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

Percentage Accurate: 92.9% → 99.5%

Time: 12.7s

Alternatives: 12

Speedup: 1.0×

• 24.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+287} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+243}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -1e+287) (not (<= t_1 2e+243)))
     (+ x (/ y (/ a (- z t))))
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -1e+287) || !(t_1 <= 2e+243)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (t_1 / 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z - t)
    if ((t_1 <= (-1d+287)) .or. (.not. (t_1 <= 2d+243))) then
        tmp = x + (y / (a / (z - t)))
    else
        tmp = x + (t_1 / a)
    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);
	double tmp;
	if ((t_1 <= -1e+287) || !(t_1 <= 2e+243)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if (t_1 <= -1e+287) or not (t_1 <= 2e+243):
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x + (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -1e+287) || !(t_1 <= 2e+243))
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if ((t_1 <= -1e+287) || ~((t_1 <= 2e+243)))
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x + (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+287], N[Not[LessEqual[t$95$1, 2e+243]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -1.0000000000000001e287 or 2.0000000000000001e243 < (*.f64 y (-.f64 z t))

   1. Initial program 66.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -1.0000000000000001e287 < (*.f64 y (-.f64 z t)) < 2.0000000000000001e243

   1. Initial program 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -1 \cdot 10^{+287} \lor \neg \left(y \cdot \left(z - t\right) \leq 2 \cdot 10^{+243}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

   1. +-commutative 90.6%

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

   2. associate-*l/ 97.7%

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

   3. fma-def 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 3: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(-t\right)\\ t_2 := \frac{y}{a} \cdot z\\ \mathbf{if}\;x \leq -4.9 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t))) (t_2 (* (/ y a) z)))
   (if (<= x -4.9e+79)
     x
     (if (<= x -7.8e-202)
       t_2
       (if (<= x 5.5e-195)
         t_1
         (if (<= x 2.6e-111) t_2 (if (<= x 3.7e+46) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -t;
	double t_2 = (y / a) * z;
	double tmp;
	if (x <= -4.9e+79) {
		tmp = x;
	} else if (x <= -7.8e-202) {
		tmp = t_2;
	} else if (x <= 5.5e-195) {
		tmp = t_1;
	} else if (x <= 2.6e-111) {
		tmp = t_2;
	} else if (x <= 3.7e+46) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / a) * -t
    t_2 = (y / a) * z
    if (x <= (-4.9d+79)) then
        tmp = x
    else if (x <= (-7.8d-202)) then
        tmp = t_2
    else if (x <= 5.5d-195) then
        tmp = t_1
    else if (x <= 2.6d-111) then
        tmp = t_2
    else if (x <= 3.7d+46) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -t;
	double t_2 = (y / a) * z;
	double tmp;
	if (x <= -4.9e+79) {
		tmp = x;
	} else if (x <= -7.8e-202) {
		tmp = t_2;
	} else if (x <= 5.5e-195) {
		tmp = t_1;
	} else if (x <= 2.6e-111) {
		tmp = t_2;
	} else if (x <= 3.7e+46) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * -t
	t_2 = (y / a) * z
	tmp = 0
	if x <= -4.9e+79:
		tmp = x
	elif x <= -7.8e-202:
		tmp = t_2
	elif x <= 5.5e-195:
		tmp = t_1
	elif x <= 2.6e-111:
		tmp = t_2
	elif x <= 3.7e+46:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(-t))
	t_2 = Float64(Float64(y / a) * z)
	tmp = 0.0
	if (x <= -4.9e+79)
		tmp = x;
	elseif (x <= -7.8e-202)
		tmp = t_2;
	elseif (x <= 5.5e-195)
		tmp = t_1;
	elseif (x <= 2.6e-111)
		tmp = t_2;
	elseif (x <= 3.7e+46)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * -t;
	t_2 = (y / a) * z;
	tmp = 0.0;
	if (x <= -4.9e+79)
		tmp = x;
	elseif (x <= -7.8e-202)
		tmp = t_2;
	elseif (x <= 5.5e-195)
		tmp = t_1;
	elseif (x <= 2.6e-111)
		tmp = t_2;
	elseif (x <= 3.7e+46)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[x, -4.9e+79], x, If[LessEqual[x, -7.8e-202], t$95$2, If[LessEqual[x, 5.5e-195], t$95$1, If[LessEqual[x, 2.6e-111], t$95$2, If[LessEqual[x, 3.7e+46], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8999999999999999e79 or 3.6999999999999999e46 < x

   1. Initial program 90.8%

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

      1. +-commutative 90.8%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 61.8%

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

   if -4.8999999999999999e79 < x < -7.7999999999999998e-202 or 5.5000000000000003e-195 < x < 2.59999999999999982e-111

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-*l/ 97.0%

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

      3. fma-def 97.0%

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

   3. Simplified 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]
   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* 51.4%

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

   7. Simplified 51.4%

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

      1. associate-/r/ 59.7%

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

   9. Applied egg-rr 59.7%

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

   if -7.7999999999999998e-202 < x < 5.5000000000000003e-195 or 2.59999999999999982e-111 < x < 3.6999999999999999e46

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-*l/ 95.2%

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

      3. fma-def 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around inf 48.3%

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

      1. associate-*r/ 53.7%

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

      2. neg-mul-1 53.7%

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

      3. distribute-rgt-neg-in 53.7%

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

      4. distribute-neg-frac 53.7%

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

   7. Simplified 53.7%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-202}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-195}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-111}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{a} \cdot z\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+138}:\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y a) z))))
   (if (<= z -3.4e+32)
     t_1
     (if (<= z -1.15e-33)
       (* y (/ (- z t) a))
       (if (<= z 5e+138) (- x (* (/ y a) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * z);
	double tmp;
	if (z <= -3.4e+32) {
		tmp = t_1;
	} else if (z <= -1.15e-33) {
		tmp = y * ((z - t) / a);
	} else if (z <= 5e+138) {
		tmp = x - ((y / a) * t);
	} else {
		tmp = 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 = x + ((y / a) * z)
    if (z <= (-3.4d+32)) then
        tmp = t_1
    else if (z <= (-1.15d-33)) then
        tmp = y * ((z - t) / a)
    else if (z <= 5d+138) then
        tmp = x - ((y / a) * t)
    else
        tmp = 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 = x + ((y / a) * z);
	double tmp;
	if (z <= -3.4e+32) {
		tmp = t_1;
	} else if (z <= -1.15e-33) {
		tmp = y * ((z - t) / a);
	} else if (z <= 5e+138) {
		tmp = x - ((y / a) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y / a) * z)
	tmp = 0
	if z <= -3.4e+32:
		tmp = t_1
	elif z <= -1.15e-33:
		tmp = y * ((z - t) / a)
	elif z <= 5e+138:
		tmp = x - ((y / a) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y / a) * z))
	tmp = 0.0
	if (z <= -3.4e+32)
		tmp = t_1;
	elseif (z <= -1.15e-33)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (z <= 5e+138)
		tmp = Float64(x - Float64(Float64(y / a) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y / a) * z);
	tmp = 0.0;
	if (z <= -3.4e+32)
		tmp = t_1;
	elseif (z <= -1.15e-33)
		tmp = y * ((z - t) / a);
	elseif (z <= 5e+138)
		tmp = x - ((y / a) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+32], t$95$1, If[LessEqual[z, -1.15e-33], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+138], N[(x - N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.39999999999999979e32 or 5.00000000000000016e138 < z

   1. Initial program 83.9%

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

      1. +-commutative 83.9%

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

      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. Taylor expanded in t around 0 82.1%

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

      1. associate-/l* 87.3%

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

      2. associate-/r/ 93.4%

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

   7. Applied egg-rr 93.4%

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

   if -3.39999999999999979e32 < z < -1.14999999999999993e-33

   1. Initial program 88.9%

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

      1. +-commutative 88.9%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 90.5%

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

      1. div-sub 96.4%

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

   7. Simplified 96.4%

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

   if -1.14999999999999993e-33 < z < 5.00000000000000016e138

   1. Initial program 94.6%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

      1. clear-num 94.2%

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

      2. associate-/r/ 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in z around 0 85.5%

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

      1. mul-1-neg 85.5%

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

      2. associate-*l/ 86.1%

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

      3. distribute-lft-neg-in 86.1%

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

      4. cancel-sign-sub-inv 86.1%

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

   9. Simplified 86.1%

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

   10. Taylor expanded in t around 0 85.5%

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

       1. associate-*r/ 89.0%

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

   12. Simplified 89.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+138}:\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.8e+132) x (if (<= x 8.4e+55) (* y (/ (- z t) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.8e+132) {
		tmp = x;
	} else if (x <= 8.4e+55) {
		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 <= (-8.8d+132)) then
        tmp = x
    else if (x <= 8.4d+55) 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 <= -8.8e+132) {
		tmp = x;
	} else if (x <= 8.4e+55) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.8e+132:
		tmp = x
	elif x <= 8.4e+55:
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.8e+132)
		tmp = x;
	elseif (x <= 8.4e+55)
		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 <= -8.8e+132)
		tmp = x;
	elseif (x <= 8.4e+55)
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.8e+132], x, If[LessEqual[x, 8.4e+55], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.79999999999999954e132 or 8.4000000000000002e55 < x

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 65.7%

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

   if -8.79999999999999954e132 < x < 8.4000000000000002e55

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-*l/ 96.3%

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

      3. fma-def 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around inf 67.3%

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

      1. div-sub 70.1%

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

   7. Simplified 70.1%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+162}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+147)
   (* (/ y a) (- t))
   (if (<= t 2.6e+162) (+ x (* (/ y a) z)) (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+147) {
		tmp = (y / a) * -t;
	} else if (t <= 2.6e+162) {
		tmp = x + ((y / a) * z);
	} else {
		tmp = y * ((z - 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 (t <= (-2.5d+147)) then
        tmp = (y / a) * -t
    else if (t <= 2.6d+162) then
        tmp = x + ((y / a) * z)
    else
        tmp = y * ((z - 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 (t <= -2.5e+147) {
		tmp = (y / a) * -t;
	} else if (t <= 2.6e+162) {
		tmp = x + ((y / a) * z);
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e+147:
		tmp = (y / a) * -t
	elif t <= 2.6e+162:
		tmp = x + ((y / a) * z)
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e+147)
		tmp = Float64(Float64(y / a) * Float64(-t));
	elseif (t <= 2.6e+162)
		tmp = Float64(x + Float64(Float64(y / a) * z));
	else
		tmp = Float64(y * Float64(Float64(z - t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.5e+147)
		tmp = (y / a) * -t;
	elseif (t <= 2.6e+162)
		tmp = x + ((y / a) * z);
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e+147], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[t, 2.6e+162], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5000000000000001e147

   1. Initial program 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 62.3%

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

      1. associate-*r/ 75.9%

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

      2. neg-mul-1 75.9%

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

      3. distribute-rgt-neg-in 75.9%

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

      4. distribute-neg-frac 75.9%

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

   7. Simplified 75.9%

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

   if -2.5000000000000001e147 < t < 2.6e162

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. associate-*l/ 97.2%

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

      3. fma-def 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in t around 0 77.7%

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

      1. associate-/l* 78.3%

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

      2. associate-/r/ 83.0%

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

   7. Applied egg-rr 83.0%

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

   if 2.6e162 < t

   1. Initial program 82.9%

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

      1. +-commutative 82.9%

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

      2. associate-*l/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 77.7%

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

      1. div-sub 88.8%

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

   7. Simplified 88.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+162}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-33} \lor \neg \left(z \leq 1.2 \cdot 10^{+147}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e-33) (not (<= z 1.2e+147))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e-33) || !(z <= 1.2e+147)) {
		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 ((z <= (-1.15d-33)) .or. (.not. (z <= 1.2d+147))) 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 ((z <= -1.15e-33) || !(z <= 1.2e+147)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e-33) or not (z <= 1.2e+147):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e-33) || !(z <= 1.2e+147))
		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 ((z <= -1.15e-33) || ~((z <= 1.2e+147)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e-33], N[Not[LessEqual[z, 1.2e+147]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999993e-33 or 1.20000000000000001e147 < z

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. associate-*l/ 98.2%

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

      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 z around inf 55.3%

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

      1. associate-*r/ 59.5%

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

   7. Simplified 59.5%

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

   if -1.14999999999999993e-33 < z < 1.20000000000000001e147

   1. Initial program 94.7%

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

      1. +-commutative 94.7%

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

      2. associate-*l/ 97.4%

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

      3. fma-def 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around 0 50.9%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-33} \lor \neg \left(z \leq 1.2 \cdot 10^{+147}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-36} \lor \neg \left(z \leq 2.7 \cdot 10^{+146}\right):\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.02e-36) (not (<= z 2.7e+146))) (* (/ y a) z) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.02e-36) || !(z <= 2.7e+146)) {
		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 ((z <= (-1.02d-36)) .or. (.not. (z <= 2.7d+146))) 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 ((z <= -1.02e-36) || !(z <= 2.7e+146)) {
		tmp = (y / a) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.02e-36) or not (z <= 2.7e+146):
		tmp = (y / a) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.02e-36) || !(z <= 2.7e+146))
		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 ((z <= -1.02e-36) || ~((z <= 2.7e+146)))
		tmp = (y / a) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.02e-36], N[Not[LessEqual[z, 2.7e+146]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e-36 or 2.69999999999999989e146 < z

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. associate-*l/ 98.2%

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

      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 z around inf 55.3%

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

      1. associate-/l* 59.8%

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

   7. Simplified 59.8%

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

      1. associate-/r/ 64.1%

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

   9. Applied egg-rr 64.1%

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

   if -1.02e-36 < z < 2.69999999999999989e146

   1. Initial program 94.7%

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

      1. +-commutative 94.7%

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

      2. associate-*l/ 97.4%

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

      3. fma-def 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around 0 50.9%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-36} \lor \neg \left(z \leq 2.7 \cdot 10^{+146}\right):\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a}{z - t}} \end{array} \]

FPCore

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

C

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

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 / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

   1. associate-/l* 93.4%

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

3. Simplified 93.4%

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

5. Final simplification 93.4%

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

Alternative 10: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{z - t}{\frac{a}{y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

   1. *-commutative 90.6%

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

   2. associate-/l* 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 11: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (z - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

   1. +-commutative 90.6%

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

   2. associate-*l/ 97.7%

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

   3. fma-def 97.7%

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

3. Simplified 97.7%

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

   1. fma-udef 97.7%

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

6. Applied egg-rr 97.7%

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

7. Final simplification 97.7%

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

Alternative 12: 39.7% 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 90.6%

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

   1. +-commutative 90.6%

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

   2. associate-*l/ 97.7%

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

   3. fma-def 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in y around 0 39.3%

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

6. Final simplification 39.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 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 2024036 
(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)))