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

Percentage Accurate: 92.9% → 97.0%

Time: 9.0s

Alternatives: 10

Speedup: 1.0×

• 24.7% 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: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.8%

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

   1. sub-neg N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

   3. distribute-neg-frac N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

   5. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

   8. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

   10. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

   11. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

   12. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

   13. --lowering--.f64 97.3%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

3. Simplified 97.3%

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

Alternative 2: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+29}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+29)
   (- x (/ y (/ a z)))
   (if (<= z 1.02e+108) (+ x (* (/ y a) t)) (- x (/ (* y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+29) {
		tmp = x - (y / (a / z));
	} else if (z <= 1.02e+108) {
		tmp = x + ((y / a) * t);
	} 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 (z <= (-1.8d+29)) then
        tmp = x - (y / (a / z))
    else if (z <= 1.02d+108) then
        tmp = x + ((y / a) * t)
    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 (z <= -1.8e+29) {
		tmp = x - (y / (a / z));
	} else if (z <= 1.02e+108) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+29:
		tmp = x - (y / (a / z))
	elif z <= 1.02e+108:
		tmp = x + ((y / a) * t)
	else:
		tmp = x - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+29)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif (z <= 1.02e+108)
		tmp = Float64(x + Float64(Float64(y / a) * t));
	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 (z <= -1.8e+29)
		tmp = x - (y / (a / z));
	elseif (z <= 1.02e+108)
		tmp = x + ((y / a) * t);
	else
		tmp = x - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+29], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+108], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999988e29

   1. Initial program 84.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{\left(y \cdot z\right)}, a\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 77.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right)\right) \]

   5. Simplified 77.7%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      6. /-lowering-/.f64 84.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 84.3%

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

   if -1.79999999999999988e29 < z < 1.02e108

   1. Initial program 95.9%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 96.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \color{blue}{t}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 88.7%

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

   if 1.02e108 < z

   1. Initial program 93.9%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{\left(y \cdot z\right)}, a\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 85.5%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right)\right) \]

   5. Simplified 85.5%

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

Alternative 3: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+31}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+115}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+31)
   (- x (/ y (/ a z)))
   (if (<= z 3.6e+115) (+ x (* (/ y a) t)) (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+31) {
		tmp = x - (y / (a / z));
	} else if (z <= 3.6e+115) {
		tmp = x + ((y / a) * t);
	} 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 <= (-4d+31)) then
        tmp = x - (y / (a / z))
    else if (z <= 3.6d+115) then
        tmp = x + ((y / a) * t)
    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 <= -4e+31) {
		tmp = x - (y / (a / z));
	} else if (z <= 3.6e+115) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+31:
		tmp = x - (y / (a / z))
	elif z <= 3.6e+115:
		tmp = x + ((y / a) * t)
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+31)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif (z <= 3.6e+115)
		tmp = Float64(x + Float64(Float64(y / a) * t));
	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 <= -4e+31)
		tmp = x - (y / (a / z));
	elseif (z <= 3.6e+115)
		tmp = x + ((y / a) * t);
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+31], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+115], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9999999999999999e31

   1. Initial program 84.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{\left(y \cdot z\right)}, a\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 77.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right)\right) \]

   5. Simplified 77.7%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      6. /-lowering-/.f64 84.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 84.3%

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

   if -3.9999999999999999e31 < z < 3.6000000000000001e115

   1. Initial program 96.0%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 96.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \color{blue}{t}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 88.3%

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

   if 3.6000000000000001e115 < z

   1. Initial program 93.5%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{\left(\frac{y}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\frac{\color{blue}{y}}{a}\right)\right) \]

      5. /-lowering-/.f64 82.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   7. Simplified 82.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+31}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+115}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+27}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+115}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+27)
   (- x (* y (/ z a)))
   (if (<= z 2.2e+115) (+ x (* (/ y a) t)) (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+27) {
		tmp = x - (y * (z / a));
	} else if (z <= 2.2e+115) {
		tmp = x + ((y / a) * t);
	} 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 <= (-9d+27)) then
        tmp = x - (y * (z / a))
    else if (z <= 2.2d+115) then
        tmp = x + ((y / a) * t)
    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 <= -9e+27) {
		tmp = x - (y * (z / a));
	} else if (z <= 2.2e+115) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+27:
		tmp = x - (y * (z / a))
	elif z <= 2.2e+115:
		tmp = x + ((y / a) * t)
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+27)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (z <= 2.2e+115)
		tmp = Float64(x + Float64(Float64(y / a) * t));
	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 <= -9e+27)
		tmp = x - (y * (z / a));
	elseif (z <= 2.2e+115)
		tmp = x + ((y / a) * t);
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+27], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+115], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999998e27

   1. Initial program 84.5%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 96.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 96.3%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      6. /-lowering-/.f64 82.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 82.9%

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

   if -8.9999999999999998e27 < z < 2.2e115

   1. Initial program 96.0%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 96.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \color{blue}{t}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 88.3%

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

   if 2.2e115 < z

   1. Initial program 93.5%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{\left(\frac{y}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\frac{\color{blue}{y}}{a}\right)\right) \]

      5. /-lowering-/.f64 82.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   7. Simplified 82.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+27}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+115}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t z))))
   (if (<= z -1.1e+35) t_1 (if (<= z 2.7e+114) (+ x (* (/ y a) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (z <= -1.1e+35) {
		tmp = t_1;
	} else if (z <= 2.7e+114) {
		tmp = x + ((y / a) * t);
	} 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 = (y / a) * (t - z)
    if (z <= (-1.1d+35)) then
        tmp = t_1
    else if (z <= 2.7d+114) then
        tmp = x + ((y / a) * t)
    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 = (y / a) * (t - z);
	double tmp;
	if (z <= -1.1e+35) {
		tmp = t_1;
	} else if (z <= 2.7e+114) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (t - z)
	tmp = 0
	if z <= -1.1e+35:
		tmp = t_1
	elif z <= 2.7e+114:
		tmp = x + ((y / a) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(t - z))
	tmp = 0.0
	if (z <= -1.1e+35)
		tmp = t_1;
	elseif (z <= 2.7e+114)
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * (t - z);
	tmp = 0.0;
	if (z <= -1.1e+35)
		tmp = t_1;
	elseif (z <= 2.7e+114)
		tmp = x + ((y / a) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+35], t$95$1, If[LessEqual[z, 2.7e+114], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0999999999999999e35 or 2.7e114 < z

   1. Initial program 88.3%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 97.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{\left(\frac{y}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\frac{\color{blue}{y}}{a}\right)\right) \]

      5. /-lowering-/.f64 76.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   7. Simplified 76.9%

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

   if -1.0999999999999999e35 < z < 2.7e114

   1. Initial program 96.0%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 96.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \color{blue}{t}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 88.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+35}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+115}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t z))))
   (if (<= z -4.6e+37) t_1 (if (<= z 3.5e+115) (+ x (* y (/ t a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (z <= -4.6e+37) {
		tmp = t_1;
	} else if (z <= 3.5e+115) {
		tmp = x + (y * (t / a));
	} 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 = (y / a) * (t - z)
    if (z <= (-4.6d+37)) then
        tmp = t_1
    else if (z <= 3.5d+115) then
        tmp = x + (y * (t / a))
    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 = (y / a) * (t - z);
	double tmp;
	if (z <= -4.6e+37) {
		tmp = t_1;
	} else if (z <= 3.5e+115) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (t - z)
	tmp = 0
	if z <= -4.6e+37:
		tmp = t_1
	elif z <= 3.5e+115:
		tmp = x + (y * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(t - z))
	tmp = 0.0
	if (z <= -4.6e+37)
		tmp = t_1;
	elseif (z <= 3.5e+115)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * (t - z);
	tmp = 0.0;
	if (z <= -4.6e+37)
		tmp = t_1;
	elseif (z <= 3.5e+115)
		tmp = x + (y * (t / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+37], t$95$1, If[LessEqual[z, 3.5e+115], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.60000000000000005e37 or 3.50000000000000005e115 < z

   1. Initial program 88.3%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 97.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{\left(\frac{y}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\frac{\color{blue}{y}}{a}\right)\right) \]

      5. /-lowering-/.f64 76.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   7. Simplified 76.9%

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

   if -4.60000000000000005e37 < z < 3.50000000000000005e115

   1. Initial program 96.0%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 96.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 96.9%

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

   5. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot t}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 88.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 88.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+115}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.06e+71) x (if (<= a 1.6e+38) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.06e+71) {
		tmp = x;
	} else if (a <= 1.6e+38) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.06d+71)) then
        tmp = x
    else if (a <= 1.6d+38) then
        tmp = (y / a) * (t - z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.06e+71) {
		tmp = x;
	} else if (a <= 1.6e+38) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.06e+71:
		tmp = x
	elif a <= 1.6e+38:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.06e+71)
		tmp = x;
	elseif (a <= 1.6e+38)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.06e+71)
		tmp = x;
	elseif (a <= 1.6e+38)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.06e+71], x, If[LessEqual[a, 1.6e+38], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.06e71 or 1.59999999999999993e38 < a

   1. Initial program 83.2%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 97.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 63.1%

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

   if -1.06e71 < a < 1.59999999999999993e38

   1. Initial program 99.2%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 96.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 96.9%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{\left(\frac{y}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\frac{\color{blue}{y}}{a}\right)\right) \]

      5. /-lowering-/.f64 78.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   7. Simplified 78.3%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.3e+106) (/ t (/ a y)) (if (<= t 2.8e-23) x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e+106) {
		tmp = t / (a / y);
	} else if (t <= 2.8e-23) {
		tmp = x;
	} else {
		tmp = (y / a) * 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 (t <= (-2.3d+106)) then
        tmp = t / (a / y)
    else if (t <= 2.8d-23) then
        tmp = x
    else
        tmp = (y / a) * 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 (t <= -2.3e+106) {
		tmp = t / (a / y);
	} else if (t <= 2.8e-23) {
		tmp = x;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.3e+106:
		tmp = t / (a / y)
	elif t <= 2.8e-23:
		tmp = x
	else:
		tmp = (y / a) * t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.3e+106)
		tmp = Float64(t / Float64(a / y));
	elseif (t <= 2.8e-23)
		tmp = x;
	else
		tmp = Float64(Float64(y / a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.3e+106)
		tmp = t / (a / y);
	elseif (t <= 2.8e-23)
		tmp = x;
	else
		tmp = (y / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.3e+106], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-23], x, N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3000000000000002e106

   1. Initial program 86.7%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{\left(\frac{y}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\frac{\color{blue}{y}}{a}\right)\right) \]

      5. /-lowering-/.f64 78.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   7. Simplified 78.1%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(y, a\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 66.4%

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

       1. clear-num N/A

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

       2. div-inv N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{y}\right)}\right) \]

       4. /-lowering-/.f64 66.5%

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right) \]

   12. Applied egg-rr 66.5%

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

   if -2.3000000000000002e106 < t < 2.7999999999999997e-23

   1. Initial program 94.9%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 95.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 95.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 48.1%

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

   if 2.7999999999999997e-23 < t

   1. Initial program 92.1%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 99.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.0%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{\left(\frac{y}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\frac{\color{blue}{y}}{a}\right)\right) \]

      5. /-lowering-/.f64 73.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   7. Simplified 73.7%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(y, a\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 55.1%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot t\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) t)))
   (if (<= t -2.1e+106) t_1 (if (<= t 1.45e-23) x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * t;
	double tmp;
	if (t <= -2.1e+106) {
		tmp = t_1;
	} else if (t <= 1.45e-23) {
		tmp = x;
	} 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 = (y / a) * t
    if (t <= (-2.1d+106)) then
        tmp = t_1
    else if (t <= 1.45d-23) then
        tmp = x
    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 = (y / a) * t;
	double tmp;
	if (t <= -2.1e+106) {
		tmp = t_1;
	} else if (t <= 1.45e-23) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * t
	tmp = 0
	if t <= -2.1e+106:
		tmp = t_1
	elif t <= 1.45e-23:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * t)
	tmp = 0.0
	if (t <= -2.1e+106)
		tmp = t_1;
	elseif (t <= 1.45e-23)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * t;
	tmp = 0.0;
	if (t <= -2.1e+106)
		tmp = t_1;
	elseif (t <= 1.45e-23)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.1e+106], t$95$1, If[LessEqual[t, 1.45e-23], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.10000000000000005e106 or 1.4500000000000001e-23 < t

   1. Initial program 90.5%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{\left(\frac{y}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\frac{\color{blue}{y}}{a}\right)\right) \]

      5. /-lowering-/.f64 75.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   7. Simplified 75.0%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(y, a\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 58.5%

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

   if -2.10000000000000005e106 < t < 1.4500000000000001e-23

   1. Initial program 94.9%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

      5. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

      13. --lowering--.f64 95.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 95.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 48.1%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.5% 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 92.8%

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

   1. sub-neg N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot \left(z - t\right)}{a}\right)\right)}\right) \]

   3. distribute-neg-frac N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\mathsf{neg}\left(y \cdot \left(z - t\right)\right)}{\color{blue}{a}}\right)\right) \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}{a}\right)\right) \]

   5. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(z - t\right)\right)\right)}\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(z - t\right)}\right)\right)\right)\right) \]

   8. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)\right)\right)\right) \]

   10. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

   11. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - \color{blue}{z}\right)\right)\right) \]

   12. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(t - z\right)\right)\right) \]

   13. --lowering--.f64 97.3%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

3. Simplified 97.3%

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

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 36.9%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 99.0% 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 2024138 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t)))))))

  (- x (/ (* y (- z t)) a)))