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

Percentage Accurate: 93.1% → 97.1%

Time: 10.2s

Alternatives: 10

Speedup: 1.0×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

   1. sub-neg 91.9%

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

   2. distribute-frac-neg 91.9%

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

   3. distribute-lft-neg-out 91.9%

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

   4. +-commutative 91.9%

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

   5. distribute-lft-neg-out 91.9%

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

   6. distribute-rgt-neg-in 91.9%

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

   7. associate-*l/ 96.9%

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

   8. fma-def 96.9%

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

   9. sub-neg 96.9%

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

   10. distribute-neg-in 96.9%

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

   11. remove-double-neg 96.9%

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

   12. +-commutative 96.9%

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

   13. sub-neg 96.9%

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

3. Simplified 96.9%

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

5. Final simplification 96.9%

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

Alternative 2: 49.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot t\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) t)))
   (if (<= y -7.5e+40)
     t_1
     (if (<= y 1.15e-87)
       x
       (if (<= y 1.55e-39)
         t_1
         (if (<= y 1.12e+85) x (if (<= y 2.6e+218) t_1 (/ (- y) (/ a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * t;
	double tmp;
	if (y <= -7.5e+40) {
		tmp = t_1;
	} else if (y <= 1.15e-87) {
		tmp = x;
	} else if (y <= 1.55e-39) {
		tmp = t_1;
	} else if (y <= 1.12e+85) {
		tmp = x;
	} else if (y <= 2.6e+218) {
		tmp = t_1;
	} else {
		tmp = -y / (a / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / a) * t
    if (y <= (-7.5d+40)) then
        tmp = t_1
    else if (y <= 1.15d-87) then
        tmp = x
    else if (y <= 1.55d-39) then
        tmp = t_1
    else if (y <= 1.12d+85) then
        tmp = x
    else if (y <= 2.6d+218) then
        tmp = t_1
    else
        tmp = -y / (a / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * t;
	double tmp;
	if (y <= -7.5e+40) {
		tmp = t_1;
	} else if (y <= 1.15e-87) {
		tmp = x;
	} else if (y <= 1.55e-39) {
		tmp = t_1;
	} else if (y <= 1.12e+85) {
		tmp = x;
	} else if (y <= 2.6e+218) {
		tmp = t_1;
	} else {
		tmp = -y / (a / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * t
	tmp = 0
	if y <= -7.5e+40:
		tmp = t_1
	elif y <= 1.15e-87:
		tmp = x
	elif y <= 1.55e-39:
		tmp = t_1
	elif y <= 1.12e+85:
		tmp = x
	elif y <= 2.6e+218:
		tmp = t_1
	else:
		tmp = -y / (a / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * t)
	tmp = 0.0
	if (y <= -7.5e+40)
		tmp = t_1;
	elseif (y <= 1.15e-87)
		tmp = x;
	elseif (y <= 1.55e-39)
		tmp = t_1;
	elseif (y <= 1.12e+85)
		tmp = x;
	elseif (y <= 2.6e+218)
		tmp = t_1;
	else
		tmp = Float64(Float64(-y) / Float64(a / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * t;
	tmp = 0.0;
	if (y <= -7.5e+40)
		tmp = t_1;
	elseif (y <= 1.15e-87)
		tmp = x;
	elseif (y <= 1.55e-39)
		tmp = t_1;
	elseif (y <= 1.12e+85)
		tmp = x;
	elseif (y <= 2.6e+218)
		tmp = t_1;
	else
		tmp = -y / (a / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -7.5e+40], t$95$1, If[LessEqual[y, 1.15e-87], x, If[LessEqual[y, 1.55e-39], t$95$1, If[LessEqual[y, 1.12e+85], x, If[LessEqual[y, 2.6e+218], t$95$1, N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999996e40 or 1.1500000000000001e-87 < y < 1.54999999999999985e-39 or 1.11999999999999993e85 < y < 2.60000000000000002e218

   1. Initial program 84.7%

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

   5. Taylor expanded in t around inf 45.6%

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

      1. associate-*r/ 53.2%

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

   7. Simplified 53.2%

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

   if -7.4999999999999996e40 < y < 1.1500000000000001e-87 or 1.54999999999999985e-39 < y < 1.11999999999999993e85

   1. Initial program 98.1%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around inf 59.8%

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

   if 2.60000000000000002e218 < y

   1. Initial program 86.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Add Preprocessing
   5. 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 95.7%

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

   6. Applied egg-rr 95.7%

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

   7. Taylor expanded in z around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. associate-/l* 68.8%

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

   9. Simplified 68.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-39}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+218}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot t\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) t)))
   (if (<= y -1.85e+38)
     t_1
     (if (<= y 1.2e-87)
       x
       (if (<= y 8.2e-40)
         t_1
         (if (<= y 5.5e+78) x (if (<= y 3.3e+218) t_1 (* (/ z a) (- y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * t;
	double tmp;
	if (y <= -1.85e+38) {
		tmp = t_1;
	} else if (y <= 1.2e-87) {
		tmp = x;
	} else if (y <= 8.2e-40) {
		tmp = t_1;
	} else if (y <= 5.5e+78) {
		tmp = x;
	} else if (y <= 3.3e+218) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = (y / a) * t
    if (y <= (-1.85d+38)) then
        tmp = t_1
    else if (y <= 1.2d-87) then
        tmp = x
    else if (y <= 8.2d-40) then
        tmp = t_1
    else if (y <= 5.5d+78) then
        tmp = x
    else if (y <= 3.3d+218) then
        tmp = t_1
    else
        tmp = (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 t_1 = (y / a) * t;
	double tmp;
	if (y <= -1.85e+38) {
		tmp = t_1;
	} else if (y <= 1.2e-87) {
		tmp = x;
	} else if (y <= 8.2e-40) {
		tmp = t_1;
	} else if (y <= 5.5e+78) {
		tmp = x;
	} else if (y <= 3.3e+218) {
		tmp = t_1;
	} else {
		tmp = (z / a) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * t
	tmp = 0
	if y <= -1.85e+38:
		tmp = t_1
	elif y <= 1.2e-87:
		tmp = x
	elif y <= 8.2e-40:
		tmp = t_1
	elif y <= 5.5e+78:
		tmp = x
	elif y <= 3.3e+218:
		tmp = t_1
	else:
		tmp = (z / a) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * t)
	tmp = 0.0
	if (y <= -1.85e+38)
		tmp = t_1;
	elseif (y <= 1.2e-87)
		tmp = x;
	elseif (y <= 8.2e-40)
		tmp = t_1;
	elseif (y <= 5.5e+78)
		tmp = x;
	elseif (y <= 3.3e+218)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / a) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * t;
	tmp = 0.0;
	if (y <= -1.85e+38)
		tmp = t_1;
	elseif (y <= 1.2e-87)
		tmp = x;
	elseif (y <= 8.2e-40)
		tmp = t_1;
	elseif (y <= 5.5e+78)
		tmp = x;
	elseif (y <= 3.3e+218)
		tmp = t_1;
	else
		tmp = (z / a) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -1.85e+38], t$95$1, If[LessEqual[y, 1.2e-87], x, If[LessEqual[y, 8.2e-40], t$95$1, If[LessEqual[y, 5.5e+78], x, If[LessEqual[y, 3.3e+218], t$95$1, N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8500000000000001e38 or 1.2e-87 < y < 8.19999999999999926e-40 or 5.4999999999999997e78 < y < 3.29999999999999998e218

   1. Initial program 84.7%

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

   5. Taylor expanded in t around inf 45.6%

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

      1. associate-*r/ 53.2%

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

   7. Simplified 53.2%

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

   if -1.8500000000000001e38 < y < 1.2e-87 or 8.19999999999999926e-40 < y < 5.4999999999999997e78

   1. Initial program 98.1%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around inf 59.8%

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

   if 3.29999999999999998e218 < y

   1. Initial program 86.8%

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

   5. Taylor expanded in x around 0 82.7%

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

      1. mul-1-neg 82.7%

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

      2. associate-*r/ 91.4%

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

      3. distribute-rgt-neg-out 91.4%

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

      4. distribute-neg-frac 91.4%

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

      5. neg-sub0 91.4%

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

      6. associate--r- 91.4%

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

      7. neg-sub0 91.4%

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

      8. +-commutative 91.4%

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

      9. sub-neg 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in t around 0 69.0%

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

      1. neg-mul-1 69.0%

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

      2. distribute-neg-frac 69.0%

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

   10. Simplified 69.0%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+218}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+136}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-165}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.8e+136)
   (/ y (/ a t))
   (if (<= t 2.1e-246)
     x
     (if (<= t 2.4e-165)
       (/ (- y) (/ a z))
       (if (<= t 1.45e-127)
         x
         (if (<= t 1.7e-12) (* (/ y a) (- z)) (* (/ y a) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e+136) {
		tmp = y / (a / t);
	} else if (t <= 2.1e-246) {
		tmp = x;
	} else if (t <= 2.4e-165) {
		tmp = -y / (a / z);
	} else if (t <= 1.45e-127) {
		tmp = x;
	} else if (t <= 1.7e-12) {
		tmp = (y / a) * -z;
	} else {
		tmp = (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 (t <= (-6.8d+136)) then
        tmp = y / (a / t)
    else if (t <= 2.1d-246) then
        tmp = x
    else if (t <= 2.4d-165) then
        tmp = -y / (a / z)
    else if (t <= 1.45d-127) then
        tmp = x
    else if (t <= 1.7d-12) then
        tmp = (y / a) * -z
    else
        tmp = (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 (t <= -6.8e+136) {
		tmp = y / (a / t);
	} else if (t <= 2.1e-246) {
		tmp = x;
	} else if (t <= 2.4e-165) {
		tmp = -y / (a / z);
	} else if (t <= 1.45e-127) {
		tmp = x;
	} else if (t <= 1.7e-12) {
		tmp = (y / a) * -z;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.8e+136:
		tmp = y / (a / t)
	elif t <= 2.1e-246:
		tmp = x
	elif t <= 2.4e-165:
		tmp = -y / (a / z)
	elif t <= 1.45e-127:
		tmp = x
	elif t <= 1.7e-12:
		tmp = (y / a) * -z
	else:
		tmp = (y / a) * t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.8e+136)
		tmp = Float64(y / Float64(a / t));
	elseif (t <= 2.1e-246)
		tmp = x;
	elseif (t <= 2.4e-165)
		tmp = Float64(Float64(-y) / Float64(a / z));
	elseif (t <= 1.45e-127)
		tmp = x;
	elseif (t <= 1.7e-12)
		tmp = Float64(Float64(y / a) * Float64(-z));
	else
		tmp = Float64(Float64(y / a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.8e+136)
		tmp = y / (a / t);
	elseif (t <= 2.1e-246)
		tmp = x;
	elseif (t <= 2.4e-165)
		tmp = -y / (a / z);
	elseif (t <= 1.45e-127)
		tmp = x;
	elseif (t <= 1.7e-12)
		tmp = (y / a) * -z;
	else
		tmp = (y / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.8e+136], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-246], x, If[LessEqual[t, 2.4e-165], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e-127], x, If[LessEqual[t, 1.7e-12], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.79999999999999993e136

   1. Initial program 84.2%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around inf 63.3%

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

      1. associate-*r/ 72.0%

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

   7. Simplified 72.0%

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

      1. associate-*r/ 63.3%

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

      2. *-commutative 63.3%

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

      3. associate-/l* 74.9%

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

   9. Applied egg-rr 74.9%

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

   if -6.79999999999999993e136 < t < 2.09999999999999995e-246 or 2.4000000000000002e-165 < t < 1.45e-127

   1. Initial program 97.4%

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

   5. Taylor expanded in x around inf 52.2%

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

   if 2.09999999999999995e-246 < t < 2.4000000000000002e-165

   1. Initial program 87.4%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

      1. *-commutative 93.5%

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

      2. clear-num 93.5%

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

      3. un-div-inv 93.6%

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

   6. Applied egg-rr 93.6%

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

   7. Taylor expanded in z around inf 54.8%

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

      1. mul-1-neg 54.8%

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

      2. associate-/l* 67.4%

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

   9. Simplified 67.4%

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

   if 1.45e-127 < t < 1.7e-12

   1. Initial program 89.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 50.3%

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

      1. mul-1-neg 50.3%

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

      2. associate-*l/ 61.7%

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

      3. distribute-rgt-neg-in 61.7%

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

   7. Simplified 61.7%

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

   if 1.7e-12 < t

   1. Initial program 87.8%

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

   5. Taylor expanded in t around inf 54.4%

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

      1. associate-*r/ 59.6%

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

   7. Simplified 59.6%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+136}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-165}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-40} \lor \neg \left(y \leq 4.55 \cdot 10^{-91}\right) \land \left(y \leq 1.06 \cdot 10^{-37} \lor \neg \left(y \leq 20.5\right)\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.9e-40)
         (and (not (<= y 4.55e-91)) (or (<= y 1.06e-37) (not (<= y 20.5)))))
   (* y (/ (- t z) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.9e-40) || (!(y <= 4.55e-91) && ((y <= 1.06e-37) || !(y <= 20.5)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.9d-40)) .or. (.not. (y <= 4.55d-91)) .and. (y <= 1.06d-37) .or. (.not. (y <= 20.5d0))) then
        tmp = y * ((t - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.9e-40) || (!(y <= 4.55e-91) && ((y <= 1.06e-37) || !(y <= 20.5)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.9e-40) or (not (y <= 4.55e-91) and ((y <= 1.06e-37) or not (y <= 20.5))):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.9e-40) || (!(y <= 4.55e-91) && ((y <= 1.06e-37) || !(y <= 20.5))))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.9e-40) || (~((y <= 4.55e-91)) && ((y <= 1.06e-37) || ~((y <= 20.5)))))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.9e-40], And[N[Not[LessEqual[y, 4.55e-91]], $MachinePrecision], Or[LessEqual[y, 1.06e-37], N[Not[LessEqual[y, 20.5]], $MachinePrecision]]]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.8999999999999999e-40 or 4.5499999999999998e-91 < y < 1.06000000000000003e-37 or 20.5 < y

   1. Initial program 86.9%

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

   5. Taylor expanded in x around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. associate-*r/ 77.8%

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

      3. distribute-rgt-neg-out 77.8%

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

      4. distribute-neg-frac 77.8%

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

      5. neg-sub0 77.8%

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

      6. associate--r- 77.8%

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

      7. neg-sub0 77.8%

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

      8. +-commutative 77.8%

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

      9. sub-neg 77.8%

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

   7. Simplified 77.8%

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

   if -1.8999999999999999e-40 < y < 4.5499999999999998e-91 or 1.06000000000000003e-37 < y < 20.5

   1. Initial program 99.4%

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

   5. Taylor expanded in x around inf 65.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-40} \lor \neg \left(y \leq 4.55 \cdot 10^{-91}\right) \land \left(y \leq 1.06 \cdot 10^{-37} \lor \neg \left(y \leq 20.5\right)\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+38} \lor \neg \left(y \leq 1.2 \cdot 10^{-87}\right) \land \left(y \leq 8 \cdot 10^{-40} \lor \neg \left(y \leq 1.15 \cdot 10^{+73}\right)\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.75e+38)
         (and (not (<= y 1.2e-87)) (or (<= y 8e-40) (not (<= y 1.15e+73)))))
   (* (/ y a) t)
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.75e+38) || (!(y <= 1.2e-87) && ((y <= 8e-40) || !(y <= 1.15e+73)))) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.75d+38)) .or. (.not. (y <= 1.2d-87)) .and. (y <= 8d-40) .or. (.not. (y <= 1.15d+73))) then
        tmp = (y / a) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.75e+38) || (!(y <= 1.2e-87) && ((y <= 8e-40) || !(y <= 1.15e+73)))) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.75e+38) or (not (y <= 1.2e-87) and ((y <= 8e-40) or not (y <= 1.15e+73))):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.75e+38) || (!(y <= 1.2e-87) && ((y <= 8e-40) || !(y <= 1.15e+73))))
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.75e+38) || (~((y <= 1.2e-87)) && ((y <= 8e-40) || ~((y <= 1.15e+73)))))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.75e+38], And[N[Not[LessEqual[y, 1.2e-87]], $MachinePrecision], Or[LessEqual[y, 8e-40], N[Not[LessEqual[y, 1.15e+73]], $MachinePrecision]]]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.7500000000000002e38 or 1.2e-87 < y < 7.9999999999999994e-40 or 1.15e73 < y

   1. Initial program 85.1%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in t around inf 44.3%

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

      1. associate-*r/ 52.1%

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

   7. Simplified 52.1%

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

   if -2.7500000000000002e38 < y < 1.2e-87 or 7.9999999999999994e-40 < y < 1.15e73

   1. Initial program 98.1%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around inf 59.8%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+38} \lor \neg \left(y \leq 1.2 \cdot 10^{-87}\right) \land \left(y \leq 8 \cdot 10^{-40} \lor \neg \left(y \leq 1.15 \cdot 10^{+73}\right)\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+75} \lor \neg \left(y \leq 14500\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.5e+75) (not (<= y 14500.0)))
   (* y (/ (- t z) a))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.5e+75) || !(y <= 14500.0)) {
		tmp = y * ((t - 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 ((y <= (-4.5d+75)) .or. (.not. (y <= 14500.0d0))) then
        tmp = y * ((t - 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 ((y <= -4.5e+75) || !(y <= 14500.0)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.5e+75) or not (y <= 14500.0):
		tmp = y * ((t - z) / a)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.5e+75) || !(y <= 14500.0))
		tmp = Float64(y * Float64(Float64(t - 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 ((y <= -4.5e+75) || ~((y <= 14500.0)))
		tmp = y * ((t - z) / a);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.5e+75], N[Not[LessEqual[y, 14500.0]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5000000000000004e75 or 14500 < y

   1. Initial program 83.0%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in x around 0 69.5%

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

      1. mul-1-neg 69.5%

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

      2. associate-*r/ 81.3%

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

      3. distribute-rgt-neg-out 81.3%

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

      4. distribute-neg-frac 81.3%

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

      5. neg-sub0 81.3%

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

      6. associate--r- 81.3%

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

      7. neg-sub0 81.3%

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

      8. +-commutative 81.3%

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

      9. sub-neg 81.3%

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

   7. Simplified 81.3%

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

   if -4.5000000000000004e75 < y < 14500

   1. Initial program 98.8%

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

      1. sub-neg 98.8%

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

      2. distribute-frac-neg 98.8%

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

      3. distribute-lft-neg-out 98.8%

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

      4. +-commutative 98.8%

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

      5. distribute-lft-neg-out 98.8%

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

      6. distribute-rgt-neg-in 98.8%

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

      7. associate-*l/ 97.3%

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

      8. fma-def 97.3%

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

      9. sub-neg 97.3%

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

      10. distribute-neg-in 97.3%

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

      11. remove-double-neg 97.3%

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

      12. +-commutative 97.3%

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

      13. sub-neg 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around 0 77.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+75} \lor \neg \left(y \leq 14500\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+118} \lor \neg \left(t \leq 2.35 \cdot 10^{-12}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.1e+118) (not (<= t 2.35e-12)))
   (+ x (* (/ y a) t))
   (- x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+118) || !(t <= 2.35e-12)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - ((y / a) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.1d+118)) .or. (.not. (t <= 2.35d-12))) then
        tmp = x + ((y / a) * t)
    else
        tmp = x - ((y / a) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+118) || !(t <= 2.35e-12)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.1e+118) or not (t <= 2.35e-12):
		tmp = x + ((y / a) * t)
	else:
		tmp = x - ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.1e+118) || !(t <= 2.35e-12))
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(x - Float64(Float64(y / a) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.1e+118) || ~((t <= 2.35e-12)))
		tmp = x + ((y / a) * t);
	else
		tmp = x - ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.1e+118], N[Not[LessEqual[t, 2.35e-12]], $MachinePrecision]], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.09999999999999993e118 or 2.34999999999999988e-12 < t

   1. Initial program 86.6%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. sub-neg 81.7%

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

      2. mul-1-neg 81.7%

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

      3. remove-double-neg 81.7%

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

      4. +-commutative 81.7%

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

      5. associate-*r/ 89.4%

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

   7. Simplified 89.4%

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

   if -1.09999999999999993e118 < t < 2.34999999999999988e-12

   1. Initial program 95.3%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around inf 86.0%

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

      1. associate-*l/ 89.6%

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

      2. *-commutative 89.6%

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

   7. Simplified 89.6%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+118} \lor \neg \left(t \leq 2.35 \cdot 10^{-12}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.1% 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 91.9%

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

5. Final simplification 96.9%

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

Alternative 10: 39.8% 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 91.9%

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

5. Taylor expanded in x around inf 38.5%

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

6. Final simplification 38.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024019 
(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)))