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

Percentage Accurate: 93.4% → 93.7%

Time: 10.9s

Alternatives: 13

Speedup: 1.0×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+143}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -2e+143) (+ x (/ (* (- z t) y) a)) (+ x (/ y (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -2e+143) {
		tmp = x + (((z - t) * y) / a);
	} 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 ((z - t) <= (-2d+143)) then
        tmp = x + (((z - t) * y) / a)
    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 ((z - t) <= -2e+143) {
		tmp = x + (((z - t) * y) / a);
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -2e+143:
		tmp = x + (((z - t) * y) / a)
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -2e+143)
		tmp = Float64(x + Float64(Float64(Float64(z - t) * y) / 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)
	tmp = 0.0;
	if ((z - t) <= -2e+143)
		tmp = x + (((z - t) * y) / a);
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -2e+143], N[(x + N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -2e143

   1. Initial program 98.5%

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

   if -2e143 < (-.f64 z t)

   1. Initial program 96.0%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+143}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 2: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* y (/ t a)))))
   (if (<= a -1.8e-13)
     x
     (if (<= a -1.7e-130)
       (/ z (/ a y))
       (if (<= a 4.2e-277)
         t_1
         (if (<= a 1.35e-236) (* z (/ y a)) (if (<= a 5e-80) 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 (a <= -1.8e-13) {
		tmp = x;
	} else if (a <= -1.7e-130) {
		tmp = z / (a / y);
	} else if (a <= 4.2e-277) {
		tmp = t_1;
	} else if (a <= 1.35e-236) {
		tmp = z * (y / a);
	} else if (a <= 5e-80) {
		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 (a <= (-1.8d-13)) then
        tmp = x
    else if (a <= (-1.7d-130)) then
        tmp = z / (a / y)
    else if (a <= 4.2d-277) then
        tmp = t_1
    else if (a <= 1.35d-236) then
        tmp = z * (y / a)
    else if (a <= 5d-80) 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 (a <= -1.8e-13) {
		tmp = x;
	} else if (a <= -1.7e-130) {
		tmp = z / (a / y);
	} else if (a <= 4.2e-277) {
		tmp = t_1;
	} else if (a <= 1.35e-236) {
		tmp = z * (y / a);
	} else if (a <= 5e-80) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -(y * (t / a))
	tmp = 0
	if a <= -1.8e-13:
		tmp = x
	elif a <= -1.7e-130:
		tmp = z / (a / y)
	elif a <= 4.2e-277:
		tmp = t_1
	elif a <= 1.35e-236:
		tmp = z * (y / a)
	elif a <= 5e-80:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(y * Float64(t / a)))
	tmp = 0.0
	if (a <= -1.8e-13)
		tmp = x;
	elseif (a <= -1.7e-130)
		tmp = Float64(z / Float64(a / y));
	elseif (a <= 4.2e-277)
		tmp = t_1;
	elseif (a <= 1.35e-236)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= 5e-80)
		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 (a <= -1.8e-13)
		tmp = x;
	elseif (a <= -1.7e-130)
		tmp = z / (a / y);
	elseif (a <= 4.2e-277)
		tmp = t_1;
	elseif (a <= 1.35e-236)
		tmp = z * (y / a);
	elseif (a <= 5e-80)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = (-N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[a, -1.8e-13], x, If[LessEqual[a, -1.7e-130], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-277], t$95$1, If[LessEqual[a, 1.35e-236], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-80], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.7999999999999999e-13 or 5e-80 < a

   1. Initial program 95.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 59.5%

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

   if -1.7999999999999999e-13 < a < -1.70000000000000003e-130

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around inf 89.6%

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

   5. Taylor expanded in z around inf 64.1%

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

      1. associate-*l/ 69.0%

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

      2. associate-/l* 74.1%

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

   7. Applied egg-rr 74.1%

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

   if -1.70000000000000003e-130 < a < 4.1999999999999999e-277 or 1.35e-236 < a < 5e-80

   1. Initial program 99.8%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around inf 77.4%

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

   5. Taylor expanded in z around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-frac-neg 59.2%

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

   7. Simplified 59.2%

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

   if 4.1999999999999999e-277 < a < 1.35e-236

   1. Initial program 94.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around inf 67.4%

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

   5. Taylor expanded in z around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-frac-neg 67.4%

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

      3. +-commutative 67.4%

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

      4. distribute-frac-neg 67.4%

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

      5. sub-neg 67.4%

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

      6. div-sub 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in z around inf 48.7%

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

      1. associate-*l/ 64.5%

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

   10. Simplified 64.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-277}:\\ \;\;\;\;-y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-80}:\\ \;\;\;\;-y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-277}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-80}:\\ \;\;\;\;-y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.4e-12)
   x
   (if (<= a -1.75e-130)
     (/ z (/ a y))
     (if (<= a 4e-277)
       (/ (* t (- y)) a)
       (if (<= a 7e-236)
         (* z (/ y a))
         (if (<= a 5.2e-80) (- (* y (/ t a))) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.4e-12) {
		tmp = x;
	} else if (a <= -1.75e-130) {
		tmp = z / (a / y);
	} else if (a <= 4e-277) {
		tmp = (t * -y) / a;
	} else if (a <= 7e-236) {
		tmp = z * (y / a);
	} else if (a <= 5.2e-80) {
		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 (a <= (-6.4d-12)) then
        tmp = x
    else if (a <= (-1.75d-130)) then
        tmp = z / (a / y)
    else if (a <= 4d-277) then
        tmp = (t * -y) / a
    else if (a <= 7d-236) then
        tmp = z * (y / a)
    else if (a <= 5.2d-80) 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 (a <= -6.4e-12) {
		tmp = x;
	} else if (a <= -1.75e-130) {
		tmp = z / (a / y);
	} else if (a <= 4e-277) {
		tmp = (t * -y) / a;
	} else if (a <= 7e-236) {
		tmp = z * (y / a);
	} else if (a <= 5.2e-80) {
		tmp = -(y * (t / a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.4e-12:
		tmp = x
	elif a <= -1.75e-130:
		tmp = z / (a / y)
	elif a <= 4e-277:
		tmp = (t * -y) / a
	elif a <= 7e-236:
		tmp = z * (y / a)
	elif a <= 5.2e-80:
		tmp = -(y * (t / a))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.4e-12)
		tmp = x;
	elseif (a <= -1.75e-130)
		tmp = Float64(z / Float64(a / y));
	elseif (a <= 4e-277)
		tmp = Float64(Float64(t * Float64(-y)) / a);
	elseif (a <= 7e-236)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= 5.2e-80)
		tmp = Float64(-Float64(y * Float64(t / a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.4e-12)
		tmp = x;
	elseif (a <= -1.75e-130)
		tmp = z / (a / y);
	elseif (a <= 4e-277)
		tmp = (t * -y) / a;
	elseif (a <= 7e-236)
		tmp = z * (y / a);
	elseif (a <= 5.2e-80)
		tmp = -(y * (t / a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.4e-12], x, If[LessEqual[a, -1.75e-130], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-277], N[(N[(t * (-y)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 7e-236], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-80], (-N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.4000000000000002e-12 or 5.2000000000000002e-80 < a

   1. Initial program 95.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 59.5%

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

   if -6.4000000000000002e-12 < a < -1.75e-130

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around inf 89.6%

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

   5. Taylor expanded in z around inf 64.1%

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

      1. associate-*l/ 69.0%

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

      2. associate-/l* 74.1%

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

   7. Applied egg-rr 74.1%

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

   if -1.75e-130 < a < 3.99999999999999988e-277

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around inf 79.9%

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

      1. sub-div 84.7%

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

      2. associate-*l/ 91.1%

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

   6. Applied egg-rr 91.1%

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

   7. Taylor expanded in z around 0 63.7%

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

      1. associate-*r* 63.7%

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

      2. neg-mul-1 63.7%

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

   9. Simplified 63.7%

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

   if 3.99999999999999988e-277 < a < 6.99999999999999988e-236

   1. Initial program 94.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around inf 67.4%

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

   5. Taylor expanded in z around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-frac-neg 67.4%

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

      3. +-commutative 67.4%

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

      4. distribute-frac-neg 67.4%

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

      5. sub-neg 67.4%

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

      6. div-sub 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in z around inf 48.7%

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

      1. associate-*l/ 64.5%

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

   10. Simplified 64.5%

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

   if 6.99999999999999988e-236 < a < 5.2000000000000002e-80

   1. Initial program 99.8%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 73.0%

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

   5. Taylor expanded in z around 0 55.2%

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

      1. mul-1-neg 55.2%

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

      2. distribute-frac-neg 55.2%

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

   7. Simplified 55.2%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-277}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-80}:\\ \;\;\;\;-y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 68.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-108} \lor \neg \left(y \leq 8 \cdot 10^{-114}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.25e-108) (not (<= y 8e-114))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.25e-108) || !(y <= 8e-114)) {
		tmp = y * ((z - 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 ((y <= (-1.25d-108)) .or. (.not. (y <= 8d-114))) then
        tmp = y * ((z - 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 ((y <= -1.25e-108) || !(y <= 8e-114)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.25e-108) or not (y <= 8e-114):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.25e-108) || !(y <= 8e-114))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.25e-108) || ~((y <= 8e-114)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.25e-108], N[Not[LessEqual[y, 8e-114]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e-108 or 8.0000000000000004e-114 < y

   1. Initial program 95.6%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around inf 71.3%

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

   5. Taylor expanded in z around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. distribute-frac-neg 71.3%

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

      3. +-commutative 71.3%

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

      4. distribute-frac-neg 71.3%

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

      5. sub-neg 71.3%

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

      6. div-sub 74.2%

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

   7. Simplified 74.2%

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

   if -1.25e-108 < y < 8.0000000000000004e-114

   1. Initial program 98.8%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in x around inf 70.2%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-108} \lor \neg \left(y \leq 8 \cdot 10^{-114}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 78.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+120} \lor \neg \left(y \leq 44\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.02e+120) (not (<= y 44.0)))
   (* y (/ (- z t) a))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.02e+120) || !(y <= 44.0)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (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 ((y <= (-1.02d+120)) .or. (.not. (y <= 44.0d0))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x + (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 ((y <= -1.02e+120) || !(y <= 44.0)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.02e+120) or not (y <= 44.0):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.02e+120) || !(y <= 44.0))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.02e+120) || ~((y <= 44.0)))
		tmp = y * ((z - t) / a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.02e+120], N[Not[LessEqual[y, 44.0]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.01999999999999997e120 or 44 < y

   1. Initial program 92.8%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around inf 82.0%

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

   5. Taylor expanded in z around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-frac-neg 82.0%

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

      3. +-commutative 82.0%

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

      4. distribute-frac-neg 82.0%

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

      5. sub-neg 82.0%

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

      6. div-sub 85.8%

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

   7. Simplified 85.8%

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

   if -1.01999999999999997e120 < y < 44

   1. Initial program 99.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around 0 76.2%

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

      1. associate-*l/ 77.5%

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

      2. *-commutative 77.5%

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

   6. Simplified 77.5%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+120} \lor \neg \left(y \leq 44\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 77.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+120} \lor \neg \left(y \leq 230\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9.2e+120) (not (<= y 230.0)))
   (* y (/ (- z t) a))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9.2e+120) || !(y <= 230.0)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-9.2d+120)) .or. (.not. (y <= 230.0d0))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9.2e+120) || !(y <= 230.0)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9.2e+120) or not (y <= 230.0):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9.2e+120) || !(y <= 230.0))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -9.2e+120) || ~((y <= 230.0)))
		tmp = y * ((z - t) / a);
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9.2e+120], N[Not[LessEqual[y, 230.0]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.1999999999999997e120 or 230 < y

   1. Initial program 92.8%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around inf 82.0%

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

   5. Taylor expanded in z around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-frac-neg 82.0%

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

      3. +-commutative 82.0%

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

      4. distribute-frac-neg 82.0%

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

      5. sub-neg 82.0%

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

      6. div-sub 85.8%

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

   7. Simplified 85.8%

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

   if -9.1999999999999997e120 < y < 230

   1. Initial program 99.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around 0 76.2%

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

      1. associate-*l/ 77.5%

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

      2. *-commutative 77.5%

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

   6. Simplified 77.5%

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

      1. clear-num 77.4%

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

      2. div-inv 77.5%

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

   8. Applied egg-rr 77.5%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+120} \lor \neg \left(y \leq 230\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+52} \lor \neg \left(z \leq 8500000000\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.8e+52) (not (<= z 8500000000.0)))
   (+ x (/ z (/ a y)))
   (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e+52) || !(z <= 8500000000.0)) {
		tmp = x + (z / (a / y));
	} 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 <= (-1.8d+52)) .or. (.not. (z <= 8500000000.0d0))) then
        tmp = x + (z / (a / y))
    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 <= -1.8e+52) || !(z <= 8500000000.0)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.8e+52) or not (z <= 8500000000.0):
		tmp = x + (z / (a / y))
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.8e+52) || !(z <= 8500000000.0))
		tmp = Float64(x + Float64(z / Float64(a / y)));
	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 <= -1.8e+52) || ~((z <= 8500000000.0)))
		tmp = x + (z / (a / y));
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.8e+52], N[Not[LessEqual[z, 8500000000.0]], $MachinePrecision]], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e52 or 8.5e9 < z

   1. Initial program 96.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 89.2%

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

      1. associate-*l/ 91.9%

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

      2. *-commutative 91.9%

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

   6. Simplified 91.9%

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

      1. clear-num 91.9%

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

      2. div-inv 92.0%

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

   8. Applied egg-rr 92.0%

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

   if -1.8e52 < z < 8.5e9

   1. Initial program 96.9%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. associate-*l/ 88.5%

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

      3. distribute-rgt-neg-out 88.5%

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

      4. +-commutative 88.5%

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

      5. *-commutative 88.5%

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

      6. distribute-lft-neg-out 88.5%

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

      7. unsub-neg 88.5%

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

   6. Simplified 88.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+52} \lor \neg \left(z \leq 8500000000\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+54} \lor \neg \left(z \leq 14500000000\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+54) (not (<= z 14500000000.0)))
   (+ x (/ z (/ a y)))
   (- x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+54) || !(z <= 14500000000.0)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.85d+54)) .or. (.not. (z <= 14500000000.0d0))) then
        tmp = x + (z / (a / y))
    else
        tmp = x - (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+54) || !(z <= 14500000000.0)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+54) or not (z <= 14500000000.0):
		tmp = x + (z / (a / y))
	else:
		tmp = x - (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+54) || !(z <= 14500000000.0))
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x - Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.85e+54) || ~((z <= 14500000000.0)))
		tmp = x + (z / (a / y));
	else
		tmp = x - (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+54], N[Not[LessEqual[z, 14500000000.0]], $MachinePrecision]], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e54 or 1.45e10 < z

   1. Initial program 96.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 89.2%

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

      1. associate-*l/ 91.9%

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

      2. *-commutative 91.9%

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

   6. Simplified 91.9%

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

      1. clear-num 91.9%

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

      2. div-inv 92.0%

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

   8. Applied egg-rr 92.0%

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

   if -1.8500000000000001e54 < z < 1.45e10

   1. Initial program 96.9%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. associate-*l/ 88.5%

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

      3. distribute-rgt-neg-out 88.5%

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

      4. +-commutative 88.5%

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

      5. *-commutative 88.5%

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

      6. distribute-lft-neg-out 88.5%

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

      7. unsub-neg 88.5%

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

   6. Simplified 88.5%

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

      1. clear-num 88.5%

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

      2. div-inv 88.6%

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

   8. Applied egg-rr 88.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+54} \lor \neg \left(z \leq 14500000000\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+60} \lor \neg \left(z \leq 20000000000\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e+60) (not (<= z 20000000000.0)))
   (+ x (/ z (/ a y)))
   (- x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+60) || !(z <= 20000000000.0)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (y / (a / 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 ((z <= (-8.5d+60)) .or. (.not. (z <= 20000000000.0d0))) then
        tmp = x + (z / (a / y))
    else
        tmp = x - (y / (a / 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 ((z <= -8.5e+60) || !(z <= 20000000000.0)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.5e+60) or not (z <= 20000000000.0):
		tmp = x + (z / (a / y))
	else:
		tmp = x - (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.5e+60) || !(z <= 20000000000.0))
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x - Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.5e+60) || ~((z <= 20000000000.0)))
		tmp = x + (z / (a / y));
	else
		tmp = x - (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.5e+60], N[Not[LessEqual[z, 20000000000.0]], $MachinePrecision]], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000064e60 or 2e10 < z

   1. Initial program 96.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 89.2%

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

      1. associate-*l/ 91.9%

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

      2. *-commutative 91.9%

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

   6. Simplified 91.9%

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

      1. clear-num 91.9%

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

      2. div-inv 92.0%

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

   8. Applied egg-rr 92.0%

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

   if -8.50000000000000064e60 < z < 2e10

   1. Initial program 96.9%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

      1. *-commutative 95.7%

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

      2. clear-num 95.7%

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

      3. un-div-inv 96.1%

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

   5. Applied egg-rr 96.1%

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

   6. Taylor expanded in z around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. mul-1-neg 88.4%

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

      3. associate-*l/ 88.5%

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

      4. distribute-lft-neg-out 88.5%

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

      5. cancel-sign-sub-inv 88.5%

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

      6. associate-/r/ 89.6%

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

   8. Simplified 89.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+60} \lor \neg \left(z \leq 20000000000\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 10: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-154}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e-13) x (if (<= a 9.6e-154) (* z (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-13) {
		tmp = x;
	} else if (a <= 9.6e-154) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.5d-13)) then
        tmp = x
    else if (a <= 9.6d-154) then
        tmp = z * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-13) {
		tmp = x;
	} else if (a <= 9.6e-154) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e-13:
		tmp = x
	elif a <= 9.6e-154:
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e-13)
		tmp = x;
	elseif (a <= 9.6e-154)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e-13)
		tmp = x;
	elseif (a <= 9.6e-154)
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e-13], x, If[LessEqual[a, 9.6e-154], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -8.5000000000000001e-13 or 9.59999999999999947e-154 < a

   1. Initial program 95.3%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around inf 56.8%

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

   if -8.5000000000000001e-13 < a < 9.59999999999999947e-154

   1. Initial program 98.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around inf 79.2%

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

   5. Taylor expanded in z around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. distribute-frac-neg 79.2%

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

      3. +-commutative 79.2%

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

      4. distribute-frac-neg 79.2%

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

      5. sub-neg 79.2%

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

      6. div-sub 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in z around inf 50.0%

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

      1. associate-*l/ 54.1%

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

   10. Simplified 54.1%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-154}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.55e-11) x (if (<= a 2.5e-156) (/ z (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.55e-11) {
		tmp = x;
	} else if (a <= 2.5e-156) {
		tmp = z / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.55d-11)) then
        tmp = x
    else if (a <= 2.5d-156) then
        tmp = z / (a / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.55e-11) {
		tmp = x;
	} else if (a <= 2.5e-156) {
		tmp = z / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.55e-11:
		tmp = x
	elif a <= 2.5e-156:
		tmp = z / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.55e-11)
		tmp = x;
	elseif (a <= 2.5e-156)
		tmp = Float64(z / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.55e-11)
		tmp = x;
	elseif (a <= 2.5e-156)
		tmp = z / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.55e-11], x, If[LessEqual[a, 2.5e-156], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.54999999999999992e-11 or 2.50000000000000004e-156 < a

   1. Initial program 95.3%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around inf 56.8%

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

   if -2.54999999999999992e-11 < a < 2.50000000000000004e-156

   1. Initial program 98.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around inf 79.2%

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

   5. Taylor expanded in z around inf 48.7%

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

      1. associate-*l/ 50.0%

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

      2. associate-/l* 54.6%

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

   7. Applied egg-rr 54.6%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

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

Alternative 13: 39.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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 x around inf 40.6%

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

5. Final simplification 40.6%

   \[\leadsto x \]

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 2023174 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))