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

Percentage Accurate: 93.0% → 99.6%

Time: 16.4s

Alternatives: 14

Speedup: 1.0×

• 24.9% 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: 93.0% 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: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 (- INFINITY))
     (- x (* (- z t) (/ y a)))
     (if (<= t_1 5e+275)
       (+ x (/ (* y (- t z)) a))
       (- x (/ y (/ a (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - ((z - t) * (y / a));
	} else if (t_1 <= 5e+275) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - ((z - t) * (y / a));
	} else if (t_1 <= 5e+275) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - ((z - t) * (y / a))
	elif t_1 <= 5e+275:
		tmp = x + ((y * (t - z)) / a)
	else:
		tmp = x - (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(Float64(z - t) * Float64(y / a)));
	elseif (t_1 <= 5e+275)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - ((z - t) * (y / a));
	elseif (t_1 <= 5e+275)
		tmp = x + ((y * (t - z)) / a);
	else
		tmp = x - (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+275], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -inf.0

   1. Initial program 73.2%

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

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 5.0000000000000003e275

   1. Initial program 99.9%

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

   if 5.0000000000000003e275 < (*.f64 y (-.f64 z t))

   1. Initial program 73.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -\infty:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 2: 47.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{a}{z}}\\ t_2 := \frac{y \cdot t}{a}\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-87}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (/ a z))) (t_2 (/ (* y t) a)))
   (if (<= x -9.2e+17)
     x
     (if (<= x -1.3e-87)
       (/ y (/ a t))
       (if (<= x -9.2e-201)
         t_1
         (if (<= x 2.8e-300)
           t_2
           (if (<= x 2.2e-228) t_1 (if (<= x 1.75e-39) t_2 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / (a / z);
	double t_2 = (y * t) / a;
	double tmp;
	if (x <= -9.2e+17) {
		tmp = x;
	} else if (x <= -1.3e-87) {
		tmp = y / (a / t);
	} else if (x <= -9.2e-201) {
		tmp = t_1;
	} else if (x <= 2.8e-300) {
		tmp = t_2;
	} else if (x <= 2.2e-228) {
		tmp = t_1;
	} else if (x <= 1.75e-39) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = -y / (a / z)
    t_2 = (y * t) / a
    if (x <= (-9.2d+17)) then
        tmp = x
    else if (x <= (-1.3d-87)) then
        tmp = y / (a / t)
    else if (x <= (-9.2d-201)) then
        tmp = t_1
    else if (x <= 2.8d-300) then
        tmp = t_2
    else if (x <= 2.2d-228) then
        tmp = t_1
    else if (x <= 1.75d-39) then
        tmp = t_2
    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 = -y / (a / z);
	double t_2 = (y * t) / a;
	double tmp;
	if (x <= -9.2e+17) {
		tmp = x;
	} else if (x <= -1.3e-87) {
		tmp = y / (a / t);
	} else if (x <= -9.2e-201) {
		tmp = t_1;
	} else if (x <= 2.8e-300) {
		tmp = t_2;
	} else if (x <= 2.2e-228) {
		tmp = t_1;
	} else if (x <= 1.75e-39) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / (a / z)
	t_2 = (y * t) / a
	tmp = 0
	if x <= -9.2e+17:
		tmp = x
	elif x <= -1.3e-87:
		tmp = y / (a / t)
	elif x <= -9.2e-201:
		tmp = t_1
	elif x <= 2.8e-300:
		tmp = t_2
	elif x <= 2.2e-228:
		tmp = t_1
	elif x <= 1.75e-39:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(a / z))
	t_2 = Float64(Float64(y * t) / a)
	tmp = 0.0
	if (x <= -9.2e+17)
		tmp = x;
	elseif (x <= -1.3e-87)
		tmp = Float64(y / Float64(a / t));
	elseif (x <= -9.2e-201)
		tmp = t_1;
	elseif (x <= 2.8e-300)
		tmp = t_2;
	elseif (x <= 2.2e-228)
		tmp = t_1;
	elseif (x <= 1.75e-39)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / (a / z);
	t_2 = (y * t) / a;
	tmp = 0.0;
	if (x <= -9.2e+17)
		tmp = x;
	elseif (x <= -1.3e-87)
		tmp = y / (a / t);
	elseif (x <= -9.2e-201)
		tmp = t_1;
	elseif (x <= 2.8e-300)
		tmp = t_2;
	elseif (x <= 2.2e-228)
		tmp = t_1;
	elseif (x <= 1.75e-39)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[x, -9.2e+17], x, If[LessEqual[x, -1.3e-87], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.2e-201], t$95$1, If[LessEqual[x, 2.8e-300], t$95$2, If[LessEqual[x, 2.2e-228], t$95$1, If[LessEqual[x, 1.75e-39], t$95$2, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.2e17 or 1.75e-39 < x

   1. Initial program 93.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 63.5%

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

   if -9.2e17 < x < -1.30000000000000001e-87

   1. Initial program 87.9%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

      1. *-commutative 93.9%

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

      2. clear-num 93.6%

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

      3. un-div-inv 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in t around inf 58.3%

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

      1. associate-/l* 64.3%

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

   8. Simplified 64.3%

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

   if -1.30000000000000001e-87 < x < -9.19999999999999943e-201 or 2.79999999999999994e-300 < x < 2.2e-228

   1. Initial program 97.6%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. associate-/l* 55.5%

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

   6. Simplified 55.5%

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

   if -9.19999999999999943e-201 < x < 2.79999999999999994e-300 or 2.2e-228 < x < 1.75e-39

   1. Initial program 94.9%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in t around inf 55.7%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-87}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-300}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-228}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-39}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 47.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot t}{a}\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-207}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-231}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y t) a)))
   (if (<= x -2.8e+16)
     x
     (if (<= x -7.6e-88)
       (/ y (/ a t))
       (if (<= x -2.5e-207)
         (/ (* y (- z)) a)
         (if (<= x 5.4e-300)
           t_1
           (if (<= x 7e-231) (/ (- y) (/ a z)) (if (<= x 6.5e-42) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * t) / a;
	double tmp;
	if (x <= -2.8e+16) {
		tmp = x;
	} else if (x <= -7.6e-88) {
		tmp = y / (a / t);
	} else if (x <= -2.5e-207) {
		tmp = (y * -z) / a;
	} else if (x <= 5.4e-300) {
		tmp = t_1;
	} else if (x <= 7e-231) {
		tmp = -y / (a / z);
	} else if (x <= 6.5e-42) {
		tmp = t_1;
	} 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 = (y * t) / a
    if (x <= (-2.8d+16)) then
        tmp = x
    else if (x <= (-7.6d-88)) then
        tmp = y / (a / t)
    else if (x <= (-2.5d-207)) then
        tmp = (y * -z) / a
    else if (x <= 5.4d-300) then
        tmp = t_1
    else if (x <= 7d-231) then
        tmp = -y / (a / z)
    else if (x <= 6.5d-42) then
        tmp = t_1
    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 = (y * t) / a;
	double tmp;
	if (x <= -2.8e+16) {
		tmp = x;
	} else if (x <= -7.6e-88) {
		tmp = y / (a / t);
	} else if (x <= -2.5e-207) {
		tmp = (y * -z) / a;
	} else if (x <= 5.4e-300) {
		tmp = t_1;
	} else if (x <= 7e-231) {
		tmp = -y / (a / z);
	} else if (x <= 6.5e-42) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * t) / a
	tmp = 0
	if x <= -2.8e+16:
		tmp = x
	elif x <= -7.6e-88:
		tmp = y / (a / t)
	elif x <= -2.5e-207:
		tmp = (y * -z) / a
	elif x <= 5.4e-300:
		tmp = t_1
	elif x <= 7e-231:
		tmp = -y / (a / z)
	elif x <= 6.5e-42:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * t) / a)
	tmp = 0.0
	if (x <= -2.8e+16)
		tmp = x;
	elseif (x <= -7.6e-88)
		tmp = Float64(y / Float64(a / t));
	elseif (x <= -2.5e-207)
		tmp = Float64(Float64(y * Float64(-z)) / a);
	elseif (x <= 5.4e-300)
		tmp = t_1;
	elseif (x <= 7e-231)
		tmp = Float64(Float64(-y) / Float64(a / z));
	elseif (x <= 6.5e-42)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * t) / a;
	tmp = 0.0;
	if (x <= -2.8e+16)
		tmp = x;
	elseif (x <= -7.6e-88)
		tmp = y / (a / t);
	elseif (x <= -2.5e-207)
		tmp = (y * -z) / a;
	elseif (x <= 5.4e-300)
		tmp = t_1;
	elseif (x <= 7e-231)
		tmp = -y / (a / z);
	elseif (x <= 6.5e-42)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[x, -2.8e+16], x, If[LessEqual[x, -7.6e-88], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e-207], N[(N[(y * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[x, 5.4e-300], t$95$1, If[LessEqual[x, 7e-231], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e-42], t$95$1, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.8e16 or 6.4999999999999998e-42 < x

   1. Initial program 93.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 63.5%

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

   if -2.8e16 < x < -7.60000000000000022e-88

   1. Initial program 87.9%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

      1. *-commutative 93.9%

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

      2. clear-num 93.6%

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

      3. un-div-inv 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in t around inf 58.3%

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

      1. associate-/l* 64.3%

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

   8. Simplified 64.3%

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

   if -7.60000000000000022e-88 < x < -2.50000000000000007e-207

   1. Initial program 99.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-frac-neg 91.8%

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

      3. distribute-rgt-neg-in 91.8%

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

      4. associate-*r/ 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in y around 0 91.8%

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

   8. Taylor expanded in t around 0 57.7%

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

      1. mul-1-neg 57.7%

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

      2. distribute-lft-neg-out 57.7%

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

      3. *-commutative 57.7%

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

   10. Simplified 57.7%

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

   if -2.50000000000000007e-207 < x < 5.3999999999999999e-300 or 7.0000000000000002e-231 < x < 6.4999999999999998e-42

   1. Initial program 94.9%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in t around inf 55.7%

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

   if 5.3999999999999999e-300 < x < 7.0000000000000002e-231

   1. Initial program 94.2%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. associate-/l* 64.4%

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

   6. Simplified 64.4%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-207}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-300}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-231}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+78}:\\ \;\;\;\;\frac{z}{\frac{-a}{y}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+282}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -1.26e+78)
     (/ z (/ (- a) y))
     (if (<= z 1.3e+131)
       t_1
       (if (<= z 9.6e+198)
         (* y (/ (- z) a))
         (if (<= z 3e+282) t_1 (/ (* y (- 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 (z <= -1.26e+78) {
		tmp = z / (-a / y);
	} else if (z <= 1.3e+131) {
		tmp = t_1;
	} else if (z <= 9.6e+198) {
		tmp = y * (-z / a);
	} else if (z <= 3e+282) {
		tmp = t_1;
	} else {
		tmp = (y * -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 (z <= (-1.26d+78)) then
        tmp = z / (-a / y)
    else if (z <= 1.3d+131) then
        tmp = t_1
    else if (z <= 9.6d+198) then
        tmp = y * (-z / a)
    else if (z <= 3d+282) then
        tmp = t_1
    else
        tmp = (y * -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 (z <= -1.26e+78) {
		tmp = z / (-a / y);
	} else if (z <= 1.3e+131) {
		tmp = t_1;
	} else if (z <= 9.6e+198) {
		tmp = y * (-z / a);
	} else if (z <= 3e+282) {
		tmp = t_1;
	} else {
		tmp = (y * -z) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -1.26e+78:
		tmp = z / (-a / y)
	elif z <= 1.3e+131:
		tmp = t_1
	elif z <= 9.6e+198:
		tmp = y * (-z / a)
	elif z <= 3e+282:
		tmp = t_1
	else:
		tmp = (y * -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 (z <= -1.26e+78)
		tmp = Float64(z / Float64(Float64(-a) / y));
	elseif (z <= 1.3e+131)
		tmp = t_1;
	elseif (z <= 9.6e+198)
		tmp = Float64(y * Float64(Float64(-z) / a));
	elseif (z <= 3e+282)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(-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 (z <= -1.26e+78)
		tmp = z / (-a / y);
	elseif (z <= 1.3e+131)
		tmp = t_1;
	elseif (z <= 9.6e+198)
		tmp = y * (-z / a);
	elseif (z <= 3e+282)
		tmp = t_1;
	else
		tmp = (y * -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[z, -1.26e+78], N[(z / N[((-a) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+131], t$95$1, If[LessEqual[z, 9.6e+198], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+282], t$95$1, N[(N[(y * (-z)), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25999999999999992e78

   1. Initial program 87.2%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

      1. *-commutative 95.5%

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

      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 z around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. associate-*l/ 76.6%

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

      3. distribute-rgt-neg-in 76.6%

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

   8. Simplified 76.6%

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

      1. associate-*l/ 68.2%

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

      2. frac-2neg 68.2%

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

      3. add-sqr-sqrt 68.0%

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

      4. sqrt-unprod 54.4%

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

      5. sqr-neg 54.4%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 3.2%

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

      8. distribute-rgt-neg-out 3.2%

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

      9. add-sqr-sqrt 3.2%

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

      10. sqrt-unprod 3.1%

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

      11. sqr-neg 3.1%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 68.2%

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

   10. Applied egg-rr 68.2%

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

       1. *-commutative 68.2%

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

       2. associate-/l* 76.6%

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

       3. distribute-frac-neg 76.6%

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

   12. Simplified 76.6%

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

   if -1.25999999999999992e78 < z < 1.3e131 or 9.6000000000000006e198 < z < 2.99999999999999997e282

   1. Initial program 96.4%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 84.0%

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

      1. cancel-sign-sub-inv 84.0%

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

      2. metadata-eval 84.0%

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

      3. *-lft-identity 84.0%

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

      4. +-commutative 84.0%

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

      5. associate-*l/ 84.3%

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

      6. *-commutative 84.3%

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

   6. Simplified 84.3%

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

   if 1.3e131 < z < 9.6000000000000006e198

   1. Initial program 83.1%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. distribute-frac-neg 60.2%

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

      3. distribute-rgt-neg-in 60.2%

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

      4. associate-*r/ 76.9%

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

   6. Simplified 76.9%

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

   7. Taylor expanded in z around inf 71.7%

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

      1. associate-*r/ 71.7%

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

      2. neg-mul-1 71.7%

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

   9. Simplified 71.7%

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

   if 2.99999999999999997e282 < z

   1. Initial program 100.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. distribute-frac-neg 84.1%

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

      3. distribute-rgt-neg-in 84.1%

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

      4. associate-*r/ 53.1%

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

   6. Simplified 53.1%

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

   7. Taylor expanded in y around 0 84.1%

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

   8. Taylor expanded in t around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. distribute-lft-neg-out 84.1%

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

      3. *-commutative 84.1%

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

   10. Simplified 84.1%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+78}:\\ \;\;\;\;\frac{z}{\frac{-a}{y}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+131}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+282}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \end{array} \]

Alternative 5: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+78}:\\ \;\;\;\;\frac{z}{\frac{-a}{y}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+131}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+207}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+283}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.26e+78)
   (/ z (/ (- a) y))
   (if (<= z 1.3e+131)
     (+ x (* t (/ y a)))
     (if (<= z 9e+207)
       (* y (/ (- z) a))
       (if (<= z 2.5e+283) (+ x (/ (* y t) a)) (/ (* y (- z)) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.26e+78) {
		tmp = z / (-a / y);
	} else if (z <= 1.3e+131) {
		tmp = x + (t * (y / a));
	} else if (z <= 9e+207) {
		tmp = y * (-z / a);
	} else if (z <= 2.5e+283) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = (y * -z) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.26d+78)) then
        tmp = z / (-a / y)
    else if (z <= 1.3d+131) then
        tmp = x + (t * (y / a))
    else if (z <= 9d+207) then
        tmp = y * (-z / a)
    else if (z <= 2.5d+283) then
        tmp = x + ((y * t) / a)
    else
        tmp = (y * -z) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.26e+78) {
		tmp = z / (-a / y);
	} else if (z <= 1.3e+131) {
		tmp = x + (t * (y / a));
	} else if (z <= 9e+207) {
		tmp = y * (-z / a);
	} else if (z <= 2.5e+283) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = (y * -z) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.26e+78:
		tmp = z / (-a / y)
	elif z <= 1.3e+131:
		tmp = x + (t * (y / a))
	elif z <= 9e+207:
		tmp = y * (-z / a)
	elif z <= 2.5e+283:
		tmp = x + ((y * t) / a)
	else:
		tmp = (y * -z) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.26e+78)
		tmp = Float64(z / Float64(Float64(-a) / y));
	elseif (z <= 1.3e+131)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 9e+207)
		tmp = Float64(y * Float64(Float64(-z) / a));
	elseif (z <= 2.5e+283)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(Float64(y * Float64(-z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.26e+78)
		tmp = z / (-a / y);
	elseif (z <= 1.3e+131)
		tmp = x + (t * (y / a));
	elseif (z <= 9e+207)
		tmp = y * (-z / a);
	elseif (z <= 2.5e+283)
		tmp = x + ((y * t) / a);
	else
		tmp = (y * -z) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.26e+78], N[(z / N[((-a) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+131], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+207], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+283], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y * (-z)), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.25999999999999992e78

   1. Initial program 87.2%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

      1. *-commutative 95.5%

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

      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 z around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. associate-*l/ 76.6%

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

      3. distribute-rgt-neg-in 76.6%

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

   8. Simplified 76.6%

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

      1. associate-*l/ 68.2%

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

      2. frac-2neg 68.2%

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

      3. add-sqr-sqrt 68.0%

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

      4. sqrt-unprod 54.4%

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

      5. sqr-neg 54.4%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 3.2%

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

      8. distribute-rgt-neg-out 3.2%

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

      9. add-sqr-sqrt 3.2%

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

      10. sqrt-unprod 3.1%

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

      11. sqr-neg 3.1%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 68.2%

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

   10. Applied egg-rr 68.2%

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

       1. *-commutative 68.2%

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

       2. associate-/l* 76.6%

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

       3. distribute-frac-neg 76.6%

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

   12. Simplified 76.6%

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

   if -1.25999999999999992e78 < z < 1.3e131

   1. Initial program 97.2%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 84.4%

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

      1. cancel-sign-sub-inv 84.4%

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

      2. metadata-eval 84.4%

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

      3. *-lft-identity 84.4%

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

      4. +-commutative 84.4%

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

      5. associate-*l/ 85.3%

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

      6. *-commutative 85.3%

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

   6. Simplified 85.3%

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

   if 1.3e131 < z < 9.00000000000000006e207

   1. Initial program 83.1%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. distribute-frac-neg 60.2%

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

      3. distribute-rgt-neg-in 60.2%

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

      4. associate-*r/ 76.9%

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

   6. Simplified 76.9%

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

   7. Taylor expanded in z around inf 71.7%

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

      1. associate-*r/ 71.7%

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

      2. neg-mul-1 71.7%

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

   9. Simplified 71.7%

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

   if 9.00000000000000006e207 < z < 2.5000000000000002e283

   1. Initial program 82.4%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in z around 0 77.5%

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

      1. cancel-sign-sub-inv 77.5%

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

      2. metadata-eval 77.5%

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

      3. *-lft-identity 77.5%

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

      4. +-commutative 77.5%

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

      5. associate-*l/ 68.6%

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

      6. *-commutative 68.6%

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

   6. Simplified 68.6%

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

      1. associate-*r/ 77.5%

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

   8. Applied egg-rr 77.5%

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

   if 2.5000000000000002e283 < z

   1. Initial program 100.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. distribute-frac-neg 84.1%

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

      3. distribute-rgt-neg-in 84.1%

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

      4. associate-*r/ 53.1%

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

   6. Simplified 53.1%

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

   7. Taylor expanded in y around 0 84.1%

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

   8. Taylor expanded in t around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. distribute-lft-neg-out 84.1%

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

      3. *-commutative 84.1%

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

   10. Simplified 84.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+78}:\\ \;\;\;\;\frac{z}{\frac{-a}{y}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+131}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+207}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+283}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \end{array} \]

Alternative 6: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-278}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))))
   (if (<= z -1.05e+78)
     t_1
     (if (<= z -4.5e-228)
       x
       (if (<= z -1.06e-278) (* t (/ y a)) (if (<= z 1.75e+20) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (z <= -1.05e+78) {
		tmp = t_1;
	} else if (z <= -4.5e-228) {
		tmp = x;
	} else if (z <= -1.06e-278) {
		tmp = t * (y / a);
	} else if (z <= 1.75e+20) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / -a)
    if (z <= (-1.05d+78)) then
        tmp = t_1
    else if (z <= (-4.5d-228)) then
        tmp = x
    else if (z <= (-1.06d-278)) then
        tmp = t * (y / a)
    else if (z <= 1.75d+20) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (z <= -1.05e+78) {
		tmp = t_1;
	} else if (z <= -4.5e-228) {
		tmp = x;
	} else if (z <= -1.06e-278) {
		tmp = t * (y / a);
	} else if (z <= 1.75e+20) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	tmp = 0
	if z <= -1.05e+78:
		tmp = t_1
	elif z <= -4.5e-228:
		tmp = x
	elif z <= -1.06e-278:
		tmp = t * (y / a)
	elif z <= 1.75e+20:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	tmp = 0.0
	if (z <= -1.05e+78)
		tmp = t_1;
	elseif (z <= -4.5e-228)
		tmp = x;
	elseif (z <= -1.06e-278)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.75e+20)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	tmp = 0.0;
	if (z <= -1.05e+78)
		tmp = t_1;
	elseif (z <= -4.5e-228)
		tmp = x;
	elseif (z <= -1.06e-278)
		tmp = t * (y / a);
	elseif (z <= 1.75e+20)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+78], t$95$1, If[LessEqual[z, -4.5e-228], x, If[LessEqual[z, -1.06e-278], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+20], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e78 or 1.75e20 < z

   1. Initial program 89.6%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. associate-*l/ 63.4%

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

      3. *-commutative 63.4%

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

      4. distribute-rgt-neg-in 63.4%

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

      5. distribute-frac-neg 63.4%

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

      6. *-lft-identity 63.4%

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

      7. metadata-eval 63.4%

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

      8. times-frac 63.4%

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

      9. neg-mul-1 63.4%

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

      10. neg-mul-1 63.4%

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

      11. remove-double-neg 63.4%

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

   6. Simplified 63.4%

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

   if -1.05e78 < z < -4.4999999999999999e-228 or -1.0600000000000001e-278 < z < 1.75e20

   1. Initial program 96.6%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in x around inf 53.2%

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

   if -4.4999999999999999e-228 < z < -1.0600000000000001e-278

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 78.6%

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

      1. associate-*l/ 78.6%

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

      2. *-commutative 78.6%

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

   6. Simplified 78.6%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-278}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]

Alternative 7: 50.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+77}:\\ \;\;\;\;\frac{z}{\frac{-a}{y}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-229}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-280}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.34 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+77)
   (/ z (/ (- a) y))
   (if (<= z -4e-229)
     x
     (if (<= z -9e-280)
       (* t (/ y a))
       (if (<= z 1.34e+20) x (* z (/ y (- a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+77) {
		tmp = z / (-a / y);
	} else if (z <= -4e-229) {
		tmp = x;
	} else if (z <= -9e-280) {
		tmp = t * (y / a);
	} else if (z <= 1.34e+20) {
		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 <= (-6d+77)) then
        tmp = z / (-a / y)
    else if (z <= (-4d-229)) then
        tmp = x
    else if (z <= (-9d-280)) then
        tmp = t * (y / a)
    else if (z <= 1.34d+20) 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 <= -6e+77) {
		tmp = z / (-a / y);
	} else if (z <= -4e-229) {
		tmp = x;
	} else if (z <= -9e-280) {
		tmp = t * (y / a);
	} else if (z <= 1.34e+20) {
		tmp = x;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+77:
		tmp = z / (-a / y)
	elif z <= -4e-229:
		tmp = x
	elif z <= -9e-280:
		tmp = t * (y / a)
	elif z <= 1.34e+20:
		tmp = x
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+77)
		tmp = Float64(z / Float64(Float64(-a) / y));
	elseif (z <= -4e-229)
		tmp = x;
	elseif (z <= -9e-280)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.34e+20)
		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 <= -6e+77)
		tmp = z / (-a / y);
	elseif (z <= -4e-229)
		tmp = x;
	elseif (z <= -9e-280)
		tmp = t * (y / a);
	elseif (z <= 1.34e+20)
		tmp = x;
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+77], N[(z / N[((-a) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-229], x, If[LessEqual[z, -9e-280], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.34e+20], x, N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.9999999999999996e77

   1. Initial program 87.2%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

      1. *-commutative 95.5%

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

      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 z around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. associate-*l/ 76.6%

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

      3. distribute-rgt-neg-in 76.6%

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

   8. Simplified 76.6%

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

      1. associate-*l/ 68.2%

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

      2. frac-2neg 68.2%

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

      3. add-sqr-sqrt 68.0%

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

      4. sqrt-unprod 54.4%

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

      5. sqr-neg 54.4%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 3.2%

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

      8. distribute-rgt-neg-out 3.2%

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

      9. add-sqr-sqrt 3.2%

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

      10. sqrt-unprod 3.1%

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

      11. sqr-neg 3.1%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 68.2%

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

   10. Applied egg-rr 68.2%

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

       1. *-commutative 68.2%

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

       2. associate-/l* 76.6%

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

       3. distribute-frac-neg 76.6%

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

   12. Simplified 76.6%

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

   if -5.9999999999999996e77 < z < -4.00000000000000028e-229 or -8.9999999999999991e-280 < z < 1.34e20

   1. Initial program 96.6%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in x around inf 53.2%

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

   if -4.00000000000000028e-229 < z < -8.9999999999999991e-280

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 78.6%

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

      1. associate-*l/ 78.6%

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

      2. *-commutative 78.6%

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

   6. Simplified 78.6%

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

   if 1.34e20 < z

   1. Initial program 91.5%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around inf 48.2%

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

      1. mul-1-neg 48.2%

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

      2. associate-*l/ 53.2%

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

      3. *-commutative 53.2%

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

      4. distribute-rgt-neg-in 53.2%

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

      5. distribute-frac-neg 53.2%

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

      6. *-lft-identity 53.2%

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

      7. metadata-eval 53.2%

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

      8. times-frac 53.2%

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

      9. neg-mul-1 53.2%

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

      10. neg-mul-1 53.2%

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

      11. remove-double-neg 53.2%

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

   6. Simplified 53.2%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+77}:\\ \;\;\;\;\frac{z}{\frac{-a}{y}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-229}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-280}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.34 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]

Alternative 8: 81.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -64000000 \lor \neg \left(z \leq 1.22 \cdot 10^{-15}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -64000000.0) (not (<= z 1.22e-15)))
   (- x (* y (/ z a)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -64000000.0) || !(z <= 1.22e-15)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-64000000.0d0)) .or. (.not. (z <= 1.22d-15))) then
        tmp = x - (y * (z / a))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -64000000.0) || !(z <= 1.22e-15)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -64000000.0) or not (z <= 1.22e-15):
		tmp = x - (y * (z / a))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -64000000.0) || !(z <= 1.22e-15))
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -64000000.0) || ~((z <= 1.22e-15)))
		tmp = x - (y * (z / a));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -64000000.0], N[Not[LessEqual[z, 1.22e-15]], $MachinePrecision]], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4e7 or 1.21999999999999991e-15 < z

   1. Initial program 91.6%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

      1. *-commutative 96.9%

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

      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. Taylor expanded in z around inf 81.4%

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

      1. associate-*r/ 82.1%

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

   8. Simplified 82.1%

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

   if -6.4e7 < z < 1.21999999999999991e-15

   1. Initial program 96.3%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around 0 89.8%

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

      1. cancel-sign-sub-inv 89.8%

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

      2. metadata-eval 89.8%

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

      3. *-lft-identity 89.8%

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

      4. +-commutative 89.8%

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

      5. associate-*l/ 89.5%

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

      6. *-commutative 89.5%

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

   6. Simplified 89.5%

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

      1. associate-*r/ 89.8%

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

   8. Applied egg-rr 89.8%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -64000000 \lor \neg \left(z \leq 1.22 \cdot 10^{-15}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 9: 95.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{-199}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.2e-199) (- x (* (- z t) (/ y a))) (+ x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.2e-199) {
		tmp = x - ((z - t) * (y / a));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 1.2d-199) then
        tmp = x - ((z - t) * (y / a))
    else
        tmp = x + (y * ((t - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.2e-199) {
		tmp = x - ((z - t) * (y / a));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.2e-199:
		tmp = x - ((z - t) * (y / a))
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.2e-199)
		tmp = Float64(x - Float64(Float64(z - t) * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.2e-199)
		tmp = x - ((z - t) * (y / a));
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.2e-199], N[(x - N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.19999999999999998e-199

   1. Initial program 93.9%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   if 1.19999999999999998e-199 < t

   1. Initial program 94.1%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

      1. clear-num 97.3%

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

      2. associate-/r/ 95.7%

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

      3. clear-num 95.8%

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

   5. Applied egg-rr 95.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{-199}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]

Alternative 10: 95.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.4 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2.4e-205) (+ x (* (/ y a) (- t z))) (- x (/ y (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.4e-205) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	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 <= 2.4d-205) then
        tmp = x + ((y / a) * (t - z))
    else
        tmp = x - (y / (a / (z - t)))
    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 <= 2.4e-205) {
		tmp = x + ((y / a) * (t - z));
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.4e-205:
		tmp = x + ((y / a) * (t - z))
	else:
		tmp = x - (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.4e-205)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	else
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 2.4e-205)
		tmp = x + ((y / a) * (t - z));
	else
		tmp = x - (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.4e-205], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.4000000000000002e-205

   1. Initial program 94.5%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   if 2.4000000000000002e-205 < t

   1. Initial program 93.4%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.4 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 11: 49.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.72 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.8e+18) x (if (<= x 1.72e-34) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.8e+18) {
		tmp = x;
	} else if (x <= 1.72e-34) {
		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 (x <= (-4.8d+18)) then
        tmp = x
    else if (x <= 1.72d-34) 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 (x <= -4.8e+18) {
		tmp = x;
	} else if (x <= 1.72e-34) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.8e+18:
		tmp = x
	elif x <= 1.72e-34:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.8e+18)
		tmp = x;
	elseif (x <= 1.72e-34)
		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 (x <= -4.8e+18)
		tmp = x;
	elseif (x <= 1.72e-34)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.8e+18], x, If[LessEqual[x, 1.72e-34], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8e18 or 1.7200000000000001e-34 < x

   1. Initial program 93.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 63.5%

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

   if -4.8e18 < x < 1.7200000000000001e-34

   1. Initial program 94.9%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 47.9%

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

      1. associate-*l/ 46.4%

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

      2. *-commutative 46.4%

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

   6. Simplified 46.4%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.72 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 47.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8e+15) x (if (<= x 4.6e-47) (/ (* y t) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8e+15) {
		tmp = x;
	} else if (x <= 4.6e-47) {
		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) :: tmp
    if (x <= (-8d+15)) then
        tmp = x
    else if (x <= 4.6d-47) 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 tmp;
	if (x <= -8e+15) {
		tmp = x;
	} else if (x <= 4.6e-47) {
		tmp = (y * t) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8e+15:
		tmp = x
	elif x <= 4.6e-47:
		tmp = (y * t) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8e+15)
		tmp = x;
	elseif (x <= 4.6e-47)
		tmp = Float64(Float64(y * t) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8e+15)
		tmp = x;
	elseif (x <= 4.6e-47)
		tmp = (y * t) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8e+15], x, If[LessEqual[x, 4.6e-47], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8e15 or 4.59999999999999964e-47 < x

   1. Initial program 93.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 63.5%

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

   if -8e15 < x < 4.59999999999999964e-47

   1. Initial program 94.9%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 47.9%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.0%

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

   1. associate-*l/ 95.2%

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

3. Simplified 95.2%

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

4. Final simplification 95.2%

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

Alternative 14: 38.9% 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 94.0%

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

   1. associate-*l/ 95.2%

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

3. Simplified 95.2%

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

4. Taylor expanded in x around inf 41.6%

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

5. Final simplification 41.6%

   \[\leadsto x \]

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 2023274 
(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)))