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

Percentage Accurate: 93.2% → 93.7%

Time: 9.9s

Alternatives: 11

Speedup: 1.0×

• 24.5% 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: 93.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-170} \lor \neg \left(a \leq 2.7 \cdot 10^{-194}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.5e-170) (not (<= a 2.7e-194)))
   (+ x (* y (/ (- t z) a)))
   (/ (* y (- t z)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.5e-170) || !(a <= 2.7e-194)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = (y * (t - z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.5d-170)) .or. (.not. (a <= 2.7d-194))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = (y * (t - z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.5e-170) || !(a <= 2.7e-194)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = (y * (t - z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.5e-170) or not (a <= 2.7e-194):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = (y * (t - z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.5e-170) || !(a <= 2.7e-194))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(Float64(y * Float64(t - z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.5e-170) || ~((a <= 2.7e-194)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = (y * (t - z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.5e-170], N[Not[LessEqual[a, 2.7e-194]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.50000000000000005e-170 or 2.7e-194 < a

   1. Initial program 90.0%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   if -2.50000000000000005e-170 < a < 2.7e-194

   1. Initial program 98.2%

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

      1. sub-neg 98.2%

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

      2. distribute-frac-neg2 98.2%

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

      3. +-commutative 98.2%

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

      4. associate-/l* 74.7%

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

      5. fma-define 74.7%

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

      6. distribute-frac-neg2 74.7%

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

      7. distribute-neg-frac 74.7%

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

      8. sub-neg 74.7%

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

      9. distribute-neg-in 74.7%

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

      10. remove-double-neg 74.7%

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

      11. +-commutative 74.7%

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

      12. sub-neg 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in y around -inf 96.7%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-170} \lor \neg \left(a \leq 2.7 \cdot 10^{-194}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-40} \lor \neg \left(t \leq 1.95 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e-40) (not (<= t 1.95e+27)))
   (+ 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 <= -2.8e-40) || !(t <= 1.95e+27)) {
		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 <= (-2.8d-40)) .or. (.not. (t <= 1.95d+27))) 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 <= -2.8e-40) || !(t <= 1.95e+27)) {
		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 <= -2.8e-40) or not (t <= 1.95e+27):
		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 <= -2.8e-40) || !(t <= 1.95e+27))
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.8e-40) || ~((t <= 1.95e+27)))
		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, -2.8e-40], N[Not[LessEqual[t, 1.95e+27]], $MachinePrecision]], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e-40 or 1.9499999999999999e27 < t

   1. Initial program 88.9%

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

      1. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in y around 0 88.9%

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

      1. associate-*l/ 97.0%

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

      2. *-commutative 97.0%

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

   7. Simplified 97.0%

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

   8. Taylor expanded in z around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. associate-*r/ 86.3%

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

      3. distribute-rgt-neg-in 86.3%

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

      4. *-commutative 86.3%

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

      5. distribute-frac-neg 86.3%

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

      6. associate-/r/ 82.1%

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

   10. Simplified 82.1%

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

   if -2.8e-40 < t < 1.9499999999999999e27

   1. Initial program 95.2%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

      1. clear-num 95.3%

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

      2. un-div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

   7. Taylor expanded in z around inf 90.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-40} \lor \neg \left(t \leq 1.95 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-40} \lor \neg \left(t \leq 2.4 \cdot 10^{+28}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.7e-40) (not (<= t 2.4e+28)))
   (+ x (/ (* t y) a))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e-40) || !(t <= 2.4e+28)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.7d-40)) .or. (.not. (t <= 2.4d+28))) then
        tmp = x + ((t * y) / a)
    else
        tmp = x - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e-40) || !(t <= 2.4e+28)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.7e-40) or not (t <= 2.4e+28):
		tmp = x + ((t * y) / a)
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.7e-40) || !(t <= 2.4e+28))
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.7e-40) || ~((t <= 2.4e+28)))
		tmp = x + ((t * y) / a);
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.7e-40], N[Not[LessEqual[t, 2.4e+28]], $MachinePrecision]], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7e-40 or 2.39999999999999981e28 < t

   1. Initial program 88.9%

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

      1. sub-neg 88.9%

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

      2. distribute-frac-neg2 88.9%

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

      3. +-commutative 88.9%

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

      4. associate-/l* 88.7%

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

      5. fma-define 88.7%

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

      6. distribute-frac-neg2 88.7%

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

      7. distribute-neg-frac 88.7%

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

      8. sub-neg 88.7%

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

      9. distribute-neg-in 88.7%

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

      10. remove-double-neg 88.7%

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

      11. +-commutative 88.7%

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

      12. sub-neg 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in z around 0 81.1%

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

   if -2.7e-40 < t < 2.39999999999999981e28

   1. Initial program 95.2%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

      1. clear-num 95.3%

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

      2. un-div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

   7. Taylor expanded in z around inf 90.1%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-40} \lor \neg \left(t \leq 2.4 \cdot 10^{+28}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-170} \lor \neg \left(a \leq 3.7 \cdot 10^{-131}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.5e-170) (not (<= a 3.7e-131)))
   (+ x (* y (/ t a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.5e-170) || !(a <= 3.7e-131)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - 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 ((a <= (-2.5d-170)) .or. (.not. (a <= 3.7d-131))) then
        tmp = x + (y * (t / a))
    else
        tmp = (y / a) * (t - 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 ((a <= -2.5e-170) || !(a <= 3.7e-131)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.5e-170) or not (a <= 3.7e-131):
		tmp = x + (y * (t / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.5e-170) || !(a <= 3.7e-131))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.5e-170) || ~((a <= 3.7e-131)))
		tmp = x + (y * (t / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.5e-170], N[Not[LessEqual[a, 3.7e-131]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.50000000000000005e-170 or 3.7000000000000002e-131 < a

   1. Initial program 89.4%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around 0 78.7%

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

      1. neg-mul-1 78.7%

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

   7. Simplified 78.7%

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

      1. cancel-sign-sub-inv 78.7%

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

      2. distribute-lft-neg-in 78.7%

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

      3. *-commutative 78.7%

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

      4. associate-*l/ 75.5%

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

      5. distribute-lft-neg-in 75.5%

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

      6. distribute-frac-neg2 75.5%

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

      7. frac-2neg 75.5%

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

      8. +-commutative 75.5%

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

      9. div-inv 75.5%

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

      10. *-commutative 75.5%

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

      11. associate-*l* 78.7%

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

      12. div-inv 78.7%

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

   9. Applied egg-rr 78.7%

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

   if -2.50000000000000005e-170 < a < 3.7000000000000002e-131

   1. Initial program 98.5%

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

      1. associate-/l* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in y around 0 98.5%

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

      1. associate-*l/ 94.5%

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

      2. *-commutative 94.5%

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

   7. Simplified 94.5%

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

   8. Taylor expanded in y around inf 64.6%

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

      1. distribute-lft-out-- 58.9%

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

      2. associate-/l* 66.8%

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

      3. associate-*r/ 83.0%

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

      4. associate-*l/ 72.0%

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

      5. associate-*l/ 69.0%

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

      6. distribute-lft-out-- 89.1%

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

   10. Simplified 89.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-170} \lor \neg \left(a \leq 3.7 \cdot 10^{-131}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-170} \lor \neg \left(a \leq 8.5 \cdot 10^{-140}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.5e-170) (not (<= a 8.5e-140)))
   (+ x (/ (* t y) a))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.5e-170) || !(a <= 8.5e-140)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = (y / a) * (t - 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 ((a <= (-2.5d-170)) .or. (.not. (a <= 8.5d-140))) then
        tmp = x + ((t * y) / a)
    else
        tmp = (y / a) * (t - 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 ((a <= -2.5e-170) || !(a <= 8.5e-140)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.5e-170) or not (a <= 8.5e-140):
		tmp = x + ((t * y) / a)
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.5e-170) || !(a <= 8.5e-140))
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.5e-170) || ~((a <= 8.5e-140)))
		tmp = x + ((t * y) / a);
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.5e-170], N[Not[LessEqual[a, 8.5e-140]], $MachinePrecision]], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.50000000000000005e-170 or 8.49999999999999997e-140 < a

   1. Initial program 89.5%

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

      1. sub-neg 89.5%

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

      2. distribute-frac-neg2 89.5%

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

      3. +-commutative 89.5%

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

      4. associate-/l* 96.8%

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

      5. fma-define 96.8%

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

      6. distribute-frac-neg2 96.8%

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

      7. distribute-neg-frac 96.8%

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

      8. sub-neg 96.8%

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

      9. distribute-neg-in 96.8%

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

      10. remove-double-neg 96.8%

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

      11. +-commutative 96.8%

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

      12. sub-neg 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around 0 75.8%

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

   if -2.50000000000000005e-170 < a < 8.49999999999999997e-140

   1. Initial program 98.5%

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

      1. associate-/l* 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in y around 0 98.5%

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

      1. associate-*l/ 94.4%

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

      2. *-commutative 94.4%

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

   7. Simplified 94.4%

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

   8. Taylor expanded in y around inf 65.0%

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

      1. distribute-lft-out-- 59.2%

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

      2. associate-/l* 67.3%

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

      3. associate-*r/ 84.0%

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

      4. associate-*l/ 72.6%

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

      5. associate-*l/ 69.6%

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

      6. distribute-lft-out-- 90.3%

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

   10. Simplified 90.3%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-170} \lor \neg \left(a \leq 8.5 \cdot 10^{-140}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e+80) x (if (<= a 7.6e+103) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+80) {
		tmp = x;
	} else if (a <= 7.6e+103) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.5d+80)) then
        tmp = x
    else if (a <= 7.6d+103) then
        tmp = (y / a) * (t - z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+80) {
		tmp = x;
	} else if (a <= 7.6e+103) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.5e+80:
		tmp = x
	elif a <= 7.6e+103:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e+80)
		tmp = x;
	elseif (a <= 7.6e+103)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.5e+80)
		tmp = x;
	elseif (a <= 7.6e+103)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e+80], x, If[LessEqual[a, 7.6e+103], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.4999999999999998e80 or 7.5999999999999994e103 < a

   1. Initial program 85.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 75.1%

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

   if -6.4999999999999998e80 < a < 7.5999999999999994e103

   1. Initial program 95.1%

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

      1. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around 0 95.1%

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

      1. associate-*l/ 96.5%

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

      2. *-commutative 96.5%

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

   7. Simplified 96.5%

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

   8. Taylor expanded in y around inf 63.0%

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

      1. distribute-lft-out-- 60.7%

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

      2. associate-/l* 61.2%

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

      3. associate-*r/ 67.8%

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

      4. associate-*l/ 64.3%

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

      5. associate-*l/ 65.1%

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

      6. distribute-lft-out-- 73.8%

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

   10. Simplified 73.8%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(t - z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e+80) x (if (<= a 6.2e+102) (* y (/ (- t z) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e+80) {
		tmp = x;
	} else if (a <= 6.2e+102) {
		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 <= (-5.5d+80)) then
        tmp = x
    else if (a <= 6.2d+102) 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 <= -5.5e+80) {
		tmp = x;
	} else if (a <= 6.2e+102) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e+80:
		tmp = x
	elif a <= 6.2e+102:
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e+80)
		tmp = x;
	elseif (a <= 6.2e+102)
		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 <= -5.5e+80)
		tmp = x;
	elseif (a <= 6.2e+102)
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e+80], x, If[LessEqual[a, 6.2e+102], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.49999999999999967e80 or 6.19999999999999973e102 < a

   1. Initial program 85.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 75.1%

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

   if -5.49999999999999967e80 < a < 6.19999999999999973e102

   1. Initial program 95.1%

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

      1. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in x around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. distribute-frac-neg 71.9%

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

      3. distribute-rgt-neg-in 71.9%

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

      4. sub-neg 71.9%

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

      5. distribute-neg-in 71.9%

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

      6. remove-double-neg 71.9%

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

      7. +-commutative 71.9%

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

      8. sub-neg 71.9%

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

      9. associate-*r/ 66.5%

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

   7. Simplified 66.5%

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

Alternative 8: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.2e-23) x (if (<= a 1.4e-9) (/ t (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e-23) {
		tmp = x;
	} else if (a <= 1.4e-9) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.2d-23)) then
        tmp = x
    else if (a <= 1.4d-9) then
        tmp = t / (a / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e-23) {
		tmp = x;
	} else if (a <= 1.4e-9) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.2e-23:
		tmp = x
	elif a <= 1.4e-9:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.2e-23)
		tmp = x;
	elseif (a <= 1.4e-9)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.2e-23)
		tmp = x;
	elseif (a <= 1.4e-9)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.2e-23], x, If[LessEqual[a, 1.4e-9], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.2000000000000002e-23 or 1.39999999999999992e-9 < a

   1. Initial program 84.7%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 62.9%

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

   if -4.2000000000000002e-23 < a < 1.39999999999999992e-9

   1. Initial program 99.2%

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

      1. associate-/l* 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in t around inf 48.6%

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

      1. associate-/l* 51.6%

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

      2. *-commutative 51.6%

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

   7. Applied egg-rr 51.6%

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

      1. *-commutative 51.6%

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

      2. clear-num 51.6%

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

      3. un-div-inv 51.8%

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

   9. Applied egg-rr 51.8%

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

Alternative 9: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.25e-26) x (if (<= a 1.35e-8) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.25e-26) {
		tmp = x;
	} else if (a <= 1.35e-8) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.25d-26)) then
        tmp = x
    else if (a <= 1.35d-8) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.25e-26) {
		tmp = x;
	} else if (a <= 1.35e-8) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.25e-26:
		tmp = x
	elif a <= 1.35e-8:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.25e-26)
		tmp = x;
	elseif (a <= 1.35e-8)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.25e-26)
		tmp = x;
	elseif (a <= 1.35e-8)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.25e-26], x, If[LessEqual[a, 1.35e-8], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2499999999999999e-26 or 1.35000000000000001e-8 < a

   1. Initial program 84.7%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 62.9%

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

   if -2.2499999999999999e-26 < a < 1.35000000000000001e-8

   1. Initial program 99.2%

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

      1. associate-/l* 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in t around inf 48.6%

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

      1. associate-/l* 51.6%

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

   7. Simplified 51.6%

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

Alternative 10: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

   1. associate-/l* 91.8%

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

3. Simplified 91.8%

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

5. Taylor expanded in y around 0 91.9%

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

   1. associate-*l/ 96.8%

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

   2. *-commutative 96.8%

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

7. Simplified 96.8%

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

8. Final simplification 96.8%

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

Alternative 11: 39.5% 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* 91.8%

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

3. Simplified 91.8%

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

5. Taylor expanded in x around inf 40.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.2% 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 2024144 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t)))))))

  (- x (/ (* y (- z t)) a)))