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

Percentage Accurate: 92.8% → 97.8%

Time: 9.3s

Alternatives: 10

Speedup: 1.0×

• 24.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.8% 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: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e-19) (+ x (* y (/ (- t z) a))) (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e-19) {
		tmp = x + (y * ((t - z) / a));
	} 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 <= (-2d-19)) then
        tmp = x + (y * ((t - z) / a))
    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 <= -2e-19) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e-19:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e-19)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	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 <= -2e-19)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e-19], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $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 < -2e-19

   1. Initial program 94.0%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   if -2e-19 < a

   1. Initial program 94.9%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 2: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := x - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+176}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (- x (/ y (/ a z)))))
   (if (<= z -1.02e+176)
     (* (/ y a) (- t z))
     (if (<= z -2.65e+67)
       t_1
       (if (<= z -4.6e+44)
         t_2
         (if (<= z -1.45e+31)
           (+ x (* y (/ t a)))
           (if (<= z 1.7e+75) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = x - (y / (a / z));
	double tmp;
	if (z <= -1.02e+176) {
		tmp = (y / a) * (t - z);
	} else if (z <= -2.65e+67) {
		tmp = t_1;
	} else if (z <= -4.6e+44) {
		tmp = t_2;
	} else if (z <= -1.45e+31) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.7e+75) {
		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 * t) / a)
    t_2 = x - (y / (a / z))
    if (z <= (-1.02d+176)) then
        tmp = (y / a) * (t - z)
    else if (z <= (-2.65d+67)) then
        tmp = t_1
    else if (z <= (-4.6d+44)) then
        tmp = t_2
    else if (z <= (-1.45d+31)) then
        tmp = x + (y * (t / a))
    else if (z <= 1.7d+75) 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 * t) / a);
	double t_2 = x - (y / (a / z));
	double tmp;
	if (z <= -1.02e+176) {
		tmp = (y / a) * (t - z);
	} else if (z <= -2.65e+67) {
		tmp = t_1;
	} else if (z <= -4.6e+44) {
		tmp = t_2;
	} else if (z <= -1.45e+31) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.7e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = x - (y / (a / z))
	tmp = 0
	if z <= -1.02e+176:
		tmp = (y / a) * (t - z)
	elif z <= -2.65e+67:
		tmp = t_1
	elif z <= -4.6e+44:
		tmp = t_2
	elif z <= -1.45e+31:
		tmp = x + (y * (t / a))
	elif z <= 1.7e+75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(x - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (z <= -1.02e+176)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (z <= -2.65e+67)
		tmp = t_1;
	elseif (z <= -4.6e+44)
		tmp = t_2;
	elseif (z <= -1.45e+31)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.7e+75)
		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 * t) / a);
	t_2 = x - (y / (a / z));
	tmp = 0.0;
	if (z <= -1.02e+176)
		tmp = (y / a) * (t - z);
	elseif (z <= -2.65e+67)
		tmp = t_1;
	elseif (z <= -4.6e+44)
		tmp = t_2;
	elseif (z <= -1.45e+31)
		tmp = x + (y * (t / a));
	elseif (z <= 1.7e+75)
		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[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+176], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.65e+67], t$95$1, If[LessEqual[z, -4.6e+44], t$95$2, If[LessEqual[z, -1.45e+31], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+75], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.02000000000000001e176

   1. Initial program 95.8%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around 0 87.7%

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

      1. associate-*r/ 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 72.4%

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

      4. neg-mul-1 72.4%

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

      5. neg-sub0 72.4%

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

      6. div-sub 71.8%

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

      7. associate-+l- 71.8%

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

      8. neg-sub0 71.8%

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

      9. +-commutative 71.8%

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

      10. sub-neg 71.8%

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

      11. div-sub 72.4%

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

      12. *-rgt-identity 72.4%

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

      13. associate-*r/ 72.5%

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

      14. associate-*l* 83.5%

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

      15. associate-*l/ 83.7%

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

      16. associate-*r/ 83.7%

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

      17. *-lft-identity 83.7%

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

   6. Simplified 83.7%

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

   if -1.02000000000000001e176 < z < -2.65e67 or -1.45e31 < z < 1.70000000000000006e75

   1. Initial program 96.6%

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

      1. sub-neg 96.6%

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

      2. +-commutative 96.6%

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

      3. distribute-neg-frac 96.6%

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

      4. distribute-rgt-neg-in 96.6%

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

      5. associate-*r/ 93.2%

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

      6. distribute-frac-neg 93.2%

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

      7. fma-def 93.2%

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

      8. distribute-frac-neg 93.2%

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

      9. sub-neg 93.2%

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

      10. +-commutative 93.2%

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

      11. distribute-neg-in 93.2%

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

      12. unsub-neg 93.2%

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

      13. remove-double-neg 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 88.5%

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

   if -2.65e67 < z < -4.60000000000000009e44 or 1.70000000000000006e75 < z

   1. Initial program 91.6%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in z around inf 91.3%

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

   if -4.60000000000000009e44 < z < -1.45e31

   1. Initial program 62.4%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-neg-frac 100.0%

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

   6. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. cancel-sign-sub 100.0%

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

      4. add-sqr-sqrt 40.0%

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

      5. sqrt-unprod 2.4%

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

      6. sqr-neg 2.4%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 20.1%

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

      9. *-commutative 20.1%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 2.4%

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

      12. sqr-neg 2.4%

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

      13. sqrt-unprod 40.0%

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

      14. add-sqr-sqrt 100.0%

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

   8. Applied egg-rr 100.0%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+176}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+44}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 3: 65.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-40} \lor \neg \left(x \leq -6.6 \cdot 10^{-74}\right) \land x \leq 4 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5e+67)
   x
   (if (or (<= x -5e-40) (and (not (<= x -6.6e-74)) (<= x 4e+83)))
     (* y (/ (- t z) a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5e+67) {
		tmp = x;
	} else if ((x <= -5e-40) || (!(x <= -6.6e-74) && (x <= 4e+83))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-5d+67)) then
        tmp = x
    else if ((x <= (-5d-40)) .or. (.not. (x <= (-6.6d-74))) .and. (x <= 4d+83)) then
        tmp = y * ((t - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5e+67) {
		tmp = x;
	} else if ((x <= -5e-40) || (!(x <= -6.6e-74) && (x <= 4e+83))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5e+67:
		tmp = x
	elif (x <= -5e-40) or (not (x <= -6.6e-74) and (x <= 4e+83)):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5e+67)
		tmp = x;
	elseif ((x <= -5e-40) || (!(x <= -6.6e-74) && (x <= 4e+83)))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5e+67)
		tmp = x;
	elseif ((x <= -5e-40) || (~((x <= -6.6e-74)) && (x <= 4e+83)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5e+67], x, If[Or[LessEqual[x, -5e-40], And[N[Not[LessEqual[x, -6.6e-74]], $MachinePrecision], LessEqual[x, 4e+83]]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.99999999999999976e67 or -4.99999999999999965e-40 < x < -6.59999999999999992e-74 or 4.00000000000000012e83 < x

   1. Initial program 95.4%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 75.3%

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

   if -4.99999999999999976e67 < x < -4.99999999999999965e-40 or -6.59999999999999992e-74 < x < 4.00000000000000012e83

   1. Initial program 94.2%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

      1. associate-/l* 94.2%

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

      2. clear-num 94.1%

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

      3. associate-/r/ 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in x around 0 74.5%

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

      1. associate-*l/ 71.5%

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

      2. associate-*r* 71.5%

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

      3. neg-mul-1 71.5%

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

      4. neg-sub0 71.5%

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

      5. div-sub 70.0%

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

      6. associate--r- 70.0%

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

      7. neg-sub0 70.0%

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

      8. +-commutative 70.0%

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

      9. sub-neg 70.0%

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

      10. *-commutative 70.0%

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

      11. div-sub 71.5%

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

   8. Simplified 71.5%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-40} \lor \neg \left(x \leq -6.6 \cdot 10^{-74}\right) \land x \leq 4 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-40} \lor \neg \left(x \leq -6.6 \cdot 10^{-74}\right) \land x \leq 7.5 \cdot 10^{+129}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.8e+68)
   x
   (if (or (<= x -5.4e-40) (and (not (<= x -6.6e-74)) (<= x 7.5e+129)))
     (* (/ y a) (- t z))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.8e+68) {
		tmp = x;
	} else if ((x <= -5.4e-40) || (!(x <= -6.6e-74) && (x <= 7.5e+129))) {
		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 (x <= (-8.8d+68)) then
        tmp = x
    else if ((x <= (-5.4d-40)) .or. (.not. (x <= (-6.6d-74))) .and. (x <= 7.5d+129)) 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 (x <= -8.8e+68) {
		tmp = x;
	} else if ((x <= -5.4e-40) || (!(x <= -6.6e-74) && (x <= 7.5e+129))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.8e+68:
		tmp = x
	elif (x <= -5.4e-40) or (not (x <= -6.6e-74) and (x <= 7.5e+129)):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.8e+68)
		tmp = x;
	elseif ((x <= -5.4e-40) || (!(x <= -6.6e-74) && (x <= 7.5e+129)))
		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 (x <= -8.8e+68)
		tmp = x;
	elseif ((x <= -5.4e-40) || (~((x <= -6.6e-74)) && (x <= 7.5e+129)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.8e+68], x, If[Or[LessEqual[x, -5.4e-40], And[N[Not[LessEqual[x, -6.6e-74]], $MachinePrecision], LessEqual[x, 7.5e+129]]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.79999999999999949e68 or -5.4e-40 < x < -6.59999999999999992e-74 or 7.4999999999999998e129 < x

   1. Initial program 95.1%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 77.4%

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

   if -8.79999999999999949e68 < x < -5.4e-40 or -6.59999999999999992e-74 < x < 7.4999999999999998e129

   1. Initial program 94.5%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around 0 73.3%

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

      1. associate-*r/ 69.8%

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

      2. *-commutative 69.8%

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

      3. associate-*r* 69.8%

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

      4. neg-mul-1 69.8%

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

      5. neg-sub0 69.8%

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

      6. div-sub 68.4%

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

      7. associate-+l- 68.4%

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

      8. neg-sub0 68.4%

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

      9. +-commutative 68.4%

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

      10. sub-neg 68.4%

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

      11. div-sub 69.8%

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

      12. *-rgt-identity 69.8%

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

      13. associate-*r/ 69.7%

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

      14. associate-*l* 75.0%

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

      15. associate-*l/ 75.1%

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

      16. associate-*r/ 75.1%

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

      17. *-lft-identity 75.1%

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

   6. Simplified 75.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-40} \lor \neg \left(x \leq -6.6 \cdot 10^{-74}\right) \land x \leq 7.5 \cdot 10^{+129}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 77.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.55 \cdot 10^{-37} \lor \neg \left(a \leq 11000\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.55e-37) (not (<= a 11000.0)))
   (+ 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 <= -3.55e-37) || !(a <= 11000.0)) {
		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 <= (-3.55d-37)) .or. (.not. (a <= 11000.0d0))) 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 <= -3.55e-37) || !(a <= 11000.0)) {
		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 <= -3.55e-37) or not (a <= 11000.0):
		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 <= -3.55e-37) || !(a <= 11000.0))
		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 <= -3.55e-37) || ~((a <= 11000.0)))
		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, -3.55e-37], N[Not[LessEqual[a, 11000.0]], $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 < -3.54999999999999989e-37 or 11000 < a

   1. Initial program 90.9%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 83.6%

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

      1. neg-mul-1 83.6%

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

      2. distribute-neg-frac 83.6%

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

   6. Simplified 83.6%

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

      1. *-commutative 83.6%

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

      2. distribute-frac-neg 83.6%

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

      3. cancel-sign-sub 83.6%

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

      4. add-sqr-sqrt 46.7%

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

      5. sqrt-unprod 66.8%

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

      6. sqr-neg 66.8%

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

      7. sqrt-unprod 27.5%

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

      8. add-sqr-sqrt 63.0%

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

      9. *-commutative 63.0%

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

      10. add-sqr-sqrt 27.5%

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

      11. sqrt-unprod 66.8%

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

      12. sqr-neg 66.8%

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

      13. sqrt-unprod 46.7%

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

      14. add-sqr-sqrt 83.6%

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

   8. Applied egg-rr 83.6%

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

   if -3.54999999999999989e-37 < a < 11000

   1. Initial program 99.8%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around 0 82.7%

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

      1. associate-*r/ 68.3%

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

      2. *-commutative 68.3%

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

      3. associate-*r* 68.3%

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

      4. neg-mul-1 68.3%

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

      5. neg-sub0 68.3%

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

      6. div-sub 65.5%

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

      7. associate-+l- 65.5%

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

      8. neg-sub0 65.5%

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

      9. +-commutative 65.5%

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

      10. sub-neg 65.5%

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

      11. div-sub 68.3%

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

      12. *-rgt-identity 68.3%

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

      13. associate-*r/ 68.3%

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

      14. associate-*l* 82.8%

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

      15. associate-*l/ 82.8%

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

      16. associate-*r/ 82.8%

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

      17. *-lft-identity 82.8%

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

   6. Simplified 82.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.55 \cdot 10^{-37} \lor \neg \left(a \leq 11000\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 6: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+129}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+174)
   (* (/ y a) (- t z))
   (if (<= z 2.05e+129) (+ x (/ (* y t) a)) (* z (/ (- y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+174) {
		tmp = (y / a) * (t - z);
	} else if (z <= 2.05e+129) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = z * (-y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.5d+174)) then
        tmp = (y / a) * (t - z)
    else if (z <= 2.05d+129) then
        tmp = x + ((y * t) / a)
    else
        tmp = z * (-y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+174) {
		tmp = (y / a) * (t - z);
	} else if (z <= 2.05e+129) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = z * (-y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+174:
		tmp = (y / a) * (t - z)
	elif z <= 2.05e+129:
		tmp = x + ((y * t) / a)
	else:
		tmp = z * (-y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+174)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (z <= 2.05e+129)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(z * Float64(Float64(-y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+174)
		tmp = (y / a) * (t - z);
	elseif (z <= 2.05e+129)
		tmp = x + ((y * t) / a);
	else
		tmp = z * (-y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+174], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+129], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999992e174

   1. Initial program 95.8%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around 0 87.7%

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

      1. associate-*r/ 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 72.4%

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

      4. neg-mul-1 72.4%

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

      5. neg-sub0 72.4%

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

      6. div-sub 71.8%

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

      7. associate-+l- 71.8%

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

      8. neg-sub0 71.8%

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

      9. +-commutative 71.8%

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

      10. sub-neg 71.8%

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

      11. div-sub 72.4%

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

      12. *-rgt-identity 72.4%

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

      13. associate-*r/ 72.5%

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

      14. associate-*l* 83.5%

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

      15. associate-*l/ 83.7%

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

      16. associate-*r/ 83.7%

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

      17. *-lft-identity 83.7%

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

   6. Simplified 83.7%

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

   if -9.4999999999999992e174 < z < 2.0500000000000001e129

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. +-commutative 95.4%

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

      3. distribute-neg-frac 95.4%

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

      4. distribute-rgt-neg-in 95.4%

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

      5. associate-*r/ 93.9%

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

      6. distribute-frac-neg 93.9%

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

      7. fma-def 93.9%

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

      8. distribute-frac-neg 93.9%

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

      9. sub-neg 93.9%

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

      10. +-commutative 93.9%

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

      11. distribute-neg-in 93.9%

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

      12. unsub-neg 93.9%

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

      13. remove-double-neg 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 85.9%

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

   if 2.0500000000000001e129 < z

   1. Initial program 91.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. associate-*l/ 74.4%

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

      3. distribute-rgt-neg-in 74.4%

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

   6. Simplified 74.4%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+129}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \end{array} \]

Alternative 7: 78.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+174)
   (/ (* y (- t z)) a)
   (if (<= z 1.35e+75) (+ x (/ (* y t) a)) (- x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+174) {
		tmp = (y * (t - z)) / a;
	} else if (z <= 1.35e+75) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d+174)) then
        tmp = (y * (t - z)) / a
    else if (z <= 1.35d+75) then
        tmp = x + ((y * t) / a)
    else
        tmp = x - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+174) {
		tmp = (y * (t - z)) / a;
	} else if (z <= 1.35e+75) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+174:
		tmp = (y * (t - z)) / a
	elif z <= 1.35e+75:
		tmp = x + ((y * t) / a)
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+174)
		tmp = Float64(Float64(y * Float64(t - z)) / a);
	elseif (z <= 1.35e+75)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+174)
		tmp = (y * (t - z)) / a;
	elseif (z <= 1.35e+75)
		tmp = x + ((y * t) / a);
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+174], N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.35e+75], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999998e174

   1. Initial program 95.8%

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

      1. sub-neg 95.8%

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

      2. +-commutative 95.8%

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

      3. distribute-neg-frac 95.8%

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

      4. distribute-rgt-neg-in 95.8%

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

      5. associate-*r/ 80.6%

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

      6. distribute-frac-neg 80.6%

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

      7. fma-def 80.6%

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

      8. distribute-frac-neg 80.6%

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

      9. sub-neg 80.6%

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

      10. +-commutative 80.6%

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

      11. distribute-neg-in 80.6%

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

      12. unsub-neg 80.6%

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

      13. remove-double-neg 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in y around -inf 87.7%

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

   if -5.4999999999999998e174 < z < 1.34999999999999999e75

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. +-commutative 95.7%

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

      3. distribute-neg-frac 95.7%

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

      4. distribute-rgt-neg-in 95.7%

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

      5. associate-*r/ 93.6%

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

      6. distribute-frac-neg 93.6%

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

      7. fma-def 93.6%

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

      8. distribute-frac-neg 93.6%

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

      9. sub-neg 93.6%

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

      10. +-commutative 93.6%

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

      11. distribute-neg-in 93.6%

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

      12. unsub-neg 93.6%

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

      13. remove-double-neg 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around 0 86.2%

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

   if 1.34999999999999999e75 < z

   1. Initial program 90.8%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around inf 90.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 8: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1650000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.4e-38) x (if (<= a 1650000.0) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.4e-38) {
		tmp = x;
	} else if (a <= 1650000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.4d-38)) then
        tmp = x
    else if (a <= 1650000.0d0) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.4e-38) {
		tmp = x;
	} else if (a <= 1650000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.4e-38:
		tmp = x
	elif a <= 1650000.0:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.4e-38)
		tmp = x;
	elseif (a <= 1650000.0)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.4e-38)
		tmp = x;
	elseif (a <= 1650000.0)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.4e-38], x, If[LessEqual[a, 1650000.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.39999999999999955e-38 or 1.65e6 < a

   1. Initial program 90.8%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in x around inf 62.5%

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

   if -6.39999999999999955e-38 < a < 1.65e6

   1. Initial program 99.8%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in t around inf 48.0%

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

      1. *-commutative 48.0%

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

      2. associate-*r/ 49.7%

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

   6. Simplified 49.7%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1650000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

   1. associate-*r/ 91.8%

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

3. Simplified 91.8%

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

4. Final simplification 91.8%

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

Alternative 10: 39.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in x around inf 43.3%

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

5. Final simplification 43.3%

   \[\leadsto x \]

Developer target: 99.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023200 
(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)))