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

Percentage Accurate: 92.9% → 97.1%

Time: 11.0s

Alternatives: 12

Speedup: 1.0×

• 24.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

   1. sub-neg 94.8%

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

   2. distribute-frac-neg 94.8%

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

   3. distribute-lft-neg-out 94.8%

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

   4. +-commutative 94.8%

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

   5. distribute-lft-neg-out 94.8%

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

   6. distribute-rgt-neg-in 94.8%

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

   7. associate-*l/ 98.3%

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

   8. fma-def 98.3%

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

   9. sub-neg 98.3%

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

   10. distribute-neg-in 98.3%

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

   11. remove-double-neg 98.3%

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

   12. +-commutative 98.3%

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

   13. sub-neg 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 2: 47.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-\frac{z}{a}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-307}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-234}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- (/ z a)))))
   (if (<= z -1.8e+118)
     t_1
     (if (<= z -1.2e-22)
       x
       (if (<= z -1.75e-51)
         (/ t (/ a y))
         (if (<= z -7.2e-129)
           x
           (if (<= z -1.04e-187)
             (* y (/ t a))
             (if (<= z 2.6e-307)
               x
               (if (<= z 2.1e-234)
                 (/ (* y t) a)
                 (if (<= z 1.2e+101) x t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * -(z / a);
	double tmp;
	if (z <= -1.8e+118) {
		tmp = t_1;
	} else if (z <= -1.2e-22) {
		tmp = x;
	} else if (z <= -1.75e-51) {
		tmp = t / (a / y);
	} else if (z <= -7.2e-129) {
		tmp = x;
	} else if (z <= -1.04e-187) {
		tmp = y * (t / a);
	} else if (z <= 2.6e-307) {
		tmp = x;
	} else if (z <= 2.1e-234) {
		tmp = (y * t) / a;
	} else if (z <= 1.2e+101) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -(z / a)
    if (z <= (-1.8d+118)) then
        tmp = t_1
    else if (z <= (-1.2d-22)) then
        tmp = x
    else if (z <= (-1.75d-51)) then
        tmp = t / (a / y)
    else if (z <= (-7.2d-129)) then
        tmp = x
    else if (z <= (-1.04d-187)) then
        tmp = y * (t / a)
    else if (z <= 2.6d-307) then
        tmp = x
    else if (z <= 2.1d-234) then
        tmp = (y * t) / a
    else if (z <= 1.2d+101) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * -(z / a);
	double tmp;
	if (z <= -1.8e+118) {
		tmp = t_1;
	} else if (z <= -1.2e-22) {
		tmp = x;
	} else if (z <= -1.75e-51) {
		tmp = t / (a / y);
	} else if (z <= -7.2e-129) {
		tmp = x;
	} else if (z <= -1.04e-187) {
		tmp = y * (t / a);
	} else if (z <= 2.6e-307) {
		tmp = x;
	} else if (z <= 2.1e-234) {
		tmp = (y * t) / a;
	} else if (z <= 1.2e+101) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * -(z / a)
	tmp = 0
	if z <= -1.8e+118:
		tmp = t_1
	elif z <= -1.2e-22:
		tmp = x
	elif z <= -1.75e-51:
		tmp = t / (a / y)
	elif z <= -7.2e-129:
		tmp = x
	elif z <= -1.04e-187:
		tmp = y * (t / a)
	elif z <= 2.6e-307:
		tmp = x
	elif z <= 2.1e-234:
		tmp = (y * t) / a
	elif z <= 1.2e+101:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(-Float64(z / a)))
	tmp = 0.0
	if (z <= -1.8e+118)
		tmp = t_1;
	elseif (z <= -1.2e-22)
		tmp = x;
	elseif (z <= -1.75e-51)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= -7.2e-129)
		tmp = x;
	elseif (z <= -1.04e-187)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 2.6e-307)
		tmp = x;
	elseif (z <= 2.1e-234)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 1.2e+101)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * -(z / a);
	tmp = 0.0;
	if (z <= -1.8e+118)
		tmp = t_1;
	elseif (z <= -1.2e-22)
		tmp = x;
	elseif (z <= -1.75e-51)
		tmp = t / (a / y);
	elseif (z <= -7.2e-129)
		tmp = x;
	elseif (z <= -1.04e-187)
		tmp = y * (t / a);
	elseif (z <= 2.6e-307)
		tmp = x;
	elseif (z <= 2.1e-234)
		tmp = (y * t) / a;
	elseif (z <= 1.2e+101)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * (-N[(z / a), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -1.8e+118], t$95$1, If[LessEqual[z, -1.2e-22], x, If[LessEqual[z, -1.75e-51], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-129], x, If[LessEqual[z, -1.04e-187], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-307], x, If[LessEqual[z, 2.1e-234], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.2e+101], x, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.8e118 or 1.19999999999999994e101 < z

   1. Initial program 93.4%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. clear-num 98.4%

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

      3. un-div-inv 98.5%

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

   5. Applied egg-rr 98.5%

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

   6. Taylor expanded in z around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-*r/ 68.7%

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

      3. distribute-rgt-neg-in 68.7%

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

      4. distribute-neg-frac 68.7%

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

   8. Simplified 68.7%

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

   if -1.8e118 < z < -1.20000000000000001e-22 or -1.7499999999999999e-51 < z < -7.2e-129 or -1.04e-187 < z < 2.59999999999999996e-307 or 2.09999999999999991e-234 < z < 1.19999999999999994e101

   1. Initial program 96.9%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in x around inf 58.9%

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

   if -1.20000000000000001e-22 < z < -1.7499999999999999e-51

   1. Initial program 85.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 59.1%

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

      1. associate-/l* 72.5%

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

   6. Simplified 72.5%

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

   if -7.2e-129 < z < -1.04e-187

   1. Initial program 78.0%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 48.2%

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

      1. associate-/l* 63.2%

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

      2. associate-/r/ 63.6%

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

   6. Applied egg-rr 63.6%

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

   if 2.59999999999999996e-307 < z < 2.09999999999999991e-234

   1. Initial program 99.5%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in t around inf 77.5%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \left(-\frac{z}{a}\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-307}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-234}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{z}{a}\right)\\ \end{array} \]

Alternative 3: 48.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-y}{a}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-238}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y) a))))
   (if (<= z -2.1e+155)
     t_1
     (if (<= z -8.4e-22)
       x
       (if (<= z -7.8e-49)
         (/ t (/ a y))
         (if (<= z -2e-128)
           x
           (if (<= z -1.05e-187)
             (* y (/ t a))
             (if (<= z 4.2e-298)
               x
               (if (<= z 2.3e-238)
                 (/ (* y t) a)
                 (if (<= z 1.8e+101) x t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / a);
	double tmp;
	if (z <= -2.1e+155) {
		tmp = t_1;
	} else if (z <= -8.4e-22) {
		tmp = x;
	} else if (z <= -7.8e-49) {
		tmp = t / (a / y);
	} else if (z <= -2e-128) {
		tmp = x;
	} else if (z <= -1.05e-187) {
		tmp = y * (t / a);
	} else if (z <= 4.2e-298) {
		tmp = x;
	} else if (z <= 2.3e-238) {
		tmp = (y * t) / a;
	} else if (z <= 1.8e+101) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (-y / a)
    if (z <= (-2.1d+155)) then
        tmp = t_1
    else if (z <= (-8.4d-22)) then
        tmp = x
    else if (z <= (-7.8d-49)) then
        tmp = t / (a / y)
    else if (z <= (-2d-128)) then
        tmp = x
    else if (z <= (-1.05d-187)) then
        tmp = y * (t / a)
    else if (z <= 4.2d-298) then
        tmp = x
    else if (z <= 2.3d-238) then
        tmp = (y * t) / a
    else if (z <= 1.8d+101) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / a);
	double tmp;
	if (z <= -2.1e+155) {
		tmp = t_1;
	} else if (z <= -8.4e-22) {
		tmp = x;
	} else if (z <= -7.8e-49) {
		tmp = t / (a / y);
	} else if (z <= -2e-128) {
		tmp = x;
	} else if (z <= -1.05e-187) {
		tmp = y * (t / a);
	} else if (z <= 4.2e-298) {
		tmp = x;
	} else if (z <= 2.3e-238) {
		tmp = (y * t) / a;
	} else if (z <= 1.8e+101) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (-y / a)
	tmp = 0
	if z <= -2.1e+155:
		tmp = t_1
	elif z <= -8.4e-22:
		tmp = x
	elif z <= -7.8e-49:
		tmp = t / (a / y)
	elif z <= -2e-128:
		tmp = x
	elif z <= -1.05e-187:
		tmp = y * (t / a)
	elif z <= 4.2e-298:
		tmp = x
	elif z <= 2.3e-238:
		tmp = (y * t) / a
	elif z <= 1.8e+101:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-y) / a))
	tmp = 0.0
	if (z <= -2.1e+155)
		tmp = t_1;
	elseif (z <= -8.4e-22)
		tmp = x;
	elseif (z <= -7.8e-49)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= -2e-128)
		tmp = x;
	elseif (z <= -1.05e-187)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 4.2e-298)
		tmp = x;
	elseif (z <= 2.3e-238)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 1.8e+101)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-y / a);
	tmp = 0.0;
	if (z <= -2.1e+155)
		tmp = t_1;
	elseif (z <= -8.4e-22)
		tmp = x;
	elseif (z <= -7.8e-49)
		tmp = t / (a / y);
	elseif (z <= -2e-128)
		tmp = x;
	elseif (z <= -1.05e-187)
		tmp = y * (t / a);
	elseif (z <= 4.2e-298)
		tmp = x;
	elseif (z <= 2.3e-238)
		tmp = (y * t) / a;
	elseif (z <= 1.8e+101)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+155], t$95$1, If[LessEqual[z, -8.4e-22], x, If[LessEqual[z, -7.8e-49], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-128], x, If[LessEqual[z, -1.05e-187], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-298], x, If[LessEqual[z, 2.3e-238], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.8e+101], x, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.1e155 or 1.80000000000000015e101 < z

   1. Initial program 93.8%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. associate-*l/ 80.1%

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

      3. distribute-rgt-neg-in 80.1%

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

   6. Simplified 80.1%

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

   if -2.1e155 < z < -8.40000000000000031e-22 or -7.80000000000000023e-49 < z < -2.00000000000000011e-128 or -1.04999999999999996e-187 < z < 4.2000000000000001e-298 or 2.30000000000000005e-238 < z < 1.80000000000000015e101

   1. Initial program 96.5%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 57.8%

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

   if -8.40000000000000031e-22 < z < -7.80000000000000023e-49

   1. Initial program 85.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 59.1%

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

      1. associate-/l* 72.5%

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

   6. Simplified 72.5%

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

   if -2.00000000000000011e-128 < z < -1.04999999999999996e-187

   1. Initial program 78.0%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 48.2%

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

      1. associate-/l* 63.2%

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

      2. associate-/r/ 63.6%

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

   6. Applied egg-rr 63.6%

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

   if 4.2000000000000001e-298 < z < 2.30000000000000005e-238

   1. Initial program 99.5%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in t around inf 77.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-238}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \end{array} \]

Alternative 4: 48.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-188}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-237}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{-a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e+155)
   (* z (/ (- y) a))
   (if (<= z -2.6e-23)
     x
     (if (<= z -5.4e-53)
       (/ t (/ a y))
       (if (<= z -2.8e-127)
         x
         (if (<= z -6e-188)
           (* y (/ t a))
           (if (<= z 6.2e-298)
             x
             (if (<= z 5.8e-237)
               (/ (* y t) a)
               (if (<= z 1.2e+101) x (/ z (/ (- a) y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+155) {
		tmp = z * (-y / a);
	} else if (z <= -2.6e-23) {
		tmp = x;
	} else if (z <= -5.4e-53) {
		tmp = t / (a / y);
	} else if (z <= -2.8e-127) {
		tmp = x;
	} else if (z <= -6e-188) {
		tmp = y * (t / a);
	} else if (z <= 6.2e-298) {
		tmp = x;
	} else if (z <= 5.8e-237) {
		tmp = (y * t) / a;
	} else if (z <= 1.2e+101) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-2.1d+155)) then
        tmp = z * (-y / a)
    else if (z <= (-2.6d-23)) then
        tmp = x
    else if (z <= (-5.4d-53)) then
        tmp = t / (a / y)
    else if (z <= (-2.8d-127)) then
        tmp = x
    else if (z <= (-6d-188)) then
        tmp = y * (t / a)
    else if (z <= 6.2d-298) then
        tmp = x
    else if (z <= 5.8d-237) then
        tmp = (y * t) / a
    else if (z <= 1.2d+101) then
        tmp = x
    else
        tmp = 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 (z <= -2.1e+155) {
		tmp = z * (-y / a);
	} else if (z <= -2.6e-23) {
		tmp = x;
	} else if (z <= -5.4e-53) {
		tmp = t / (a / y);
	} else if (z <= -2.8e-127) {
		tmp = x;
	} else if (z <= -6e-188) {
		tmp = y * (t / a);
	} else if (z <= 6.2e-298) {
		tmp = x;
	} else if (z <= 5.8e-237) {
		tmp = (y * t) / a;
	} else if (z <= 1.2e+101) {
		tmp = x;
	} else {
		tmp = z / (-a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e+155:
		tmp = z * (-y / a)
	elif z <= -2.6e-23:
		tmp = x
	elif z <= -5.4e-53:
		tmp = t / (a / y)
	elif z <= -2.8e-127:
		tmp = x
	elif z <= -6e-188:
		tmp = y * (t / a)
	elif z <= 6.2e-298:
		tmp = x
	elif z <= 5.8e-237:
		tmp = (y * t) / a
	elif z <= 1.2e+101:
		tmp = x
	else:
		tmp = z / (-a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e+155)
		tmp = Float64(z * Float64(Float64(-y) / a));
	elseif (z <= -2.6e-23)
		tmp = x;
	elseif (z <= -5.4e-53)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= -2.8e-127)
		tmp = x;
	elseif (z <= -6e-188)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 6.2e-298)
		tmp = x;
	elseif (z <= 5.8e-237)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 1.2e+101)
		tmp = x;
	else
		tmp = Float64(z / Float64(Float64(-a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.1e+155)
		tmp = z * (-y / a);
	elseif (z <= -2.6e-23)
		tmp = x;
	elseif (z <= -5.4e-53)
		tmp = t / (a / y);
	elseif (z <= -2.8e-127)
		tmp = x;
	elseif (z <= -6e-188)
		tmp = y * (t / a);
	elseif (z <= 6.2e-298)
		tmp = x;
	elseif (z <= 5.8e-237)
		tmp = (y * t) / a;
	elseif (z <= 1.2e+101)
		tmp = x;
	else
		tmp = z / (-a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e+155], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-23], x, If[LessEqual[z, -5.4e-53], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-127], x, If[LessEqual[z, -6e-188], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-298], x, If[LessEqual[z, 5.8e-237], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.2e+101], x, N[(z / N[((-a) / y), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.1e155

   1. Initial program 96.4%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 79.2%

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

      1. mul-1-neg 79.2%

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

      2. associate-*l/ 79.3%

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

      3. distribute-rgt-neg-in 79.3%

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

   6. Simplified 79.3%

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

   if -2.1e155 < z < -2.6e-23 or -5.3999999999999998e-53 < z < -2.8e-127 or -6.00000000000000033e-188 < z < 6.2000000000000003e-298 or 5.80000000000000022e-237 < z < 1.19999999999999994e101

   1. Initial program 96.5%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 57.8%

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

   if -2.6e-23 < z < -5.3999999999999998e-53

   1. Initial program 85.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 59.1%

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

      1. associate-/l* 72.5%

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

   6. Simplified 72.5%

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

   if -2.8e-127 < z < -6.00000000000000033e-188

   1. Initial program 78.0%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 48.2%

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

      1. associate-/l* 63.2%

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

      2. associate-/r/ 63.6%

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

   6. Applied egg-rr 63.6%

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

   if 6.2000000000000003e-298 < z < 5.80000000000000022e-237

   1. Initial program 99.5%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in t around inf 77.5%

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

   if 1.19999999999999994e101 < z

   1. Initial program 91.8%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. associate-*l/ 80.8%

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

      3. distribute-rgt-neg-in 80.8%

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

   6. Simplified 80.8%

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

      1. clear-num 80.7%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 0.7%

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

      4. sqr-neg 0.7%

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

      5. sqrt-unprod 1.1%

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

      6. add-sqr-sqrt 1.1%

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

      7. associate-/r/ 1.1%

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

      8. frac-2neg 1.1%

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

      9. clear-num 1.1%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 64.1%

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

      12. sqr-neg 64.1%

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

      13. sqrt-unprod 80.6%

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

      14. add-sqr-sqrt 80.9%

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

      15. distribute-neg-frac 80.9%

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

   8. Applied egg-rr 80.9%

      \[\leadsto \color{blue}{\frac{z}{\frac{-a}{y}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-188}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-237}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{-a}{y}}\\ \end{array} \]

Alternative 5: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+87} \lor \neg \left(x \leq 1.8 \cdot 10^{+117}\right) \land x \leq 1.3 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.6e+111)
   x
   (if (or (<= x 4.5e+87) (and (not (<= x 1.8e+117)) (<= x 1.3e+151)))
     (* y (/ (- t z) a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.6e+111) {
		tmp = x;
	} else if ((x <= 4.5e+87) || (!(x <= 1.8e+117) && (x <= 1.3e+151))) {
		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 <= (-3.6d+111)) then
        tmp = x
    else if ((x <= 4.5d+87) .or. (.not. (x <= 1.8d+117)) .and. (x <= 1.3d+151)) 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 <= -3.6e+111) {
		tmp = x;
	} else if ((x <= 4.5e+87) || (!(x <= 1.8e+117) && (x <= 1.3e+151))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.6e+111:
		tmp = x
	elif (x <= 4.5e+87) or (not (x <= 1.8e+117) and (x <= 1.3e+151)):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.6e+111)
		tmp = x;
	elseif ((x <= 4.5e+87) || (!(x <= 1.8e+117) && (x <= 1.3e+151)))
		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 <= -3.6e+111)
		tmp = x;
	elseif ((x <= 4.5e+87) || (~((x <= 1.8e+117)) && (x <= 1.3e+151)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.6e+111], x, If[Or[LessEqual[x, 4.5e+87], And[N[Not[LessEqual[x, 1.8e+117]], $MachinePrecision], LessEqual[x, 1.3e+151]]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6000000000000002e111 or 4.5000000000000003e87 < x < 1.80000000000000006e117 or 1.30000000000000007e151 < x

   1. Initial program 96.9%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 79.5%

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

   if -3.6000000000000002e111 < x < 4.5000000000000003e87 or 1.80000000000000006e117 < x < 1.30000000000000007e151

   1. Initial program 93.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. associate-*r/ 71.0%

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

      3. distribute-rgt-neg-out 71.0%

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

      4. *-rgt-identity 71.0%

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

      5. *-rgt-identity 71.0%

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

      6. distribute-neg-frac 71.0%

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

      7. neg-sub0 71.0%

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

      8. associate--r- 71.0%

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

      9. neg-sub0 71.0%

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

      10. +-commutative 71.0%

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

      11. sub-neg 71.0%

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

   6. Simplified 71.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+87} \lor \neg \left(x \leq 1.8 \cdot 10^{+117}\right) \land x \leq 1.3 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 68.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.1e+115)
   x
   (if (<= x 9.2e+86)
     (* (/ y a) (- t z))
     (if (<= x 1.85e+121) x (if (<= x 3.8e+148) (* y (/ (- t z) a)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e+115) {
		tmp = x;
	} else if (x <= 9.2e+86) {
		tmp = (y / a) * (t - z);
	} else if (x <= 1.85e+121) {
		tmp = x;
	} else if (x <= 3.8e+148) {
		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 <= (-1.1d+115)) then
        tmp = x
    else if (x <= 9.2d+86) then
        tmp = (y / a) * (t - z)
    else if (x <= 1.85d+121) then
        tmp = x
    else if (x <= 3.8d+148) 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 <= -1.1e+115) {
		tmp = x;
	} else if (x <= 9.2e+86) {
		tmp = (y / a) * (t - z);
	} else if (x <= 1.85e+121) {
		tmp = x;
	} else if (x <= 3.8e+148) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.1e+115:
		tmp = x
	elif x <= 9.2e+86:
		tmp = (y / a) * (t - z)
	elif x <= 1.85e+121:
		tmp = x
	elif x <= 3.8e+148:
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.1e+115)
		tmp = x;
	elseif (x <= 9.2e+86)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (x <= 1.85e+121)
		tmp = x;
	elseif (x <= 3.8e+148)
		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 <= -1.1e+115)
		tmp = x;
	elseif (x <= 9.2e+86)
		tmp = (y / a) * (t - z);
	elseif (x <= 1.85e+121)
		tmp = x;
	elseif (x <= 3.8e+148)
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.1e+115], x, If[LessEqual[x, 9.2e+86], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+121], x, If[LessEqual[x, 3.8e+148], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e115 or 9.19999999999999958e86 < x < 1.85000000000000006e121 or 3.7999999999999998e148 < x

   1. Initial program 96.9%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 79.5%

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

   if -1.1e115 < x < 9.19999999999999958e86

   1. Initial program 93.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*r/ 69.9%

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

      3. distribute-rgt-neg-out 69.9%

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

      4. *-rgt-identity 69.9%

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

      5. *-rgt-identity 69.9%

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

      6. distribute-neg-frac 69.9%

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

      7. neg-sub0 69.9%

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

      8. associate--r- 69.9%

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

      9. neg-sub0 69.9%

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

      10. +-commutative 69.9%

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

      11. sub-neg 69.9%

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

   6. Simplified 69.9%

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

      1. clear-num 69.9%

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

      2. un-div-inv 70.4%

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

   8. Applied egg-rr 70.4%

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

   9. Taylor expanded in y around 0 70.3%

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

       1. associate-/l* 70.4%

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

       2. associate-/r/ 74.4%

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

   11. Simplified 74.4%

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

   if 1.85000000000000006e121 < x < 3.7999999999999998e148

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

      4. *-rgt-identity 100.0%

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

      5. *-rgt-identity 100.0%

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

      6. distribute-neg-frac 100.0%

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

      7. neg-sub0 100.0%

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

      8. associate--r- 100.0%

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

      9. neg-sub0 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-27} \lor \neg \left(z \leq 7.8 \cdot 10^{-31}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.22e-27) (not (<= z 7.8e-31)))
   (- x (* (/ y a) z))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.22e-27) || !(z <= 7.8e-31)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.22d-27)) .or. (.not. (z <= 7.8d-31))) then
        tmp = x - ((y / a) * z)
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.22e-27) || !(z <= 7.8e-31)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.22e-27) or not (z <= 7.8e-31):
		tmp = x - ((y / a) * z)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.22e-27) || !(z <= 7.8e-31))
		tmp = Float64(x - Float64(Float64(y / a) * z));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.22e-27) || ~((z <= 7.8e-31)))
		tmp = x - ((y / a) * z);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.22e-27], N[Not[LessEqual[z, 7.8e-31]], $MachinePrecision]], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e-27 or 7.8000000000000003e-31 < z

   1. Initial program 93.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 81.9%

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

      1. associate-*l/ 84.6%

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

      2. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   if -1.22e-27 < z < 7.8000000000000003e-31

   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. distribute-frac-neg 96.6%

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

      3. distribute-lft-neg-out 96.6%

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

      4. +-commutative 96.6%

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

      5. distribute-lft-neg-out 96.6%

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

      6. distribute-rgt-neg-in 96.6%

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

      7. associate-*l/ 97.3%

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

      8. fma-def 97.3%

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

      9. sub-neg 97.3%

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

      10. distribute-neg-in 97.3%

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

      11. remove-double-neg 97.3%

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

      12. +-commutative 97.3%

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

      13. sub-neg 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 91.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-27} \lor \neg \left(z \leq 7.8 \cdot 10^{-31}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 8: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-29} \lor \neg \left(z \leq 9.6 \cdot 10^{-34}\right):\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e-29) (not (<= z 9.6e-34)))
   (- x (/ z (/ a y)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e-29) || !(z <= 9.6e-34)) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.95d-29)) .or. (.not. (z <= 9.6d-34))) then
        tmp = x - (z / (a / y))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e-29) || !(z <= 9.6e-34)) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e-29) or not (z <= 9.6e-34):
		tmp = x - (z / (a / y))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e-29) || !(z <= 9.6e-34))
		tmp = Float64(x - Float64(z / Float64(a / y)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e-29) || ~((z <= 9.6e-34)))
		tmp = x - (z / (a / y));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e-29], N[Not[LessEqual[z, 9.6e-34]], $MachinePrecision]], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9499999999999999e-29 or 9.59999999999999965e-34 < z

   1. Initial program 93.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 81.9%

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

      1. associate-*l/ 84.6%

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

      2. *-commutative 84.6%

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

   6. Simplified 84.6%

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

      1. clear-num 84.6%

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

      2. div-inv 84.7%

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

   8. Applied egg-rr 84.7%

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

   if -1.9499999999999999e-29 < z < 9.59999999999999965e-34

   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. distribute-frac-neg 96.6%

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

      3. distribute-lft-neg-out 96.6%

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

      4. +-commutative 96.6%

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

      5. distribute-lft-neg-out 96.6%

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

      6. distribute-rgt-neg-in 96.6%

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

      7. associate-*l/ 97.3%

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

      8. fma-def 97.3%

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

      9. sub-neg 97.3%

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

      10. distribute-neg-in 97.3%

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

      11. remove-double-neg 97.3%

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

      12. +-commutative 97.3%

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

      13. sub-neg 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 91.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-29} \lor \neg \left(z \leq 9.6 \cdot 10^{-34}\right):\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 9: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+172}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.45e+172)
   (* (/ y a) (- t z))
   (if (<= z 1.2e+95) (+ x (/ (* y t) a)) (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.45e+172) {
		tmp = (y / a) * (t - z);
	} else if (z <= 1.2e+95) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.45d+172)) then
        tmp = (y / a) * (t - z)
    else if (z <= 1.2d+95) then
        tmp = x + ((y * t) / a)
    else
        tmp = y * ((t - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.45e+172) {
		tmp = (y / a) * (t - z);
	} else if (z <= 1.2e+95) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.45e+172:
		tmp = (y / a) * (t - z)
	elif z <= 1.2e+95:
		tmp = x + ((y * t) / a)
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.45e+172)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (z <= 1.2e+95)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(y * Float64(Float64(t - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.45e+172)
		tmp = (y / a) * (t - z);
	elseif (z <= 1.2e+95)
		tmp = x + ((y * t) / a);
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.45e+172], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+95], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45e172

   1. Initial program 96.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around 0 88.7%

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

      1. mul-1-neg 88.7%

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

      2. associate-*r/ 70.8%

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

      3. distribute-rgt-neg-out 70.8%

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

      4. *-rgt-identity 70.8%

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

      5. *-rgt-identity 70.8%

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

      6. distribute-neg-frac 70.8%

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

      7. neg-sub0 70.8%

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

      8. associate--r- 70.8%

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

      9. neg-sub0 70.8%

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

      10. +-commutative 70.8%

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

      11. sub-neg 70.8%

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

   6. Simplified 70.8%

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

      1. clear-num 70.6%

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

      2. un-div-inv 70.6%

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

   8. Applied egg-rr 70.6%

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

   9. Taylor expanded in y around 0 88.7%

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

       1. associate-/l* 70.6%

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

       2. associate-/r/ 92.4%

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

   11. Simplified 92.4%

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

   if -2.45e172 < z < 1.2e95

   1. Initial program 95.1%

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

      1. sub-neg 95.1%

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

      2. distribute-frac-neg 95.1%

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

      3. distribute-lft-neg-out 95.1%

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

      4. +-commutative 95.1%

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

      5. distribute-lft-neg-out 95.1%

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

      6. distribute-rgt-neg-in 95.1%

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

      7. associate-*l/ 98.3%

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

      8. fma-def 98.3%

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

      9. sub-neg 98.3%

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

      10. distribute-neg-in 98.3%

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

      11. remove-double-neg 98.3%

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

      12. +-commutative 98.3%

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

      13. sub-neg 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 81.8%

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

   if 1.2e95 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. associate-*r/ 86.1%

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

      3. distribute-rgt-neg-out 86.1%

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

      4. *-rgt-identity 86.1%

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

      5. *-rgt-identity 86.1%

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

      6. distribute-neg-frac 86.1%

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

      7. neg-sub0 86.1%

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

      8. associate--r- 86.1%

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

      9. neg-sub0 86.1%

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

      10. +-commutative 86.1%

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

      11. sub-neg 86.1%

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

   6. Simplified 86.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+172}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]

Alternative 10: 51.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+146} \lor \neg \left(t \leq 2.9 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.5e+146) (not (<= t 2.9e+54))) (* (/ y a) t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e+146) || !(t <= 2.9e+54)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.5d+146)) .or. (.not. (t <= 2.9d+54))) then
        tmp = (y / a) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e+146) || !(t <= 2.9e+54)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.5e+146) or not (t <= 2.9e+54):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.5e+146) || !(t <= 2.9e+54))
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.5e+146) || ~((t <= 2.9e+54)))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.5e+146], N[Not[LessEqual[t, 2.9e+54]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -6.4999999999999997e146 or 2.8999999999999999e54 < t

   1. Initial program 91.2%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 57.8%

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

      1. associate-*r/ 64.0%

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

   6. Simplified 64.0%

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

   if -6.4999999999999997e146 < t < 2.8999999999999999e54

   1. Initial program 96.5%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around inf 50.1%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+146} \lor \neg \left(t \leq 2.9 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 97.1% 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 94.8%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 12: 39.2% 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 94.8%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Taylor expanded in x around inf 41.7%

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

5. Final simplification 41.7%

   \[\leadsto x \]

Developer target: 99.0% 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 2023320 
(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)))