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

Percentage Accurate: 93.4% → 97.1%

Time: 12.2s

Alternatives: 13

Speedup: 1.0×

• 25.1% 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: 93.4% 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, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((t - z) / (a / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. *-commutative 97.0%

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

   2. clear-num 96.9%

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

   3. un-div-inv 97.3%

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

5. Applied egg-rr 97.3%

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

6. Final simplification 97.3%

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

Alternative 2: 47.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a} \cdot \left(-y\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-159}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 1400:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z a) (- y))))
   (if (<= a -3.5e+73)
     x
     (if (<= a 1.25e-274)
       t_1
       (if (<= a 1.25e-159)
         (/ (* t y) a)
         (if (<= a 1400.0)
           t_1
           (if (<= a 6.5e+70)
             x
             (if (<= a 2.6e+80)
               t_1
               (if (<= a 1.04e+142) (* y (/ t a)) x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / a) * -y;
	double tmp;
	if (a <= -3.5e+73) {
		tmp = x;
	} else if (a <= 1.25e-274) {
		tmp = t_1;
	} else if (a <= 1.25e-159) {
		tmp = (t * y) / a;
	} else if (a <= 1400.0) {
		tmp = t_1;
	} else if (a <= 6.5e+70) {
		tmp = x;
	} else if (a <= 2.6e+80) {
		tmp = t_1;
	} else if (a <= 1.04e+142) {
		tmp = y * (t / 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) :: t_1
    real(8) :: tmp
    t_1 = (z / a) * -y
    if (a <= (-3.5d+73)) then
        tmp = x
    else if (a <= 1.25d-274) then
        tmp = t_1
    else if (a <= 1.25d-159) then
        tmp = (t * y) / a
    else if (a <= 1400.0d0) then
        tmp = t_1
    else if (a <= 6.5d+70) then
        tmp = x
    else if (a <= 2.6d+80) then
        tmp = t_1
    else if (a <= 1.04d+142) then
        tmp = y * (t / 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 t_1 = (z / a) * -y;
	double tmp;
	if (a <= -3.5e+73) {
		tmp = x;
	} else if (a <= 1.25e-274) {
		tmp = t_1;
	} else if (a <= 1.25e-159) {
		tmp = (t * y) / a;
	} else if (a <= 1400.0) {
		tmp = t_1;
	} else if (a <= 6.5e+70) {
		tmp = x;
	} else if (a <= 2.6e+80) {
		tmp = t_1;
	} else if (a <= 1.04e+142) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / a) * -y
	tmp = 0
	if a <= -3.5e+73:
		tmp = x
	elif a <= 1.25e-274:
		tmp = t_1
	elif a <= 1.25e-159:
		tmp = (t * y) / a
	elif a <= 1400.0:
		tmp = t_1
	elif a <= 6.5e+70:
		tmp = x
	elif a <= 2.6e+80:
		tmp = t_1
	elif a <= 1.04e+142:
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / a) * Float64(-y))
	tmp = 0.0
	if (a <= -3.5e+73)
		tmp = x;
	elseif (a <= 1.25e-274)
		tmp = t_1;
	elseif (a <= 1.25e-159)
		tmp = Float64(Float64(t * y) / a);
	elseif (a <= 1400.0)
		tmp = t_1;
	elseif (a <= 6.5e+70)
		tmp = x;
	elseif (a <= 2.6e+80)
		tmp = t_1;
	elseif (a <= 1.04e+142)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / a) * -y;
	tmp = 0.0;
	if (a <= -3.5e+73)
		tmp = x;
	elseif (a <= 1.25e-274)
		tmp = t_1;
	elseif (a <= 1.25e-159)
		tmp = (t * y) / a;
	elseif (a <= 1400.0)
		tmp = t_1;
	elseif (a <= 6.5e+70)
		tmp = x;
	elseif (a <= 2.6e+80)
		tmp = t_1;
	elseif (a <= 1.04e+142)
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision]}, If[LessEqual[a, -3.5e+73], x, If[LessEqual[a, 1.25e-274], t$95$1, If[LessEqual[a, 1.25e-159], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 1400.0], t$95$1, If[LessEqual[a, 6.5e+70], x, If[LessEqual[a, 2.6e+80], t$95$1, If[LessEqual[a, 1.04e+142], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.50000000000000002e73 or 1400 < a < 6.49999999999999978e70 or 1.04e142 < a

   1. Initial program 87.5%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 62.9%

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

   if -3.50000000000000002e73 < a < 1.25e-274 or 1.25000000000000008e-159 < a < 1400 or 6.49999999999999978e70 < a < 2.59999999999999982e80

   1. Initial program 97.5%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

      1. *-commutative 98.4%

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

      2. clear-num 98.2%

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

      3. un-div-inv 98.2%

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

   5. Applied egg-rr 98.2%

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

   6. Taylor expanded in z around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. associate-*r/ 56.0%

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

      3. distribute-rgt-neg-in 56.0%

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

      4. distribute-frac-neg 56.0%

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

   8. Simplified 56.0%

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

   if 1.25e-274 < a < 1.25000000000000008e-159

   1. Initial program 99.8%

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

      1. associate-*l/ 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in t around inf 70.3%

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

   if 2.59999999999999982e80 < a < 1.04e142

   1. Initial program 77.5%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

      1. *-commutative 94.1%

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

      2. clear-num 93.7%

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

      3. un-div-inv 93.9%

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

   5. Applied egg-rr 93.9%

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

   6. Taylor expanded in t around inf 27.2%

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

      1. associate-*l/ 43.3%

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

   8. Simplified 43.3%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-274}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-159}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 1400:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 49.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-159}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+81}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))))
   (if (<= a -3.8e+73)
     x
     (if (<= a 1.15e-273)
       t_1
       (if (<= a 1.12e-159)
         (/ (* t y) a)
         (if (<= a 9.5e-9)
           t_1
           (if (<= a 8.2e+70)
             x
             (if (<= a 3.1e+81)
               (* (/ z a) (- y))
               (if (<= a 3.3e+143) (* y (/ t a)) x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (a <= -3.8e+73) {
		tmp = x;
	} else if (a <= 1.15e-273) {
		tmp = t_1;
	} else if (a <= 1.12e-159) {
		tmp = (t * y) / a;
	} else if (a <= 9.5e-9) {
		tmp = t_1;
	} else if (a <= 8.2e+70) {
		tmp = x;
	} else if (a <= 3.1e+81) {
		tmp = (z / a) * -y;
	} else if (a <= 3.3e+143) {
		tmp = y * (t / 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) :: t_1
    real(8) :: tmp
    t_1 = z * (y / -a)
    if (a <= (-3.8d+73)) then
        tmp = x
    else if (a <= 1.15d-273) then
        tmp = t_1
    else if (a <= 1.12d-159) then
        tmp = (t * y) / a
    else if (a <= 9.5d-9) then
        tmp = t_1
    else if (a <= 8.2d+70) then
        tmp = x
    else if (a <= 3.1d+81) then
        tmp = (z / a) * -y
    else if (a <= 3.3d+143) then
        tmp = y * (t / 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 t_1 = z * (y / -a);
	double tmp;
	if (a <= -3.8e+73) {
		tmp = x;
	} else if (a <= 1.15e-273) {
		tmp = t_1;
	} else if (a <= 1.12e-159) {
		tmp = (t * y) / a;
	} else if (a <= 9.5e-9) {
		tmp = t_1;
	} else if (a <= 8.2e+70) {
		tmp = x;
	} else if (a <= 3.1e+81) {
		tmp = (z / a) * -y;
	} else if (a <= 3.3e+143) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	tmp = 0
	if a <= -3.8e+73:
		tmp = x
	elif a <= 1.15e-273:
		tmp = t_1
	elif a <= 1.12e-159:
		tmp = (t * y) / a
	elif a <= 9.5e-9:
		tmp = t_1
	elif a <= 8.2e+70:
		tmp = x
	elif a <= 3.1e+81:
		tmp = (z / a) * -y
	elif a <= 3.3e+143:
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	tmp = 0.0
	if (a <= -3.8e+73)
		tmp = x;
	elseif (a <= 1.15e-273)
		tmp = t_1;
	elseif (a <= 1.12e-159)
		tmp = Float64(Float64(t * y) / a);
	elseif (a <= 9.5e-9)
		tmp = t_1;
	elseif (a <= 8.2e+70)
		tmp = x;
	elseif (a <= 3.1e+81)
		tmp = Float64(Float64(z / a) * Float64(-y));
	elseif (a <= 3.3e+143)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	tmp = 0.0;
	if (a <= -3.8e+73)
		tmp = x;
	elseif (a <= 1.15e-273)
		tmp = t_1;
	elseif (a <= 1.12e-159)
		tmp = (t * y) / a;
	elseif (a <= 9.5e-9)
		tmp = t_1;
	elseif (a <= 8.2e+70)
		tmp = x;
	elseif (a <= 3.1e+81)
		tmp = (z / a) * -y;
	elseif (a <= 3.3e+143)
		tmp = y * (t / a);
	else
		tmp = x;
	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[a, -3.8e+73], x, If[LessEqual[a, 1.15e-273], t$95$1, If[LessEqual[a, 1.12e-159], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 9.5e-9], t$95$1, If[LessEqual[a, 8.2e+70], x, If[LessEqual[a, 3.1e+81], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[a, 3.3e+143], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.80000000000000022e73 or 9.5000000000000007e-9 < a < 8.2000000000000004e70 or 3.3e143 < a

   1. Initial program 87.5%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 62.9%

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

   if -3.80000000000000022e73 < a < 1.1499999999999999e-273 or 1.12000000000000006e-159 < a < 9.5000000000000007e-9

   1. Initial program 98.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 59.7%

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

      1. mul-1-neg 59.7%

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

      2. associate-*l/ 61.8%

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

      3. *-commutative 61.8%

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

      4. distribute-rgt-neg-in 61.8%

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

      5. *-lft-identity 61.8%

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

      6. associate-*l/ 61.7%

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

      7. remove-double-neg 61.7%

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

      8. neg-mul-1 61.7%

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

      9. associate-*r* 61.7%

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

      10. *-commutative 61.7%

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

      11. associate-*r/ 61.7%

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

      12. metadata-eval 61.7%

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

      13. metadata-eval 61.7%

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

      14. associate-/r* 61.7%

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

      15. neg-mul-1 61.7%

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

      16. *-commutative 61.7%

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

      17. associate-*r/ 61.8%

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

      18. *-rgt-identity 61.8%

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

      19. distribute-frac-neg 61.8%

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

      20. remove-double-neg 61.8%

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

   6. Simplified 61.8%

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

   if 1.1499999999999999e-273 < a < 1.12000000000000006e-159

   1. Initial program 99.8%

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

      1. associate-*l/ 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in t around inf 70.3%

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

   if 8.2000000000000004e70 < a < 3.1e81

   1. Initial program 69.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

   8. Simplified 100.0%

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

   if 3.1e81 < a < 3.3e143

   1. Initial program 77.5%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

      1. *-commutative 94.1%

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

      2. clear-num 93.7%

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

      3. un-div-inv 93.9%

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

   5. Applied egg-rr 93.9%

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

   6. Taylor expanded in t around inf 27.2%

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

      1. associate-*l/ 43.3%

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

   8. Simplified 43.3%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-159}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+81}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+223}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (* (/ y a) (- t z))))
   (if (<= z -1.1e+18)
     t_2
     (if (<= z 1.05e+64)
       t_1
       (if (<= z 4.8e+120)
         t_2
         (if (<= z 3.3e+168) t_1 (if (<= z 2e+223) (/ (- z) (/ a y)) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = (y / a) * (t - z);
	double tmp;
	if (z <= -1.1e+18) {
		tmp = t_2;
	} else if (z <= 1.05e+64) {
		tmp = t_1;
	} else if (z <= 4.8e+120) {
		tmp = t_2;
	} else if (z <= 3.3e+168) {
		tmp = t_1;
	} else if (z <= 2e+223) {
		tmp = -z / (a / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    t_2 = (y / a) * (t - z)
    if (z <= (-1.1d+18)) then
        tmp = t_2
    else if (z <= 1.05d+64) then
        tmp = t_1
    else if (z <= 4.8d+120) then
        tmp = t_2
    else if (z <= 3.3d+168) then
        tmp = t_1
    else if (z <= 2d+223) then
        tmp = -z / (a / y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = (y / a) * (t - z);
	double tmp;
	if (z <= -1.1e+18) {
		tmp = t_2;
	} else if (z <= 1.05e+64) {
		tmp = t_1;
	} else if (z <= 4.8e+120) {
		tmp = t_2;
	} else if (z <= 3.3e+168) {
		tmp = t_1;
	} else if (z <= 2e+223) {
		tmp = -z / (a / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = (y / a) * (t - z)
	tmp = 0
	if z <= -1.1e+18:
		tmp = t_2
	elif z <= 1.05e+64:
		tmp = t_1
	elif z <= 4.8e+120:
		tmp = t_2
	elif z <= 3.3e+168:
		tmp = t_1
	elif z <= 2e+223:
		tmp = -z / (a / y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(Float64(y / a) * Float64(t - z))
	tmp = 0.0
	if (z <= -1.1e+18)
		tmp = t_2;
	elseif (z <= 1.05e+64)
		tmp = t_1;
	elseif (z <= 4.8e+120)
		tmp = t_2;
	elseif (z <= 3.3e+168)
		tmp = t_1;
	elseif (z <= 2e+223)
		tmp = Float64(Float64(-z) / Float64(a / y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = (y / a) * (t - z);
	tmp = 0.0;
	if (z <= -1.1e+18)
		tmp = t_2;
	elseif (z <= 1.05e+64)
		tmp = t_1;
	elseif (z <= 4.8e+120)
		tmp = t_2;
	elseif (z <= 3.3e+168)
		tmp = t_1;
	elseif (z <= 2e+223)
		tmp = -z / (a / y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+18], t$95$2, If[LessEqual[z, 1.05e+64], t$95$1, If[LessEqual[z, 4.8e+120], t$95$2, If[LessEqual[z, 3.3e+168], t$95$1, If[LessEqual[z, 2e+223], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e18 or 1.05e64 < z < 4.80000000000000002e120 or 2.00000000000000009e223 < z

   1. Initial program 88.9%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

      1. *-commutative 97.1%

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

      2. clear-num 96.7%

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

      3. un-div-inv 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in x around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-*r/ 73.5%

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

      3. distribute-rgt-neg-in 73.5%

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

      4. neg-sub0 73.5%

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

      5. div-sub 71.4%

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

      6. associate--r- 71.4%

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

      7. neg-sub0 71.4%

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

      8. distribute-frac-neg 71.4%

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

      9. +-commutative 71.4%

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

      10. distribute-frac-neg 71.4%

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

      11. sub-neg 71.4%

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

      12. distribute-rgt-out-- 69.2%

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

      13. associate-*l/ 69.4%

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

      14. associate-*r/ 67.1%

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

      15. associate-*l/ 63.0%

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

      16. associate-*r/ 71.2%

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

      17. distribute-rgt-out-- 78.6%

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

   8. Simplified 78.6%

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

   if -1.1e18 < z < 1.05e64 or 4.80000000000000002e120 < z < 3.2999999999999999e168

   1. Initial program 93.7%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around 0 82.9%

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

      1. cancel-sign-sub-inv 82.9%

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

      2. metadata-eval 82.9%

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

      3. *-lft-identity 82.9%

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

      4. +-commutative 82.9%

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

      5. associate-*r/ 87.3%

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

   6. Simplified 87.3%

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

   if 3.2999999999999999e168 < z < 2.00000000000000009e223

   1. Initial program 99.8%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around inf 89.6%

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

      1. mul-1-neg 89.6%

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

      2. associate-*l/ 78.9%

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

      3. *-commutative 78.9%

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

      4. distribute-rgt-neg-in 78.9%

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

      5. *-lft-identity 78.9%

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

      6. associate-*l/ 79.0%

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

      7. remove-double-neg 79.0%

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

      8. neg-mul-1 79.0%

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

      9. associate-*r* 79.0%

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

      10. *-commutative 79.0%

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

      11. associate-*r/ 79.0%

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

      12. metadata-eval 79.0%

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

      13. metadata-eval 79.0%

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

      14. associate-/r* 79.0%

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

      15. neg-mul-1 79.0%

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

      16. *-commutative 79.0%

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

      17. associate-*r/ 78.9%

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

      18. *-rgt-identity 78.9%

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

      19. distribute-frac-neg 78.9%

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

      20. remove-double-neg 78.9%

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

   6. Simplified 78.9%

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

      1. associate-*r/ 89.6%

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

      2. add-sqr-sqrt 56.3%

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

      3. sqrt-unprod 55.8%

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

      4. sqr-neg 55.8%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 0.8%

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

      7. associate-/l* 1.0%

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

      8. frac-2neg 1.0%

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

      9. distribute-frac-neg 1.0%

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

      10. add-sqr-sqrt 0.9%

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

      11. sqrt-unprod 23.9%

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

      12. sqr-neg 23.9%

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

      13. sqrt-unprod 33.2%

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

      14. add-sqr-sqrt 79.2%

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

   8. Applied egg-rr 79.2%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+64}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+168}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+223}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 5: 78.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+167}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+229}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t z))))
   (if (<= z -6.2e+22)
     t_1
     (if (<= z 6.4e+63)
       (+ x (/ t (/ a y)))
       (if (<= z 4.4e+120)
         t_1
         (if (<= z 4.6e+167)
           (+ x (* t (/ y a)))
           (if (<= z 7.2e+229) (/ (- z) (/ a y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (z <= -6.2e+22) {
		tmp = t_1;
	} else if (z <= 6.4e+63) {
		tmp = x + (t / (a / y));
	} else if (z <= 4.4e+120) {
		tmp = t_1;
	} else if (z <= 4.6e+167) {
		tmp = x + (t * (y / a));
	} else if (z <= 7.2e+229) {
		tmp = -z / (a / y);
	} 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) * (t - z)
    if (z <= (-6.2d+22)) then
        tmp = t_1
    else if (z <= 6.4d+63) then
        tmp = x + (t / (a / y))
    else if (z <= 4.4d+120) then
        tmp = t_1
    else if (z <= 4.6d+167) then
        tmp = x + (t * (y / a))
    else if (z <= 7.2d+229) then
        tmp = -z / (a / y)
    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) * (t - z);
	double tmp;
	if (z <= -6.2e+22) {
		tmp = t_1;
	} else if (z <= 6.4e+63) {
		tmp = x + (t / (a / y));
	} else if (z <= 4.4e+120) {
		tmp = t_1;
	} else if (z <= 4.6e+167) {
		tmp = x + (t * (y / a));
	} else if (z <= 7.2e+229) {
		tmp = -z / (a / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (t - z)
	tmp = 0
	if z <= -6.2e+22:
		tmp = t_1
	elif z <= 6.4e+63:
		tmp = x + (t / (a / y))
	elif z <= 4.4e+120:
		tmp = t_1
	elif z <= 4.6e+167:
		tmp = x + (t * (y / a))
	elif z <= 7.2e+229:
		tmp = -z / (a / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(t - z))
	tmp = 0.0
	if (z <= -6.2e+22)
		tmp = t_1;
	elseif (z <= 6.4e+63)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 4.4e+120)
		tmp = t_1;
	elseif (z <= 4.6e+167)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 7.2e+229)
		tmp = Float64(Float64(-z) / Float64(a / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * (t - z);
	tmp = 0.0;
	if (z <= -6.2e+22)
		tmp = t_1;
	elseif (z <= 6.4e+63)
		tmp = x + (t / (a / y));
	elseif (z <= 4.4e+120)
		tmp = t_1;
	elseif (z <= 4.6e+167)
		tmp = x + (t * (y / a));
	elseif (z <= 7.2e+229)
		tmp = -z / (a / y);
	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] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+22], t$95$1, If[LessEqual[z, 6.4e+63], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+120], t$95$1, If[LessEqual[z, 4.6e+167], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+229], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.2000000000000004e22 or 6.40000000000000022e63 < z < 4.4000000000000003e120 or 7.19999999999999973e229 < z

   1. Initial program 88.9%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

      1. *-commutative 97.1%

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

      2. clear-num 96.7%

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

      3. un-div-inv 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in x around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-*r/ 73.5%

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

      3. distribute-rgt-neg-in 73.5%

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

      4. neg-sub0 73.5%

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

      5. div-sub 71.4%

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

      6. associate--r- 71.4%

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

      7. neg-sub0 71.4%

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

      8. distribute-frac-neg 71.4%

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

      9. +-commutative 71.4%

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

      10. distribute-frac-neg 71.4%

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

      11. sub-neg 71.4%

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

      12. distribute-rgt-out-- 69.2%

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

      13. associate-*l/ 69.4%

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

      14. associate-*r/ 67.1%

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

      15. associate-*l/ 63.0%

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

      16. associate-*r/ 71.2%

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

      17. distribute-rgt-out-- 78.6%

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

   8. Simplified 78.6%

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

   if -6.2000000000000004e22 < z < 6.40000000000000022e63

   1. Initial program 94.0%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 83.2%

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

      1. cancel-sign-sub-inv 83.2%

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

      2. metadata-eval 83.2%

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

      3. *-lft-identity 83.2%

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

      4. +-commutative 83.2%

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

      5. associate-*r/ 87.1%

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

   6. Simplified 87.1%

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

      1. clear-num 87.1%

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

      2. div-inv 87.7%

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

   8. Applied egg-rr 87.7%

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

   if 4.4000000000000003e120 < z < 4.59999999999999976e167

   1. Initial program 88.9%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around 0 78.7%

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

      1. cancel-sign-sub-inv 78.7%

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

      2. metadata-eval 78.7%

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

      3. *-lft-identity 78.7%

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

      4. +-commutative 78.7%

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

      5. associate-*r/ 89.8%

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

   6. Simplified 89.8%

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

   if 4.59999999999999976e167 < z < 7.19999999999999973e229

   1. Initial program 99.8%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around inf 89.6%

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

      1. mul-1-neg 89.6%

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

      2. associate-*l/ 78.9%

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

      3. *-commutative 78.9%

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

      4. distribute-rgt-neg-in 78.9%

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

      5. *-lft-identity 78.9%

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

      6. associate-*l/ 79.0%

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

      7. remove-double-neg 79.0%

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

      8. neg-mul-1 79.0%

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

      9. associate-*r* 79.0%

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

      10. *-commutative 79.0%

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

      11. associate-*r/ 79.0%

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

      12. metadata-eval 79.0%

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

      13. metadata-eval 79.0%

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

      14. associate-/r* 79.0%

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

      15. neg-mul-1 79.0%

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

      16. *-commutative 79.0%

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

      17. associate-*r/ 78.9%

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

      18. *-rgt-identity 78.9%

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

      19. distribute-frac-neg 78.9%

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

      20. remove-double-neg 78.9%

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

   6. Simplified 78.9%

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

      1. associate-*r/ 89.6%

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

      2. add-sqr-sqrt 56.3%

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

      3. sqrt-unprod 55.8%

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

      4. sqr-neg 55.8%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 0.8%

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

      7. associate-/l* 1.0%

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

      8. frac-2neg 1.0%

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

      9. distribute-frac-neg 1.0%

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

      10. add-sqr-sqrt 0.9%

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

      11. sqrt-unprod 23.9%

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

      12. sqr-neg 23.9%

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

      13. sqrt-unprod 33.2%

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

      14. add-sqr-sqrt 79.2%

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

   8. Applied egg-rr 79.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+167}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+229}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 6: 67.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-194} \lor \neg \left(y \leq 5.2 \cdot 10^{-91}\right) \land \left(y \leq 1.2 \cdot 10^{-27} \lor \neg \left(y \leq 8.5 \cdot 10^{-20}\right)\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9.4e-194)
         (and (not (<= y 5.2e-91)) (or (<= y 1.2e-27) (not (<= y 8.5e-20)))))
   (* y (/ (- t z) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9.4e-194) || (!(y <= 5.2e-91) && ((y <= 1.2e-27) || !(y <= 8.5e-20)))) {
		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 <= (-9.4d-194)) .or. (.not. (y <= 5.2d-91)) .and. (y <= 1.2d-27) .or. (.not. (y <= 8.5d-20))) 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 <= -9.4e-194) || (!(y <= 5.2e-91) && ((y <= 1.2e-27) || !(y <= 8.5e-20)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9.4e-194) or (not (y <= 5.2e-91) and ((y <= 1.2e-27) or not (y <= 8.5e-20))):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9.4e-194) || (!(y <= 5.2e-91) && ((y <= 1.2e-27) || !(y <= 8.5e-20))))
		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 <= -9.4e-194) || (~((y <= 5.2e-91)) && ((y <= 1.2e-27) || ~((y <= 8.5e-20)))))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9.4e-194], And[N[Not[LessEqual[y, 5.2e-91]], $MachinePrecision], Or[LessEqual[y, 1.2e-27], N[Not[LessEqual[y, 8.5e-20]], $MachinePrecision]]]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.4000000000000005e-194 or 5.20000000000000028e-91 < y < 1.20000000000000001e-27 or 8.5000000000000005e-20 < y

   1. Initial program 90.1%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in x around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. associate-*r/ 70.9%

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

      3. distribute-rgt-neg-out 70.9%

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

      4. distribute-neg-frac 70.9%

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

      5. neg-sub0 70.9%

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

      6. associate--r- 70.9%

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

      7. neg-sub0 70.9%

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

      8. +-commutative 70.9%

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

      9. sub-neg 70.9%

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

   6. Simplified 70.9%

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

   if -9.4000000000000005e-194 < y < 5.20000000000000028e-91 or 1.20000000000000001e-27 < y < 8.5000000000000005e-20

   1. Initial program 98.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 71.4%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-194} \lor \neg \left(y \leq 5.2 \cdot 10^{-91}\right) \land \left(y \leq 1.2 \cdot 10^{-27} \lor \neg \left(y \leq 8.5 \cdot 10^{-20}\right)\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 67.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t z))))
   (if (<= y -9e-194)
     t_1
     (if (<= y 3.4e-93)
       x
       (if (<= y 9.5e-28) t_1 (if (<= y 5.8e-20) x (* y (/ (- t z) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (y <= -9e-194) {
		tmp = t_1;
	} else if (y <= 3.4e-93) {
		tmp = x;
	} else if (y <= 9.5e-28) {
		tmp = t_1;
	} else if (y <= 5.8e-20) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (y / a) * (t - z)
    if (y <= (-9d-194)) then
        tmp = t_1
    else if (y <= 3.4d-93) then
        tmp = x
    else if (y <= 9.5d-28) then
        tmp = t_1
    else if (y <= 5.8d-20) 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 t_1 = (y / a) * (t - z);
	double tmp;
	if (y <= -9e-194) {
		tmp = t_1;
	} else if (y <= 3.4e-93) {
		tmp = x;
	} else if (y <= 9.5e-28) {
		tmp = t_1;
	} else if (y <= 5.8e-20) {
		tmp = x;
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (t - z)
	tmp = 0
	if y <= -9e-194:
		tmp = t_1
	elif y <= 3.4e-93:
		tmp = x
	elif y <= 9.5e-28:
		tmp = t_1
	elif y <= 5.8e-20:
		tmp = x
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(t - z))
	tmp = 0.0
	if (y <= -9e-194)
		tmp = t_1;
	elseif (y <= 3.4e-93)
		tmp = x;
	elseif (y <= 9.5e-28)
		tmp = t_1;
	elseif (y <= 5.8e-20)
		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)
	t_1 = (y / a) * (t - z);
	tmp = 0.0;
	if (y <= -9e-194)
		tmp = t_1;
	elseif (y <= 3.4e-93)
		tmp = x;
	elseif (y <= 9.5e-28)
		tmp = t_1;
	elseif (y <= 5.8e-20)
		tmp = x;
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-194], t$95$1, If[LessEqual[y, 3.4e-93], x, If[LessEqual[y, 9.5e-28], t$95$1, If[LessEqual[y, 5.8e-20], x, N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999997e-194 or 3.40000000000000001e-93 < y < 9.50000000000000001e-28

   1. Initial program 94.3%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

      1. *-commutative 97.5%

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

      2. clear-num 97.5%

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

      3. un-div-inv 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in x around 0 67.1%

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

      1. mul-1-neg 67.1%

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

      2. associate-*r/ 65.2%

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

      3. distribute-rgt-neg-in 65.2%

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

      4. neg-sub0 65.2%

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

      5. div-sub 63.5%

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

      6. associate--r- 63.5%

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

      7. neg-sub0 63.5%

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

      8. distribute-frac-neg 63.5%

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

      9. +-commutative 63.5%

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

      10. distribute-frac-neg 63.5%

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

      11. sub-neg 63.5%

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

      12. distribute-rgt-out-- 59.2%

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

      13. associate-*l/ 60.6%

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

      14. associate-*r/ 60.5%

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

      15. associate-*l/ 61.2%

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

      16. associate-*r/ 61.3%

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

      17. distribute-rgt-out-- 68.1%

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

   8. Simplified 68.1%

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

   if -8.9999999999999997e-194 < y < 3.40000000000000001e-93 or 9.50000000000000001e-28 < y < 5.8e-20

   1. Initial program 98.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 71.4%

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

   if 5.8e-20 < y

   1. Initial program 83.3%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. associate-*r/ 80.0%

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

      3. distribute-rgt-neg-out 80.0%

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

      4. distribute-neg-frac 80.0%

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

      5. neg-sub0 80.0%

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

      6. associate--r- 80.0%

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

      7. neg-sub0 80.0%

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

      8. +-commutative 80.0%

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

      9. sub-neg 80.0%

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

   6. Simplified 80.0%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-194}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]

Alternative 8: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-84} \lor \neg \left(z \leq 6.2 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e-84) (not (<= z 6.2e+63)))
   (* (/ y a) (- t z))
   (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e-84) || !(z <= 6.2e+63)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2d-84)) .or. (.not. (z <= 6.2d+63))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + ((t * y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e-84) || !(z <= 6.2e+63)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e-84) or not (z <= 6.2e+63):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e-84) || !(z <= 6.2e+63))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e-84) || ~((z <= 6.2e+63)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e-84], N[Not[LessEqual[z, 6.2e+63]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-84 or 6.2000000000000001e63 < z

   1. Initial program 90.8%

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

      1. *-commutative 97.0%

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

      2. clear-num 96.8%

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

      3. un-div-inv 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in x around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-*r/ 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

      4. neg-sub0 69.2%

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

      5. div-sub 65.9%

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

      6. associate--r- 65.9%

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

      7. neg-sub0 65.9%

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

      8. distribute-frac-neg 65.9%

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

      9. +-commutative 65.9%

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

      10. distribute-frac-neg 65.9%

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

      11. sub-neg 65.9%

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

      12. distribute-rgt-out-- 61.9%

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

      13. associate-*l/ 62.1%

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

      14. associate-*r/ 59.6%

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

      15. associate-*l/ 58.8%

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

      16. associate-*r/ 64.2%

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

      17. distribute-rgt-out-- 74.6%

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

   8. Simplified 74.6%

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

   if -2.0000000000000001e-84 < z < 6.2000000000000001e63

   1. Initial program 93.5%

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

      1. sub-neg 93.5%

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

      2. distribute-frac-neg 93.5%

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

      3. distribute-lft-neg-out 93.5%

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

      4. +-commutative 93.5%

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

      5. distribute-lft-neg-out 93.5%

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

      6. distribute-rgt-neg-in 93.5%

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

      7. associate-*l/ 97.0%

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

      8. fma-def 97.0%

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

      9. sub-neg 97.0%

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

      10. distribute-neg-in 97.0%

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

      11. remove-double-neg 97.0%

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

      12. +-commutative 97.0%

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

      13. sub-neg 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around 0 85.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-84} \lor \neg \left(z \leq 6.2 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]

Alternative 9: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-84} \lor \neg \left(z \leq 3.6 \cdot 10^{-36}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e-84) (not (<= z 3.6e-36)))
   (- x (* z (/ y a)))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e-84) || !(z <= 3.6e-36)) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + (t / (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 <= (-2d-84)) .or. (.not. (z <= 3.6d-36))) then
        tmp = x - (z * (y / a))
    else
        tmp = x + (t / (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 <= -2e-84) || !(z <= 3.6e-36)) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e-84) or not (z <= 3.6e-36):
		tmp = x - (z * (y / a))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e-84) || !(z <= 3.6e-36))
		tmp = Float64(x - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e-84) || ~((z <= 3.6e-36)))
		tmp = x - (z * (y / a));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e-84], N[Not[LessEqual[z, 3.6e-36]], $MachinePrecision]], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-84 or 3.60000000000000032e-36 < z

   1. Initial program 90.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 80.9%

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

      1. associate-*l/ 84.9%

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

      2. *-commutative 84.9%

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

   6. Simplified 84.9%

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

   if -2.0000000000000001e-84 < z < 3.60000000000000032e-36

   1. Initial program 93.9%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 90.5%

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

      1. cancel-sign-sub-inv 90.5%

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

      2. metadata-eval 90.5%

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

      3. *-lft-identity 90.5%

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

      4. +-commutative 90.5%

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

      5. associate-*r/ 91.4%

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

   6. Simplified 91.4%

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

      1. clear-num 91.4%

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

      2. div-inv 92.3%

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

   8. Applied egg-rr 92.3%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-84} \lor \neg \left(z \leq 3.6 \cdot 10^{-36}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.6e+54) x (if (<= a 1.8e-55) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.6e+54) {
		tmp = x;
	} else if (a <= 1.8e-55) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.6d+54)) then
        tmp = x
    else if (a <= 1.8d-55) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.6e+54) {
		tmp = x;
	} else if (a <= 1.8e-55) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.6e+54:
		tmp = x
	elif a <= 1.8e-55:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.6e+54)
		tmp = x;
	elseif (a <= 1.8e-55)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.6e+54)
		tmp = x;
	elseif (a <= 1.8e-55)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.6e+54], x, If[LessEqual[a, 1.8e-55], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.6e54 or 1.8e-55 < a

   1. Initial program 87.0%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around inf 55.2%

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

   if -6.6e54 < a < 1.8e-55

   1. Initial program 98.3%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in t around inf 41.7%

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

      1. associate-*r/ 43.3%

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

   6. Simplified 43.3%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.42e+56) x (if (<= a 4.4e-54) (/ t (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.42e+56) {
		tmp = x;
	} else if (a <= 4.4e-54) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.42d+56)) then
        tmp = x
    else if (a <= 4.4d-54) then
        tmp = t / (a / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.42e+56) {
		tmp = x;
	} else if (a <= 4.4e-54) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.42e+56:
		tmp = x
	elif a <= 4.4e-54:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.42e+56)
		tmp = x;
	elseif (a <= 4.4e-54)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.42e+56)
		tmp = x;
	elseif (a <= 4.4e-54)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.42e+56], x, If[LessEqual[a, 4.4e-54], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.42e56 or 4.3999999999999999e-54 < a

   1. Initial program 87.0%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around inf 55.2%

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

   if -1.42e56 < a < 4.3999999999999999e-54

   1. Initial program 98.3%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in t around inf 41.7%

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

      1. associate-/l* 44.1%

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

   6. Simplified 44.1%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 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 92.2%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. Final simplification 97.0%

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

Alternative 13: 39.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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 inf 37.5%

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

5. Final simplification 37.5%

   \[\leadsto x \]

Developer target: 99.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023336 
(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)))