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

Percentage Accurate: 92.7% → 97.3%

Time: 11.0s

Alternatives: 11

Speedup: 1.0×

• 25.6% 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: 92.7% 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: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-*l/ 96.2%

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

3. Simplified 96.2%

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

5. Final simplification 96.2%

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

Alternative 2: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot t\\ t_2 := \frac{y}{a} \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -8.3 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3800000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) t)) (t_2 (* (/ y a) (- z))))
   (if (<= z -8.3e+77)
     t_2
     (if (<= z -2.7e-102)
       x
       (if (<= z -5.7e-238)
         t_1
         (if (<= z 5.2e-241) x (if (<= z 3800000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * t;
	double t_2 = (y / a) * -z;
	double tmp;
	if (z <= -8.3e+77) {
		tmp = t_2;
	} else if (z <= -2.7e-102) {
		tmp = x;
	} else if (z <= -5.7e-238) {
		tmp = t_1;
	} else if (z <= 5.2e-241) {
		tmp = x;
	} else if (z <= 3800000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (y / a) * t
    t_2 = (y / a) * -z
    if (z <= (-8.3d+77)) then
        tmp = t_2
    else if (z <= (-2.7d-102)) then
        tmp = x
    else if (z <= (-5.7d-238)) then
        tmp = t_1
    else if (z <= 5.2d-241) then
        tmp = x
    else if (z <= 3800000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = (y / a) * -z;
	double tmp;
	if (z <= -8.3e+77) {
		tmp = t_2;
	} else if (z <= -2.7e-102) {
		tmp = x;
	} else if (z <= -5.7e-238) {
		tmp = t_1;
	} else if (z <= 5.2e-241) {
		tmp = x;
	} else if (z <= 3800000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * t
	t_2 = (y / a) * -z
	tmp = 0
	if z <= -8.3e+77:
		tmp = t_2
	elif z <= -2.7e-102:
		tmp = x
	elif z <= -5.7e-238:
		tmp = t_1
	elif z <= 5.2e-241:
		tmp = x
	elif z <= 3800000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * t)
	t_2 = Float64(Float64(y / a) * Float64(-z))
	tmp = 0.0
	if (z <= -8.3e+77)
		tmp = t_2;
	elseif (z <= -2.7e-102)
		tmp = x;
	elseif (z <= -5.7e-238)
		tmp = t_1;
	elseif (z <= 5.2e-241)
		tmp = x;
	elseif (z <= 3800000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * t;
	t_2 = (y / a) * -z;
	tmp = 0.0;
	if (z <= -8.3e+77)
		tmp = t_2;
	elseif (z <= -2.7e-102)
		tmp = x;
	elseif (z <= -5.7e-238)
		tmp = t_1;
	elseif (z <= 5.2e-241)
		tmp = x;
	elseif (z <= 3800000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -8.3e+77], t$95$2, If[LessEqual[z, -2.7e-102], x, If[LessEqual[z, -5.7e-238], t$95$1, If[LessEqual[z, 5.2e-241], x, If[LessEqual[z, 3800000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2999999999999998e77 or 3.8e6 < z

   1. Initial program 93.1%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around inf 82.7%

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

      1. associate-*l/ 86.1%

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

      2. *-commutative 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in x around 0 53.4%

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

      1. associate-*r/ 53.4%

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

      2. *-commutative 53.4%

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

      3. associate-*r/ 53.4%

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

      4. associate-*r/ 56.3%

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

      5. neg-mul-1 56.3%

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

      6. distribute-rgt-neg-in 56.3%

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

   10. Simplified 56.3%

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

   if -8.2999999999999998e77 < z < -2.7e-102 or -5.70000000000000022e-238 < z < 5.1999999999999998e-241

   1. Initial program 96.9%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around inf 75.5%

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

      1. associate-*l/ 77.2%

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

      2. *-commutative 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in x around inf 68.1%

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

   if -2.7e-102 < z < -5.70000000000000022e-238 or 5.1999999999999998e-241 < z < 3.8e6

   1. Initial program 89.8%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around 0 84.8%

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

      1. associate-*r/ 84.8%

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

      2. neg-mul-1 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in x around 0 47.7%

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

      1. associate-*r/ 55.6%

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

   10. Simplified 55.6%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-238}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3800000:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= t -4.1e+96)
     t_1
     (if (<= t 4.5e-60)
       x
       (if (<= t 9e-39) t_1 (if (<= t 3.2e+119) x (* (/ y a) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (t <= -4.1e+96) {
		tmp = t_1;
	} else if (t <= 4.5e-60) {
		tmp = x;
	} else if (t <= 9e-39) {
		tmp = t_1;
	} else if (t <= 3.2e+119) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (t / a)
    if (t <= (-4.1d+96)) then
        tmp = t_1
    else if (t <= 4.5d-60) then
        tmp = x
    else if (t <= 9d-39) then
        tmp = t_1
    else if (t <= 3.2d+119) 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 t_1 = y * (t / a);
	double tmp;
	if (t <= -4.1e+96) {
		tmp = t_1;
	} else if (t <= 4.5e-60) {
		tmp = x;
	} else if (t <= 9e-39) {
		tmp = t_1;
	} else if (t <= 3.2e+119) {
		tmp = x;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if t <= -4.1e+96:
		tmp = t_1
	elif t <= 4.5e-60:
		tmp = x
	elif t <= 9e-39:
		tmp = t_1
	elif t <= 3.2e+119:
		tmp = x
	else:
		tmp = (y / a) * t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (t <= -4.1e+96)
		tmp = t_1;
	elseif (t <= 4.5e-60)
		tmp = x;
	elseif (t <= 9e-39)
		tmp = t_1;
	elseif (t <= 3.2e+119)
		tmp = x;
	else
		tmp = Float64(Float64(y / a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (t <= -4.1e+96)
		tmp = t_1;
	elseif (t <= 4.5e-60)
		tmp = x;
	elseif (t <= 9e-39)
		tmp = t_1;
	elseif (t <= 3.2e+119)
		tmp = x;
	else
		tmp = (y / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+96], t$95$1, If[LessEqual[t, 4.5e-60], x, If[LessEqual[t, 9e-39], t$95$1, If[LessEqual[t, 3.2e+119], x, N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.09999999999999998e96 or 4.50000000000000001e-60 < t < 9.0000000000000002e-39

   1. Initial program 85.6%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around 0 82.1%

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

      1. associate-*r/ 82.1%

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

      2. neg-mul-1 82.1%

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

   7. Simplified 82.1%

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

   8. Taylor expanded in x around 0 62.7%

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

      1. associate-/l* 68.8%

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

      2. associate-/r/ 74.6%

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

   10. Applied egg-rr 74.6%

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

   if -4.09999999999999998e96 < t < 4.50000000000000001e-60 or 9.0000000000000002e-39 < t < 3.19999999999999989e119

   1. Initial program 94.6%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around inf 82.2%

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

      1. associate-*l/ 85.7%

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

      2. *-commutative 85.7%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in x around inf 54.1%

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

   if 3.19999999999999989e119 < t

   1. Initial program 94.0%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in z around 0 74.8%

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

      1. associate-*r/ 74.8%

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

      2. neg-mul-1 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in x around 0 61.0%

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

      1. associate-*r/ 61.7%

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

   10. Simplified 61.7%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.95e+96)
   (* y (/ t a))
   (if (<= t 4.5e-60)
     x
     (if (<= t 5.3e-39) (/ (* y t) a) (if (<= t 6.8e+118) x (* (/ y a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e+96) {
		tmp = y * (t / a);
	} else if (t <= 4.5e-60) {
		tmp = x;
	} else if (t <= 5.3e-39) {
		tmp = (y * t) / a;
	} else if (t <= 6.8e+118) {
		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 <= (-1.95d+96)) then
        tmp = y * (t / a)
    else if (t <= 4.5d-60) then
        tmp = x
    else if (t <= 5.3d-39) then
        tmp = (y * t) / a
    else if (t <= 6.8d+118) 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 <= -1.95e+96) {
		tmp = y * (t / a);
	} else if (t <= 4.5e-60) {
		tmp = x;
	} else if (t <= 5.3e-39) {
		tmp = (y * t) / a;
	} else if (t <= 6.8e+118) {
		tmp = x;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.95e+96:
		tmp = y * (t / a)
	elif t <= 4.5e-60:
		tmp = x
	elif t <= 5.3e-39:
		tmp = (y * t) / a
	elif t <= 6.8e+118:
		tmp = x
	else:
		tmp = (y / a) * t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.95e+96)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= 4.5e-60)
		tmp = x;
	elseif (t <= 5.3e-39)
		tmp = Float64(Float64(y * t) / a);
	elseif (t <= 6.8e+118)
		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 <= -1.95e+96)
		tmp = y * (t / a);
	elseif (t <= 4.5e-60)
		tmp = x;
	elseif (t <= 5.3e-39)
		tmp = (y * t) / a;
	elseif (t <= 6.8e+118)
		tmp = x;
	else
		tmp = (y / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.95e+96], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-60], x, If[LessEqual[t, 5.3e-39], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 6.8e+118], x, N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.95e96

   1. Initial program 83.4%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in z around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. neg-mul-1 82.0%

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

   7. Simplified 82.0%

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

   8. Taylor expanded in x around 0 59.5%

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

      1. associate-/l* 68.9%

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

      2. associate-/r/ 73.3%

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

   10. Applied egg-rr 73.3%

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

   if -1.95e96 < t < 4.50000000000000001e-60 or 5.30000000000000003e-39 < t < 6.79999999999999973e118

   1. Initial program 94.6%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around inf 82.2%

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

      1. associate-*l/ 85.7%

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

      2. *-commutative 85.7%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in x around inf 54.1%

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

   if 4.50000000000000001e-60 < t < 5.30000000000000003e-39

   1. Initial program 100.0%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 83.2%

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

      1. associate-*r/ 83.2%

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

      2. neg-mul-1 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x around 0 83.8%

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

   if 6.79999999999999973e118 < t

   1. Initial program 94.0%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in z around 0 74.8%

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

      1. associate-*r/ 74.8%

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

      2. neg-mul-1 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in x around 0 61.0%

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

      1. associate-*r/ 61.7%

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

   10. Simplified 61.7%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+78}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -3.9e+186)
     t_1
     (if (<= z -1.42e+78)
       (/ (- z) (/ a y))
       (if (<= z 4e+174) t_1 (* (/ y a) (- z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -3.9e+186) {
		tmp = t_1;
	} else if (z <= -1.42e+78) {
		tmp = -z / (a / y);
	} else if (z <= 4e+174) {
		tmp = t_1;
	} else {
		tmp = (y / a) * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-3.9d+186)) then
        tmp = t_1
    else if (z <= (-1.42d+78)) then
        tmp = -z / (a / y)
    else if (z <= 4d+174) then
        tmp = t_1
    else
        tmp = (y / a) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -3.9e+186) {
		tmp = t_1;
	} else if (z <= -1.42e+78) {
		tmp = -z / (a / y);
	} else if (z <= 4e+174) {
		tmp = t_1;
	} else {
		tmp = (y / a) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -3.9e+186:
		tmp = t_1
	elif z <= -1.42e+78:
		tmp = -z / (a / y)
	elif z <= 4e+174:
		tmp = t_1
	else:
		tmp = (y / a) * -z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -3.9e+186)
		tmp = t_1;
	elseif (z <= -1.42e+78)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (z <= 4e+174)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / a) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -3.9e+186)
		tmp = t_1;
	elseif (z <= -1.42e+78)
		tmp = -z / (a / y);
	elseif (z <= 4e+174)
		tmp = t_1;
	else
		tmp = (y / a) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+186], t$95$1, If[LessEqual[z, -1.42e+78], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+174], t$95$1, N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9000000000000001e186 or -1.42e78 < z < 4.00000000000000028e174

   1. Initial program 93.4%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around 0 81.0%

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

      1. associate-*r/ 81.0%

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

      2. neg-mul-1 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in x around 0 79.1%

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

   if -3.9000000000000001e186 < z < -1.42e78

   1. Initial program 88.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 83.1%

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

      1. associate-*l/ 93.9%

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

      2. *-commutative 93.9%

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

   7. Simplified 93.9%

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

   8. Taylor expanded in x around 0 65.8%

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

      1. associate-*r/ 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-*r/ 65.8%

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

      4. associate-*r/ 76.6%

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

      5. neg-mul-1 76.6%

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

      6. distribute-rgt-neg-in 76.6%

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

   10. Simplified 76.6%

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

       1. distribute-rgt-neg-out 76.6%

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

       2. clear-num 76.6%

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

       3. div-inv 76.7%

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

       4. distribute-neg-frac 76.7%

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

   12. Applied egg-rr 76.7%

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

   if 4.00000000000000028e174 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around inf 84.7%

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

      1. associate-*l/ 88.9%

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

      2. *-commutative 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in x around 0 59.7%

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

      1. associate-*r/ 59.7%

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

      2. *-commutative 59.7%

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

      3. associate-*r/ 59.7%

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

      4. associate-*r/ 64.9%

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

      5. neg-mul-1 64.9%

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

      6. distribute-rgt-neg-in 64.9%

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

   10. Simplified 64.9%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+186}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+78}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+174}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+186}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+78}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+174}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+186)
   (+ x (/ (* y t) a))
   (if (<= z -1.42e+78)
     (/ (- z) (/ a y))
     (if (<= z 1.25e+174) (+ x (* y (/ t a))) (* (/ y a) (- z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+186) {
		tmp = x + ((y * t) / a);
	} else if (z <= -1.42e+78) {
		tmp = -z / (a / y);
	} else if (z <= 1.25e+174) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6d+186)) then
        tmp = x + ((y * t) / a)
    else if (z <= (-1.42d+78)) then
        tmp = -z / (a / y)
    else if (z <= 1.25d+174) then
        tmp = x + (y * (t / a))
    else
        tmp = (y / a) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+186) {
		tmp = x + ((y * t) / a);
	} else if (z <= -1.42e+78) {
		tmp = -z / (a / y);
	} else if (z <= 1.25e+174) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+186:
		tmp = x + ((y * t) / a)
	elif z <= -1.42e+78:
		tmp = -z / (a / y)
	elif z <= 1.25e+174:
		tmp = x + (y * (t / a))
	else:
		tmp = (y / a) * -z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+186)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= -1.42e+78)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (z <= 1.25e+174)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+186)
		tmp = x + ((y * t) / a);
	elseif (z <= -1.42e+78)
		tmp = -z / (a / y);
	elseif (z <= 1.25e+174)
		tmp = x + (y * (t / a));
	else
		tmp = (y / a) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+186], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.42e+78], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+174], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.99999999999999964e186

   1. Initial program 94.9%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in z around 0 57.2%

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

      1. associate-*r/ 57.2%

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

      2. neg-mul-1 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in x around 0 57.1%

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

   if -5.99999999999999964e186 < z < -1.42e78

   1. Initial program 88.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 83.1%

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

      1. associate-*l/ 93.9%

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

      2. *-commutative 93.9%

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

   7. Simplified 93.9%

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

   8. Taylor expanded in x around 0 65.8%

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

      1. associate-*r/ 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-*r/ 65.8%

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

      4. associate-*r/ 76.6%

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

      5. neg-mul-1 76.6%

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

      6. distribute-rgt-neg-in 76.6%

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

   10. Simplified 76.6%

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

       1. distribute-rgt-neg-out 76.6%

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

       2. clear-num 76.6%

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

       3. div-inv 76.7%

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

       4. distribute-neg-frac 76.7%

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

   12. Applied egg-rr 76.7%

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

   if -1.42e78 < z < 1.2499999999999999e174

   1. Initial program 93.2%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

      1. clear-num 96.2%

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

      2. associate-/r/ 96.2%

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

      3. clear-num 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in z around 0 83.3%

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

      1. neg-mul-1 83.3%

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

      2. distribute-neg-frac 83.3%

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

   9. Simplified 83.3%

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

       1. sub-neg 83.3%

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

       2. +-commutative 83.3%

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

       3. distribute-lft-neg-in 83.3%

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

       4. distribute-frac-neg 83.3%

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

       5. remove-double-neg 83.3%

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

   11. Applied egg-rr 83.3%

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

   if 1.2499999999999999e174 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around inf 84.7%

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

      1. associate-*l/ 88.9%

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

      2. *-commutative 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in x around 0 59.7%

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

      1. associate-*r/ 59.7%

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

      2. *-commutative 59.7%

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

      3. associate-*r/ 59.7%

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

      4. associate-*r/ 64.9%

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

      5. neg-mul-1 64.9%

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

      6. distribute-rgt-neg-in 64.9%

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

   10. Simplified 64.9%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+186}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+78}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+174}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+78}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= z -3.5e+186)
     t_1
     (if (<= z -1.42e+78)
       (/ (- z) (/ a y))
       (if (<= z 9.2e+173) t_1 (* (/ y a) (- z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (z <= -3.5e+186) {
		tmp = t_1;
	} else if (z <= -1.42e+78) {
		tmp = -z / (a / y);
	} else if (z <= 9.2e+173) {
		tmp = t_1;
	} else {
		tmp = (y / a) * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    if (z <= (-3.5d+186)) then
        tmp = t_1
    else if (z <= (-1.42d+78)) then
        tmp = -z / (a / y)
    else if (z <= 9.2d+173) then
        tmp = t_1
    else
        tmp = (y / a) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (z <= -3.5e+186) {
		tmp = t_1;
	} else if (z <= -1.42e+78) {
		tmp = -z / (a / y);
	} else if (z <= 9.2e+173) {
		tmp = t_1;
	} else {
		tmp = (y / a) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if z <= -3.5e+186:
		tmp = t_1
	elif z <= -1.42e+78:
		tmp = -z / (a / y)
	elif z <= 9.2e+173:
		tmp = t_1
	else:
		tmp = (y / a) * -z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (z <= -3.5e+186)
		tmp = t_1;
	elseif (z <= -1.42e+78)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (z <= 9.2e+173)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / a) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (z <= -3.5e+186)
		tmp = t_1;
	elseif (z <= -1.42e+78)
		tmp = -z / (a / y);
	elseif (z <= 9.2e+173)
		tmp = t_1;
	else
		tmp = (y / a) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+186], t$95$1, If[LessEqual[z, -1.42e+78], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+173], t$95$1, N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999987e186 or -1.42e78 < z < 9.1999999999999998e173

   1. Initial program 93.4%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

      1. clear-num 95.6%

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

      2. associate-/r/ 95.6%

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

      3. clear-num 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in z around 0 80.9%

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

      1. neg-mul-1 80.9%

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

      2. distribute-neg-frac 80.9%

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

   9. Simplified 80.9%

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

       1. sub-neg 80.9%

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

       2. +-commutative 80.9%

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

       3. distribute-lft-neg-in 80.9%

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

       4. distribute-frac-neg 80.9%

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

       5. remove-double-neg 80.9%

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

   11. Applied egg-rr 80.9%

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

       1. *-commutative 80.9%

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

       2. clear-num 80.9%

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

       3. un-div-inv 81.0%

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

   13. Applied egg-rr 81.0%

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

   if -3.49999999999999987e186 < z < -1.42e78

   1. Initial program 88.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 83.1%

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

      1. associate-*l/ 93.9%

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

      2. *-commutative 93.9%

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

   7. Simplified 93.9%

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

   8. Taylor expanded in x around 0 65.8%

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

      1. associate-*r/ 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-*r/ 65.8%

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

      4. associate-*r/ 76.6%

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

      5. neg-mul-1 76.6%

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

      6. distribute-rgt-neg-in 76.6%

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

   10. Simplified 76.6%

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

       1. distribute-rgt-neg-out 76.6%

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

       2. clear-num 76.6%

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

       3. div-inv 76.7%

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

       4. distribute-neg-frac 76.7%

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

   12. Applied egg-rr 76.7%

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

   if 9.1999999999999998e173 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around inf 84.7%

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

      1. associate-*l/ 88.9%

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

      2. *-commutative 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in x around 0 59.7%

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

      1. associate-*r/ 59.7%

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

      2. *-commutative 59.7%

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

      3. associate-*r/ 59.7%

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

      4. associate-*r/ 64.9%

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

      5. neg-mul-1 64.9%

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

      6. distribute-rgt-neg-in 64.9%

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

   10. Simplified 64.9%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+186}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+78}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+173}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+23} \lor \neg \left(z \leq 0.72\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+23) (not (<= z 0.72)))
   (- x (* (/ y a) z))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+23) || !(z <= 0.72)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + (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 ((z <= (-3.5d+23)) .or. (.not. (z <= 0.72d0))) then
        tmp = x - ((y / a) * z)
    else
        tmp = x + (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 ((z <= -3.5e+23) || !(z <= 0.72)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e+23) or not (z <= 0.72):
		tmp = x - ((y / a) * z)
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+23) || !(z <= 0.72))
		tmp = Float64(x - Float64(Float64(y / a) * z));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.5e+23) || ~((z <= 0.72)))
		tmp = x - ((y / a) * z);
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+23], N[Not[LessEqual[z, 0.72]], $MachinePrecision]], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000002e23 or 0.71999999999999997 < z

   1. Initial program 93.0%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around inf 82.9%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

   7. Simplified 86.8%

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

   if -3.5000000000000002e23 < z < 0.71999999999999997

   1. Initial program 92.8%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

      1. clear-num 96.5%

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

      2. associate-/r/ 96.5%

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

      3. clear-num 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in z around 0 87.7%

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

      1. neg-mul-1 87.7%

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

      2. distribute-neg-frac 87.7%

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

   9. Simplified 87.7%

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

       1. sub-neg 87.7%

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

       2. +-commutative 87.7%

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

       3. distribute-lft-neg-in 87.7%

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

       4. distribute-frac-neg 87.7%

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

       5. remove-double-neg 87.7%

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

   11. Applied egg-rr 87.7%

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

       1. *-commutative 87.7%

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

       2. clear-num 87.7%

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

       3. un-div-inv 87.7%

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

   13. Applied egg-rr 87.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+23} \lor \neg \left(z \leq 0.72\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+23} \lor \neg \left(z \leq 0.8\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+23) (not (<= z 0.8)))
   (- x (* (/ y a) z))
   (+ x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+23) || !(z <= 0.8)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((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 ((z <= (-4.8d+23)) .or. (.not. (z <= 0.8d0))) then
        tmp = x - ((y / a) * z)
    else
        tmp = x + ((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 ((z <= -4.8e+23) || !(z <= 0.8)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e+23) or not (z <= 0.8):
		tmp = x - ((y / a) * z)
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e+23) || !(z <= 0.8))
		tmp = Float64(x - Float64(Float64(y / a) * z));
	else
		tmp = Float64(x + Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.8e+23) || ~((z <= 0.8)))
		tmp = x - ((y / a) * z);
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e+23], N[Not[LessEqual[z, 0.8]], $MachinePrecision]], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e23 or 0.80000000000000004 < z

   1. Initial program 93.0%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around inf 82.9%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

   7. Simplified 86.8%

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

   if -4.8e23 < z < 0.80000000000000004

   1. Initial program 92.8%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-*l/ 89.6%

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

      3. neg-mul-1 89.6%

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

      4. distribute-rgt-neg-out 89.6%

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

   7. Simplified 89.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+23} \lor \neg \left(z \leq 0.8\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+97} \lor \neg \left(t \leq 7.2 \cdot 10^{+118}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.2e+97) (not (<= t 7.2e+118))) (* (/ y a) t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+97) || !(t <= 7.2e+118)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.2d+97)) .or. (.not. (t <= 7.2d+118))) then
        tmp = (y / a) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+97) || !(t <= 7.2e+118)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.2e+97) or not (t <= 7.2e+118):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.2e+97) || !(t <= 7.2e+118))
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.2e+97) || ~((t <= 7.2e+118)))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.2e+97], N[Not[LessEqual[t, 7.2e+118]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -8.19999999999999977e97 or 7.2e118 < t

   1. Initial program 88.1%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 78.8%

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

      1. associate-*r/ 78.8%

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

      2. neg-mul-1 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in x around 0 60.2%

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

      1. associate-*r/ 65.9%

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

   10. Simplified 65.9%

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

   if -8.19999999999999977e97 < t < 7.2e118

   1. Initial program 94.8%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around inf 80.2%

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

      1. associate-*l/ 84.1%

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

      2. *-commutative 84.1%

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

   7. Simplified 84.1%

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

   8. Taylor expanded in x around inf 52.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+97} \lor \neg \left(t \leq 7.2 \cdot 10^{+118}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-*l/ 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in z around inf 66.7%

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

   1. associate-*l/ 69.9%

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

   2. *-commutative 69.9%

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

7. Simplified 69.9%

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

8. Taylor expanded in x around inf 42.0%

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

9. Final simplification 42.0%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 99.3% 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 2024031 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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