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

Percentage Accurate: 93.2% → 97.0%

Time: 8.3s

Alternatives: 10

Speedup: 1.0×

• 25.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

3. Taylor expanded in z around 0 85.1%

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

   1. +-commutative 85.1%

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

   2. mul-1-neg 85.1%

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

   3. *-commutative 85.1%

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

   4. associate-*r/ 85.0%

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

   5. associate-/l* 87.1%

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

   6. distribute-lft-neg-in 87.1%

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

   7. distribute-rgt-in 98.0%

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

   8. sub-neg 98.0%

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

5. Simplified 98.0%

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

6. Final simplification 98.0%

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

Alternative 2: 47.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ t_2 := y \cdot \frac{-z}{a}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+157}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))) (t_2 (* y (/ (- z) a))))
   (if (<= y -6.6e+157)
     (/ (* y (- z)) a)
     (if (<= y -2.7e+53)
       (* (/ y a) t)
       (if (<= y -5e-42)
         t_2
         (if (<= y 1.45e-44)
           x
           (if (<= y 6.8e+65)
             t_1
             (if (<= y 1.65e+130)
               t_2
               (if (<= y 6.4e+273) t_1 (* (/ y a) (- z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double t_2 = y * (-z / a);
	double tmp;
	if (y <= -6.6e+157) {
		tmp = (y * -z) / a;
	} else if (y <= -2.7e+53) {
		tmp = (y / a) * t;
	} else if (y <= -5e-42) {
		tmp = t_2;
	} else if (y <= 1.45e-44) {
		tmp = x;
	} else if (y <= 6.8e+65) {
		tmp = t_1;
	} else if (y <= 1.65e+130) {
		tmp = t_2;
	} else if (y <= 6.4e+273) {
		tmp = t_1;
	} else {
		tmp = (y / a) * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t / a)
    t_2 = y * (-z / a)
    if (y <= (-6.6d+157)) then
        tmp = (y * -z) / a
    else if (y <= (-2.7d+53)) then
        tmp = (y / a) * t
    else if (y <= (-5d-42)) then
        tmp = t_2
    else if (y <= 1.45d-44) then
        tmp = x
    else if (y <= 6.8d+65) then
        tmp = t_1
    else if (y <= 1.65d+130) then
        tmp = t_2
    else if (y <= 6.4d+273) then
        tmp = t_1
    else
        tmp = (y / a) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double t_2 = y * (-z / a);
	double tmp;
	if (y <= -6.6e+157) {
		tmp = (y * -z) / a;
	} else if (y <= -2.7e+53) {
		tmp = (y / a) * t;
	} else if (y <= -5e-42) {
		tmp = t_2;
	} else if (y <= 1.45e-44) {
		tmp = x;
	} else if (y <= 6.8e+65) {
		tmp = t_1;
	} else if (y <= 1.65e+130) {
		tmp = t_2;
	} else if (y <= 6.4e+273) {
		tmp = t_1;
	} else {
		tmp = (y / a) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	t_2 = y * (-z / a)
	tmp = 0
	if y <= -6.6e+157:
		tmp = (y * -z) / a
	elif y <= -2.7e+53:
		tmp = (y / a) * t
	elif y <= -5e-42:
		tmp = t_2
	elif y <= 1.45e-44:
		tmp = x
	elif y <= 6.8e+65:
		tmp = t_1
	elif y <= 1.65e+130:
		tmp = t_2
	elif y <= 6.4e+273:
		tmp = t_1
	else:
		tmp = (y / a) * -z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	t_2 = Float64(y * Float64(Float64(-z) / a))
	tmp = 0.0
	if (y <= -6.6e+157)
		tmp = Float64(Float64(y * Float64(-z)) / a);
	elseif (y <= -2.7e+53)
		tmp = Float64(Float64(y / a) * t);
	elseif (y <= -5e-42)
		tmp = t_2;
	elseif (y <= 1.45e-44)
		tmp = x;
	elseif (y <= 6.8e+65)
		tmp = t_1;
	elseif (y <= 1.65e+130)
		tmp = t_2;
	elseif (y <= 6.4e+273)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / a) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	t_2 = y * (-z / a);
	tmp = 0.0;
	if (y <= -6.6e+157)
		tmp = (y * -z) / a;
	elseif (y <= -2.7e+53)
		tmp = (y / a) * t;
	elseif (y <= -5e-42)
		tmp = t_2;
	elseif (y <= 1.45e-44)
		tmp = x;
	elseif (y <= 6.8e+65)
		tmp = t_1;
	elseif (y <= 1.65e+130)
		tmp = t_2;
	elseif (y <= 6.4e+273)
		tmp = t_1;
	else
		tmp = (y / a) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e+157], N[(N[(y * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -2.7e+53], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -5e-42], t$95$2, If[LessEqual[y, 1.45e-44], x, If[LessEqual[y, 6.8e+65], t$95$1, If[LessEqual[y, 1.65e+130], t$95$2, If[LessEqual[y, 6.4e+273], t$95$1, N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -6.6000000000000003e157

   1. Initial program 87.8%

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

      1. sub-neg 87.8%

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

      2. distribute-frac-neg2 87.8%

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

      3. +-commutative 87.8%

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

      4. associate-/l* 97.0%

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

      5. fma-define 97.0%

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

      6. distribute-frac-neg2 97.0%

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

      7. distribute-neg-frac 97.0%

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

      8. sub-neg 97.0%

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

      9. distribute-neg-in 97.0%

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

      10. remove-double-neg 97.0%

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

      11. +-commutative 97.0%

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

      12. sub-neg 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around -inf 81.8%

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

   6. Taylor expanded in t around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-rgt-neg-out 72.3%

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

   8. Simplified 72.3%

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

   if -6.6000000000000003e157 < y < -2.70000000000000019e53

   1. Initial program 85.5%

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

   3. Taylor expanded in t around inf 62.7%

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

      1. associate-/l* 77.0%

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

   5. Simplified 77.0%

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

   if -2.70000000000000019e53 < y < -5.00000000000000003e-42 or 6.7999999999999999e65 < y < 1.65e130

   1. Initial program 89.5%

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

   3. Taylor expanded in z around inf 63.3%

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

      1. mul-1-neg 63.3%

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

      2. associate-/l* 68.3%

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

      3. distribute-rgt-neg-in 68.3%

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

      4. distribute-neg-frac2 68.3%

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

   5. Simplified 68.3%

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

   if -5.00000000000000003e-42 < y < 1.4500000000000001e-44

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 67.7%

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

   if 1.4500000000000001e-44 < y < 6.7999999999999999e65 or 1.65e130 < y < 6.4000000000000004e273

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. *-commutative 76.7%

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

      4. associate-*r/ 71.9%

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

      5. associate-/l* 74.5%

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

      6. distribute-lft-neg-in 74.5%

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

      7. distribute-rgt-in 96.7%

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

      8. sub-neg 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in t around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. associate-*r/ 55.5%

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

   8. Simplified 55.5%

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

   if 6.4000000000000004e273 < y

   1. Initial program 68.6%

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

   3. Taylor expanded in z around inf 46.6%

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

      1. mul-1-neg 46.6%

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

      2. associate-/l* 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

      4. distribute-neg-frac2 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in y around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. *-commutative 46.6%

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

      3. associate-*r/ 77.9%

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

      4. *-commutative 77.9%

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

      5. distribute-lft-neg-in 77.9%

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

      6. distribute-neg-frac2 77.9%

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

   8. Simplified 77.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+157}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-z}{a}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+65} \lor \neg \left(y \leq 1.85 \cdot 10^{+130}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z) a))))
   (if (<= y -2.2e+160)
     t_1
     (if (<= y -9.2e+51)
       (* (/ y a) t)
       (if (<= y -7e-37)
         t_1
         (if (<= y 2.6e-45)
           x
           (if (or (<= y 7.5e+65) (not (<= y 1.85e+130)))
             (* y (/ t a))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-z / a);
	double tmp;
	if (y <= -2.2e+160) {
		tmp = t_1;
	} else if (y <= -9.2e+51) {
		tmp = (y / a) * t;
	} else if (y <= -7e-37) {
		tmp = t_1;
	} else if (y <= 2.6e-45) {
		tmp = x;
	} else if ((y <= 7.5e+65) || !(y <= 1.85e+130)) {
		tmp = y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (-z / a)
    if (y <= (-2.2d+160)) then
        tmp = t_1
    else if (y <= (-9.2d+51)) then
        tmp = (y / a) * t
    else if (y <= (-7d-37)) then
        tmp = t_1
    else if (y <= 2.6d-45) then
        tmp = x
    else if ((y <= 7.5d+65) .or. (.not. (y <= 1.85d+130))) then
        tmp = y * (t / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-z / a);
	double tmp;
	if (y <= -2.2e+160) {
		tmp = t_1;
	} else if (y <= -9.2e+51) {
		tmp = (y / a) * t;
	} else if (y <= -7e-37) {
		tmp = t_1;
	} else if (y <= 2.6e-45) {
		tmp = x;
	} else if ((y <= 7.5e+65) || !(y <= 1.85e+130)) {
		tmp = y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-z / a)
	tmp = 0
	if y <= -2.2e+160:
		tmp = t_1
	elif y <= -9.2e+51:
		tmp = (y / a) * t
	elif y <= -7e-37:
		tmp = t_1
	elif y <= 2.6e-45:
		tmp = x
	elif (y <= 7.5e+65) or not (y <= 1.85e+130):
		tmp = y * (t / a)
	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 (y <= -2.2e+160)
		tmp = t_1;
	elseif (y <= -9.2e+51)
		tmp = Float64(Float64(y / a) * t);
	elseif (y <= -7e-37)
		tmp = t_1;
	elseif (y <= 2.6e-45)
		tmp = x;
	elseif ((y <= 7.5e+65) || !(y <= 1.85e+130))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-z / a);
	tmp = 0.0;
	if (y <= -2.2e+160)
		tmp = t_1;
	elseif (y <= -9.2e+51)
		tmp = (y / a) * t;
	elseif (y <= -7e-37)
		tmp = t_1;
	elseif (y <= 2.6e-45)
		tmp = x;
	elseif ((y <= 7.5e+65) || ~((y <= 1.85e+130)))
		tmp = y * (t / a);
	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[y, -2.2e+160], t$95$1, If[LessEqual[y, -9.2e+51], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -7e-37], t$95$1, If[LessEqual[y, 2.6e-45], x, If[Or[LessEqual[y, 7.5e+65], N[Not[LessEqual[y, 1.85e+130]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.19999999999999992e160 or -9.2000000000000002e51 < y < -7.0000000000000003e-37 or 7.50000000000000006e65 < y < 1.8500000000000001e130

   1. Initial program 88.7%

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

   3. Taylor expanded in z around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. associate-/l* 66.2%

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

      3. distribute-rgt-neg-in 66.2%

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

      4. distribute-neg-frac2 66.2%

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

   5. Simplified 66.2%

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

   if -2.19999999999999992e160 < y < -9.2000000000000002e51

   1. Initial program 85.5%

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

   3. Taylor expanded in t around inf 62.7%

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

      1. associate-/l* 77.0%

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

   5. Simplified 77.0%

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

   if -7.0000000000000003e-37 < y < 2.59999999999999987e-45

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 67.7%

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

   if 2.59999999999999987e-45 < y < 7.50000000000000006e65 or 1.8500000000000001e130 < y

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 74.3%

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

      1. +-commutative 74.3%

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

      2. mul-1-neg 74.3%

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

      3. *-commutative 74.3%

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

      4. associate-*r/ 72.7%

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

      5. associate-/l* 74.9%

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

      6. distribute-lft-neg-in 74.9%

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

      7. distribute-rgt-in 97.1%

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

      8. sub-neg 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in t around inf 49.3%

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

      1. *-commutative 49.3%

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

      2. associate-*r/ 54.3%

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

   8. Simplified 54.3%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+160}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+65} \lor \neg \left(y \leq 1.85 \cdot 10^{+130}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- z))))
   (if (<= y -3.3e+158)
     t_1
     (if (<= y -4.5e+53)
       (* (/ y a) t)
       (if (<= y -4e-38)
         (* y (/ (- z) a))
         (if (<= y 9e-45) x (if (<= y 4.5e+64) (* y (/ t a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -z;
	double tmp;
	if (y <= -3.3e+158) {
		tmp = t_1;
	} else if (y <= -4.5e+53) {
		tmp = (y / a) * t;
	} else if (y <= -4e-38) {
		tmp = y * (-z / a);
	} else if (y <= 9e-45) {
		tmp = x;
	} else if (y <= 4.5e+64) {
		tmp = y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / a) * -z
    if (y <= (-3.3d+158)) then
        tmp = t_1
    else if (y <= (-4.5d+53)) then
        tmp = (y / a) * t
    else if (y <= (-4d-38)) then
        tmp = y * (-z / a)
    else if (y <= 9d-45) then
        tmp = x
    else if (y <= 4.5d+64) then
        tmp = y * (t / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -z;
	double tmp;
	if (y <= -3.3e+158) {
		tmp = t_1;
	} else if (y <= -4.5e+53) {
		tmp = (y / a) * t;
	} else if (y <= -4e-38) {
		tmp = y * (-z / a);
	} else if (y <= 9e-45) {
		tmp = x;
	} else if (y <= 4.5e+64) {
		tmp = y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * -z
	tmp = 0
	if y <= -3.3e+158:
		tmp = t_1
	elif y <= -4.5e+53:
		tmp = (y / a) * t
	elif y <= -4e-38:
		tmp = y * (-z / a)
	elif y <= 9e-45:
		tmp = x
	elif y <= 4.5e+64:
		tmp = y * (t / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(-z))
	tmp = 0.0
	if (y <= -3.3e+158)
		tmp = t_1;
	elseif (y <= -4.5e+53)
		tmp = Float64(Float64(y / a) * t);
	elseif (y <= -4e-38)
		tmp = Float64(y * Float64(Float64(-z) / a));
	elseif (y <= 9e-45)
		tmp = x;
	elseif (y <= 4.5e+64)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * -z;
	tmp = 0.0;
	if (y <= -3.3e+158)
		tmp = t_1;
	elseif (y <= -4.5e+53)
		tmp = (y / a) * t;
	elseif (y <= -4e-38)
		tmp = y * (-z / a);
	elseif (y <= 9e-45)
		tmp = x;
	elseif (y <= 4.5e+64)
		tmp = y * (t / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[y, -3.3e+158], t$95$1, If[LessEqual[y, -4.5e+53], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -4e-38], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-45], x, If[LessEqual[y, 4.5e+64], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.30000000000000017e158 or 4.49999999999999973e64 < y

   1. Initial program 85.1%

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

   3. Taylor expanded in z around inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. associate-/l* 54.4%

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

      3. distribute-rgt-neg-in 54.4%

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

      4. distribute-neg-frac2 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in y around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-*r/ 57.3%

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

      4. *-commutative 57.3%

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

      5. distribute-lft-neg-in 57.3%

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

      6. distribute-neg-frac2 57.3%

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

   8. Simplified 57.3%

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

   if -3.30000000000000017e158 < y < -4.5000000000000002e53

   1. Initial program 85.5%

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

   3. Taylor expanded in t around inf 62.7%

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

      1. associate-/l* 77.0%

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

   5. Simplified 77.0%

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

   if -4.5000000000000002e53 < y < -3.9999999999999998e-38

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. associate-/l* 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. distribute-neg-frac2 70.9%

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

   5. Simplified 70.9%

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

   if -3.9999999999999998e-38 < y < 8.9999999999999997e-45

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 67.7%

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

   if 8.9999999999999997e-45 < y < 4.49999999999999973e64

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 95.9%

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

      1. +-commutative 95.9%

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

      2. mul-1-neg 95.9%

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

      3. *-commutative 95.9%

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

      4. associate-*r/ 95.9%

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

      5. associate-/l* 95.9%

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

      6. distribute-lft-neg-in 95.9%

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

      7. distribute-rgt-in 99.9%

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

      8. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-*r/ 52.1%

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

   8. Simplified 52.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+158}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-45} \lor \neg \left(y \leq 1.65 \cdot 10^{-142}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8e-45) (not (<= y 1.65e-142))) (* y (/ (- t z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8e-45) || !(y <= 1.65e-142)) {
		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 ((y <= (-8d-45)) .or. (.not. (y <= 1.65d-142))) 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 ((y <= -8e-45) || !(y <= 1.65e-142)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8e-45) or not (y <= 1.65e-142):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8e-45) || !(y <= 1.65e-142))
		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 ((y <= -8e-45) || ~((y <= 1.65e-142)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8e-45], N[Not[LessEqual[y, 1.65e-142]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999987e-45 or 1.6499999999999998e-142 < y

   1. Initial program 90.0%

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

   3. Taylor expanded in x around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. associate-*r/ 80.7%

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

      3. distribute-rgt-neg-in 80.7%

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

      4. neg-sub0 80.7%

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

      5. div-sub 75.5%

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

      6. associate-+l- 75.5%

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

      7. neg-sub0 75.5%

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

      8. +-commutative 75.5%

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

      9. sub-neg 75.5%

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

      10. div-sub 80.7%

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

   5. Simplified 80.7%

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

   if -7.99999999999999987e-45 < y < 1.6499999999999998e-142

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-45} \lor \neg \left(y \leq 1.65 \cdot 10^{-142}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.8e+137)
   (+ x (/ (* y t) a))
   (if (<= t 2.05e+114) (- x (/ y (/ a z))) (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.8e+137) {
		tmp = x + ((y * t) / a);
	} else if (t <= 2.05e+114) {
		tmp = x - (y / (a / z));
	} 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 (t <= (-9.8d+137)) then
        tmp = x + ((y * t) / a)
    else if (t <= 2.05d+114) then
        tmp = x - (y / (a / z))
    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 (t <= -9.8e+137) {
		tmp = x + ((y * t) / a);
	} else if (t <= 2.05e+114) {
		tmp = x - (y / (a / z));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.8e+137:
		tmp = x + ((y * t) / a)
	elif t <= 2.05e+114:
		tmp = x - (y / (a / z))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.8e+137)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (t <= 2.05e+114)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	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 (t <= -9.8e+137)
		tmp = x + ((y * t) / a);
	elseif (t <= 2.05e+114)
		tmp = x - (y / (a / z));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.8e+137], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+114], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.80000000000000065e137

   1. Initial program 94.5%

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

      1. sub-neg 94.5%

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

      2. distribute-frac-neg2 94.5%

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

      3. +-commutative 94.5%

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

      4. associate-/l* 94.2%

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

      5. fma-define 94.2%

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

      6. distribute-frac-neg2 94.2%

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

      7. distribute-neg-frac 94.2%

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

      8. sub-neg 94.2%

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

      9. distribute-neg-in 94.2%

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

      10. remove-double-neg 94.2%

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

      11. +-commutative 94.2%

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

      12. sub-neg 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around 0 85.7%

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

   if -9.80000000000000065e137 < t < 2.05e114

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf 83.6%

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

      1. associate-/l* 83.1%

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

   5. Simplified 83.1%

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

      1. clear-num 83.1%

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

      2. un-div-inv 83.2%

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

   7. Applied egg-rr 83.2%

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

   if 2.05e114 < t

   1. Initial program 85.1%

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

   3. Taylor expanded in x around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. associate-*r/ 84.7%

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

      3. distribute-rgt-neg-in 84.7%

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

      4. neg-sub0 84.7%

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

      5. div-sub 77.9%

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

      6. associate-+l- 77.9%

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

      7. neg-sub0 77.9%

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

      8. +-commutative 77.9%

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

      9. sub-neg 77.9%

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

      10. div-sub 84.7%

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

   5. Simplified 84.7%

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

      1. *-commutative 84.7%

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

      2. div-inv 84.7%

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

      3. associate-*l* 88.9%

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

      4. associate-/r/ 88.8%

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

      5. clear-num 88.9%

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

   7. Applied egg-rr 88.9%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.75e-36)
   (* (/ y a) (- t z))
   (if (<= y 1.35e+29) (+ x (/ (* y t) a)) (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.75e-36) {
		tmp = (y / a) * (t - z);
	} else if (y <= 1.35e+29) {
		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 (y <= (-2.75d-36)) then
        tmp = (y / a) * (t - z)
    else if (y <= 1.35d+29) 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 (y <= -2.75e-36) {
		tmp = (y / a) * (t - z);
	} else if (y <= 1.35e+29) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.75e-36:
		tmp = (y / a) * (t - z)
	elif y <= 1.35e+29:
		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 (y <= -2.75e-36)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (y <= 1.35e+29)
		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 (y <= -2.75e-36)
		tmp = (y / a) * (t - z);
	elseif (y <= 1.35e+29)
		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[y, -2.75e-36], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+29], 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 y < -2.74999999999999992e-36

   1. Initial program 89.5%

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

   3. Taylor expanded in x around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. associate-*r/ 86.5%

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

      3. distribute-rgt-neg-in 86.5%

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

      4. neg-sub0 86.5%

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

      5. div-sub 80.3%

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

      6. associate-+l- 80.3%

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

      7. neg-sub0 80.3%

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

      8. +-commutative 80.3%

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

      9. sub-neg 80.3%

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

      10. div-sub 86.5%

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

   5. Simplified 86.5%

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

      1. *-commutative 86.5%

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

      2. div-inv 86.4%

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

      3. associate-*l* 88.2%

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

      4. associate-/r/ 88.2%

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

      5. clear-num 88.2%

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

   7. Applied egg-rr 88.2%

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

   if -2.74999999999999992e-36 < y < 1.35e29

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-frac-neg2 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-/l* 88.9%

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

      5. fma-define 88.9%

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

      6. distribute-frac-neg2 88.9%

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

      7. distribute-neg-frac 88.9%

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

      8. sub-neg 88.9%

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

      9. distribute-neg-in 88.9%

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

      10. remove-double-neg 88.9%

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

      11. +-commutative 88.9%

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

      12. sub-neg 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in z around 0 82.1%

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

   if 1.35e29 < y

   1. Initial program 85.5%

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

   3. Taylor expanded in x around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. associate-*r/ 85.2%

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

      3. distribute-rgt-neg-in 85.2%

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

      4. neg-sub0 85.2%

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

      5. div-sub 78.3%

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

      6. associate-+l- 78.3%

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

      7. neg-sub0 78.3%

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

      8. +-commutative 78.3%

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

      9. sub-neg 78.3%

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

      10. div-sub 85.2%

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

   5. Simplified 85.2%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.7e-45)
   (* (/ y a) (- t z))
   (if (<= y 1.45e-139) x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.7e-45) {
		tmp = (y / a) * (t - z);
	} else if (y <= 1.45e-139) {
		tmp = x;
	} 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 (y <= (-1.7d-45)) then
        tmp = (y / a) * (t - z)
    else if (y <= 1.45d-139) then
        tmp = x
    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 (y <= -1.7e-45) {
		tmp = (y / a) * (t - z);
	} else if (y <= 1.45e-139) {
		tmp = x;
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.7e-45:
		tmp = (y / a) * (t - z)
	elif y <= 1.45e-139:
		tmp = x
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.7e-45)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (y <= 1.45e-139)
		tmp = x;
	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 (y <= -1.7e-45)
		tmp = (y / a) * (t - z);
	elseif (y <= 1.45e-139)
		tmp = x;
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.7e-45], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-139], x, N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000002e-45

   1. Initial program 89.9%

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

   3. Taylor expanded in x around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. associate-*r/ 85.1%

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

      3. distribute-rgt-neg-in 85.1%

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

      4. neg-sub0 85.1%

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

      5. div-sub 79.1%

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

      6. associate-+l- 79.1%

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

      7. neg-sub0 79.1%

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

      8. +-commutative 79.1%

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

      9. sub-neg 79.1%

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

      10. div-sub 85.1%

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

   5. Simplified 85.1%

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

      1. *-commutative 85.1%

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

      2. div-inv 84.9%

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

      3. associate-*l* 86.6%

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

      4. associate-/r/ 86.6%

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

      5. clear-num 86.7%

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

   7. Applied egg-rr 86.7%

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

   if -1.70000000000000002e-45 < y < 1.4499999999999999e-139

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.2%

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

   if 1.4499999999999999e-139 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. associate-*r/ 77.9%

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

      3. distribute-rgt-neg-in 77.9%

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

      4. neg-sub0 77.9%

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

      5. div-sub 73.2%

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

      6. associate-+l- 73.2%

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

      7. neg-sub0 73.2%

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

      8. +-commutative 73.2%

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

      9. sub-neg 73.2%

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

      10. div-sub 77.9%

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

   5. Simplified 77.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-36} \lor \neg \left(y \leq 9.5 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.6e-36) (not (<= y 9.5e-45))) (* (/ y a) t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.6e-36) || !(y <= 9.5e-45)) {
		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 ((y <= (-1.6d-36)) .or. (.not. (y <= 9.5d-45))) 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 ((y <= -1.6e-36) || !(y <= 9.5e-45)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.6e-36) or not (y <= 9.5e-45):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.6e-36) || !(y <= 9.5e-45))
		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 ((y <= -1.6e-36) || ~((y <= 9.5e-45)))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.6e-36], N[Not[LessEqual[y, 9.5e-45]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000011e-36 or 9.5000000000000002e-45 < y

   1. Initial program 88.8%

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

   3. Taylor expanded in t around inf 38.8%

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

      1. associate-/l* 45.4%

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

   5. Simplified 45.4%

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

   if -1.60000000000000011e-36 < y < 9.5000000000000002e-45

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 67.7%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-36} \lor \neg \left(y \leq 9.5 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

3. Taylor expanded in x around inf 36.5%

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

Developer target: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (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)))