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

Percentage Accurate: 93.3% → 97.6%

Time: 10.4s

Alternatives: 14

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e-25) (- x (/ y (/ a (- z t)))) (+ x (/ (- t z) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e-25) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((t - z) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.5d-25)) then
        tmp = x - (y / (a / (z - t)))
    else
        tmp = x + ((t - z) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e-25) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((t - z) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e-25:
		tmp = x - (y / (a / (z - t)))
	else:
		tmp = x + ((t - z) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e-25)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.5e-25)
		tmp = x - (y / (a / (z - t)));
	else
		tmp = x + ((t - z) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e-25], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5000000000000002e-25

   1. Initial program 87.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -3.5000000000000002e-25 < a

   1. Initial program 94.3%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 96.5%

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

   6. Simplified 96.5%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \]

Alternative 2: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ t_2 := z \cdot \frac{y}{-a}\\ \mathbf{if}\;a \leq -2.45 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))) (t_2 (* z (/ y (- a)))))
   (if (<= a -2.45e-24)
     x
     (if (<= a -1.45e-208)
       t_2
       (if (<= a -3e-256)
         t_1
         (if (<= a 4.5e-7) t_2 (if (<= a 2.4e+40) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double t_2 = z * (y / -a);
	double tmp;
	if (a <= -2.45e-24) {
		tmp = x;
	} else if (a <= -1.45e-208) {
		tmp = t_2;
	} else if (a <= -3e-256) {
		tmp = t_1;
	} else if (a <= 4.5e-7) {
		tmp = t_2;
	} else if (a <= 2.4e+40) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y / a)
    t_2 = z * (y / -a)
    if (a <= (-2.45d-24)) then
        tmp = x
    else if (a <= (-1.45d-208)) then
        tmp = t_2
    else if (a <= (-3d-256)) then
        tmp = t_1
    else if (a <= 4.5d-7) then
        tmp = t_2
    else if (a <= 2.4d+40) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double t_2 = z * (y / -a);
	double tmp;
	if (a <= -2.45e-24) {
		tmp = x;
	} else if (a <= -1.45e-208) {
		tmp = t_2;
	} else if (a <= -3e-256) {
		tmp = t_1;
	} else if (a <= 4.5e-7) {
		tmp = t_2;
	} else if (a <= 2.4e+40) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	t_2 = z * (y / -a)
	tmp = 0
	if a <= -2.45e-24:
		tmp = x
	elif a <= -1.45e-208:
		tmp = t_2
	elif a <= -3e-256:
		tmp = t_1
	elif a <= 4.5e-7:
		tmp = t_2
	elif a <= 2.4e+40:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	t_2 = Float64(z * Float64(y / Float64(-a)))
	tmp = 0.0
	if (a <= -2.45e-24)
		tmp = x;
	elseif (a <= -1.45e-208)
		tmp = t_2;
	elseif (a <= -3e-256)
		tmp = t_1;
	elseif (a <= 4.5e-7)
		tmp = t_2;
	elseif (a <= 2.4e+40)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	t_2 = z * (y / -a);
	tmp = 0.0;
	if (a <= -2.45e-24)
		tmp = x;
	elseif (a <= -1.45e-208)
		tmp = t_2;
	elseif (a <= -3e-256)
		tmp = t_1;
	elseif (a <= 4.5e-7)
		tmp = t_2;
	elseif (a <= 2.4e+40)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.45e-24], x, If[LessEqual[a, -1.45e-208], t$95$2, If[LessEqual[a, -3e-256], t$95$1, If[LessEqual[a, 4.5e-7], t$95$2, If[LessEqual[a, 2.4e+40], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.45e-24 or 2.4e40 < a

   1. Initial program 86.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in x around inf 62.4%

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

   if -2.45e-24 < a < -1.45e-208 or -2.9999999999999998e-256 < a < 4.4999999999999998e-7

   1. Initial program 97.2%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. associate-*l/ 55.7%

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

      3. *-commutative 55.7%

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

      4. distribute-rgt-neg-in 55.7%

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

      5. *-lft-identity 55.7%

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

      6. associate-*l/ 55.7%

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

      7. remove-double-neg 55.7%

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

      8. neg-mul-1 55.7%

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

      9. associate-*r* 55.7%

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

      10. *-commutative 55.7%

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

      11. neg-mul-1 55.7%

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

      12. *-commutative 55.7%

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

      13. distribute-neg-frac 55.7%

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

      14. metadata-eval 55.7%

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

      15. metadata-eval 55.7%

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

      16. associate-/r* 55.7%

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

      17. neg-mul-1 55.7%

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

      18. associate-*r/ 55.7%

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

      19. *-rgt-identity 55.7%

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

      20. distribute-frac-neg 55.7%

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

      21. remove-double-neg 55.7%

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

   6. Simplified 55.7%

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

   if -1.45e-208 < a < -2.9999999999999998e-256 or 4.4999999999999998e-7 < a < 2.4e40

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in t around inf 78.3%

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

      1. associate-*r/ 78.3%

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

   9. Simplified 78.3%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-207}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-5}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= a -8.8e-15)
     x
     (if (<= a -9.2e-207)
       (/ (- z) (/ a y))
       (if (<= a -1.55e-253)
         t_1
         (if (<= a 1e-5) (* z (/ y (- a))) (if (<= a 6e+32) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -8.8e-15) {
		tmp = x;
	} else if (a <= -9.2e-207) {
		tmp = -z / (a / y);
	} else if (a <= -1.55e-253) {
		tmp = t_1;
	} else if (a <= 1e-5) {
		tmp = z * (y / -a);
	} else if (a <= 6e+32) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (a <= (-8.8d-15)) then
        tmp = x
    else if (a <= (-9.2d-207)) then
        tmp = -z / (a / y)
    else if (a <= (-1.55d-253)) then
        tmp = t_1
    else if (a <= 1d-5) then
        tmp = z * (y / -a)
    else if (a <= 6d+32) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -8.8e-15) {
		tmp = x;
	} else if (a <= -9.2e-207) {
		tmp = -z / (a / y);
	} else if (a <= -1.55e-253) {
		tmp = t_1;
	} else if (a <= 1e-5) {
		tmp = z * (y / -a);
	} else if (a <= 6e+32) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if a <= -8.8e-15:
		tmp = x
	elif a <= -9.2e-207:
		tmp = -z / (a / y)
	elif a <= -1.55e-253:
		tmp = t_1
	elif a <= 1e-5:
		tmp = z * (y / -a)
	elif a <= 6e+32:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (a <= -8.8e-15)
		tmp = x;
	elseif (a <= -9.2e-207)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (a <= -1.55e-253)
		tmp = t_1;
	elseif (a <= 1e-5)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (a <= 6e+32)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (a <= -8.8e-15)
		tmp = x;
	elseif (a <= -9.2e-207)
		tmp = -z / (a / y);
	elseif (a <= -1.55e-253)
		tmp = t_1;
	elseif (a <= 1e-5)
		tmp = z * (y / -a);
	elseif (a <= 6e+32)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e-15], x, If[LessEqual[a, -9.2e-207], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.55e-253], t$95$1, If[LessEqual[a, 1e-5], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+32], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.79999999999999942e-15 or 6e32 < a

   1. Initial program 86.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in x around inf 62.4%

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

   if -8.79999999999999942e-15 < a < -9.2000000000000002e-207

   1. Initial program 99.7%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. associate-*l/ 53.4%

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

      3. *-commutative 53.4%

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

      4. distribute-rgt-neg-in 53.4%

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

      5. *-lft-identity 53.4%

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

      6. associate-*l/ 53.4%

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

      7. remove-double-neg 53.4%

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

      8. neg-mul-1 53.4%

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

      9. associate-*r* 53.4%

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

      10. *-commutative 53.4%

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

      11. neg-mul-1 53.4%

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

      12. *-commutative 53.4%

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

      13. distribute-neg-frac 53.4%

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

      14. metadata-eval 53.4%

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

      15. metadata-eval 53.4%

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

      16. associate-/r* 53.4%

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

      17. neg-mul-1 53.4%

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

      18. associate-*r/ 53.4%

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

      19. *-rgt-identity 53.4%

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

      20. distribute-frac-neg 53.4%

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

      21. remove-double-neg 53.4%

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

   6. Simplified 53.4%

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

      1. associate-*r/ 55.7%

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

      2. add-sqr-sqrt 55.5%

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

      3. sqrt-unprod 47.0%

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

      4. sqr-neg 47.0%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 1.3%

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

      7. associate-/l* 1.3%

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

      8. frac-2neg 1.3%

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

      9. distribute-frac-neg 1.3%

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

      10. add-sqr-sqrt 1.3%

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

      11. sqrt-unprod 1.2%

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

      12. sqr-neg 1.2%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 54.4%

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

   8. Applied egg-rr 54.4%

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

   if -9.2000000000000002e-207 < a < -1.54999999999999998e-253 or 1.00000000000000008e-5 < a < 6e32

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in t around inf 78.3%

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

      1. associate-*r/ 78.3%

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

   9. Simplified 78.3%

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

   if -1.54999999999999998e-253 < a < 1.00000000000000008e-5

   1. Initial program 95.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. associate-*l/ 56.9%

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

      3. *-commutative 56.9%

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

      4. distribute-rgt-neg-in 56.9%

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

      5. *-lft-identity 56.9%

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

      6. associate-*l/ 56.8%

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

      7. remove-double-neg 56.8%

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

      8. neg-mul-1 56.8%

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

      9. associate-*r* 56.8%

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

      10. *-commutative 56.8%

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

      11. neg-mul-1 56.8%

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

      12. *-commutative 56.8%

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

      13. distribute-neg-frac 56.8%

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

      14. metadata-eval 56.8%

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

      15. metadata-eval 56.8%

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

      16. associate-/r* 56.8%

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

      17. neg-mul-1 56.8%

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

      18. associate-*r/ 56.9%

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

      19. *-rgt-identity 56.9%

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

      20. distribute-frac-neg 56.9%

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

      21. remove-double-neg 56.9%

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

   6. Simplified 56.9%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-207}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-253}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 10^{-5}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= a -1.1e-14)
     x
     (if (<= a -9.8e-209)
       (/ (* y (- z)) a)
       (if (<= a -1.8e-258)
         t_1
         (if (<= a 1.35e-6) (* z (/ y (- a))) (if (<= a 7e+31) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -1.1e-14) {
		tmp = x;
	} else if (a <= -9.8e-209) {
		tmp = (y * -z) / a;
	} else if (a <= -1.8e-258) {
		tmp = t_1;
	} else if (a <= 1.35e-6) {
		tmp = z * (y / -a);
	} else if (a <= 7e+31) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (a <= (-1.1d-14)) then
        tmp = x
    else if (a <= (-9.8d-209)) then
        tmp = (y * -z) / a
    else if (a <= (-1.8d-258)) then
        tmp = t_1
    else if (a <= 1.35d-6) then
        tmp = z * (y / -a)
    else if (a <= 7d+31) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -1.1e-14) {
		tmp = x;
	} else if (a <= -9.8e-209) {
		tmp = (y * -z) / a;
	} else if (a <= -1.8e-258) {
		tmp = t_1;
	} else if (a <= 1.35e-6) {
		tmp = z * (y / -a);
	} else if (a <= 7e+31) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if a <= -1.1e-14:
		tmp = x
	elif a <= -9.8e-209:
		tmp = (y * -z) / a
	elif a <= -1.8e-258:
		tmp = t_1
	elif a <= 1.35e-6:
		tmp = z * (y / -a)
	elif a <= 7e+31:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (a <= -1.1e-14)
		tmp = x;
	elseif (a <= -9.8e-209)
		tmp = Float64(Float64(y * Float64(-z)) / a);
	elseif (a <= -1.8e-258)
		tmp = t_1;
	elseif (a <= 1.35e-6)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (a <= 7e+31)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (a <= -1.1e-14)
		tmp = x;
	elseif (a <= -9.8e-209)
		tmp = (y * -z) / a;
	elseif (a <= -1.8e-258)
		tmp = t_1;
	elseif (a <= 1.35e-6)
		tmp = z * (y / -a);
	elseif (a <= 7e+31)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e-14], x, If[LessEqual[a, -9.8e-209], N[(N[(y * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -1.8e-258], t$95$1, If[LessEqual[a, 1.35e-6], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+31], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.1e-14 or 7e31 < a

   1. Initial program 86.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in x around inf 62.4%

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

   if -1.1e-14 < a < -9.8000000000000007e-209

   1. Initial program 99.7%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. associate-*l/ 53.4%

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

      3. *-commutative 53.4%

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

      4. distribute-rgt-neg-in 53.4%

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

      5. *-lft-identity 53.4%

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

      6. associate-*l/ 53.4%

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

      7. remove-double-neg 53.4%

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

      8. neg-mul-1 53.4%

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

      9. associate-*r* 53.4%

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

      10. *-commutative 53.4%

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

      11. neg-mul-1 53.4%

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

      12. *-commutative 53.4%

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

      13. distribute-neg-frac 53.4%

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

      14. metadata-eval 53.4%

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

      15. metadata-eval 53.4%

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

      16. associate-/r* 53.4%

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

      17. neg-mul-1 53.4%

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

      18. associate-*r/ 53.4%

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

      19. *-rgt-identity 53.4%

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

      20. distribute-frac-neg 53.4%

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

      21. remove-double-neg 53.4%

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

   6. Simplified 53.4%

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

      1. associate-*r/ 55.7%

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

      2. add-sqr-sqrt 55.5%

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

      3. sqrt-unprod 47.0%

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

      4. sqr-neg 47.0%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 1.3%

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

      7. associate-*l/ 1.3%

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

      8. frac-2neg 1.3%

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

      9. associate-*l/ 1.3%

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

      10. add-sqr-sqrt 1.3%

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

      11. sqrt-unprod 1.2%

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

      12. sqr-neg 1.2%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 55.7%

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

   8. Applied egg-rr 55.7%

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

   if -9.8000000000000007e-209 < a < -1.79999999999999989e-258 or 1.34999999999999999e-6 < a < 7e31

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in t around inf 78.3%

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

      1. associate-*r/ 78.3%

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

   9. Simplified 78.3%

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

   if -1.79999999999999989e-258 < a < 1.34999999999999999e-6

   1. Initial program 95.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. associate-*l/ 56.9%

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

      3. *-commutative 56.9%

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

      4. distribute-rgt-neg-in 56.9%

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

      5. *-lft-identity 56.9%

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

      6. associate-*l/ 56.8%

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

      7. remove-double-neg 56.8%

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

      8. neg-mul-1 56.8%

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

      9. associate-*r* 56.8%

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

      10. *-commutative 56.8%

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

      11. neg-mul-1 56.8%

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

      12. *-commutative 56.8%

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

      13. distribute-neg-frac 56.8%

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

      14. metadata-eval 56.8%

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

      15. metadata-eval 56.8%

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

      16. associate-/r* 56.8%

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

      17. neg-mul-1 56.8%

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

      18. associate-*r/ 56.9%

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

      19. *-rgt-identity 56.9%

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

      20. distribute-frac-neg 56.9%

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

      21. remove-double-neg 56.9%

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

   6. Simplified 56.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-258}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 67.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+150} \lor \neg \left(a \leq -1.95 \cdot 10^{-7}\right) \land a \leq 1.95 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e+184)
   x
   (if (or (<= a -5.8e+150) (and (not (<= a -1.95e-7)) (<= a 1.95e+40)))
     (* (/ y a) (- t z))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e+184) {
		tmp = x;
	} else if ((a <= -5.8e+150) || (!(a <= -1.95e-7) && (a <= 1.95e+40))) {
		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 <= (-1.45d+184)) then
        tmp = x
    else if ((a <= (-5.8d+150)) .or. (.not. (a <= (-1.95d-7))) .and. (a <= 1.95d+40)) 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 <= -1.45e+184) {
		tmp = x;
	} else if ((a <= -5.8e+150) || (!(a <= -1.95e-7) && (a <= 1.95e+40))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e+184:
		tmp = x
	elif (a <= -5.8e+150) or (not (a <= -1.95e-7) and (a <= 1.95e+40)):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.45e+184)
		tmp = x;
	elseif ((a <= -5.8e+150) || (!(a <= -1.95e-7) && (a <= 1.95e+40)))
		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 <= -1.45e+184)
		tmp = x;
	elseif ((a <= -5.8e+150) || (~((a <= -1.95e-7)) && (a <= 1.95e+40)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e+184], x, If[Or[LessEqual[a, -5.8e+150], And[N[Not[LessEqual[a, -1.95e-7]], $MachinePrecision], LessEqual[a, 1.95e+40]]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4499999999999999e184 or -5.80000000000000022e150 < a < -1.95000000000000012e-7 or 1.95e40 < a

   1. Initial program 87.8%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in x around inf 67.0%

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

   if -1.4499999999999999e184 < a < -5.80000000000000022e150 or -1.95000000000000012e-7 < a < 1.95e40

   1. Initial program 95.4%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in y around 0 95.4%

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

      1. *-commutative 95.4%

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

      2. associate-/l* 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in x around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-*r/ 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

      4. neg-sub0 73.2%

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

      5. div-sub 70.6%

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

      6. associate--r- 70.6%

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

      7. neg-sub0 70.6%

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

      8. distribute-frac-neg 70.6%

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

      9. +-commutative 70.6%

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

      10. distribute-frac-neg 70.6%

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

      11. sub-neg 70.6%

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

      12. distribute-rgt-out-- 63.5%

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

      13. associate-/r/ 66.7%

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

      14. associate-*l/ 68.4%

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

      15. associate-*r/ 69.7%

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

      16. *-commutative 69.7%

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

      17. associate-/l* 68.3%

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

      18. *-commutative 68.3%

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

      19. associate-*l/ 69.7%

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

      20. distribute-lft-out-- 82.0%

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

   9. Simplified 82.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+150} \lor \neg \left(a \leq -1.95 \cdot 10^{-7}\right) \land a \leq 1.95 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 81.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z}{a}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ z a)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= t -1.1e+95)
     t_2
     (if (<= t 1.9e-108)
       t_1
       (if (<= t 1.6e+26) (* (/ y a) (- t z)) (if (<= t 4.4e+70) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / a));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (t <= -1.1e+95) {
		tmp = t_2;
	} else if (t <= 1.9e-108) {
		tmp = t_1;
	} else if (t <= 1.6e+26) {
		tmp = (y / a) * (t - z);
	} else if (t <= 4.4e+70) {
		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 = x - (y * (z / a))
    t_2 = x + (t * (y / a))
    if (t <= (-1.1d+95)) then
        tmp = t_2
    else if (t <= 1.9d-108) then
        tmp = t_1
    else if (t <= 1.6d+26) then
        tmp = (y / a) * (t - z)
    else if (t <= 4.4d+70) 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 = x - (y * (z / a));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (t <= -1.1e+95) {
		tmp = t_2;
	} else if (t <= 1.9e-108) {
		tmp = t_1;
	} else if (t <= 1.6e+26) {
		tmp = (y / a) * (t - z);
	} else if (t <= 4.4e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (z / a))
	t_2 = x + (t * (y / a))
	tmp = 0
	if t <= -1.1e+95:
		tmp = t_2
	elif t <= 1.9e-108:
		tmp = t_1
	elif t <= 1.6e+26:
		tmp = (y / a) * (t - z)
	elif t <= 4.4e+70:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(z / a)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (t <= -1.1e+95)
		tmp = t_2;
	elseif (t <= 1.9e-108)
		tmp = t_1;
	elseif (t <= 1.6e+26)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (t <= 4.4e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (z / a));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (t <= -1.1e+95)
		tmp = t_2;
	elseif (t <= 1.9e-108)
		tmp = t_1;
	elseif (t <= 1.6e+26)
		tmp = (y / a) * (t - z);
	elseif (t <= 4.4e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+95], t$95$2, If[LessEqual[t, 1.9e-108], t$95$1, If[LessEqual[t, 1.6e+26], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+70], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0999999999999999e95 or 4.40000000000000001e70 < t

   1. Initial program 89.8%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-/l* 95.5%

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

   6. Simplified 95.5%

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

   7. Taylor expanded in z around 0 84.7%

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

      1. cancel-sign-sub-inv 84.7%

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

      2. metadata-eval 84.7%

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

      3. associate-*l/ 85.2%

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

      4. *-commutative 85.2%

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

      5. *-lft-identity 85.2%

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

      6. *-commutative 85.2%

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

      7. associate-*l/ 84.7%

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

      8. associate-*r/ 87.8%

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

   9. Simplified 87.8%

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

   if -1.0999999999999999e95 < t < 1.89999999999999987e-108 or 1.60000000000000014e26 < t < 4.40000000000000001e70

   1. Initial program 94.6%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around inf 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-/l* 89.3%

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

      3. associate-/r/ 88.1%

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

   6. Simplified 88.1%

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

   if 1.89999999999999987e-108 < t < 1.60000000000000014e26

   1. Initial program 91.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in x around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. associate-*r/ 69.7%

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

      3. distribute-rgt-neg-in 69.7%

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

      4. neg-sub0 69.7%

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

      5. div-sub 69.7%

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

      6. associate--r- 69.7%

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

      7. neg-sub0 69.7%

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

      8. distribute-frac-neg 69.7%

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

      9. +-commutative 69.7%

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

      10. distribute-frac-neg 69.7%

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

      11. sub-neg 69.7%

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

      12. distribute-rgt-out-- 61.0%

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

      13. associate-/r/ 69.3%

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

      14. associate-*l/ 65.6%

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

      15. associate-*r/ 69.3%

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

      16. *-commutative 69.3%

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

      17. associate-/l* 65.3%

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

      18. *-commutative 65.3%

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

      19. associate-*l/ 69.4%

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

      20. distribute-lft-out-- 78.0%

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

   9. Simplified 78.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+95}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-108}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+70}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 49.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-203} \lor \neg \left(a \leq 1.75 \cdot 10^{-144}\right) \land a \leq 8.6 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e-46)
   x
   (if (or (<= a 1.4e-203) (and (not (<= a 1.75e-144)) (<= a 8.6e+34)))
     (* t (/ y a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e-46) {
		tmp = x;
	} else if ((a <= 1.4e-203) || (!(a <= 1.75e-144) && (a <= 8.6e+34))) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.5d-46)) then
        tmp = x
    else if ((a <= 1.4d-203) .or. (.not. (a <= 1.75d-144)) .and. (a <= 8.6d+34)) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e-46) {
		tmp = x;
	} else if ((a <= 1.4e-203) || (!(a <= 1.75e-144) && (a <= 8.6e+34))) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e-46:
		tmp = x
	elif (a <= 1.4e-203) or (not (a <= 1.75e-144) and (a <= 8.6e+34)):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e-46)
		tmp = x;
	elseif ((a <= 1.4e-203) || (!(a <= 1.75e-144) && (a <= 8.6e+34)))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e-46)
		tmp = x;
	elseif ((a <= 1.4e-203) || (~((a <= 1.75e-144)) && (a <= 8.6e+34)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e-46], x, If[Or[LessEqual[a, 1.4e-203], And[N[Not[LessEqual[a, 1.75e-144]], $MachinePrecision], LessEqual[a, 8.6e+34]]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.49999999999999996e-46 or 1.40000000000000011e-203 < a < 1.7499999999999999e-144 or 8.59999999999999988e34 < a

   1. Initial program 87.9%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around inf 61.0%

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

   if -2.49999999999999996e-46 < a < 1.40000000000000011e-203 or 1.7499999999999999e-144 < a < 8.59999999999999988e34

   1. Initial program 97.3%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 97.3%

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

      1. *-commutative 97.3%

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

      2. associate-/l* 98.6%

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

   6. Simplified 98.6%

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

   7. Taylor expanded in t around inf 47.5%

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

      1. associate-*r/ 49.6%

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

   9. Simplified 49.6%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-203} \lor \neg \left(a \leq 1.75 \cdot 10^{-144}\right) \land a \leq 8.6 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 50.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.000112:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= a -2.5e-37)
     x
     (if (<= a -9.2e-260)
       t_1
       (if (<= a 0.000112) (/ (- y) (/ a z)) (if (<= a 1.7e+32) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -2.5e-37) {
		tmp = x;
	} else if (a <= -9.2e-260) {
		tmp = t_1;
	} else if (a <= 0.000112) {
		tmp = -y / (a / z);
	} else if (a <= 1.7e+32) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (a <= (-2.5d-37)) then
        tmp = x
    else if (a <= (-9.2d-260)) then
        tmp = t_1
    else if (a <= 0.000112d0) then
        tmp = -y / (a / z)
    else if (a <= 1.7d+32) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -2.5e-37) {
		tmp = x;
	} else if (a <= -9.2e-260) {
		tmp = t_1;
	} else if (a <= 0.000112) {
		tmp = -y / (a / z);
	} else if (a <= 1.7e+32) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if a <= -2.5e-37:
		tmp = x
	elif a <= -9.2e-260:
		tmp = t_1
	elif a <= 0.000112:
		tmp = -y / (a / z)
	elif a <= 1.7e+32:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (a <= -2.5e-37)
		tmp = x;
	elseif (a <= -9.2e-260)
		tmp = t_1;
	elseif (a <= 0.000112)
		tmp = Float64(Float64(-y) / Float64(a / z));
	elseif (a <= 1.7e+32)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (a <= -2.5e-37)
		tmp = x;
	elseif (a <= -9.2e-260)
		tmp = t_1;
	elseif (a <= 0.000112)
		tmp = -y / (a / z);
	elseif (a <= 1.7e+32)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e-37], x, If[LessEqual[a, -9.2e-260], t$95$1, If[LessEqual[a, 0.000112], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+32], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4999999999999999e-37 or 1.69999999999999989e32 < a

   1. Initial program 86.9%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around inf 61.8%

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

   if -2.4999999999999999e-37 < a < -9.2e-260 or 1.11999999999999998e-4 < a < 1.69999999999999989e32

   1. Initial program 99.7%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in t around inf 54.6%

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

      1. associate-*r/ 54.6%

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

   9. Simplified 54.6%

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

   if -9.2e-260 < a < 1.11999999999999998e-4

   1. Initial program 95.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. associate-/l* 53.7%

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

   6. Simplified 53.7%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 0.000112:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-8} \lor \neg \left(a \leq 3.6 \cdot 10^{+29}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.15e-8) (not (<= a 3.6e+29)))
   (+ x (* t (/ y a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.15e-8) || !(a <= 3.6e+29)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.15d-8)) .or. (.not. (a <= 3.6d+29))) then
        tmp = x + (t * (y / a))
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.15e-8) || !(a <= 3.6e+29)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.15e-8) or not (a <= 3.6e+29):
		tmp = x + (t * (y / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.15e-8) || !(a <= 3.6e+29))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.15e-8) || ~((a <= 3.6e+29)))
		tmp = x + (t * (y / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.15e-8], N[Not[LessEqual[a, 3.6e+29]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1500000000000001e-8 or 3.59999999999999976e29 < a

   1. Initial program 86.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around 0 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-/l* 93.0%

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

   6. Simplified 93.0%

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

   7. Taylor expanded in z around 0 76.0%

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

      1. cancel-sign-sub-inv 76.0%

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

      2. metadata-eval 76.0%

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

      3. associate-*l/ 81.8%

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

      4. *-commutative 81.8%

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

      5. *-lft-identity 81.8%

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

      6. *-commutative 81.8%

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

      7. associate-*l/ 76.0%

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

      8. associate-*r/ 78.8%

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

   9. Simplified 78.8%

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

   if -2.1500000000000001e-8 < a < 3.59999999999999976e29

   1. Initial program 97.6%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around 0 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in x around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. associate-*r/ 73.1%

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

      3. distribute-rgt-neg-in 73.1%

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

      4. neg-sub0 73.1%

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

      5. div-sub 70.2%

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

      6. associate--r- 70.2%

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

      7. neg-sub0 70.2%

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

      8. distribute-frac-neg 70.2%

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

      9. +-commutative 70.2%

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

      10. distribute-frac-neg 70.2%

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

      11. sub-neg 70.2%

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

      12. distribute-rgt-out-- 63.8%

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

      13. associate-/r/ 67.3%

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

      14. associate-*l/ 71.2%

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

      15. associate-*r/ 70.6%

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

      16. *-commutative 70.6%

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

      17. associate-/l* 71.1%

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

      18. *-commutative 71.1%

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

      19. associate-*l/ 70.6%

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

      20. distribute-lft-out-- 82.8%

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

   9. Simplified 82.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-8} \lor \neg \left(a \leq 3.6 \cdot 10^{+29}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 10: 77.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-9} \lor \neg \left(a \leq 2.8 \cdot 10^{+29}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e-9) (not (<= a 2.8e+29)))
   (+ x (* y (/ t a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-9) || !(a <= 2.8e+29)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.8d-9)) .or. (.not. (a <= 2.8d+29))) then
        tmp = x + (y * (t / a))
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-9) || !(a <= 2.8e+29)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e-9) or not (a <= 2.8e+29):
		tmp = x + (y * (t / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e-9) || !(a <= 2.8e+29))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e-9) || ~((a <= 2.8e+29)))
		tmp = x + (y * (t / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e-9], N[Not[LessEqual[a, 2.8e+29]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.79999999999999984e-9 or 2.8e29 < a

   1. Initial program 86.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in z around 0 76.2%

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

      1. cancel-sign-sub-inv 76.2%

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

      2. metadata-eval 76.2%

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

      3. *-lft-identity 76.2%

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

      4. +-commutative 76.2%

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

      5. associate-/l* 78.9%

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

      6. associate-/r/ 81.9%

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

   6. Simplified 81.9%

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

   if -2.79999999999999984e-9 < a < 2.8e29

   1. Initial program 97.6%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around 0 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in x around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. associate-*r/ 72.9%

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

      3. distribute-rgt-neg-in 72.9%

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

      4. neg-sub0 72.9%

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

      5. div-sub 70.0%

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

      6. associate--r- 70.0%

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

      7. neg-sub0 70.0%

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

      8. distribute-frac-neg 70.0%

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

      9. +-commutative 70.0%

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

      10. distribute-frac-neg 70.0%

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

      11. sub-neg 70.0%

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

      12. distribute-rgt-out-- 63.5%

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

      13. associate-/r/ 67.0%

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

      14. associate-*l/ 71.0%

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

      15. associate-*r/ 70.4%

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

      16. *-commutative 70.4%

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

      17. associate-/l* 70.9%

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

      18. *-commutative 70.9%

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

      19. associate-*l/ 70.4%

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

      20. distribute-lft-out-- 82.7%

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

   9. Simplified 82.7%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-9} \lor \neg \left(a \leq 2.8 \cdot 10^{+29}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 11: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+96} \lor \neg \left(t \leq 5.4 \cdot 10^{+71}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.5e+96) (not (<= t 5.4e+71)))
   (+ x (* t (/ y a)))
   (- x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e+96) || !(t <= 5.4e+71)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.5d+96)) .or. (.not. (t <= 5.4d+71))) then
        tmp = x + (t * (y / a))
    else
        tmp = x - ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e+96) || !(t <= 5.4e+71)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.5e+96) or not (t <= 5.4e+71):
		tmp = x + (t * (y / a))
	else:
		tmp = x - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.5e+96) || !(t <= 5.4e+71))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.5e+96) || ~((t <= 5.4e+71)))
		tmp = x + (t * (y / a));
	else
		tmp = x - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.5e+96], N[Not[LessEqual[t, 5.4e+71]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5e96 or 5.39999999999999993e71 < t

   1. Initial program 89.8%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-/l* 95.5%

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

   6. Simplified 95.5%

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

   7. Taylor expanded in z around 0 84.7%

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

      1. cancel-sign-sub-inv 84.7%

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

      2. metadata-eval 84.7%

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

      3. associate-*l/ 85.2%

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

      4. *-commutative 85.2%

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

      5. *-lft-identity 85.2%

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

      6. *-commutative 85.2%

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

      7. associate-*l/ 84.7%

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

      8. associate-*r/ 87.8%

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

   9. Simplified 87.8%

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

   if -6.5e96 < t < 5.39999999999999993e71

   1. Initial program 94.2%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around inf 84.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+96} \lor \neg \left(t \leq 5.4 \cdot 10^{+71}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 12: 97.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-9}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e-9) (- x (/ y (/ a (- z t)))) (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-9) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((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 (a <= (-1.2d-9)) then
        tmp = x - (y / (a / (z - t)))
    else
        tmp = x + ((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 (a <= -1.2e-9) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e-9:
		tmp = x - (y / (a / (z - t)))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e-9)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + 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 (a <= -1.2e-9)
		tmp = x - (y / (a / (z - t)));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e-9], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2e-9

   1. Initial program 86.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -1.2e-9 < a

   1. Initial program 94.3%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-9}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 13: 97.2% 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 92.4%

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

   1. associate-*l/ 95.7%

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

3. Simplified 95.7%

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

4. Final simplification 95.7%

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

Alternative 14: 39.1% 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 92.4%

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

   1. associate-*l/ 95.7%

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

3. Simplified 95.7%

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

4. Taylor expanded in x around inf 37.3%

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

5. Final simplification 37.3%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023318 
(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)))