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

Percentage Accurate: 93.1% → 97.3%

Time: 11.5s

Alternatives: 10

Speedup: 1.0×

• 24.7% 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: 97.3% 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 97.2%

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

   1. sub-neg 97.2%

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

   2. distribute-frac-neg 97.2%

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

   3. distribute-lft-neg-out 97.2%

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

   4. +-commutative 97.2%

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

   5. distribute-lft-neg-out 97.2%

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

   6. distribute-rgt-neg-in 97.2%

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

   7. associate-*l/ 98.2%

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

   8. fma-def 98.3%

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

   9. sub-neg 98.3%

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

   10. distribute-neg-in 98.3%

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

   11. remove-double-neg 98.3%

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

   12. +-commutative 98.3%

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

   13. sub-neg 98.3%

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

3. Simplified 98.3%

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

5. Final simplification 98.3%

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

Alternative 2: 48.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a} \cdot \left(-y\right)\\ t_2 := \frac{y}{a} \cdot t\\ \mathbf{if}\;a \leq -1.16 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z a) (- y))) (t_2 (* (/ y a) t)))
   (if (<= a -1.16e+36)
     x
     (if (<= a -3.8e-147)
       t_2
       (if (<= a -4e-207)
         t_1
         (if (<= a -9e-307) t_2 (if (<= a 1e-49) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / a) * -y;
	double t_2 = (y / a) * t;
	double tmp;
	if (a <= -1.16e+36) {
		tmp = x;
	} else if (a <= -3.8e-147) {
		tmp = t_2;
	} else if (a <= -4e-207) {
		tmp = t_1;
	} else if (a <= -9e-307) {
		tmp = t_2;
	} else if (a <= 1e-49) {
		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) :: t_2
    real(8) :: tmp
    t_1 = (z / a) * -y
    t_2 = (y / a) * t
    if (a <= (-1.16d+36)) then
        tmp = x
    else if (a <= (-3.8d-147)) then
        tmp = t_2
    else if (a <= (-4d-207)) then
        tmp = t_1
    else if (a <= (-9d-307)) then
        tmp = t_2
    else if (a <= 1d-49) 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 = (z / a) * -y;
	double t_2 = (y / a) * t;
	double tmp;
	if (a <= -1.16e+36) {
		tmp = x;
	} else if (a <= -3.8e-147) {
		tmp = t_2;
	} else if (a <= -4e-207) {
		tmp = t_1;
	} else if (a <= -9e-307) {
		tmp = t_2;
	} else if (a <= 1e-49) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / a) * -y
	t_2 = (y / a) * t
	tmp = 0
	if a <= -1.16e+36:
		tmp = x
	elif a <= -3.8e-147:
		tmp = t_2
	elif a <= -4e-207:
		tmp = t_1
	elif a <= -9e-307:
		tmp = t_2
	elif a <= 1e-49:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / a) * Float64(-y))
	t_2 = Float64(Float64(y / a) * t)
	tmp = 0.0
	if (a <= -1.16e+36)
		tmp = x;
	elseif (a <= -3.8e-147)
		tmp = t_2;
	elseif (a <= -4e-207)
		tmp = t_1;
	elseif (a <= -9e-307)
		tmp = t_2;
	elseif (a <= 1e-49)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / a) * -y;
	t_2 = (y / a) * t;
	tmp = 0.0;
	if (a <= -1.16e+36)
		tmp = x;
	elseif (a <= -3.8e-147)
		tmp = t_2;
	elseif (a <= -4e-207)
		tmp = t_1;
	elseif (a <= -9e-307)
		tmp = t_2;
	elseif (a <= 1e-49)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[a, -1.16e+36], x, If[LessEqual[a, -3.8e-147], t$95$2, If[LessEqual[a, -4e-207], t$95$1, If[LessEqual[a, -9e-307], t$95$2, If[LessEqual[a, 1e-49], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15999999999999998e36 or 9.99999999999999936e-50 < a

   1. Initial program 94.5%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around inf 63.4%

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

   if -1.15999999999999998e36 < a < -3.80000000000000028e-147 or -3.9999999999999997e-207 < a < -8.99999999999999978e-307

   1. Initial program 99.8%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 56.8%

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

      1. associate-*r/ 58.2%

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

   7. Simplified 58.2%

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

   if -3.80000000000000028e-147 < a < -3.9999999999999997e-207 or -8.99999999999999978e-307 < a < 9.99999999999999936e-50

   1. Initial program 99.4%

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

      1. associate-/l* 87.2%

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

   3. Simplified 87.2%

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

      1. clear-num 86.6%

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

      2. associate-/r/ 87.2%

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

   6. Applied egg-rr 87.2%

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

   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. associate-*r/ 60.2%

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

      2. neg-mul-1 60.2%

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

      3. distribute-rgt-neg-in 60.2%

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

      4. distribute-neg-frac 60.2%

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

   9. Simplified 60.2%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-147}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-207}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-307}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;a \leq 10^{-49}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ t_2 := \frac{y}{a} \cdot t\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))) (t_2 (* (/ y a) t)))
   (if (<= a -7.6e+35)
     x
     (if (<= a -2.4e-132)
       t_2
       (if (<= a -1.1e-230)
         t_1
         (if (<= a -5e-307) t_2 (if (<= a 1.05e-49) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double t_2 = (y / a) * t;
	double tmp;
	if (a <= -7.6e+35) {
		tmp = x;
	} else if (a <= -2.4e-132) {
		tmp = t_2;
	} else if (a <= -1.1e-230) {
		tmp = t_1;
	} else if (a <= -5e-307) {
		tmp = t_2;
	} else if (a <= 1.05e-49) {
		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) :: t_2
    real(8) :: tmp
    t_1 = z * (y / -a)
    t_2 = (y / a) * t
    if (a <= (-7.6d+35)) then
        tmp = x
    else if (a <= (-2.4d-132)) then
        tmp = t_2
    else if (a <= (-1.1d-230)) then
        tmp = t_1
    else if (a <= (-5d-307)) then
        tmp = t_2
    else if (a <= 1.05d-49) 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 = z * (y / -a);
	double t_2 = (y / a) * t;
	double tmp;
	if (a <= -7.6e+35) {
		tmp = x;
	} else if (a <= -2.4e-132) {
		tmp = t_2;
	} else if (a <= -1.1e-230) {
		tmp = t_1;
	} else if (a <= -5e-307) {
		tmp = t_2;
	} else if (a <= 1.05e-49) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	t_2 = (y / a) * t
	tmp = 0
	if a <= -7.6e+35:
		tmp = x
	elif a <= -2.4e-132:
		tmp = t_2
	elif a <= -1.1e-230:
		tmp = t_1
	elif a <= -5e-307:
		tmp = t_2
	elif a <= 1.05e-49:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	t_2 = Float64(Float64(y / a) * t)
	tmp = 0.0
	if (a <= -7.6e+35)
		tmp = x;
	elseif (a <= -2.4e-132)
		tmp = t_2;
	elseif (a <= -1.1e-230)
		tmp = t_1;
	elseif (a <= -5e-307)
		tmp = t_2;
	elseif (a <= 1.05e-49)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	t_2 = (y / a) * t;
	tmp = 0.0;
	if (a <= -7.6e+35)
		tmp = x;
	elseif (a <= -2.4e-132)
		tmp = t_2;
	elseif (a <= -1.1e-230)
		tmp = t_1;
	elseif (a <= -5e-307)
		tmp = t_2;
	elseif (a <= 1.05e-49)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[a, -7.6e+35], x, If[LessEqual[a, -2.4e-132], t$95$2, If[LessEqual[a, -1.1e-230], t$95$1, If[LessEqual[a, -5e-307], t$95$2, If[LessEqual[a, 1.05e-49], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.5999999999999999e35 or 1.0499999999999999e-49 < a

   1. Initial program 94.5%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around inf 63.4%

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

   if -7.5999999999999999e35 < a < -2.40000000000000015e-132 or -1.0999999999999999e-230 < a < -5.00000000000000014e-307

   1. Initial program 99.8%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 61.8%

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

      1. associate-*r/ 63.4%

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

   7. Simplified 63.4%

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

   if -2.40000000000000015e-132 < a < -1.0999999999999999e-230 or -5.00000000000000014e-307 < a < 1.0499999999999999e-49

   1. Initial program 99.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. associate-*l/ 62.5%

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

      3. *-commutative 62.5%

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

      4. distribute-rgt-neg-in 62.5%

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

      5. *-lft-identity 62.5%

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

      6. associate-*l/ 62.5%

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

      7. remove-double-neg 62.5%

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

      8. neg-mul-1 62.5%

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

      9. associate-*r* 62.5%

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

      10. *-commutative 62.5%

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

      11. neg-mul-1 62.5%

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

      12. *-commutative 62.5%

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

      13. distribute-neg-frac 62.5%

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

      14. metadata-eval 62.5%

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

      15. metadata-eval 62.5%

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

      16. associate-/r* 62.5%

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

      17. neg-mul-1 62.5%

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

      18. associate-*r/ 62.5%

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

      19. *-rgt-identity 62.5%

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

      20. distribute-frac-neg 62.5%

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

      21. remove-double-neg 62.5%

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

   7. Simplified 62.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-132}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-230}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-307}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+140} \lor \neg \left(z \leq 5.6 \cdot 10^{+102}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e+140) (not (<= z 5.6e+102)))
   (* z (/ y (- a)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e+140) || !(z <= 5.6e+102)) {
		tmp = z * (y / -a);
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1d+140)) .or. (.not. (z <= 5.6d+102))) then
        tmp = z * (y / -a)
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e+140) || !(z <= 5.6e+102)) {
		tmp = z * (y / -a);
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e+140) or not (z <= 5.6e+102):
		tmp = z * (y / -a)
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e+140) || !(z <= 5.6e+102))
		tmp = Float64(z * Float64(y / Float64(-a)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1e+140) || ~((z <= 5.6e+102)))
		tmp = z * (y / -a);
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e+140], N[Not[LessEqual[z, 5.6e+102]], $MachinePrecision]], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000006e140 or 5.60000000000000037e102 < z

   1. Initial program 94.3%

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

      1. associate-*l/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. associate-*l/ 70.7%

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

      3. *-commutative 70.7%

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

      4. distribute-rgt-neg-in 70.7%

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

      5. *-lft-identity 70.7%

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

      6. associate-*l/ 70.7%

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

      7. remove-double-neg 70.7%

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

      8. neg-mul-1 70.7%

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

      9. associate-*r* 70.7%

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

      10. *-commutative 70.7%

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

      11. neg-mul-1 70.7%

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

      12. *-commutative 70.7%

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

      13. distribute-neg-frac 70.7%

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

      14. metadata-eval 70.7%

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

      15. metadata-eval 70.7%

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

      16. associate-/r* 70.7%

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

      17. neg-mul-1 70.7%

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

      18. associate-*r/ 70.7%

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

      19. *-rgt-identity 70.7%

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

      20. distribute-frac-neg 70.7%

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

      21. remove-double-neg 70.7%

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

   7. Simplified 70.7%

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

   if -1.00000000000000006e140 < z < 5.60000000000000037e102

   1. Initial program 98.6%

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

      1. sub-neg 98.6%

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

      2. distribute-frac-neg 98.6%

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

      3. distribute-lft-neg-out 98.6%

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

      4. +-commutative 98.6%

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

      5. distribute-lft-neg-out 98.6%

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

      6. distribute-rgt-neg-in 98.6%

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

      7. associate-*l/ 97.7%

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

      8. fma-def 97.7%

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

      9. sub-neg 97.7%

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

      10. distribute-neg-in 97.7%

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

      11. remove-double-neg 97.7%

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

      12. +-commutative 97.7%

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

      13. sub-neg 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 87.1%

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

      1. associate-/l* 87.9%

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

      2. associate-/r/ 82.9%

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

   7. Applied egg-rr 82.9%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+140} \lor \neg \left(z \leq 5.6 \cdot 10^{+102}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+143} \lor \neg \left(z \leq 1.7 \cdot 10^{+102}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.3e+143) (not (<= z 1.7e+102)))
   (* z (/ y (- a)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e+143) || !(z <= 1.7e+102)) {
		tmp = z * (y / -a);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.3d+143)) .or. (.not. (z <= 1.7d+102))) then
        tmp = z * (y / -a)
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e+143) || !(z <= 1.7e+102)) {
		tmp = z * (y / -a);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.3e+143) or not (z <= 1.7e+102):
		tmp = z * (y / -a)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.3e+143) || !(z <= 1.7e+102))
		tmp = Float64(z * Float64(y / Float64(-a)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.3e+143) || ~((z <= 1.7e+102)))
		tmp = z * (y / -a);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.3e+143], N[Not[LessEqual[z, 1.7e+102]], $MachinePrecision]], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e143 or 1.7e102 < z

   1. Initial program 94.3%

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

      1. associate-*l/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. associate-*l/ 70.7%

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

      3. *-commutative 70.7%

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

      4. distribute-rgt-neg-in 70.7%

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

      5. *-lft-identity 70.7%

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

      6. associate-*l/ 70.7%

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

      7. remove-double-neg 70.7%

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

      8. neg-mul-1 70.7%

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

      9. associate-*r* 70.7%

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

      10. *-commutative 70.7%

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

      11. neg-mul-1 70.7%

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

      12. *-commutative 70.7%

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

      13. distribute-neg-frac 70.7%

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

      14. metadata-eval 70.7%

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

      15. metadata-eval 70.7%

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

      16. associate-/r* 70.7%

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

      17. neg-mul-1 70.7%

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

      18. associate-*r/ 70.7%

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

      19. *-rgt-identity 70.7%

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

      20. distribute-frac-neg 70.7%

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

      21. remove-double-neg 70.7%

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

   7. Simplified 70.7%

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

   if -3.3e143 < z < 1.7e102

   1. Initial program 98.6%

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

      1. sub-neg 98.6%

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

      2. distribute-frac-neg 98.6%

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

      3. distribute-lft-neg-out 98.6%

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

      4. +-commutative 98.6%

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

      5. distribute-lft-neg-out 98.6%

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

      6. distribute-rgt-neg-in 98.6%

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

      7. associate-*l/ 97.7%

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

      8. fma-def 97.7%

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

      9. sub-neg 97.7%

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

      10. distribute-neg-in 97.7%

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

      11. remove-double-neg 97.7%

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

      12. +-commutative 97.7%

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

      13. sub-neg 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 87.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+143} \lor \neg \left(z \leq 1.7 \cdot 10^{+102}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+136} \lor \neg \left(z \leq 1.1 \cdot 10^{+37}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e+136) (not (<= z 1.1e+37)))
   (- x (* (/ y a) z))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+136) || !(z <= 1.1e+37)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.5d+136)) .or. (.not. (z <= 1.1d+37))) then
        tmp = x - ((y / a) * z)
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+136) || !(z <= 1.1e+37)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e+136) or not (z <= 1.1e+37):
		tmp = x - ((y / a) * z)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e+136) || !(z <= 1.1e+37))
		tmp = Float64(x - Float64(Float64(y / a) * z));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.5e+136) || ~((z <= 1.1e+37)))
		tmp = x - ((y / a) * z);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e+136], N[Not[LessEqual[z, 1.1e+37]], $MachinePrecision]], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000039e136 or 1.1e37 < z

   1. Initial program 94.7%

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

      1. associate-*l/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around inf 89.1%

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

      1. associate-*l/ 92.8%

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

      2. *-commutative 92.8%

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

   7. Simplified 92.8%

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

   if -5.50000000000000039e136 < z < 1.1e37

   1. Initial program 98.5%

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

      1. sub-neg 98.5%

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

      2. distribute-frac-neg 98.5%

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

      3. distribute-lft-neg-out 98.5%

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

      4. +-commutative 98.5%

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

      5. distribute-lft-neg-out 98.5%

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

      6. distribute-rgt-neg-in 98.5%

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

      7. associate-*l/ 97.6%

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

      8. fma-def 97.6%

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

      9. sub-neg 97.6%

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

      10. distribute-neg-in 97.6%

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

      11. remove-double-neg 97.6%

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

      12. +-commutative 97.6%

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

      13. sub-neg 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around 0 87.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+136} \lor \neg \left(z \leq 1.1 \cdot 10^{+37}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e+65) x (if (<= a 1.75) (* y (/ (- t z) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+65) {
		tmp = x;
	} else if (a <= 1.75) {
		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 (a <= (-1.6d+65)) then
        tmp = x
    else if (a <= 1.75d0) 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 (a <= -1.6e+65) {
		tmp = x;
	} else if (a <= 1.75) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e+65:
		tmp = x
	elif a <= 1.75:
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e+65)
		tmp = x;
	elseif (a <= 1.75)
		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 (a <= -1.6e+65)
		tmp = x;
	elseif (a <= 1.75)
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e+65], x, If[LessEqual[a, 1.75], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.60000000000000003e65 or 1.75 < a

   1. Initial program 94.0%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around inf 66.3%

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

   if -1.60000000000000003e65 < a < 1.75

   1. Initial program 99.6%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in x around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. associate-*r/ 67.3%

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

      3. distribute-rgt-neg-out 67.3%

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

      4. *-rgt-identity 67.3%

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

      5. *-rgt-identity 67.3%

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

      6. distribute-neg-frac 67.3%

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

      7. neg-sub0 67.3%

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

      8. associate--r- 67.3%

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

      9. neg-sub0 67.3%

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

      10. +-commutative 67.3%

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

      11. sub-neg 67.3%

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

   7. Simplified 67.3%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e+36) x (if (<= a 5.5e-49) (* (/ y a) t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e+36) {
		tmp = x;
	} else if (a <= 5.5e-49) {
		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 (a <= (-3.1d+36)) then
        tmp = x
    else if (a <= 5.5d-49) 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 (a <= -3.1e+36) {
		tmp = x;
	} else if (a <= 5.5e-49) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e+36:
		tmp = x
	elif a <= 5.5e-49:
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e+36)
		tmp = x;
	elseif (a <= 5.5e-49)
		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 (a <= -3.1e+36)
		tmp = x;
	elseif (a <= 5.5e-49)
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e+36], x, If[LessEqual[a, 5.5e-49], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0999999999999999e36 or 5.50000000000000031e-49 < a

   1. Initial program 94.5%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around inf 63.4%

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

   if -3.0999999999999999e36 < a < 5.50000000000000031e-49

   1. Initial program 99.6%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in t around inf 48.0%

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

      1. associate-*r/ 51.1%

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

   7. Simplified 51.1%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. associate-*l/ 98.2%

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

3. Simplified 98.2%

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

5. Final simplification 98.2%

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

Alternative 10: 39.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. associate-*l/ 98.2%

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

3. Simplified 98.2%

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

5. Taylor expanded in x around inf 40.8%

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

6. Final simplification 40.8%

   \[\leadsto x \]
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 2024017 
(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)))