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

Percentage Accurate: 92.7% → 97.9%

Time: 7.7s

Alternatives: 13

Speedup: 1.0×

• 25.0% 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: 92.7% 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: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - x) / (t / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(z - x), $MachinePrecision] / N[(t / y), $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/ 87.1%

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

   4. mul-1-neg 87.1%

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

   5. associate-/l* 89.2%

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

   6. distribute-lft-neg-in 89.2%

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

   7. distribute-rgt-in 98.2%

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

   8. sub-neg 98.2%

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

5. Simplified 98.2%

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

   1. *-commutative 98.2%

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

   2. clear-num 98.1%

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

   3. un-div-inv 98.5%

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

7. Applied egg-rr 98.5%

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

8. Final simplification 98.5%

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

Alternative 2: 54.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ t_2 := y \cdot \frac{x}{-t}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+207}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+243} \lor \neg \left(y \leq 6.2 \cdot 10^{+287}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))) (t_2 (* y (/ x (- t)))))
   (if (<= y -5.6e+207)
     t_2
     (if (<= y -4.8e-63)
       t_1
       (if (<= y 7e-87)
         x
         (if (or (<= y 4.4e+243) (not (<= y 6.2e+287))) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double t_2 = y * (x / -t);
	double tmp;
	if (y <= -5.6e+207) {
		tmp = t_2;
	} else if (y <= -4.8e-63) {
		tmp = t_1;
	} else if (y <= 7e-87) {
		tmp = x;
	} else if ((y <= 4.4e+243) || !(y <= 6.2e+287)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = z * (y / t)
    t_2 = y * (x / -t)
    if (y <= (-5.6d+207)) then
        tmp = t_2
    else if (y <= (-4.8d-63)) then
        tmp = t_1
    else if (y <= 7d-87) then
        tmp = x
    else if ((y <= 4.4d+243) .or. (.not. (y <= 6.2d+287))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double t_2 = y * (x / -t);
	double tmp;
	if (y <= -5.6e+207) {
		tmp = t_2;
	} else if (y <= -4.8e-63) {
		tmp = t_1;
	} else if (y <= 7e-87) {
		tmp = x;
	} else if ((y <= 4.4e+243) || !(y <= 6.2e+287)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	t_2 = y * (x / -t)
	tmp = 0
	if y <= -5.6e+207:
		tmp = t_2
	elif y <= -4.8e-63:
		tmp = t_1
	elif y <= 7e-87:
		tmp = x
	elif (y <= 4.4e+243) or not (y <= 6.2e+287):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	t_2 = Float64(y * Float64(x / Float64(-t)))
	tmp = 0.0
	if (y <= -5.6e+207)
		tmp = t_2;
	elseif (y <= -4.8e-63)
		tmp = t_1;
	elseif (y <= 7e-87)
		tmp = x;
	elseif ((y <= 4.4e+243) || !(y <= 6.2e+287))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	t_2 = y * (x / -t);
	tmp = 0.0;
	if (y <= -5.6e+207)
		tmp = t_2;
	elseif (y <= -4.8e-63)
		tmp = t_1;
	elseif (y <= 7e-87)
		tmp = x;
	elseif ((y <= 4.4e+243) || ~((y <= 6.2e+287)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+207], t$95$2, If[LessEqual[y, -4.8e-63], t$95$1, If[LessEqual[y, 7e-87], x, If[Or[LessEqual[y, 4.4e+243], N[Not[LessEqual[y, 6.2e+287]], $MachinePrecision]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000022e207 or 4.40000000000000018e243 < y < 6.2e287

   1. Initial program 79.6%

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

   3. Taylor expanded in y around -inf 79.6%

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

      1. associate-/l* 97.3%

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

      2. *-commutative 97.3%

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

   5. Applied egg-rr 97.3%

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

   6. Taylor expanded in z around 0 76.0%

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

      1. neg-mul-1 76.0%

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

      2. distribute-neg-frac 76.0%

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

   8. Simplified 76.0%

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

   if -5.60000000000000022e207 < y < -4.8000000000000001e-63 or 7.00000000000000023e-87 < y < 4.40000000000000018e243 or 6.2e287 < y

   1. Initial program 95.1%

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

   3. Taylor expanded in y around -inf 75.2%

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

   4. Taylor expanded in z around inf 52.4%

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

      1. associate-/l* 53.2%

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

   6. Simplified 53.2%

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

      1. clear-num 53.1%

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

      2. un-div-inv 53.5%

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

   8. Applied egg-rr 53.5%

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

      1. associate-/r/ 58.5%

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

   10. Applied egg-rr 58.5%

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

   if -4.8000000000000001e-63 < y < 7.00000000000000023e-87

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 69.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+207}:\\ \;\;\;\;y \cdot \frac{x}{-t}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-63}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+243} \lor \neg \left(y \leq 6.2 \cdot 10^{+287}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-222}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-211}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 10000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))))
   (if (<= z -8.4e+105)
     t_1
     (if (<= z -4.6e-222)
       x
       (if (<= z 1.75e-211)
         (* (/ y t) (- x))
         (if (<= z 10000000000.0) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (z <= -8.4e+105) {
		tmp = t_1;
	} else if (z <= -4.6e-222) {
		tmp = x;
	} else if (z <= 1.75e-211) {
		tmp = (y / t) * -x;
	} else if (z <= 10000000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = z * (y / t)
    if (z <= (-8.4d+105)) then
        tmp = t_1
    else if (z <= (-4.6d-222)) then
        tmp = x
    else if (z <= 1.75d-211) then
        tmp = (y / t) * -x
    else if (z <= 10000000000.0d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (z <= -8.4e+105) {
		tmp = t_1;
	} else if (z <= -4.6e-222) {
		tmp = x;
	} else if (z <= 1.75e-211) {
		tmp = (y / t) * -x;
	} else if (z <= 10000000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	tmp = 0
	if z <= -8.4e+105:
		tmp = t_1
	elif z <= -4.6e-222:
		tmp = x
	elif z <= 1.75e-211:
		tmp = (y / t) * -x
	elif z <= 10000000000.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (z <= -8.4e+105)
		tmp = t_1;
	elseif (z <= -4.6e-222)
		tmp = x;
	elseif (z <= 1.75e-211)
		tmp = Float64(Float64(y / t) * Float64(-x));
	elseif (z <= 10000000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	tmp = 0.0;
	if (z <= -8.4e+105)
		tmp = t_1;
	elseif (z <= -4.6e-222)
		tmp = x;
	elseif (z <= 1.75e-211)
		tmp = (y / t) * -x;
	elseif (z <= 10000000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.4e+105], t$95$1, If[LessEqual[z, -4.6e-222], x, If[LessEqual[z, 1.75e-211], N[(N[(y / t), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, 10000000000.0], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4000000000000004e105 or 1e10 < z

   1. Initial program 92.9%

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

   3. Taylor expanded in y around -inf 73.2%

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

   4. Taylor expanded in z around inf 68.4%

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

      1. associate-/l* 66.8%

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

   6. Simplified 66.8%

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

      1. clear-num 66.7%

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

      2. un-div-inv 67.2%

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

   8. Applied egg-rr 67.2%

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

      1. associate-/r/ 71.1%

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

   10. Applied egg-rr 71.1%

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

   if -8.4000000000000004e105 < z < -4.6000000000000003e-222 or 1.75e-211 < z < 1e10

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 53.3%

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

   if -4.6000000000000003e-222 < z < 1.75e-211

   1. Initial program 93.7%

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

   3. Taylor expanded in y around -inf 64.2%

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

   4. Taylor expanded in z around 0 57.8%

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

      1. mul-1-neg 57.8%

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

      2. associate-/l* 63.8%

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

      3. distribute-rgt-neg-in 63.8%

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

      4. mul-1-neg 63.8%

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

      5. associate-*r/ 63.8%

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

      6. mul-1-neg 63.8%

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

   6. Simplified 63.8%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+105}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-222}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-211}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 10000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+111} \lor \neg \left(z \leq 5.8 \cdot 10^{+32}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e+111) (not (<= z 5.8e+32)))
   (* z (/ y t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+111) || !(z <= 5.8e+32)) {
		tmp = z * (y / t);
	} else {
		tmp = x * (1.0 - (y / 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 ((z <= (-2.8d+111)) .or. (.not. (z <= 5.8d+32))) then
        tmp = z * (y / t)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+111) || !(z <= 5.8e+32)) {
		tmp = z * (y / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+111) or not (z <= 5.8e+32):
		tmp = z * (y / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e+111) || !(z <= 5.8e+32))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.8e+111) || ~((z <= 5.8e+32)))
		tmp = z * (y / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e+111], N[Not[LessEqual[z, 5.8e+32]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e111 or 5.80000000000000006e32 < z

   1. Initial program 92.6%

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

   3. Taylor expanded in y around -inf 74.0%

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

   4. Taylor expanded in z around inf 69.0%

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

      1. associate-/l* 67.3%

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

   6. Simplified 67.3%

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

      1. clear-num 67.3%

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

      2. un-div-inv 67.8%

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

   8. Applied egg-rr 67.8%

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

      1. associate-/r/ 71.8%

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

   10. Applied egg-rr 71.8%

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

   if -2.7999999999999999e111 < z < 5.80000000000000006e32

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+111} \lor \neg \left(z \leq 5.8 \cdot 10^{+32}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+85} \lor \neg \left(z \leq 2.25 \cdot 10^{+33}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.8e+85) (not (<= z 2.25e+33)))
   (* (- z x) (/ y t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e+85) || !(z <= 2.25e+33)) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x * (1.0 - (y / 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 ((z <= (-7.8d+85)) .or. (.not. (z <= 2.25d+33))) then
        tmp = (z - x) * (y / t)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e+85) || !(z <= 2.25e+33)) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.8e+85) or not (z <= 2.25e+33):
		tmp = (z - x) * (y / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e+85) || !(z <= 2.25e+33))
		tmp = Float64(Float64(z - x) * Float64(y / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.8e+85) || ~((z <= 2.25e+33)))
		tmp = (z - x) * (y / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.8e+85], N[Not[LessEqual[z, 2.25e+33]], $MachinePrecision]], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.80000000000000067e85 or 2.25e33 < z

   1. Initial program 92.0%

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

   3. Taylor expanded in y around -inf 73.0%

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

   4. Taylor expanded in z around 0 63.5%

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

      1. +-commutative 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r/ 85.8%

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

      4. mul-1-neg 85.8%

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

      5. associate-/l* 86.4%

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

      6. distribute-lft-neg-in 86.4%

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

      7. distribute-rgt-in 98.5%

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

      8. sub-neg 98.5%

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

   6. Simplified 76.5%

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

   if -7.80000000000000067e85 < z < 2.25e33

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   5. Simplified 86.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+85} \lor \neg \left(z \leq 2.25 \cdot 10^{+33}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+105} \lor \neg \left(z \leq 2.7 \cdot 10^{-108}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.8e+105) (not (<= z 2.7e-108)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e+105) || !(z <= 2.7e-108)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / 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 ((z <= (-7.8d+105)) .or. (.not. (z <= 2.7d-108))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e+105) || !(z <= 2.7e-108)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.8e+105) or not (z <= 2.7e-108):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e+105) || !(z <= 2.7e-108))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.8e+105) || ~((z <= 2.7e-108)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.8e+105], N[Not[LessEqual[z, 2.7e-108]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.79999999999999957e105 or 2.70000000000000005e-108 < z

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf 89.7%

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

      1. associate-/l* 60.2%

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

   5. Simplified 89.2%

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

   if -7.79999999999999957e105 < z < 2.70000000000000005e-108

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

   5. Simplified 87.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+105} \lor \neg \left(z \leq 2.7 \cdot 10^{-108}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+105} \lor \neg \left(z \leq 2 \cdot 10^{-104}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.8e+105) (not (<= z 2e-104)))
   (+ x (/ y (/ t z)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e+105) || !(z <= 2e-104)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (y / 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 ((z <= (-7.8d+105)) .or. (.not. (z <= 2d-104))) then
        tmp = x + (y / (t / z))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e+105) || !(z <= 2e-104)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.8e+105) or not (z <= 2e-104):
		tmp = x + (y / (t / z))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e+105) || !(z <= 2e-104))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.8e+105) || ~((z <= 2e-104)))
		tmp = x + (y / (t / z));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.8e+105], N[Not[LessEqual[z, 2e-104]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.79999999999999957e105 or 1.99999999999999985e-104 < z

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf 89.7%

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

      1. associate-/l* 60.2%

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

   5. Simplified 89.2%

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

      1. clear-num 60.2%

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

      2. un-div-inv 60.6%

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

   7. Applied egg-rr 89.6%

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

   if -7.79999999999999957e105 < z < 1.99999999999999985e-104

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

   5. Simplified 87.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+105} \lor \neg \left(z \leq 2 \cdot 10^{-104}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.8e+105)
   (+ x (/ y (/ t z)))
   (if (<= z 2.3e-104) (* x (- 1.0 (/ y t))) (+ x (/ (* z y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e+105) {
		tmp = x + (y / (t / z));
	} else if (z <= 2.3e-104) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((z * y) / 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 (z <= (-7.8d+105)) then
        tmp = x + (y / (t / z))
    else if (z <= 2.3d-104) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + ((z * y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e+105) {
		tmp = x + (y / (t / z));
	} else if (z <= 2.3e-104) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.8e+105:
		tmp = x + (y / (t / z))
	elif z <= 2.3e-104:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + ((z * y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.8e+105)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 2.3e-104)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.8e+105)
		tmp = x + (y / (t / z));
	elseif (z <= 2.3e-104)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + ((z * y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.8e+105], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-104], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.79999999999999957e105

   1. Initial program 90.4%

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

   3. Taylor expanded in z around inf 92.4%

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

      1. associate-/l* 67.8%

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

   5. Simplified 93.1%

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

      1. clear-num 67.7%

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

      2. un-div-inv 68.9%

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

   7. Applied egg-rr 94.3%

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

   if -7.79999999999999957e105 < z < 2.2999999999999999e-104

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

   5. Simplified 87.7%

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

   if 2.2999999999999999e-104 < z

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 88.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+105}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-104}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8e+105)
   (+ x (/ y (/ t z)))
   (if (<= z 2.2e-104) (- x (* x (/ y t))) (+ x (/ (* z y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e+105) {
		tmp = x + (y / (t / z));
	} else if (z <= 2.2e-104) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + ((z * y) / 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 (z <= (-8d+105)) then
        tmp = x + (y / (t / z))
    else if (z <= 2.2d-104) then
        tmp = x - (x * (y / t))
    else
        tmp = x + ((z * y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e+105) {
		tmp = x + (y / (t / z));
	} else if (z <= 2.2e-104) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8e+105:
		tmp = x + (y / (t / z))
	elif z <= 2.2e-104:
		tmp = x - (x * (y / t))
	else:
		tmp = x + ((z * y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8e+105)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 2.2e-104)
		tmp = Float64(x - Float64(x * Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8e+105)
		tmp = x + (y / (t / z));
	elseif (z <= 2.2e-104)
		tmp = x - (x * (y / t));
	else
		tmp = x + ((z * y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8e+105], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-104], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999995e105

   1. Initial program 90.4%

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

   3. Taylor expanded in z around inf 92.4%

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

      1. associate-/l* 67.8%

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

   5. Simplified 93.1%

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

      1. clear-num 67.7%

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

      2. un-div-inv 68.9%

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

   7. Applied egg-rr 94.3%

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

   if -7.9999999999999995e105 < z < 2.20000000000000012e-104

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0 84.1%

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

      1. mul-1-neg 43.4%

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

      2. associate-/l* 47.1%

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

      3. distribute-rgt-neg-in 47.1%

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

      4. mul-1-neg 47.1%

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

      5. associate-*r/ 47.1%

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

      6. mul-1-neg 47.1%

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

   5. Simplified 87.8%

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

   if 2.20000000000000012e-104 < z

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 88.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+105}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-104}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-62} \lor \neg \left(y \leq 3.05 \cdot 10^{-86}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.35e-62) (not (<= y 3.05e-86))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.35e-62) || !(y <= 3.05e-86)) {
		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 ((y <= (-1.35d-62)) .or. (.not. (y <= 3.05d-86))) 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 ((y <= -1.35e-62) || !(y <= 3.05e-86)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.35e-62) or not (y <= 3.05e-86):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.35e-62) || !(y <= 3.05e-86))
		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 ((y <= -1.35e-62) || ~((y <= 3.05e-86)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.35e-62], N[Not[LessEqual[y, 3.05e-86]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.3500000000000001e-62 or 3.05000000000000016e-86 < y

   1. Initial program 92.2%

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

   3. Taylor expanded in y around -inf 76.0%

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

   4. Taylor expanded in z around inf 47.4%

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

      1. associate-/l* 48.6%

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

   6. Simplified 48.6%

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

   if -1.3500000000000001e-62 < y < 3.05000000000000016e-86

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 69.9%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-62} \lor \neg \left(y \leq 3.05 \cdot 10^{-86}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-63} \lor \neg \left(y \leq 2.85 \cdot 10^{-89}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6e-63) (not (<= y 2.85e-89))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e-63) || !(y <= 2.85e-89)) {
		tmp = z * (y / 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 ((y <= (-6d-63)) .or. (.not. (y <= 2.85d-89))) then
        tmp = z * (y / 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 ((y <= -6e-63) || !(y <= 2.85e-89)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6e-63) or not (y <= 2.85e-89):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6e-63) || !(y <= 2.85e-89))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6e-63) || ~((y <= 2.85e-89)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6e-63], N[Not[LessEqual[y, 2.85e-89]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999959e-63 or 2.8500000000000001e-89 < y

   1. Initial program 92.2%

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

   3. Taylor expanded in y around -inf 76.0%

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

   4. Taylor expanded in z around inf 47.4%

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

      1. associate-/l* 48.6%

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

   6. Simplified 48.6%

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

      1. clear-num 48.5%

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

      2. un-div-inv 48.8%

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

   8. Applied egg-rr 48.8%

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

      1. associate-/r/ 52.6%

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

   10. Applied egg-rr 52.6%

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

   if -5.99999999999999959e-63 < y < 2.8500000000000001e-89

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 69.9%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-63} \lor \neg \left(y \leq 2.85 \cdot 10^{-89}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(z - x), $MachinePrecision] * N[(y / t), $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/ 87.1%

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

   4. mul-1-neg 87.1%

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

   5. associate-/l* 89.2%

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

   6. distribute-lft-neg-in 89.2%

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

   7. distribute-rgt-in 98.2%

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

   8. sub-neg 98.2%

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

5. Simplified 98.2%

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

6. Final simplification 98.2%

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

Alternative 13: 39.1% 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 36.7%

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

4. Final simplification 36.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 91.3% 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 2024080 
(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)))