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

Percentage Accurate: 92.7% → 95.6%

Time: 14.5s

Alternatives: 14

Speedup: 1.0×

• 25.6% 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: 92.7% 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: 95.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+255}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 2e+255) (+ x t_1) (+ x (/ y (/ a (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= 2e+255) {
		tmp = x + t_1;
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if (t_1 <= 2d+255) then
        tmp = x + t_1
    else
        tmp = x + (y / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= 2e+255) {
		tmp = x + t_1;
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= 2e+255:
		tmp = x + t_1
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= 2e+255)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= 2e+255)
		tmp = x + t_1;
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+255], N[(x + t$95$1), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < 1.99999999999999998e255

   1. Initial program 97.3%

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

   if 1.99999999999999998e255 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 67.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq 2 \cdot 10^{+255}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+155} \lor \neg \left(x \leq -5.4 \cdot 10^{+72}\right) \land \left(x \leq -1.2 \cdot 10^{-73} \lor \neg \left(x \leq -6 \cdot 10^{-114}\right) \land x \leq 1.85 \cdot 10^{-14}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.5e+170)
   x
   (if (or (<= x -1.5e+155)
           (and (not (<= x -5.4e+72))
                (or (<= x -1.2e-73)
                    (and (not (<= x -6e-114)) (<= x 1.85e-14)))))
     (* y (/ (- z t) a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.5e+170) {
		tmp = x;
	} else if ((x <= -1.5e+155) || (!(x <= -5.4e+72) && ((x <= -1.2e-73) || (!(x <= -6e-114) && (x <= 1.85e-14))))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-5.5d+170)) then
        tmp = x
    else if ((x <= (-1.5d+155)) .or. (.not. (x <= (-5.4d+72))) .and. (x <= (-1.2d-73)) .or. (.not. (x <= (-6d-114))) .and. (x <= 1.85d-14)) then
        tmp = y * ((z - t) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.5e+170) {
		tmp = x;
	} else if ((x <= -1.5e+155) || (!(x <= -5.4e+72) && ((x <= -1.2e-73) || (!(x <= -6e-114) && (x <= 1.85e-14))))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.5e+170:
		tmp = x
	elif (x <= -1.5e+155) or (not (x <= -5.4e+72) and ((x <= -1.2e-73) or (not (x <= -6e-114) and (x <= 1.85e-14)))):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.5e+170)
		tmp = x;
	elseif ((x <= -1.5e+155) || (!(x <= -5.4e+72) && ((x <= -1.2e-73) || (!(x <= -6e-114) && (x <= 1.85e-14)))))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.5e+170)
		tmp = x;
	elseif ((x <= -1.5e+155) || (~((x <= -5.4e+72)) && ((x <= -1.2e-73) || (~((x <= -6e-114)) && (x <= 1.85e-14)))))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.5e+170], x, If[Or[LessEqual[x, -1.5e+155], And[N[Not[LessEqual[x, -5.4e+72]], $MachinePrecision], Or[LessEqual[x, -1.2e-73], And[N[Not[LessEqual[x, -6e-114]], $MachinePrecision], LessEqual[x, 1.85e-14]]]]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4999999999999999e170 or -1.5000000000000001e155 < x < -5.4000000000000001e72 or -1.20000000000000003e-73 < x < -6.0000000000000003e-114 or 1.85000000000000001e-14 < x

   1. Initial program 94.8%

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

      1. +-commutative 94.8%

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

      2. associate-*l/ 98.8%

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

      3. fma-def 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around 0 74.1%

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

   if -5.4999999999999999e170 < x < -1.5000000000000001e155 or -5.4000000000000001e72 < x < -1.20000000000000003e-73 or -6.0000000000000003e-114 < x < 1.85000000000000001e-14

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. associate-*l/ 94.4%

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

      3. fma-def 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around inf 72.7%

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

      1. div-sub 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+170}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+155} \lor \neg \left(x \leq -5.4 \cdot 10^{+72}\right) \land \left(x \leq -1.2 \cdot 10^{-73} \lor \neg \left(x \leq -6 \cdot 10^{-114}\right) \land x \leq 1.85 \cdot 10^{-14}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t))))
   (if (<= z -9.5e+77)
     (/ y (/ a z))
     (if (<= z -7e-102)
       x
       (if (<= z -7.2e-238)
         t_1
         (if (<= z 3.4e-240) x (if (<= z 2.7) t_1 (* (/ y a) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -t;
	double tmp;
	if (z <= -9.5e+77) {
		tmp = y / (a / z);
	} else if (z <= -7e-102) {
		tmp = x;
	} else if (z <= -7.2e-238) {
		tmp = t_1;
	} else if (z <= 3.4e-240) {
		tmp = x;
	} else if (z <= 2.7) {
		tmp = t_1;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / a) * -t
    if (z <= (-9.5d+77)) then
        tmp = y / (a / z)
    else if (z <= (-7d-102)) then
        tmp = x
    else if (z <= (-7.2d-238)) then
        tmp = t_1
    else if (z <= 3.4d-240) then
        tmp = x
    else if (z <= 2.7d0) then
        tmp = t_1
    else
        tmp = (y / a) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -t;
	double tmp;
	if (z <= -9.5e+77) {
		tmp = y / (a / z);
	} else if (z <= -7e-102) {
		tmp = x;
	} else if (z <= -7.2e-238) {
		tmp = t_1;
	} else if (z <= 3.4e-240) {
		tmp = x;
	} else if (z <= 2.7) {
		tmp = t_1;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * -t
	tmp = 0
	if z <= -9.5e+77:
		tmp = y / (a / z)
	elif z <= -7e-102:
		tmp = x
	elif z <= -7.2e-238:
		tmp = t_1
	elif z <= 3.4e-240:
		tmp = x
	elif z <= 2.7:
		tmp = t_1
	else:
		tmp = (y / a) * z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(-t))
	tmp = 0.0
	if (z <= -9.5e+77)
		tmp = Float64(y / Float64(a / z));
	elseif (z <= -7e-102)
		tmp = x;
	elseif (z <= -7.2e-238)
		tmp = t_1;
	elseif (z <= 3.4e-240)
		tmp = x;
	elseif (z <= 2.7)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / a) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * -t;
	tmp = 0.0;
	if (z <= -9.5e+77)
		tmp = y / (a / z);
	elseif (z <= -7e-102)
		tmp = x;
	elseif (z <= -7.2e-238)
		tmp = t_1;
	elseif (z <= 3.4e-240)
		tmp = x;
	elseif (z <= 2.7)
		tmp = t_1;
	else
		tmp = (y / a) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[z, -9.5e+77], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-102], x, If[LessEqual[z, -7.2e-238], t$95$1, If[LessEqual[z, 3.4e-240], x, If[LessEqual[z, 2.7], t$95$1, N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.4999999999999998e77

   1. Initial program 92.1%

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

      1. +-commutative 92.1%

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

      2. associate-*l/ 92.8%

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

      3. fma-def 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in z around inf 52.5%

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

      1. associate-/l* 55.1%

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

   7. Simplified 55.1%

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

   if -9.4999999999999998e77 < z < -6.99999999999999973e-102 or -7.20000000000000021e-238 < z < 3.3999999999999999e-240

   1. Initial program 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-*l/ 97.1%

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

      3. fma-def 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around 0 68.6%

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

   if -6.99999999999999973e-102 < z < -7.20000000000000021e-238 or 3.3999999999999999e-240 < z < 2.7000000000000002

   1. Initial program 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-*l/ 98.8%

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

      3. fma-def 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 48.1%

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

      1. mul-1-neg 48.1%

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

      2. associate-*r/ 56.1%

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

      3. distribute-rgt-neg-in 56.1%

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

      4. distribute-neg-frac 56.1%

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

   7. Simplified 56.1%

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

   if 2.7000000000000002 < z

   1. Initial program 93.7%

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

      1. +-commutative 93.7%

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

      2. associate-*l/ 93.5%

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

      3. fma-def 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around inf 53.5%

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

      1. associate-/l* 49.9%

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

   7. Simplified 49.9%

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

      1. associate-/r/ 56.3%

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

   9. Applied egg-rr 56.3%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-238}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-238}:\\ \;\;\;\;\frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.054:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+78)
   (/ y (/ a z))
   (if (<= z -2.8e-102)
     x
     (if (<= z -5.3e-238)
       (/ y (/ (- a) t))
       (if (<= z 9e-240)
         x
         (if (<= z 0.054) (* (/ y a) (- t)) (* (/ y a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+78) {
		tmp = y / (a / z);
	} else if (z <= -2.8e-102) {
		tmp = x;
	} else if (z <= -5.3e-238) {
		tmp = y / (-a / t);
	} else if (z <= 9e-240) {
		tmp = x;
	} else if (z <= 0.054) {
		tmp = (y / a) * -t;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d+78)) then
        tmp = y / (a / z)
    else if (z <= (-2.8d-102)) then
        tmp = x
    else if (z <= (-5.3d-238)) then
        tmp = y / (-a / t)
    else if (z <= 9d-240) then
        tmp = x
    else if (z <= 0.054d0) then
        tmp = (y / a) * -t
    else
        tmp = (y / a) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+78) {
		tmp = y / (a / z);
	} else if (z <= -2.8e-102) {
		tmp = x;
	} else if (z <= -5.3e-238) {
		tmp = y / (-a / t);
	} else if (z <= 9e-240) {
		tmp = x;
	} else if (z <= 0.054) {
		tmp = (y / a) * -t;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+78:
		tmp = y / (a / z)
	elif z <= -2.8e-102:
		tmp = x
	elif z <= -5.3e-238:
		tmp = y / (-a / t)
	elif z <= 9e-240:
		tmp = x
	elif z <= 0.054:
		tmp = (y / a) * -t
	else:
		tmp = (y / a) * z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+78)
		tmp = Float64(y / Float64(a / z));
	elseif (z <= -2.8e-102)
		tmp = x;
	elseif (z <= -5.3e-238)
		tmp = Float64(y / Float64(Float64(-a) / t));
	elseif (z <= 9e-240)
		tmp = x;
	elseif (z <= 0.054)
		tmp = Float64(Float64(y / a) * Float64(-t));
	else
		tmp = Float64(Float64(y / a) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+78)
		tmp = y / (a / z);
	elseif (z <= -2.8e-102)
		tmp = x;
	elseif (z <= -5.3e-238)
		tmp = y / (-a / t);
	elseif (z <= 9e-240)
		tmp = x;
	elseif (z <= 0.054)
		tmp = (y / a) * -t;
	else
		tmp = (y / a) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+78], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-102], x, If[LessEqual[z, -5.3e-238], N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-240], x, If[LessEqual[z, 0.054], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.1500000000000001e78

   1. Initial program 92.1%

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

      1. +-commutative 92.1%

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

      2. associate-*l/ 92.8%

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

      3. fma-def 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in z around inf 52.5%

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

      1. associate-/l* 55.1%

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

   7. Simplified 55.1%

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

   if -1.1500000000000001e78 < z < -2.80000000000000013e-102 or -5.29999999999999968e-238 < z < 9.0000000000000003e-240

   1. Initial program 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-*l/ 97.1%

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

      3. fma-def 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around 0 68.6%

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

   if -2.80000000000000013e-102 < z < -5.29999999999999968e-238

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-*l/ 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. associate-*r/ 61.6%

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

      3. distribute-rgt-neg-in 61.6%

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

      4. distribute-neg-frac 61.6%

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

   7. Simplified 61.6%

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

      1. *-commutative 61.6%

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

      2. frac-2neg 61.6%

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

      3. remove-double-neg 61.6%

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

      4. associate-*l/ 54.4%

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

   9. Applied egg-rr 54.4%

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

       1. associate-/l* 61.8%

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

   11. Simplified 61.8%

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

   if 9.0000000000000003e-240 < z < 0.0539999999999999994

   1. Initial program 87.9%

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

      1. +-commutative 87.9%

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

      2. associate-*l/ 98.3%

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

      3. fma-def 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around inf 43.9%

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

      1. mul-1-neg 43.9%

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

      2. associate-*r/ 52.3%

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

      3. distribute-rgt-neg-in 52.3%

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

      4. distribute-neg-frac 52.3%

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

   7. Simplified 52.3%

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

   if 0.0539999999999999994 < z

   1. Initial program 93.7%

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

      1. +-commutative 93.7%

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

      2. associate-*l/ 93.5%

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

      3. fma-def 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around inf 53.5%

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

      1. associate-/l* 49.9%

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

   7. Simplified 49.9%

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

      1. associate-/r/ 56.3%

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

   9. Applied egg-rr 56.3%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-238}:\\ \;\;\;\;\frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.054:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-72} \lor \neg \left(x \leq -1.55 \cdot 10^{-116}\right) \land x \leq 2.9 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.3e-53)
   x
   (if (or (<= x -4.5e-72) (and (not (<= x -1.55e-116)) (<= x 2.9e-101)))
     (* y (/ z a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.3e-53) {
		tmp = x;
	} else if ((x <= -4.5e-72) || (!(x <= -1.55e-116) && (x <= 2.9e-101))) {
		tmp = y * (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 (x <= (-2.3d-53)) then
        tmp = x
    else if ((x <= (-4.5d-72)) .or. (.not. (x <= (-1.55d-116))) .and. (x <= 2.9d-101)) then
        tmp = y * (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 (x <= -2.3e-53) {
		tmp = x;
	} else if ((x <= -4.5e-72) || (!(x <= -1.55e-116) && (x <= 2.9e-101))) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.3e-53:
		tmp = x
	elif (x <= -4.5e-72) or (not (x <= -1.55e-116) and (x <= 2.9e-101)):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.3e-53)
		tmp = x;
	elseif ((x <= -4.5e-72) || (!(x <= -1.55e-116) && (x <= 2.9e-101)))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.3e-53)
		tmp = x;
	elseif ((x <= -4.5e-72) || (~((x <= -1.55e-116)) && (x <= 2.9e-101)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.3e-53], x, If[Or[LessEqual[x, -4.5e-72], And[N[Not[LessEqual[x, -1.55e-116]], $MachinePrecision], LessEqual[x, 2.9e-101]]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3000000000000001e-53 or -4.5e-72 < x < -1.55000000000000009e-116 or 2.9e-101 < x

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-*l/ 98.5%

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

      3. fma-def 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 59.9%

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

   if -2.3000000000000001e-53 < x < -4.5e-72 or -1.55000000000000009e-116 < x < 2.9e-101

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-*l/ 92.4%

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

      3. fma-def 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around inf 49.5%

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

      1. associate-*r/ 45.9%

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

   7. Simplified 45.9%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-72} \lor \neg \left(x \leq -1.55 \cdot 10^{-116}\right) \land x \leq 2.9 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.2e-52)
   x
   (if (<= x -1.5e-67)
     (* y (/ z a))
     (if (<= x -7.5e-116) x (if (<= x 5.3e-101) (* (/ y a) z) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.2e-52) {
		tmp = x;
	} else if (x <= -1.5e-67) {
		tmp = y * (z / a);
	} else if (x <= -7.5e-116) {
		tmp = x;
	} else if (x <= 5.3e-101) {
		tmp = (y / a) * 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 (x <= (-7.2d-52)) then
        tmp = x
    else if (x <= (-1.5d-67)) then
        tmp = y * (z / a)
    else if (x <= (-7.5d-116)) then
        tmp = x
    else if (x <= 5.3d-101) then
        tmp = (y / a) * 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 (x <= -7.2e-52) {
		tmp = x;
	} else if (x <= -1.5e-67) {
		tmp = y * (z / a);
	} else if (x <= -7.5e-116) {
		tmp = x;
	} else if (x <= 5.3e-101) {
		tmp = (y / a) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.2e-52:
		tmp = x
	elif x <= -1.5e-67:
		tmp = y * (z / a)
	elif x <= -7.5e-116:
		tmp = x
	elif x <= 5.3e-101:
		tmp = (y / a) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.2e-52)
		tmp = x;
	elseif (x <= -1.5e-67)
		tmp = Float64(y * Float64(z / a));
	elseif (x <= -7.5e-116)
		tmp = x;
	elseif (x <= 5.3e-101)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.2e-52)
		tmp = x;
	elseif (x <= -1.5e-67)
		tmp = y * (z / a);
	elseif (x <= -7.5e-116)
		tmp = x;
	elseif (x <= 5.3e-101)
		tmp = (y / a) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.2e-52], x, If[LessEqual[x, -1.5e-67], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e-116], x, If[LessEqual[x, 5.3e-101], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999976e-52 or -1.50000000000000016e-67 < x < -7.5000000000000004e-116 or 5.3000000000000003e-101 < x

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-*l/ 98.5%

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

      3. fma-def 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 59.9%

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

   if -7.19999999999999976e-52 < x < -1.50000000000000016e-67

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 83.8%

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

      1. associate-*r/ 83.8%

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

   7. Simplified 83.8%

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

   if -7.5000000000000004e-116 < x < 5.3000000000000003e-101

   1. Initial program 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-*l/ 91.9%

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

      3. fma-def 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in z around inf 47.2%

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

      1. associate-/l* 43.3%

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

   7. Simplified 43.3%

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

      1. associate-/r/ 46.5%

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

   9. Applied egg-rr 46.5%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-67}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.05 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.65e-48)
   x
   (if (<= x -4.8e-67)
     (/ z (/ a y))
     (if (<= x -4.8e-116) x (if (<= x 5.05e-101) (* (/ y a) z) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.65e-48) {
		tmp = x;
	} else if (x <= -4.8e-67) {
		tmp = z / (a / y);
	} else if (x <= -4.8e-116) {
		tmp = x;
	} else if (x <= 5.05e-101) {
		tmp = (y / a) * 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 (x <= (-1.65d-48)) then
        tmp = x
    else if (x <= (-4.8d-67)) then
        tmp = z / (a / y)
    else if (x <= (-4.8d-116)) then
        tmp = x
    else if (x <= 5.05d-101) then
        tmp = (y / a) * 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 (x <= -1.65e-48) {
		tmp = x;
	} else if (x <= -4.8e-67) {
		tmp = z / (a / y);
	} else if (x <= -4.8e-116) {
		tmp = x;
	} else if (x <= 5.05e-101) {
		tmp = (y / a) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.65e-48:
		tmp = x
	elif x <= -4.8e-67:
		tmp = z / (a / y)
	elif x <= -4.8e-116:
		tmp = x
	elif x <= 5.05e-101:
		tmp = (y / a) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.65e-48)
		tmp = x;
	elseif (x <= -4.8e-67)
		tmp = Float64(z / Float64(a / y));
	elseif (x <= -4.8e-116)
		tmp = x;
	elseif (x <= 5.05e-101)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.65e-48)
		tmp = x;
	elseif (x <= -4.8e-67)
		tmp = z / (a / y);
	elseif (x <= -4.8e-116)
		tmp = x;
	elseif (x <= 5.05e-101)
		tmp = (y / a) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.65e-48], x, If[LessEqual[x, -4.8e-67], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-116], x, If[LessEqual[x, 5.05e-101], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e-48 or -4.8e-67 < x < -4.79999999999999986e-116 or 5.05000000000000013e-101 < x

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-*l/ 98.5%

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

      3. fma-def 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 59.9%

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

   if -1.65e-48 < x < -4.8e-67

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

      1. associate-/r/ 83.5%

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

   9. Applied egg-rr 83.5%

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

       1. *-commutative 83.5%

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

       2. clear-num 83.5%

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

       3. un-div-inv 83.8%

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

   11. Applied egg-rr 83.8%

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

   if -4.79999999999999986e-116 < x < 5.05000000000000013e-101

   1. Initial program 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-*l/ 91.9%

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

      3. fma-def 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in z around inf 47.2%

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

      1. associate-/l* 43.3%

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

   7. Simplified 43.3%

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

      1. associate-/r/ 46.5%

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

   9. Applied egg-rr 46.5%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-67}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.05 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-70}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-101}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.9e-48)
   x
   (if (<= x -1.15e-70)
     (/ z (/ a y))
     (if (<= x -4.3e-114) x (if (<= x 2.35e-101) (/ (* y z) a) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.9e-48) {
		tmp = x;
	} else if (x <= -1.15e-70) {
		tmp = z / (a / y);
	} else if (x <= -4.3e-114) {
		tmp = x;
	} else if (x <= 2.35e-101) {
		tmp = (y * 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 (x <= (-1.9d-48)) then
        tmp = x
    else if (x <= (-1.15d-70)) then
        tmp = z / (a / y)
    else if (x <= (-4.3d-114)) then
        tmp = x
    else if (x <= 2.35d-101) then
        tmp = (y * 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 (x <= -1.9e-48) {
		tmp = x;
	} else if (x <= -1.15e-70) {
		tmp = z / (a / y);
	} else if (x <= -4.3e-114) {
		tmp = x;
	} else if (x <= 2.35e-101) {
		tmp = (y * z) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.9e-48:
		tmp = x
	elif x <= -1.15e-70:
		tmp = z / (a / y)
	elif x <= -4.3e-114:
		tmp = x
	elif x <= 2.35e-101:
		tmp = (y * z) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.9e-48)
		tmp = x;
	elseif (x <= -1.15e-70)
		tmp = Float64(z / Float64(a / y));
	elseif (x <= -4.3e-114)
		tmp = x;
	elseif (x <= 2.35e-101)
		tmp = Float64(Float64(y * z) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.9e-48)
		tmp = x;
	elseif (x <= -1.15e-70)
		tmp = z / (a / y);
	elseif (x <= -4.3e-114)
		tmp = x;
	elseif (x <= 2.35e-101)
		tmp = (y * z) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.9e-48], x, If[LessEqual[x, -1.15e-70], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.3e-114], x, If[LessEqual[x, 2.35e-101], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.90000000000000001e-48 or -1.15e-70 < x < -4.3e-114 or 2.35e-101 < x

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-*l/ 98.5%

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

      3. fma-def 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 59.9%

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

   if -1.90000000000000001e-48 < x < -1.15e-70

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

      1. associate-/r/ 83.5%

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

   9. Applied egg-rr 83.5%

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

       1. *-commutative 83.5%

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

       2. clear-num 83.5%

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

       3. un-div-inv 83.8%

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

   11. Applied egg-rr 83.8%

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

   if -4.3e-114 < x < 2.35e-101

   1. Initial program 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-*l/ 91.9%

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

      3. fma-def 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in z around inf 47.2%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-70}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-101}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 -2e+110) t_1 (+ x (/ y (/ a (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -2e+110) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if (t_1 <= (-2d+110)) then
        tmp = t_1
    else
        tmp = x + (y / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -2e+110) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -2e+110:
		tmp = t_1
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= -2e+110)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= -2e+110)
		tmp = t_1;
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+110], t$95$1, N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2e110

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-*l/ 96.5%

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

      3. fma-def 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around -inf 87.9%

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

   if -2e110 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 92.8%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -2 \cdot 10^{+110}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+23} \lor \neg \left(z \leq 0.0065\right):\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+23) (not (<= z 0.0065)))
   (+ x (* (/ y a) z))
   (+ x (/ y (/ (- a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+23) || !(z <= 0.0065)) {
		tmp = x + ((y / a) * z);
	} else {
		tmp = x + (y / (-a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.8d+23)) .or. (.not. (z <= 0.0065d0))) then
        tmp = x + ((y / a) * z)
    else
        tmp = x + (y / (-a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+23) || !(z <= 0.0065)) {
		tmp = x + ((y / a) * z);
	} else {
		tmp = x + (y / (-a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e+23) or not (z <= 0.0065):
		tmp = x + ((y / a) * z)
	else:
		tmp = x + (y / (-a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e+23) || !(z <= 0.0065))
		tmp = Float64(x + Float64(Float64(y / a) * z));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(-a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.8e+23) || ~((z <= 0.0065)))
		tmp = x + ((y / a) * z);
	else
		tmp = x + (y / (-a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e+23], N[Not[LessEqual[z, 0.0065]], $MachinePrecision]], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e23 or 0.0064999999999999997 < z

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-*l/ 94.0%

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

      3. fma-def 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around 0 82.9%

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

      1. associate-/l* 80.0%

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

   7. Simplified 80.0%

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

      1. associate-/r/ 53.6%

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

   9. Applied egg-rr 86.9%

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

   if -4.8e23 < z < 0.0064999999999999997

   1. Initial program 92.9%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around 0 87.7%

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

      1. associate-*r/ 87.7%

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

      2. neg-mul-1 87.7%

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

   7. Simplified 87.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+23} \lor \neg \left(z \leq 0.0065\right):\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+96} \lor \neg \left(t \leq 1.15 \cdot 10^{+121}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.2e+96) (not (<= t 1.15e+121)))
   (* y (/ (- z t) a))
   (+ x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+96) || !(t <= 1.15e+121)) {
		tmp = y * ((z - t) / 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 <= (-8.2d+96)) .or. (.not. (t <= 1.15d+121))) then
        tmp = y * ((z - t) / 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 <= -8.2e+96) || !(t <= 1.15e+121)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.2e+96) or not (t <= 1.15e+121):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.2e+96) || !(t <= 1.15e+121))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(Float64(y / a) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.2e+96) || ~((t <= 1.15e+121)))
		tmp = y * ((z - t) / a);
	else
		tmp = x + ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.2e+96], N[Not[LessEqual[t, 1.15e+121]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.19999999999999996e96 or 1.1499999999999999e121 < t

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-*l/ 95.1%

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

      3. fma-def 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around inf 72.0%

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

      1. div-sub 74.8%

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

   7. Simplified 74.8%

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

   if -8.19999999999999996e96 < t < 1.1499999999999999e121

   1. Initial program 94.8%

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

      1. +-commutative 94.8%

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

      2. associate-*l/ 96.7%

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

      3. fma-def 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 80.1%

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

      1. associate-/l* 79.9%

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

   7. Simplified 79.9%

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

      1. associate-/r/ 33.4%

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

   9. Applied egg-rr 84.2%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+96} \lor \neg \left(t \leq 1.15 \cdot 10^{+121}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+23} \lor \neg \left(z \leq 0.72\right):\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+23) (not (<= z 0.72)))
   (+ 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 <= -3.5e+23) || !(z <= 0.72)) {
		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 <= (-3.5d+23)) .or. (.not. (z <= 0.72d0))) 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 <= -3.5e+23) || !(z <= 0.72)) {
		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 <= -3.5e+23) or not (z <= 0.72):
		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 <= -3.5e+23) || !(z <= 0.72))
		tmp = Float64(x + Float64(Float64(y / a) * z));
	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 <= -3.5e+23) || ~((z <= 0.72)))
		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, -3.5e+23], N[Not[LessEqual[z, 0.72]], $MachinePrecision]], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000002e23 or 0.71999999999999997 < z

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-*l/ 94.0%

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

      3. fma-def 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around 0 82.9%

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

      1. associate-/l* 80.0%

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

   7. Simplified 80.0%

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

      1. associate-/r/ 53.6%

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

   9. Applied egg-rr 86.9%

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

   if -3.5000000000000002e23 < z < 0.71999999999999997

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-*l/ 97.9%

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

      3. fma-def 97.9%

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

   3. Simplified 97.9%

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

      1. fma-udef 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. associate-/l* 89.6%

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

      3. unsub-neg 89.6%

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

      4. associate-/r/ 87.6%

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

      5. *-commutative 87.6%

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

   9. Simplified 87.6%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+23} \lor \neg \left(z \leq 0.72\right):\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. +-commutative 92.9%

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

   2. associate-*l/ 96.2%

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

   3. fma-def 96.2%

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

3. Simplified 96.2%

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

   1. fma-udef 96.2%

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

6. Applied egg-rr 96.2%

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

7. Final simplification 96.2%

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

Alternative 14: 38.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. +-commutative 92.9%

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

   2. associate-*l/ 96.2%

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

   3. fma-def 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in y around 0 42.2%

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

6. Final simplification 42.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.3% 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 2024031 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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