <= 6e-149) and (y <= 1.85e-78))):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.3e-190) || !((y <= 2.4e-164) || (!(y <= 6e-149) && (y <= 1.85e-78))))
		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 ((y <= -1.3e-190) || ~(((y <= 2.4e-164) || (~((y <= 6e-149)) && (y <= 1.85e-78)))))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.3e-190], N[Not[Or[LessEqual[y, 2.4e-164], And[N[Not[LessEqual[y, 6e-149]], $MachinePrecision], LessEqual[y, 1.85e-78]]]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.2999999999999999e-190 or 2.39999999999999983e-164 < y < 6.0000000000000003e-149 or 1.85000000000000003e-78 < y

   1. Initial program 93.0%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. distribute-frac-neg2 70.1%

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

      3. sub-neg 70.1%

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

      4. +-commutative 70.1%

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

      5. neg-sub0 70.1%

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(0 - t\right)} + z\right)}{-a} \]

      6. associate--r- 70.1%

         \[\leadsto \frac{y \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}}{-a} \]

      7. neg-sub0 70.1%

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

      8. associate-*r/ 74.3%

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

      9. distribute-neg-frac 74.3%

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

      10. distribute-neg-frac2 74.3%

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

      11. remove-double-neg 74.3%

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

   7. Simplified 74.3%

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

   if -1.2999999999999999e-190 < y < 2.39999999999999983e-164 or 6.0000000000000003e-149 < y < 1.85000000000000003e-78

   1. Initial program 99.9%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in x around inf 80.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-190} \lor \neg \left(y \leq 2.4 \cdot 10^{-164} \lor \neg \left(y \leq 6 \cdot 10^{-149}\right) \land y \leq 1.85 \cdot 10^{-78}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-190}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-164} \lor \neg \left(y \leq 6 \cdot 10^{-149}\right) \land y \leq 8 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.25e-190)
   (* (/ y a) (- t z))
   (if (or (<= y 2.6e-164) (and (not (<= y 6e-149)) (<= y 8e-79)))
     x
     (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.25e-190) {
		tmp = (y / a) * (t - z);
	} else if ((y <= 2.6e-164) || (!(y <= 6e-149) && (y <= 8e-79))) {
		tmp = x;
	} else {
		tmp = y * ((t - z) / 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 <= (-1.25d-190)) then
        tmp = (y / a) * (t - z)
    else if ((y <= 2.6d-164) .or. (.not. (y <= 6d-149)) .and. (y <= 8d-79)) then
        tmp = x
    else
        tmp = y * ((t - z) / 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 <= -1.25e-190) {
		tmp = (y / a) * (t - z);
	} else if ((y <= 2.6e-164) || (!(y <= 6e-149) && (y <= 8e-79))) {
		tmp = x;
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.25e-190:
		tmp = (y / a) * (t - z)
	elif (y <= 2.6e-164) or (not (y <= 6e-149) and (y <= 8e-79)):
		tmp = x
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.25e-190)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif ((y <= 2.6e-164) || (!(y <= 6e-149) && (y <= 8e-79)))
		tmp = x;
	else
		tmp = Float64(y * Float64(Float64(t - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.25e-190)
		tmp = (y / a) * (t - z);
	elseif ((y <= 2.6e-164) || (~((y <= 6e-149)) && (y <= 8e-79)))
		tmp = x;
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.25e-190], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.6e-164], And[N[Not[LessEqual[y, 6e-149]], $MachinePrecision], LessEqual[y, 8e-79]]], x, N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25000000000000009e-190

   1. Initial program 92.7%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around 0 92.7%

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

      1. associate-*l/ 98.8%

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

      2. *-commutative 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in x around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. *-commutative 64.1%

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

      3. associate-*r/ 70.1%

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

      4. *-commutative 70.1%

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

      5. distribute-rgt-neg-in 70.1%

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

      6. neg-sub0 70.1%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(0 - \left(z - t\right)\right)} \]

      7. associate--r- 70.1%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(\left(0 - z\right) + t\right)} \]

      8. neg-sub0 70.1%

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

      9. +-commutative 70.1%

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

      10. sub-neg 70.1%

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

   10. Simplified 70.1%

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

   if -1.25000000000000009e-190 < y < 2.6000000000000002e-164 or 6.0000000000000003e-149 < y < 8e-79

   1. Initial program 99.9%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in x around inf 80.0%

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

   if 2.6000000000000002e-164 < y < 6.0000000000000003e-149 or 8e-79 < y

   1. Initial program 93.2%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. distribute-frac-neg2 76.6%

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

      3. sub-neg 76.6%

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

      4. +-commutative 76.6%

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

      5. neg-sub0 76.6%

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(0 - t\right)} + z\right)}{-a} \]

      6. associate--r- 76.6%

         \[\leadsto \frac{y \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}}{-a} \]

      7. neg-sub0 76.6%

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

      8. associate-*r/ 81.0%

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

      9. distribute-neg-frac 81.0%

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

      10. distribute-neg-frac2 81.0%

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

      11. remove-double-neg 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-190}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-164} \lor \neg \left(y \leq 6 \cdot 10^{-149}\right) \land y \leq 8 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 25500000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.6e-58)
   (* y (/ z (- a)))
   (if (<= z 1.65e-250)
     x
     (if (<= z 2.25e-175)
       (/ y (/ a t))
       (if (<= z 25500000000.0) x (* z (/ y (- a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e-58) {
		tmp = y * (z / -a);
	} else if (z <= 1.65e-250) {
		tmp = x;
	} else if (z <= 2.25e-175) {
		tmp = y / (a / t);
	} else if (z <= 25500000000.0) {
		tmp = x;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.6d-58)) then
        tmp = y * (z / -a)
    else if (z <= 1.65d-250) then
        tmp = x
    else if (z <= 2.25d-175) then
        tmp = y / (a / t)
    else if (z <= 25500000000.0d0) then
        tmp = x
    else
        tmp = z * (y / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e-58) {
		tmp = y * (z / -a);
	} else if (z <= 1.65e-250) {
		tmp = x;
	} else if (z <= 2.25e-175) {
		tmp = y / (a / t);
	} else if (z <= 25500000000.0) {
		tmp = x;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.6e-58:
		tmp = y * (z / -a)
	elif z <= 1.65e-250:
		tmp = x
	elif z <= 2.25e-175:
		tmp = y / (a / t)
	elif z <= 25500000000.0:
		tmp = x
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.6e-58)
		tmp = Float64(y * Float64(z / Float64(-a)));
	elseif (z <= 1.65e-250)
		tmp = x;
	elseif (z <= 2.25e-175)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 25500000000.0)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.6e-58)
		tmp = y * (z / -a);
	elseif (z <= 1.65e-250)
		tmp = x;
	elseif (z <= 2.25e-175)
		tmp = y / (a / t);
	elseif (z <= 25500000000.0)
		tmp = x;
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.6e-58], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-250], x, If[LessEqual[z, 2.25e-175], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 25500000000.0], x, N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.6000000000000001e-58

   1. Initial program 90.2%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around inf 52.7%

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

      1. mul-1-neg 52.7%

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

      2. associate-/l* 57.2%

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

      3. distribute-rgt-neg-in 57.2%

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

      4. distribute-neg-frac2 57.2%

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

   7. Simplified 57.2%

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

   if -5.6000000000000001e-58 < z < 1.65e-250 or 2.24999999999999999e-175 < z < 2.55e10

   1. Initial program 99.9%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around inf 63.9%

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

   if 1.65e-250 < z < 2.24999999999999999e-175

   1. Initial program 93.7%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in t around inf 67.7%

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

      1. *-commutative 67.7%

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

   7. Simplified 67.7%

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

      1. associate-/l* 67.6%

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

      2. *-commutative 67.6%

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

   9. Applied egg-rr 67.6%

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

       1. *-commutative 67.6%

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

       2. clear-num 67.6%

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

       3. un-div-inv 71.4%

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

   11. Applied egg-rr 71.4%

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

   if 2.55e10 < z

   1. Initial program 93.5%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in y around 0 93.5%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. associate-*l/ 56.2%

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

      3. distribute-rgt-neg-in 56.2%

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

   10. Simplified 56.2%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 25500000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.00086:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+207}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ z a)))))
   (if (<= z -5.8e-60)
     t_1
     (if (<= z 0.00086)
       (+ x (/ (* y t) a))
       (if (<= z 1.22e+207) (* (/ y a) (- t z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / a));
	double tmp;
	if (z <= -5.8e-60) {
		tmp = t_1;
	} else if (z <= 0.00086) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.22e+207) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = 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 = x - (y * (z / a))
    if (z <= (-5.8d-60)) then
        tmp = t_1
    else if (z <= 0.00086d0) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.22d+207) then
        tmp = (y / a) * (t - z)
    else
        tmp = 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 = x - (y * (z / a));
	double tmp;
	if (z <= -5.8e-60) {
		tmp = t_1;
	} else if (z <= 0.00086) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.22e+207) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (z / a))
	tmp = 0
	if z <= -5.8e-60:
		tmp = t_1
	elif z <= 0.00086:
		tmp = x + ((y * t) / a)
	elif z <= 1.22e+207:
		tmp = (y / a) * (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (z <= -5.8e-60)
		tmp = t_1;
	elseif (z <= 0.00086)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.22e+207)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (z / a));
	tmp = 0.0;
	if (z <= -5.8e-60)
		tmp = t_1;
	elseif (z <= 0.00086)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.22e+207)
		tmp = (y / a) * (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e-60], t$95$1, If[LessEqual[z, 0.00086], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+207], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.7999999999999999e-60 or 1.21999999999999993e207 < z

   1. Initial program 90.8%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in z around inf 82.8%

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

      1. associate-/l* 81.5%

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

   7. Simplified 81.5%

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

   if -5.7999999999999999e-60 < z < 8.59999999999999979e-4

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. distribute-frac-neg2 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-/l* 97.6%

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

      5. fma-define 97.6%

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

      6. distribute-frac-neg2 97.6%

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

      7. distribute-neg-frac 97.6%

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

      8. sub-neg 97.6%

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

      9. distribute-neg-in 97.6%

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

      10. remove-double-neg 97.6%

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

      11. +-commutative 97.6%

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

      12. sub-neg 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around 0 94.2%

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

   if 8.59999999999999979e-4 < z < 1.21999999999999993e207

   1. Initial program 93.9%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in y around 0 93.9%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*r/ 87.8%

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

      4. *-commutative 87.8%

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

      5. distribute-rgt-neg-in 87.8%

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

      6. neg-sub0 87.8%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(0 - \left(z - t\right)\right)} \]

      7. associate--r- 87.8%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(\left(0 - z\right) + t\right)} \]

      8. neg-sub0 87.8%

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

      9. +-commutative 87.8%

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

      10. sub-neg 87.8%

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

   10. Simplified 87.8%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-60}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 0.00086:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+207}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 38:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+206}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ z (/ a y)))))
   (if (<= z -3.5e-44)
     t_1
     (if (<= z 38.0)
       (+ x (/ (* y t) a))
       (if (<= z 3.8e+206) (* (/ y a) (- t z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z / (a / y));
	double tmp;
	if (z <= -3.5e-44) {
		tmp = t_1;
	} else if (z <= 38.0) {
		tmp = x + ((y * t) / a);
	} else if (z <= 3.8e+206) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = 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 = x - (z / (a / y))
    if (z <= (-3.5d-44)) then
        tmp = t_1
    else if (z <= 38.0d0) then
        tmp = x + ((y * t) / a)
    else if (z <= 3.8d+206) then
        tmp = (y / a) * (t - z)
    else
        tmp = 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 = x - (z / (a / y));
	double tmp;
	if (z <= -3.5e-44) {
		tmp = t_1;
	} else if (z <= 38.0) {
		tmp = x + ((y * t) / a);
	} else if (z <= 3.8e+206) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z / (a / y))
	tmp = 0
	if z <= -3.5e-44:
		tmp = t_1
	elif z <= 38.0:
		tmp = x + ((y * t) / a)
	elif z <= 3.8e+206:
		tmp = (y / a) * (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z / Float64(a / y)))
	tmp = 0.0
	if (z <= -3.5e-44)
		tmp = t_1;
	elseif (z <= 38.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 3.8e+206)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (z / (a / y));
	tmp = 0.0;
	if (z <= -3.5e-44)
		tmp = t_1;
	elseif (z <= 38.0)
		tmp = x + ((y * t) / a);
	elseif (z <= 3.8e+206)
		tmp = (y / a) * (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-44], t$95$1, If[LessEqual[z, 38.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+206], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999998e-44 or 3.7999999999999999e206 < z

   1. Initial program 90.5%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in z around inf 83.1%

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

      1. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

      1. *-commutative 81.8%

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

      2. associate-/r/ 88.7%

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

   9. Applied egg-rr 88.7%

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

   if -3.4999999999999998e-44 < z < 38

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. distribute-frac-neg2 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-/l* 97.7%

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

      5. fma-define 97.7%

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

      6. distribute-frac-neg2 97.7%

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

      7. distribute-neg-frac 97.7%

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

      8. sub-neg 97.7%

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

      9. distribute-neg-in 97.7%

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

      10. remove-double-neg 97.7%

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

      11. +-commutative 97.7%

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

      12. sub-neg 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 93.6%

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

   if 38 < z < 3.7999999999999999e206

   1. Initial program 93.9%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in y around 0 93.9%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*r/ 87.8%

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

      4. *-commutative 87.8%

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

      5. distribute-rgt-neg-in 87.8%

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

      6. neg-sub0 87.8%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(0 - \left(z - t\right)\right)} \]

      7. associate--r- 87.8%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(\left(0 - z\right) + t\right)} \]

      8. neg-sub0 87.8%

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

      9. +-commutative 87.8%

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

      10. sub-neg 87.8%

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

   10. Simplified 87.8%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-44}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 38:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+206}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-189} \lor \neg \left(y \leq 1.2 \cdot 10^{-203}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.9e-189) (not (<= y 1.2e-203)))
   (+ x (* y (/ (- t z) a)))
   (- x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e-189) || !(y <= 1.2e-203)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.9d-189)) .or. (.not. (y <= 1.2d-203))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x - ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e-189) || !(y <= 1.2e-203)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.9e-189) or not (y <= 1.2e-203):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.9e-189) || !(y <= 1.2e-203))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x - Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.9e-189) || ~((y <= 1.2e-203)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.9e-189], N[Not[LessEqual[y, 1.2e-203]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e-189 or 1.1999999999999999e-203 < y

   1. Initial program 93.9%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   if -2.9e-189 < y < 1.1999999999999999e-203

   1. Initial program 99.9%

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

      1. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in z around inf 96.0%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-189} \lor \neg \left(y \leq 1.2 \cdot 10^{-203}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;z \leq 0.92:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.45e-57)
   (* y (/ (- t z) a))
   (if (<= z 0.92) (+ x (/ (* y t) a)) (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.45e-57) {
		tmp = y * ((t - z) / a);
	} else if (z <= 0.92) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.45d-57)) then
        tmp = y * ((t - z) / a)
    else if (z <= 0.92d0) then
        tmp = x + ((y * t) / a)
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.45e-57) {
		tmp = y * ((t - z) / a);
	} else if (z <= 0.92) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.45e-57:
		tmp = y * ((t - z) / a)
	elif z <= 0.92:
		tmp = x + ((y * t) / a)
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.45e-57)
		tmp = Float64(y * Float64(Float64(t - z) / a));
	elseif (z <= 0.92)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.45e-57)
		tmp = y * ((t - z) / a);
	elseif (z <= 0.92)
		tmp = x + ((y * t) / a);
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.45e-57], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.92], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.44999999999999994e-57

   1. Initial program 90.2%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-frac-neg2 63.2%

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

      3. sub-neg 63.2%

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

      4. +-commutative 63.2%

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

      5. neg-sub0 63.2%

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(0 - t\right)} + z\right)}{-a} \]

      6. associate--r- 63.2%

         \[\leadsto \frac{y \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}}{-a} \]

      7. neg-sub0 63.2%

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

      8. associate-*r/ 69.5%

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

      9. distribute-neg-frac 69.5%

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

      10. distribute-neg-frac2 69.5%

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

      11. remove-double-neg 69.5%

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

   7. Simplified 69.5%

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

   if -2.44999999999999994e-57 < z < 0.92000000000000004

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. distribute-frac-neg2 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-/l* 97.6%

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

      5. fma-define 97.6%

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

      6. distribute-frac-neg2 97.6%

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

      7. distribute-neg-frac 97.6%

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

      8. sub-neg 97.6%

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

      9. distribute-neg-in 97.6%

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

      10. remove-double-neg 97.6%

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

      11. +-commutative 97.6%

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

      12. sub-neg 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around 0 94.2%

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

   if 0.92000000000000004 < z

   1. Initial program 93.5%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in y around 0 93.5%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-*r/ 77.8%

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

      4. *-commutative 77.8%

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

      5. distribute-rgt-neg-in 77.8%

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

      6. neg-sub0 77.8%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(0 - \left(z - t\right)\right)} \]

      7. associate--r- 77.8%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(\left(0 - z\right) + t\right)} \]

      8. neg-sub0 77.8%

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

      9. +-commutative 77.8%

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

      10. sub-neg 77.8%

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

   10. Simplified 77.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;z \leq 0.92:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+45} \lor \neg \left(y \leq 50000000000000\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.5e+45) (not (<= y 50000000000000.0))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.5e+45) || !(y <= 50000000000000.0)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5.5d+45)) .or. (.not. (y <= 50000000000000.0d0))) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.5e+45) || !(y <= 50000000000000.0)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.5e+45) or not (y <= 50000000000000.0):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.5e+45) || !(y <= 50000000000000.0))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.5e+45) || ~((y <= 50000000000000.0)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.5e+45], N[Not[LessEqual[y, 50000000000000.0]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000001e45 or 5e13 < y

   1. Initial program 88.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. associate-*l/ 96.3%

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

      2. *-commutative 96.3%

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

   7. Simplified 96.3%

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

   8. Taylor expanded in t around inf 48.7%

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

      1. associate-/l* 53.4%

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

   10. Simplified 53.4%

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

   if -5.5000000000000001e45 < y < 5e13

   1. Initial program 99.8%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in x around inf 60.7%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+45} \lor \neg \left(y \leq 50000000000000\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+41} \lor \neg \left(y \leq 25000000\right):\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.8e+41) (not (<= y 25000000.0))) (/ t (/ a y)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.8e+41) || !(y <= 25000000.0)) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5.8d+41)) .or. (.not. (y <= 25000000.0d0))) then
        tmp = t / (a / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.8e+41) || !(y <= 25000000.0)) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.8e+41) or not (y <= 25000000.0):
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.8e+41) || !(y <= 25000000.0))
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.8e+41) || ~((y <= 25000000.0)))
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.8e+41], N[Not[LessEqual[y, 25000000.0]], $MachinePrecision]], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999977e41 or 2.5e7 < y

   1. Initial program 88.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. associate-*l/ 96.3%

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

      2. *-commutative 96.3%

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

   7. Simplified 96.3%

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

   8. Taylor expanded in t around inf 48.7%

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

      1. associate-/l* 53.4%

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

   10. Simplified 53.4%

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

       1. clear-num 53.4%

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

       2. div-inv 53.5%

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

   12. Applied egg-rr 53.5%

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

   if -5.79999999999999977e41 < y < 2.5e7

   1. Initial program 99.8%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in x around inf 60.7%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+41} \lor \neg \left(y \leq 25000000\right):\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.2e-136) (+ x (* (/ y a) (- t z))) (+ x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.2e-136) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x + (y * ((t - z) / 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 <= 1.2d-136) then
        tmp = x + ((y / a) * (t - z))
    else
        tmp = x + (y * ((t - z) / 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 <= 1.2e-136) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.2e-136:
		tmp = x + ((y / a) * (t - z))
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.2e-136)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.2e-136)
		tmp = x + ((y / a) * (t - z));
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.2e-136], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.1999999999999999e-136

   1. Initial program 95.7%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in y around 0 95.7%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   if 1.1999999999999999e-136 < y

   1. Initial program 93.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.36 \cdot 10^{-114}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.36e-114) (+ x (* (/ y a) (- t z))) (- x (/ y (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.36e-114) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	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 <= 1.36d-114) then
        tmp = x + ((y / a) * (t - z))
    else
        tmp = x - (y / (a / (z - t)))
    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 <= 1.36e-114) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.36e-114:
		tmp = x + ((y / a) * (t - z))
	else:
		tmp = x - (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.36e-114)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	else
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.36e-114)
		tmp = x + ((y / a) * (t - z));
	else
		tmp = x - (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.36e-114], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.3599999999999999e-114

   1. Initial program 95.8%

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

      1. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around 0 95.8%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   if 1.3599999999999999e-114 < y

   1. Initial program 93.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.36 \cdot 10^{-114}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.7% 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 95.0%

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

   1. associate-/l* 94.0%

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

3. Simplified 94.0%

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

5. Taylor expanded in x around inf 41.7%

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

6. Final simplification 41.7%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024066 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (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)))