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

Percentage Accurate: 92.3% → 98.1%

Time: 9.7s

Alternatives: 13

Speedup: 1.0×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

3. Taylor expanded in z around 0 89.2%

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

   1. +-commutative 89.2%

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

   2. *-commutative 89.2%

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

   3. associate-*r/ 88.7%

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

   4. mul-1-neg 88.7%

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

   5. associate-/l* 88.6%

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

   6. distribute-lft-neg-in 88.6%

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

   7. distribute-rgt-in 97.6%

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

   8. sub-neg 97.6%

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

5. Simplified 97.6%

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

6. Final simplification 97.6%

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

Alternative 2: 53.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(-y\right)}{t}\\ t_2 := y \cdot \frac{z}{t}\\ t_3 := \frac{y \cdot z}{t}\\ \mathbf{if}\;t \leq -5.9 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -0.29:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-254}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+35}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y)) t)) (t_2 (* y (/ z t))) (t_3 (/ (* y z) t)))
   (if (<= t -5.9e+38)
     x
     (if (<= t -0.29)
       t_2
       (if (<= t -6.1e-34)
         x
         (if (<= t -1.04e-66)
           t_2
           (if (<= t -9.6e-153)
             t_1
             (if (<= t -2.25e-254)
               t_3
               (if (<= t 4.2e-232) t_1 (if (<= t 9.5e+35) t_3 x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * -y) / t;
	double t_2 = y * (z / t);
	double t_3 = (y * z) / t;
	double tmp;
	if (t <= -5.9e+38) {
		tmp = x;
	} else if (t <= -0.29) {
		tmp = t_2;
	} else if (t <= -6.1e-34) {
		tmp = x;
	} else if (t <= -1.04e-66) {
		tmp = t_2;
	} else if (t <= -9.6e-153) {
		tmp = t_1;
	} else if (t <= -2.25e-254) {
		tmp = t_3;
	} else if (t <= 4.2e-232) {
		tmp = t_1;
	} else if (t <= 9.5e+35) {
		tmp = t_3;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * -y) / t
    t_2 = y * (z / t)
    t_3 = (y * z) / t
    if (t <= (-5.9d+38)) then
        tmp = x
    else if (t <= (-0.29d0)) then
        tmp = t_2
    else if (t <= (-6.1d-34)) then
        tmp = x
    else if (t <= (-1.04d-66)) then
        tmp = t_2
    else if (t <= (-9.6d-153)) then
        tmp = t_1
    else if (t <= (-2.25d-254)) then
        tmp = t_3
    else if (t <= 4.2d-232) then
        tmp = t_1
    else if (t <= 9.5d+35) then
        tmp = t_3
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * -y) / t;
	double t_2 = y * (z / t);
	double t_3 = (y * z) / t;
	double tmp;
	if (t <= -5.9e+38) {
		tmp = x;
	} else if (t <= -0.29) {
		tmp = t_2;
	} else if (t <= -6.1e-34) {
		tmp = x;
	} else if (t <= -1.04e-66) {
		tmp = t_2;
	} else if (t <= -9.6e-153) {
		tmp = t_1;
	} else if (t <= -2.25e-254) {
		tmp = t_3;
	} else if (t <= 4.2e-232) {
		tmp = t_1;
	} else if (t <= 9.5e+35) {
		tmp = t_3;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * -y) / t
	t_2 = y * (z / t)
	t_3 = (y * z) / t
	tmp = 0
	if t <= -5.9e+38:
		tmp = x
	elif t <= -0.29:
		tmp = t_2
	elif t <= -6.1e-34:
		tmp = x
	elif t <= -1.04e-66:
		tmp = t_2
	elif t <= -9.6e-153:
		tmp = t_1
	elif t <= -2.25e-254:
		tmp = t_3
	elif t <= 4.2e-232:
		tmp = t_1
	elif t <= 9.5e+35:
		tmp = t_3
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(-y)) / t)
	t_2 = Float64(y * Float64(z / t))
	t_3 = Float64(Float64(y * z) / t)
	tmp = 0.0
	if (t <= -5.9e+38)
		tmp = x;
	elseif (t <= -0.29)
		tmp = t_2;
	elseif (t <= -6.1e-34)
		tmp = x;
	elseif (t <= -1.04e-66)
		tmp = t_2;
	elseif (t <= -9.6e-153)
		tmp = t_1;
	elseif (t <= -2.25e-254)
		tmp = t_3;
	elseif (t <= 4.2e-232)
		tmp = t_1;
	elseif (t <= 9.5e+35)
		tmp = t_3;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * -y) / t;
	t_2 = y * (z / t);
	t_3 = (y * z) / t;
	tmp = 0.0;
	if (t <= -5.9e+38)
		tmp = x;
	elseif (t <= -0.29)
		tmp = t_2;
	elseif (t <= -6.1e-34)
		tmp = x;
	elseif (t <= -1.04e-66)
		tmp = t_2;
	elseif (t <= -9.6e-153)
		tmp = t_1;
	elseif (t <= -2.25e-254)
		tmp = t_3;
	elseif (t <= 4.2e-232)
		tmp = t_1;
	elseif (t <= 9.5e+35)
		tmp = t_3;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * (-y)), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -5.9e+38], x, If[LessEqual[t, -0.29], t$95$2, If[LessEqual[t, -6.1e-34], x, If[LessEqual[t, -1.04e-66], t$95$2, If[LessEqual[t, -9.6e-153], t$95$1, If[LessEqual[t, -2.25e-254], t$95$3, If[LessEqual[t, 4.2e-232], t$95$1, If[LessEqual[t, 9.5e+35], t$95$3, x]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.89999999999999981e38 or -0.28999999999999998 < t < -6.0999999999999998e-34 or 9.50000000000000062e35 < t

   1. Initial program 89.6%

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

   3. Taylor expanded in y around 0 70.5%

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

   if -5.89999999999999981e38 < t < -0.28999999999999998 or -6.0999999999999998e-34 < t < -1.04e-66

   1. Initial program 94.2%

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

   3. Taylor expanded in y around -inf 88.0%

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

   4. Taylor expanded in z around inf 72.2%

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

      1. associate-/l* 77.8%

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

   6. Simplified 77.8%

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

   if -1.04e-66 < t < -9.6000000000000008e-153 or -2.25e-254 < t < 4.2000000000000001e-232

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 75.9%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{t} \]
   4. Step-by-step derivation

      1. mul-1-neg 75.9%

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

      2. distribute-lft-neg-out 75.9%

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

      3. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in t around 0 75.9%

      \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot y\right) + t \cdot x}{t}} \]
   7. Step-by-step derivation

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. *-commutative 75.9%

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

      4. unsub-neg 75.9%

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

      5. *-commutative 75.9%

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

   8. Simplified 75.9%

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

   9. Taylor expanded in t around 0 70.8%

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

       1. mul-1-neg 70.8%

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

       2. *-commutative 70.8%

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

       3. distribute-rgt-neg-in 70.8%

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

   11. Simplified 70.8%

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

   if -9.6000000000000008e-153 < t < -2.25e-254 or 4.2000000000000001e-232 < t < 9.50000000000000062e35

   1. Initial program 98.8%

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

   3. Taylor expanded in y around -inf 81.9%

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

   4. Taylor expanded in z around inf 65.3%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -0.29:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-153}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-254}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -0.3 \lor \neg \left(t \leq -6.2 \cdot 10^{-34}\right) \land t \leq 9 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8e+38)
   x
   (if (or (<= t -0.3) (and (not (<= t -6.2e-34)) (<= t 9e+37)))
     (* y (/ z t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8e+38) {
		tmp = x;
	} else if ((t <= -0.3) || (!(t <= -6.2e-34) && (t <= 9e+37))) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-8d+38)) then
        tmp = x
    else if ((t <= (-0.3d0)) .or. (.not. (t <= (-6.2d-34))) .and. (t <= 9d+37)) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8e+38) {
		tmp = x;
	} else if ((t <= -0.3) || (!(t <= -6.2e-34) && (t <= 9e+37))) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8e+38:
		tmp = x
	elif (t <= -0.3) or (not (t <= -6.2e-34) and (t <= 9e+37)):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8e+38)
		tmp = x;
	elseif ((t <= -0.3) || (!(t <= -6.2e-34) && (t <= 9e+37)))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8e+38)
		tmp = x;
	elseif ((t <= -0.3) || (~((t <= -6.2e-34)) && (t <= 9e+37)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8e+38], x, If[Or[LessEqual[t, -0.3], And[N[Not[LessEqual[t, -6.2e-34]], $MachinePrecision], LessEqual[t, 9e+37]]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -7.99999999999999982e38 or -0.299999999999999989 < t < -6.1999999999999996e-34 or 8.99999999999999923e37 < t

   1. Initial program 89.6%

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

   3. Taylor expanded in y around 0 70.5%

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

   if -7.99999999999999982e38 < t < -0.299999999999999989 or -6.1999999999999996e-34 < t < 8.99999999999999923e37

   1. Initial program 98.6%

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

   3. Taylor expanded in y around -inf 86.0%

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

   4. Taylor expanded in z around inf 57.0%

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

      1. associate-/l* 55.0%

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

   6. Simplified 55.0%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -0.3 \lor \neg \left(t \leq -6.2 \cdot 10^{-34}\right) \land t \leq 9 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;x \leq -120000000000 \lor \neg \left(x \leq 5.5 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.1e+140)
   (* x (/ y (- t)))
   (if (or (<= x -120000000000.0) (not (<= x 5.5e-12)))
     (/ (* x y) y)
     (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.1e+140) {
		tmp = x * (y / -t);
	} else if ((x <= -120000000000.0) || !(x <= 5.5e-12)) {
		tmp = (x * y) / y;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.1d+140)) then
        tmp = x * (y / -t)
    else if ((x <= (-120000000000.0d0)) .or. (.not. (x <= 5.5d-12))) then
        tmp = (x * y) / y
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.1e+140) {
		tmp = x * (y / -t);
	} else if ((x <= -120000000000.0) || !(x <= 5.5e-12)) {
		tmp = (x * y) / y;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.1e+140:
		tmp = x * (y / -t)
	elif (x <= -120000000000.0) or not (x <= 5.5e-12):
		tmp = (x * y) / y
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.1e+140)
		tmp = Float64(x * Float64(y / Float64(-t)));
	elseif ((x <= -120000000000.0) || !(x <= 5.5e-12))
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.1e+140)
		tmp = x * (y / -t);
	elseif ((x <= -120000000000.0) || ~((x <= 5.5e-12)))
		tmp = (x * y) / y;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.1e+140], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -120000000000.0], N[Not[LessEqual[x, 5.5e-12]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.1e140

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0 93.6%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{t} \]
   4. Step-by-step derivation

      1. mul-1-neg 93.6%

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

      2. distribute-lft-neg-out 93.6%

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

      3. *-commutative 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in y around inf 67.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{x}{t} + \frac{x}{y}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 67.1%

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

      2. +-commutative 67.1%

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

      3. unsub-neg 67.1%

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

   8. Simplified 67.1%

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

   9. Taylor expanded in y around inf 54.0%

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

       1. mul-1-neg 54.0%

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

       2. distribute-frac-neg2 54.0%

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

   11. Simplified 54.0%

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

   12. Taylor expanded in y around 0 62.4%

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

       1. associate-*r/ 62.4%

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

       2. associate-*r* 62.4%

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

       3. neg-mul-1 62.4%

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

       4. *-commutative 62.4%

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

   14. Simplified 62.4%

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

   if -3.1e140 < x < -1.2e11 or 5.5000000000000004e-12 < x

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 79.0%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{t} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.0%

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

      2. distribute-lft-neg-out 79.0%

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

      3. *-commutative 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in y around inf 60.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{x}{t} + \frac{x}{y}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 60.8%

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

      2. +-commutative 60.8%

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

      3. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   9. Taylor expanded in y around 0 35.7%

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

       1. associate-*r/ 57.2%

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

   11. Applied egg-rr 57.2%

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

   if -1.2e11 < x < 5.5000000000000004e-12

   1. Initial program 96.3%

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

   3. Taylor expanded in y around -inf 71.9%

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

   4. Taylor expanded in z around inf 59.2%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;x \leq -120000000000 \lor \neg \left(x \leq 5.5 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-94} \lor \neg \left(x \leq 2.25 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1e-94) (not (<= x 2.25e-85)))
   (* x (- 1.0 (/ y t)))
   (/ (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1e-94) || !(x <= 2.25e-85)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1d-94)) .or. (.not. (x <= 2.25d-85))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1e-94) || !(x <= 2.25e-85)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1e-94) or not (x <= 2.25e-85):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1e-94) || !(x <= 2.25e-85))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1e-94) || ~((x <= 2.25e-85)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1e-94], N[Not[LessEqual[x, 2.25e-85]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999996e-95 or 2.25000000000000002e-85 < x

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 80.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

   5. Simplified 80.5%

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

   if -9.9999999999999996e-95 < x < 2.25000000000000002e-85

   1. Initial program 95.6%

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

   3. Taylor expanded in y around -inf 72.8%

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

   4. Taylor expanded in z around inf 68.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-94} \lor \neg \left(x \leq 2.25 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -25000000000 \lor \neg \left(x \leq 2.3 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -25000000000.0) (not (<= x 2.3e-15)))
   (* x (- 1.0 (/ y t)))
   (* (/ y t) (- z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -25000000000.0) || !(x <= 2.3e-15)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-25000000000.0d0)) .or. (.not. (x <= 2.3d-15))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y / t) * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -25000000000.0) || !(x <= 2.3e-15)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -25000000000.0) or not (x <= 2.3e-15):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -25000000000.0) || !(x <= 2.3e-15))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -25000000000.0) || ~((x <= 2.3e-15)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -25000000000.0], N[Not[LessEqual[x, 2.3e-15]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5e10 or 2.2999999999999999e-15 < x

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf 89.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 89.0%

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

      2. unsub-neg 89.0%

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

   5. Simplified 89.0%

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

   if -2.5e10 < x < 2.2999999999999999e-15

   1. Initial program 96.2%

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

   3. Taylor expanded in y around -inf 71.6%

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

   4. Taylor expanded in z around 0 67.8%

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

      1. +-commutative 92.4%

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

      2. *-commutative 92.4%

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

      3. associate-*r/ 91.5%

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

      4. mul-1-neg 91.5%

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

      5. associate-/l* 85.4%

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

      6. distribute-lft-neg-in 85.4%

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

      7. distribute-rgt-in 95.4%

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

      8. sub-neg 95.4%

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

   6. Simplified 70.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -25000000000 \lor \neg \left(x \leq 2.3 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4300000000 \lor \neg \left(x \leq 1.3 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4300000000.0) (not (<= x 1.3e-14)))
   (* x (- 1.0 (/ y t)))
   (* y (/ (- z x) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4300000000.0) || !(x <= 1.3e-14)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4300000000.0d0)) .or. (.not. (x <= 1.3d-14))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = y * ((z - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4300000000.0) || !(x <= 1.3e-14)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4300000000.0) or not (x <= 1.3e-14):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = y * ((z - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4300000000.0) || !(x <= 1.3e-14))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(y * Float64(Float64(z - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4300000000.0) || ~((x <= 1.3e-14)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = y * ((z - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4300000000.0], N[Not[LessEqual[x, 1.3e-14]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3e9 or 1.29999999999999998e-14 < x

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf 89.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 89.0%

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

      2. unsub-neg 89.0%

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

   5. Simplified 89.0%

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

   if -4.3e9 < x < 1.29999999999999998e-14

   1. Initial program 96.2%

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

   3. Taylor expanded in y around -inf 71.6%

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

      1. associate-/l* 71.7%

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

      2. *-commutative 71.7%

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

   5. Applied egg-rr 71.7%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4300000000 \lor \neg \left(x \leq 1.3 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-48} \lor \neg \left(t \leq 4.8 \cdot 10^{-88}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.8e-48) (not (<= t 4.8e-88)))
   (+ x (* y (/ z t)))
   (* (/ y t) (- z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e-48) || !(t <= 4.8e-88)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.8d-48)) .or. (.not. (t <= 4.8d-88))) then
        tmp = x + (y * (z / t))
    else
        tmp = (y / t) * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e-48) || !(t <= 4.8e-88)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.8e-48) or not (t <= 4.8e-88):
		tmp = x + (y * (z / t))
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.8e-48) || !(t <= 4.8e-88))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.8e-48) || ~((t <= 4.8e-88)))
		tmp = x + (y * (z / t));
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.8e-48], N[Not[LessEqual[t, 4.8e-88]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.80000000000000002e-48 or 4.7999999999999999e-88 < t

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf 85.1%

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

      1. associate-/l* 33.9%

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

   5. Simplified 87.4%

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

   if -3.80000000000000002e-48 < t < 4.7999999999999999e-88

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 91.3%

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

   4. Taylor expanded in z around 0 77.9%

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

      1. +-commutative 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-*r/ 81.5%

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

      4. mul-1-neg 81.5%

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

      5. associate-/l* 73.2%

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

      6. distribute-lft-neg-in 73.2%

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

      7. distribute-rgt-in 96.1%

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

      8. sub-neg 96.1%

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

   6. Simplified 88.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-48} \lor \neg \left(t \leq 4.8 \cdot 10^{-88}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-45}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.5e-45)
   (+ x (* y (/ z t)))
   (if (<= t 2.4e-87) (* (/ y t) (- z x)) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e-45) {
		tmp = x + (y * (z / t));
	} else if (t <= 2.4e-87) {
		tmp = (y / t) * (z - x);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.5d-45)) then
        tmp = x + (y * (z / t))
    else if (t <= 2.4d-87) then
        tmp = (y / t) * (z - x)
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e-45) {
		tmp = x + (y * (z / t));
	} else if (t <= 2.4e-87) {
		tmp = (y / t) * (z - x);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.5e-45:
		tmp = x + (y * (z / t))
	elif t <= 2.4e-87:
		tmp = (y / t) * (z - x)
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.5e-45)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 2.4e-87)
		tmp = Float64(Float64(y / t) * Float64(z - x));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.5e-45)
		tmp = x + (y * (z / t));
	elseif (t <= 2.4e-87)
		tmp = (y / t) * (z - x);
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.5e-45], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-87], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5e-45

   1. Initial program 89.5%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. associate-/l* 30.3%

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

   5. Simplified 86.6%

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

   if -3.5e-45 < t < 2.4e-87

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 91.3%

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

   4. Taylor expanded in z around 0 77.9%

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

      1. +-commutative 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-*r/ 81.5%

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

      4. mul-1-neg 81.5%

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

      5. associate-/l* 73.2%

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

      6. distribute-lft-neg-in 73.2%

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

      7. distribute-rgt-in 96.1%

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

      8. sub-neg 96.1%

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

   6. Simplified 88.5%

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

   if 2.4e-87 < t

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 87.2%

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

      1. associate-/l* 38.0%

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

   5. Simplified 88.4%

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

      1. clear-num 88.4%

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

      2. un-div-inv 89.0%

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

   7. Applied egg-rr 89.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-45}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-34}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e-34)
   (+ x (* y (/ z t)))
   (if (<= t 7.5e-87) (/ (* y (- z x)) t) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-34) {
		tmp = x + (y * (z / t));
	} else if (t <= 7.5e-87) {
		tmp = (y * (z - x)) / t;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.5d-34)) then
        tmp = x + (y * (z / t))
    else if (t <= 7.5d-87) then
        tmp = (y * (z - x)) / t
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-34) {
		tmp = x + (y * (z / t));
	} else if (t <= 7.5e-87) {
		tmp = (y * (z - x)) / t;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e-34:
		tmp = x + (y * (z / t))
	elif t <= 7.5e-87:
		tmp = (y * (z - x)) / t
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e-34)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 7.5e-87)
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e-34)
		tmp = x + (y * (z / t));
	elseif (t <= 7.5e-87)
		tmp = (y * (z - x)) / t;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e-34], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-87], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5e-34

   1. Initial program 89.4%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. associate-/l* 29.4%

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

   5. Simplified 86.4%

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

   if -1.5e-34 < t < 7.5000000000000002e-87

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 91.4%

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

   if 7.5000000000000002e-87 < t

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 87.2%

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

      1. associate-/l* 38.0%

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

   5. Simplified 88.4%

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

      1. clear-num 88.4%

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

      2. un-div-inv 89.0%

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

   7. Applied egg-rr 89.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-34}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -660000000000 \lor \neg \left(x \leq 8 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -660000000000.0) (not (<= x 8e-5)))
   (/ (* x y) y)
   (* y (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -660000000000.0) || !(x <= 8e-5)) {
		tmp = (x * y) / y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-660000000000.0d0)) .or. (.not. (x <= 8d-5))) then
        tmp = (x * y) / y
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -660000000000.0) || !(x <= 8e-5)) {
		tmp = (x * y) / y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -660000000000.0) or not (x <= 8e-5):
		tmp = (x * y) / y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -660000000000.0) || !(x <= 8e-5))
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -660000000000.0) || ~((x <= 8e-5)))
		tmp = (x * y) / y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -660000000000.0], N[Not[LessEqual[x, 8e-5]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6e11 or 8.00000000000000065e-5 < x

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 82.7%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{t} \]
   4. Step-by-step derivation

      1. mul-1-neg 82.7%

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

      2. distribute-lft-neg-out 82.7%

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

      3. *-commutative 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around inf 62.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{x}{t} + \frac{x}{y}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 62.4%

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

      2. +-commutative 62.4%

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

      3. unsub-neg 62.4%

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

   8. Simplified 62.4%

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

   9. Taylor expanded in y around 0 31.2%

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

       1. associate-*r/ 54.6%

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

   11. Applied egg-rr 54.6%

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

   if -6.6e11 < x < 8.00000000000000065e-5

   1. Initial program 96.3%

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

   3. Taylor expanded in y around -inf 71.9%

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

   4. Taylor expanded in z around inf 59.2%

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

      1. associate-/l* 59.2%

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

   6. Simplified 59.2%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -660000000000 \lor \neg \left(x \leq 8 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -135000000000 \lor \neg \left(x \leq 1.55 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -135000000000.0) (not (<= x 1.55e-8)))
   (/ (* x y) y)
   (/ (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -135000000000.0) || !(x <= 1.55e-8)) {
		tmp = (x * y) / y;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-135000000000.0d0)) .or. (.not. (x <= 1.55d-8))) then
        tmp = (x * y) / y
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -135000000000.0) || !(x <= 1.55e-8)) {
		tmp = (x * y) / y;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -135000000000.0) or not (x <= 1.55e-8):
		tmp = (x * y) / y
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -135000000000.0) || !(x <= 1.55e-8))
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -135000000000.0) || ~((x <= 1.55e-8)))
		tmp = (x * y) / y;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -135000000000.0], N[Not[LessEqual[x, 1.55e-8]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e11 or 1.55e-8 < x

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 82.7%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{t} \]
   4. Step-by-step derivation

      1. mul-1-neg 82.7%

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

      2. distribute-lft-neg-out 82.7%

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

      3. *-commutative 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around inf 62.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{x}{t} + \frac{x}{y}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 62.4%

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

      2. +-commutative 62.4%

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

      3. unsub-neg 62.4%

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

   8. Simplified 62.4%

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

   9. Taylor expanded in y around 0 31.2%

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

       1. associate-*r/ 54.6%

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

   11. Applied egg-rr 54.6%

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

   if -1.35e11 < x < 1.55e-8

   1. Initial program 96.3%

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

   3. Taylor expanded in y around -inf 71.9%

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

   4. Taylor expanded in z around inf 59.2%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -135000000000 \lor \neg \left(x \leq 1.55 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

3. Taylor expanded in y around 0 38.9%

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

4. Final simplification 38.9%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 91.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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