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

Percentage Accurate: 93.1% → 97.2%

Time: 13.8s

Alternatives: 15

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: 93.1% 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: 97.2% 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/ 97.3%

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

3. Simplified 97.3%

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

   1. *-commutative 97.3%

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

   2. clear-num 97.0%

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

   3. un-div-inv 97.5%

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

5. Applied egg-rr 97.5%

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

6. Final simplification 97.5%

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

Alternative 2: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-209}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+155} \lor \neg \left(t \leq 2 \cdot 10^{+170}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= t -5.8e-19)
     t_1
     (if (<= t 2e-209)
       (- x (/ (* z y) a))
       (if (<= t 6.1e+72)
         (- x (/ y (/ a z)))
         (if (or (<= t 2.5e+155) (not (<= t 2e+170)))
           t_1
           (/ (* y (- t z)) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (t <= -5.8e-19) {
		tmp = t_1;
	} else if (t <= 2e-209) {
		tmp = x - ((z * y) / a);
	} else if (t <= 6.1e+72) {
		tmp = x - (y / (a / z));
	} else if ((t <= 2.5e+155) || !(t <= 2e+170)) {
		tmp = t_1;
	} 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 = x + (t * (y / a))
    if (t <= (-5.8d-19)) then
        tmp = t_1
    else if (t <= 2d-209) then
        tmp = x - ((z * y) / a)
    else if (t <= 6.1d+72) then
        tmp = x - (y / (a / z))
    else if ((t <= 2.5d+155) .or. (.not. (t <= 2d+170))) then
        tmp = t_1
    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 = x + (t * (y / a));
	double tmp;
	if (t <= -5.8e-19) {
		tmp = t_1;
	} else if (t <= 2e-209) {
		tmp = x - ((z * y) / a);
	} else if (t <= 6.1e+72) {
		tmp = x - (y / (a / z));
	} else if ((t <= 2.5e+155) || !(t <= 2e+170)) {
		tmp = t_1;
	} else {
		tmp = (y * (t - z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if t <= -5.8e-19:
		tmp = t_1
	elif t <= 2e-209:
		tmp = x - ((z * y) / a)
	elif t <= 6.1e+72:
		tmp = x - (y / (a / z))
	elif (t <= 2.5e+155) or not (t <= 2e+170):
		tmp = t_1
	else:
		tmp = (y * (t - z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (t <= -5.8e-19)
		tmp = t_1;
	elseif (t <= 2e-209)
		tmp = Float64(x - Float64(Float64(z * y) / a));
	elseif (t <= 6.1e+72)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif ((t <= 2.5e+155) || !(t <= 2e+170))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(t - z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (t <= -5.8e-19)
		tmp = t_1;
	elseif (t <= 2e-209)
		tmp = x - ((z * y) / a);
	elseif (t <= 6.1e+72)
		tmp = x - (y / (a / z));
	elseif ((t <= 2.5e+155) || ~((t <= 2e+170)))
		tmp = t_1;
	else
		tmp = (y * (t - z)) / a;
	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]}, If[LessEqual[t, -5.8e-19], t$95$1, If[LessEqual[t, 2e-209], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.1e+72], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.5e+155], N[Not[LessEqual[t, 2e+170]], $MachinePrecision]], t$95$1, N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.8e-19 or 6.09999999999999991e72 < t < 2.5e155 or 2.00000000000000007e170 < t

   1. Initial program 86.8%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 80.2%

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

      1. cancel-sign-sub-inv 80.2%

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

      2. metadata-eval 80.2%

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

      3. *-lft-identity 80.2%

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

      4. +-commutative 80.2%

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

      5. associate-*l/ 91.7%

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

      6. *-commutative 91.7%

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

   6. Simplified 91.7%

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

   if -5.8e-19 < t < 2.0000000000000001e-209

   1. Initial program 99.8%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 90.6%

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

   if 2.0000000000000001e-209 < t < 6.09999999999999991e72

   1. Initial program 91.0%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around inf 78.8%

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

      1. associate-/l* 86.7%

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

   6. Simplified 86.7%

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

   if 2.5e155 < t < 2.00000000000000007e170

   1. Initial program 99.6%

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

      1. associate-*l/ 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in x around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. distribute-frac-neg 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. associate-*r/ 76.0%

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

   6. Simplified 76.0%

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

   7. Taylor expanded in y around 0 99.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-19}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-209}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+155} \lor \neg \left(t \leq 2 \cdot 10^{+170}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]

Alternative 3: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-210}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+155}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+174}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= t -6.6e-18)
     t_1
     (if (<= t 2.9e-210)
       (- x (/ (* z y) a))
       (if (<= t 6.2e+72)
         (- x (/ y (/ a z)))
         (if (<= t 4.1e+155)
           (- x (/ y (/ (- a) t)))
           (if (<= t 2.9e+174) (* (/ y a) (- t z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (t <= -6.6e-18) {
		tmp = t_1;
	} else if (t <= 2.9e-210) {
		tmp = x - ((z * y) / a);
	} else if (t <= 6.2e+72) {
		tmp = x - (y / (a / z));
	} else if (t <= 4.1e+155) {
		tmp = x - (y / (-a / t));
	} else if (t <= 2.9e+174) {
		tmp = (y / a) * (t - z);
	} 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 = x + (t * (y / a))
    if (t <= (-6.6d-18)) then
        tmp = t_1
    else if (t <= 2.9d-210) then
        tmp = x - ((z * y) / a)
    else if (t <= 6.2d+72) then
        tmp = x - (y / (a / z))
    else if (t <= 4.1d+155) then
        tmp = x - (y / (-a / t))
    else if (t <= 2.9d+174) then
        tmp = (y / a) * (t - z)
    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 = x + (t * (y / a));
	double tmp;
	if (t <= -6.6e-18) {
		tmp = t_1;
	} else if (t <= 2.9e-210) {
		tmp = x - ((z * y) / a);
	} else if (t <= 6.2e+72) {
		tmp = x - (y / (a / z));
	} else if (t <= 4.1e+155) {
		tmp = x - (y / (-a / t));
	} else if (t <= 2.9e+174) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if t <= -6.6e-18:
		tmp = t_1
	elif t <= 2.9e-210:
		tmp = x - ((z * y) / a)
	elif t <= 6.2e+72:
		tmp = x - (y / (a / z))
	elif t <= 4.1e+155:
		tmp = x - (y / (-a / t))
	elif t <= 2.9e+174:
		tmp = (y / a) * (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (t <= -6.6e-18)
		tmp = t_1;
	elseif (t <= 2.9e-210)
		tmp = Float64(x - Float64(Float64(z * y) / a));
	elseif (t <= 6.2e+72)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif (t <= 4.1e+155)
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	elseif (t <= 2.9e+174)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (t <= -6.6e-18)
		tmp = t_1;
	elseif (t <= 2.9e-210)
		tmp = x - ((z * y) / a);
	elseif (t <= 6.2e+72)
		tmp = x - (y / (a / z));
	elseif (t <= 4.1e+155)
		tmp = x - (y / (-a / t));
	elseif (t <= 2.9e+174)
		tmp = (y / a) * (t - z);
	else
		tmp = t_1;
	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]}, If[LessEqual[t, -6.6e-18], t$95$1, If[LessEqual[t, 2.9e-210], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+72], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e+155], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+174], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.6000000000000003e-18 or 2.9e174 < t

   1. Initial program 87.4%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 80.1%

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

      1. cancel-sign-sub-inv 80.1%

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

      2. metadata-eval 80.1%

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

      3. *-lft-identity 80.1%

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

      4. +-commutative 80.1%

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

      5. associate-*l/ 90.9%

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

      6. *-commutative 90.9%

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

   6. Simplified 90.9%

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

   if -6.6000000000000003e-18 < t < 2.90000000000000006e-210

   1. Initial program 99.8%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 90.6%

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

   if 2.90000000000000006e-210 < t < 6.19999999999999977e72

   1. Initial program 91.0%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around inf 78.8%

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

      1. associate-/l* 86.7%

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

   6. Simplified 86.7%

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

   if 6.19999999999999977e72 < t < 4.0999999999999998e155

   1. Initial program 84.2%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. neg-mul-1 99.9%

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

   6. Simplified 99.9%

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

   if 4.0999999999999998e155 < t < 2.9e174

   1. Initial program 99.5%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 81.6%

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

      2. div-inv 81.6%

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

      3. associate-/r* 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in x around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. associate-*l/ 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-neg-in 99.7%

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

      6. remove-double-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. sub-neg 99.7%

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

   8. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(t - z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-210}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+155}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+174}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (/ a z))))
   (if (<= z -7.6e+134)
     t_1
     (if (<= z -3e-196)
       x
       (if (<= z 1.82e-273) (* y (/ t a)) (if (<= z 2.9e+67) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / (a / z);
	double tmp;
	if (z <= -7.6e+134) {
		tmp = t_1;
	} else if (z <= -3e-196) {
		tmp = x;
	} else if (z <= 1.82e-273) {
		tmp = y * (t / a);
	} else if (z <= 2.9e+67) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y / (a / z)
    if (z <= (-7.6d+134)) then
        tmp = t_1
    else if (z <= (-3d-196)) then
        tmp = x
    else if (z <= 1.82d-273) then
        tmp = y * (t / a)
    else if (z <= 2.9d+67) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / (a / z);
	double tmp;
	if (z <= -7.6e+134) {
		tmp = t_1;
	} else if (z <= -3e-196) {
		tmp = x;
	} else if (z <= 1.82e-273) {
		tmp = y * (t / a);
	} else if (z <= 2.9e+67) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / (a / z)
	tmp = 0
	if z <= -7.6e+134:
		tmp = t_1
	elif z <= -3e-196:
		tmp = x
	elif z <= 1.82e-273:
		tmp = y * (t / a)
	elif z <= 2.9e+67:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(a / z))
	tmp = 0.0
	if (z <= -7.6e+134)
		tmp = t_1;
	elseif (z <= -3e-196)
		tmp = x;
	elseif (z <= 1.82e-273)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 2.9e+67)
		tmp = x;
	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 (z <= -7.6e+134)
		tmp = t_1;
	elseif (z <= -3e-196)
		tmp = x;
	elseif (z <= 1.82e-273)
		tmp = y * (t / a);
	elseif (z <= 2.9e+67)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.6e+134], t$95$1, If[LessEqual[z, -3e-196], x, If[LessEqual[z, 1.82e-273], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+67], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.59999999999999997e134 or 2.90000000000000023e67 < z

   1. Initial program 92.5%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. associate-/l* 60.1%

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

   6. Simplified 60.1%

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

   if -7.59999999999999997e134 < z < -3e-196 or 1.81999999999999997e-273 < z < 2.90000000000000023e67

   1. Initial program 92.5%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 56.2%

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

   if -3e-196 < z < 1.81999999999999997e-273

   1. Initial program 90.9%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

      1. *-commutative 95.6%

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

      2. clear-num 95.5%

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

      3. un-div-inv 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in t around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-*l/ 61.5%

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

   8. Simplified 61.5%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+134}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \end{array} \]

Alternative 5: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+135)
   (* y (/ (- z) a))
   (if (<= z -1.95e-200)
     x
     (if (<= z 1.72e-273)
       (* y (/ t a))
       (if (<= z 7.4e+68) x (/ (- y) (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+135) {
		tmp = y * (-z / a);
	} else if (z <= -1.95e-200) {
		tmp = x;
	} else if (z <= 1.72e-273) {
		tmp = y * (t / a);
	} else if (z <= 7.4e+68) {
		tmp = x;
	} 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) :: tmp
    if (z <= (-1.35d+135)) then
        tmp = y * (-z / a)
    else if (z <= (-1.95d-200)) then
        tmp = x
    else if (z <= 1.72d-273) then
        tmp = y * (t / a)
    else if (z <= 7.4d+68) then
        tmp = x
    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 tmp;
	if (z <= -1.35e+135) {
		tmp = y * (-z / a);
	} else if (z <= -1.95e-200) {
		tmp = x;
	} else if (z <= 1.72e-273) {
		tmp = y * (t / a);
	} else if (z <= 7.4e+68) {
		tmp = x;
	} else {
		tmp = -y / (a / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+135:
		tmp = y * (-z / a)
	elif z <= -1.95e-200:
		tmp = x
	elif z <= 1.72e-273:
		tmp = y * (t / a)
	elif z <= 7.4e+68:
		tmp = x
	else:
		tmp = -y / (a / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+135)
		tmp = Float64(y * Float64(Float64(-z) / a));
	elseif (z <= -1.95e-200)
		tmp = x;
	elseif (z <= 1.72e-273)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 7.4e+68)
		tmp = x;
	else
		tmp = Float64(Float64(-y) / Float64(a / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+135)
		tmp = y * (-z / a);
	elseif (z <= -1.95e-200)
		tmp = x;
	elseif (z <= 1.72e-273)
		tmp = y * (t / a);
	elseif (z <= 7.4e+68)
		tmp = x;
	else
		tmp = -y / (a / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+135], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-200], x, If[LessEqual[z, 1.72e-273], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+68], x, N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.34999999999999992e135

   1. Initial program 94.1%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

      1. *-commutative 96.5%

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

      2. clear-num 94.9%

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

      3. un-div-inv 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in z around inf 56.6%

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

      1. mul-1-neg 56.6%

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

      2. associate-*r/ 62.6%

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

      3. distribute-rgt-neg-out 62.6%

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

   8. Simplified 62.6%

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

   if -1.34999999999999992e135 < z < -1.94999999999999999e-200 or 1.71999999999999996e-273 < z < 7.39999999999999996e68

   1. Initial program 92.5%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 56.2%

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

   if -1.94999999999999999e-200 < z < 1.71999999999999996e-273

   1. Initial program 90.9%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

      1. *-commutative 95.6%

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

      2. clear-num 95.5%

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

      3. un-div-inv 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in t around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-*l/ 61.5%

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

   8. Simplified 61.5%

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

   if 7.39999999999999996e68 < z

   1. Initial program 91.4%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. associate-/l* 58.3%

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

   6. Simplified 58.3%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \end{array} \]

Alternative 6: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+133)
   (* y (/ (- z) a))
   (if (<= z -1e-201)
     x
     (if (<= z 1.58e-273)
       (* y (/ t a))
       (if (<= z 1.9e+71) x (* z (/ y (- a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+133) {
		tmp = y * (-z / a);
	} else if (z <= -1e-201) {
		tmp = x;
	} else if (z <= 1.58e-273) {
		tmp = y * (t / a);
	} else if (z <= 1.9e+71) {
		tmp = x;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.8d+133)) then
        tmp = y * (-z / a)
    else if (z <= (-1d-201)) then
        tmp = x
    else if (z <= 1.58d-273) then
        tmp = y * (t / a)
    else if (z <= 1.9d+71) then
        tmp = x
    else
        tmp = z * (y / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+133) {
		tmp = y * (-z / a);
	} else if (z <= -1e-201) {
		tmp = x;
	} else if (z <= 1.58e-273) {
		tmp = y * (t / a);
	} else if (z <= 1.9e+71) {
		tmp = x;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+133:
		tmp = y * (-z / a)
	elif z <= -1e-201:
		tmp = x
	elif z <= 1.58e-273:
		tmp = y * (t / a)
	elif z <= 1.9e+71:
		tmp = x
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+133)
		tmp = Float64(y * Float64(Float64(-z) / a));
	elseif (z <= -1e-201)
		tmp = x;
	elseif (z <= 1.58e-273)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 1.9e+71)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+133)
		tmp = y * (-z / a);
	elseif (z <= -1e-201)
		tmp = x;
	elseif (z <= 1.58e-273)
		tmp = y * (t / a);
	elseif (z <= 1.9e+71)
		tmp = x;
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+133], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e-201], x, If[LessEqual[z, 1.58e-273], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+71], x, N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8000000000000002e133

   1. Initial program 94.1%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

      1. *-commutative 96.5%

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

      2. clear-num 94.9%

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

      3. un-div-inv 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in z around inf 56.6%

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

      1. mul-1-neg 56.6%

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

      2. associate-*r/ 62.6%

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

      3. distribute-rgt-neg-out 62.6%

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

   8. Simplified 62.6%

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

   if -3.8000000000000002e133 < z < -9.99999999999999946e-202 or 1.57999999999999994e-273 < z < 1.9e71

   1. Initial program 92.5%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 56.2%

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

   if -9.99999999999999946e-202 < z < 1.57999999999999994e-273

   1. Initial program 90.9%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

      1. *-commutative 95.6%

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

      2. clear-num 95.5%

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

      3. un-div-inv 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in t around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-*l/ 61.5%

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

   8. Simplified 61.5%

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

   if 1.9e71 < z

   1. Initial program 91.4%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. associate-*l/ 62.9%

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

      3. *-commutative 62.9%

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

      4. distribute-rgt-neg-in 62.9%

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

      5. distribute-frac-neg 62.9%

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

      6. *-lft-identity 62.9%

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

      7. metadata-eval 62.9%

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

      8. times-frac 62.9%

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

      9. neg-mul-1 62.9%

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

      10. neg-mul-1 62.9%

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

      11. remove-double-neg 62.9%

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

   6. Simplified 62.9%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]

Alternative 7: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -215:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+141}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+198}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+209}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -215.0)
   (* t (/ y a))
   (if (<= t 2.8e+141)
     x
     (if (<= t 7e+198) (/ y (/ a t)) (if (<= t 2.95e+209) x (/ t (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -215.0) {
		tmp = t * (y / a);
	} else if (t <= 2.8e+141) {
		tmp = x;
	} else if (t <= 7e+198) {
		tmp = y / (a / t);
	} else if (t <= 2.95e+209) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-215.0d0)) then
        tmp = t * (y / a)
    else if (t <= 2.8d+141) then
        tmp = x
    else if (t <= 7d+198) then
        tmp = y / (a / t)
    else if (t <= 2.95d+209) then
        tmp = x
    else
        tmp = 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 (t <= -215.0) {
		tmp = t * (y / a);
	} else if (t <= 2.8e+141) {
		tmp = x;
	} else if (t <= 7e+198) {
		tmp = y / (a / t);
	} else if (t <= 2.95e+209) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -215.0:
		tmp = t * (y / a)
	elif t <= 2.8e+141:
		tmp = x
	elif t <= 7e+198:
		tmp = y / (a / t)
	elif t <= 2.95e+209:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -215.0)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 2.8e+141)
		tmp = x;
	elseif (t <= 7e+198)
		tmp = Float64(y / Float64(a / t));
	elseif (t <= 2.95e+209)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -215.0)
		tmp = t * (y / a);
	elseif (t <= 2.8e+141)
		tmp = x;
	elseif (t <= 7e+198)
		tmp = y / (a / t);
	elseif (t <= 2.95e+209)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -215.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+141], x, If[LessEqual[t, 7e+198], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e+209], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -215

   1. Initial program 91.1%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 55.3%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if -215 < t < 2.79999999999999991e141 or 7.00000000000000026e198 < t < 2.9499999999999999e209

   1. Initial program 95.3%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around inf 54.8%

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

   if 2.79999999999999991e141 < t < 7.00000000000000026e198

   1. Initial program 87.1%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

      1. *-commutative 93.5%

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

      2. clear-num 93.4%

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

      3. un-div-inv 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in t around inf 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-*l/ 54.2%

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

   8. Simplified 54.2%

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

      1. associate-*l/ 47.8%

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

      2. *-commutative 47.8%

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

      3. associate-/l* 59.5%

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

   10. Applied egg-rr 59.5%

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

   if 2.9499999999999999e209 < t

   1. Initial program 75.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      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 t around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. associate-/l* 76.2%

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

   8. Simplified 76.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -215:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+141}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+198}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+209}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-209}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= t -7.8e-17)
     t_1
     (if (<= t 1e-209)
       (- x (/ (* z y) a))
       (if (<= t 6.1e+72) (- x (/ y (/ a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (t <= -7.8e-17) {
		tmp = t_1;
	} else if (t <= 1e-209) {
		tmp = x - ((z * y) / a);
	} else if (t <= 6.1e+72) {
		tmp = x - (y / (a / z));
	} 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 = x + (t * (y / a))
    if (t <= (-7.8d-17)) then
        tmp = t_1
    else if (t <= 1d-209) then
        tmp = x - ((z * y) / a)
    else if (t <= 6.1d+72) then
        tmp = x - (y / (a / z))
    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 = x + (t * (y / a));
	double tmp;
	if (t <= -7.8e-17) {
		tmp = t_1;
	} else if (t <= 1e-209) {
		tmp = x - ((z * y) / a);
	} else if (t <= 6.1e+72) {
		tmp = x - (y / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if t <= -7.8e-17:
		tmp = t_1
	elif t <= 1e-209:
		tmp = x - ((z * y) / a)
	elif t <= 6.1e+72:
		tmp = x - (y / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (t <= -7.8e-17)
		tmp = t_1;
	elseif (t <= 1e-209)
		tmp = Float64(x - Float64(Float64(z * y) / a));
	elseif (t <= 6.1e+72)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (t <= -7.8e-17)
		tmp = t_1;
	elseif (t <= 1e-209)
		tmp = x - ((z * y) / a);
	elseif (t <= 6.1e+72)
		tmp = x - (y / (a / z));
	else
		tmp = t_1;
	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]}, If[LessEqual[t, -7.8e-17], t$95$1, If[LessEqual[t, 1e-209], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.1e+72], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.79999999999999979e-17 or 6.09999999999999991e72 < t

   1. Initial program 87.7%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 78.2%

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

      1. cancel-sign-sub-inv 78.2%

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

      2. metadata-eval 78.2%

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

      3. *-lft-identity 78.2%

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

      4. +-commutative 78.2%

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

      5. associate-*l/ 88.1%

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

      6. *-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -7.79999999999999979e-17 < t < 1e-209

   1. Initial program 99.8%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 90.6%

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

   if 1e-209 < t < 6.09999999999999991e72

   1. Initial program 91.0%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around inf 78.8%

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

      1. associate-/l* 86.7%

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

   6. Simplified 86.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-17}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 10^{-209}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-30} \lor \neg \left(y \leq 2.2 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5e-30) (not (<= y 2.2e-77))) (* (/ y a) (- t z)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e-30) || !(y <= 2.2e-77)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5d-30)) .or. (.not. (y <= 2.2d-77))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e-30) || !(y <= 2.2e-77)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5e-30) or not (y <= 2.2e-77):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5e-30) || !(y <= 2.2e-77))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5e-30) || ~((y <= 2.2e-77)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5e-30], N[Not[LessEqual[y, 2.2e-77]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999972e-30 or 2.20000000000000007e-77 < y

   1. Initial program 86.8%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

      1. associate-/r/ 97.1%

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

      2. div-inv 97.0%

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

      3. associate-/r* 97.1%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in x around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-*l/ 74.9%

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

      3. distribute-rgt-neg-in 74.9%

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

      4. sub-neg 74.9%

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

      5. distribute-neg-in 74.9%

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

      6. remove-double-neg 74.9%

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

      7. +-commutative 74.9%

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

      8. sub-neg 74.9%

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

   8. Simplified 74.9%

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

   if -4.99999999999999972e-30 < y < 2.20000000000000007e-77

   1. Initial program 98.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 67.2%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-30} \lor \neg \left(y \leq 2.2 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+135} \lor \neg \left(z \leq 3.7 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e+135) (not (<= z 3.7e+67)))
   (* (/ 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 <= -1.25e+135) || !(z <= 3.7e+67)) {
		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 <= (-1.25d+135)) .or. (.not. (z <= 3.7d+67))) 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 <= -1.25e+135) || !(z <= 3.7e+67)) {
		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 <= -1.25e+135) or not (z <= 3.7e+67):
		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 <= -1.25e+135) || !(z <= 3.7e+67))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.25e+135) || ~((z <= 3.7e+67)))
		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, -1.25e+135], N[Not[LessEqual[z, 3.7e+67]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000007e135 or 3.6999999999999997e67 < z

   1. Initial program 92.5%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

      1. associate-/r/ 87.4%

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

      2. div-inv 87.4%

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

      3. associate-/r* 97.1%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in x around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-*l/ 74.5%

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

      3. distribute-rgt-neg-in 74.5%

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

      4. sub-neg 74.5%

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

      5. distribute-neg-in 74.5%

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

      6. remove-double-neg 74.5%

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

      7. +-commutative 74.5%

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

      8. sub-neg 74.5%

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

   8. Simplified 74.5%

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

   if -1.25000000000000007e135 < z < 3.6999999999999997e67

   1. Initial program 92.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 83.6%

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

      1. cancel-sign-sub-inv 83.6%

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

      2. metadata-eval 83.6%

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

      3. *-lft-identity 83.6%

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

      4. +-commutative 83.6%

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

      5. associate-*l/ 87.9%

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

      6. *-commutative 87.9%

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

   6. Simplified 87.9%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+135} \lor \neg \left(z \leq 3.7 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 11: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-16} \lor \neg \left(t \leq 6.1 \cdot 10^{+72}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.5e-16) (not (<= t 6.1e+72)))
   (+ x (* t (/ y a)))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e-16) || !(t <= 6.1e+72)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.5d-16)) .or. (.not. (t <= 6.1d+72))) then
        tmp = x + (t * (y / a))
    else
        tmp = x - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e-16) || !(t <= 6.1e+72)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.5e-16) or not (t <= 6.1e+72):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.5e-16) || !(t <= 6.1e+72))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.5e-16) || ~((t <= 6.1e+72)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.5e-16], N[Not[LessEqual[t, 6.1e+72]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.50000000000000011e-16 or 6.09999999999999991e72 < t

   1. Initial program 87.7%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 78.2%

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

      1. cancel-sign-sub-inv 78.2%

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

      2. metadata-eval 78.2%

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

      3. *-lft-identity 78.2%

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

      4. +-commutative 78.2%

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

      5. associate-*l/ 88.1%

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

      6. *-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -6.50000000000000011e-16 < t < 6.09999999999999991e72

   1. Initial program 96.1%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around inf 85.6%

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

      1. associate-/l* 84.1%

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

   6. Simplified 84.1%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-16} \lor \neg \left(t \leq 6.1 \cdot 10^{+72}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 12: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0019 \lor \neg \left(t \leq 2.85 \cdot 10^{+141}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.0019) (not (<= t 2.85e+141))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.0019) || !(t <= 2.85e+141)) {
		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 ((t <= (-0.0019d0)) .or. (.not. (t <= 2.85d+141))) 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 ((t <= -0.0019) || !(t <= 2.85e+141)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.0019) or not (t <= 2.85e+141):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.0019) || !(t <= 2.85e+141))
		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 ((t <= -0.0019) || ~((t <= 2.85e+141)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.0019], N[Not[LessEqual[t, 2.85e+141]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -0.0019 or 2.84999999999999999e141 < t

   1. Initial program 86.9%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in t around inf 54.8%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if -0.0019 < t < 2.84999999999999999e141

   1. Initial program 95.8%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 53.6%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0019 \lor \neg \left(t \leq 2.85 \cdot 10^{+141}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1200:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1200.0) (* t (/ y a)) (if (<= t 1.9e+142) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1200.0) {
		tmp = t * (y / a);
	} else if (t <= 1.9e+142) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-1200.0d0)) then
        tmp = t * (y / a)
    else if (t <= 1.9d+142) then
        tmp = x
    else
        tmp = 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 (t <= -1200.0) {
		tmp = t * (y / a);
	} else if (t <= 1.9e+142) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1200.0:
		tmp = t * (y / a)
	elif t <= 1.9e+142:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1200.0)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 1.9e+142)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1200.0)
		tmp = t * (y / a);
	elseif (t <= 1.9e+142)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1200.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+142], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1200

   1. Initial program 91.1%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 55.3%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if -1200 < t < 1.89999999999999995e142

   1. Initial program 95.8%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 53.6%

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

   if 1.89999999999999995e142 < t

   1. Initial program 79.8%

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

      1. *-commutative 97.4%

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

      2. clear-num 97.4%

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

      3. un-div-inv 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in t around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-/l* 59.7%

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

   8. Simplified 59.7%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1200:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 14: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. Final simplification 97.3%

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

Alternative 15: 39.6% 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/ 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in x around inf 44.1%

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

5. Final simplification 44.1%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(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)))