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

Percentage Accurate: 92.7% → 97.7%

Time: 8.1s

Alternatives: 11

Speedup: 1.0×

• 25.4% 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: 97.7% 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 95.4%

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

3. Taylor expanded in z around 0 91.9%

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

   1. +-commutative 91.9%

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

   2. *-commutative 91.9%

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

   3. associate-*r/ 90.0%

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

   4. mul-1-neg 90.0%

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

   5. associate-/l* 89.5%

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

   6. distribute-lft-neg-in 89.5%

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

   7. distribute-rgt-in 97.3%

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

   8. sub-neg 97.3%

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

5. Simplified 97.3%

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

   1. *-commutative 97.3%

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

   2. clear-num 97.3%

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

   3. un-div-inv 97.4%

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

7. Applied egg-rr 97.4%

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

Alternative 2: 75.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-155}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))))
   (if (<= x -3.8e-31)
     t_1
     (if (<= x -1.65e-155)
       (* (- z x) (/ y t))
       (if (<= x -1.32e-186) x (if (<= x 9.2e-23) (* y (/ (- z x) t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -3.8e-31) {
		tmp = t_1;
	} else if (x <= -1.65e-155) {
		tmp = (z - x) * (y / t);
	} else if (x <= -1.32e-186) {
		tmp = x;
	} else if (x <= 9.2e-23) {
		tmp = y * ((z - x) / t);
	} 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 = x * (1.0d0 - (y / t))
    if (x <= (-3.8d-31)) then
        tmp = t_1
    else if (x <= (-1.65d-155)) then
        tmp = (z - x) * (y / t)
    else if (x <= (-1.32d-186)) then
        tmp = x
    else if (x <= 9.2d-23) then
        tmp = y * ((z - x) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -3.8e-31) {
		tmp = t_1;
	} else if (x <= -1.65e-155) {
		tmp = (z - x) * (y / t);
	} else if (x <= -1.32e-186) {
		tmp = x;
	} else if (x <= 9.2e-23) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -3.8e-31:
		tmp = t_1
	elif x <= -1.65e-155:
		tmp = (z - x) * (y / t)
	elif x <= -1.32e-186:
		tmp = x
	elif x <= 9.2e-23:
		tmp = y * ((z - x) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -3.8e-31)
		tmp = t_1;
	elseif (x <= -1.65e-155)
		tmp = Float64(Float64(z - x) * Float64(y / t));
	elseif (x <= -1.32e-186)
		tmp = x;
	elseif (x <= 9.2e-23)
		tmp = Float64(y * Float64(Float64(z - x) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (x <= -3.8e-31)
		tmp = t_1;
	elseif (x <= -1.65e-155)
		tmp = (z - x) * (y / t);
	elseif (x <= -1.32e-186)
		tmp = x;
	elseif (x <= 9.2e-23)
		tmp = y * ((z - x) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e-31], t$95$1, If[LessEqual[x, -1.65e-155], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.32e-186], x, If[LessEqual[x, 9.2e-23], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.8e-31 or 9.2000000000000004e-23 < x

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

   5. Simplified 85.2%

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

   if -3.8e-31 < x < -1.64999999999999993e-155

   1. Initial program 95.4%

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

   3. Taylor expanded in y around -inf 70.8%

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

   4. Taylor expanded in z around 0 70.8%

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

      1. +-commutative 95.4%

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

      2. *-commutative 95.4%

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

      3. associate-*r/ 95.4%

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

      4. mul-1-neg 95.4%

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

      5. associate-/l* 91.3%

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

      6. distribute-lft-neg-in 91.3%

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

      7. distribute-rgt-in 95.9%

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

      8. sub-neg 95.9%

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

   6. Simplified 71.3%

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

   if -1.64999999999999993e-155 < x < -1.32e-186

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.6%

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

   if -1.32e-186 < x < 9.2000000000000004e-23

   1. Initial program 95.7%

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

   3. Taylor expanded in y around -inf 80.1%

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

      1. associate-/l* 79.0%

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

      2. *-commutative 79.0%

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

   5. Applied egg-rr 79.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-155}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - x\right) \cdot \frac{y}{t}\\ t_2 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z x) (/ y t))) (t_2 (* x (- 1.0 (/ y t)))))
   (if (<= x -3.4e-30)
     t_2
     (if (<= x -1.65e-155)
       t_1
       (if (<= x -4e-189) x (if (<= x 9.2e-23) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z - x) * (y / t);
	double t_2 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -3.4e-30) {
		tmp = t_2;
	} else if (x <= -1.65e-155) {
		tmp = t_1;
	} else if (x <= -4e-189) {
		tmp = x;
	} else if (x <= 9.2e-23) {
		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 - x) * (y / t)
    t_2 = x * (1.0d0 - (y / t))
    if (x <= (-3.4d-30)) then
        tmp = t_2
    else if (x <= (-1.65d-155)) then
        tmp = t_1
    else if (x <= (-4d-189)) then
        tmp = x
    else if (x <= 9.2d-23) 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 - x) * (y / t);
	double t_2 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -3.4e-30) {
		tmp = t_2;
	} else if (x <= -1.65e-155) {
		tmp = t_1;
	} else if (x <= -4e-189) {
		tmp = x;
	} else if (x <= 9.2e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z - x) * (y / t)
	t_2 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -3.4e-30:
		tmp = t_2
	elif x <= -1.65e-155:
		tmp = t_1
	elif x <= -4e-189:
		tmp = x
	elif x <= 9.2e-23:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z - x) * Float64(y / t))
	t_2 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -3.4e-30)
		tmp = t_2;
	elseif (x <= -1.65e-155)
		tmp = t_1;
	elseif (x <= -4e-189)
		tmp = x;
	elseif (x <= 9.2e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z - x) * (y / t);
	t_2 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (x <= -3.4e-30)
		tmp = t_2;
	elseif (x <= -1.65e-155)
		tmp = t_1;
	elseif (x <= -4e-189)
		tmp = x;
	elseif (x <= 9.2e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e-30], t$95$2, If[LessEqual[x, -1.65e-155], t$95$1, If[LessEqual[x, -4e-189], x, If[LessEqual[x, 9.2e-23], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4000000000000003e-30 or 9.2000000000000004e-23 < x

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

   5. Simplified 85.2%

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

   if -3.4000000000000003e-30 < x < -1.64999999999999993e-155 or -4.00000000000000027e-189 < x < 9.2000000000000004e-23

   1. Initial program 95.7%

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

   3. Taylor expanded in y around -inf 78.3%

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

   4. Taylor expanded in z around 0 77.4%

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

      1. +-commutative 94.8%

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

      2. *-commutative 94.8%

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

      3. associate-*r/ 93.1%

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

      4. mul-1-neg 93.1%

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

      5. associate-/l* 87.1%

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

      6. distribute-lft-neg-in 87.1%

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

      7. distribute-rgt-in 94.2%

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

      8. sub-neg 94.2%

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

   6. Simplified 77.0%

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

   if -1.64999999999999993e-155 < x < -4.00000000000000027e-189

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.6%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-155}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-23}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{t}\\ t_2 := z \cdot \frac{y}{t}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x t))) (t_2 (* z (/ y t))))
   (if (<= x -2.6e-28)
     t_1
     (if (<= x -1.12e-151)
       t_2
       (if (<= x -1.32e-186) x (if (<= x 1.2e-21) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / t);
	double t_2 = z * (y / t);
	double tmp;
	if (x <= -2.6e-28) {
		tmp = t_1;
	} else if (x <= -1.12e-151) {
		tmp = t_2;
	} else if (x <= -1.32e-186) {
		tmp = x;
	} else if (x <= 1.2e-21) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t * (x / t)
    t_2 = z * (y / t)
    if (x <= (-2.6d-28)) then
        tmp = t_1
    else if (x <= (-1.12d-151)) then
        tmp = t_2
    else if (x <= (-1.32d-186)) then
        tmp = x
    else if (x <= 1.2d-21) then
        tmp = t_2
    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 = t * (x / t);
	double t_2 = z * (y / t);
	double tmp;
	if (x <= -2.6e-28) {
		tmp = t_1;
	} else if (x <= -1.12e-151) {
		tmp = t_2;
	} else if (x <= -1.32e-186) {
		tmp = x;
	} else if (x <= 1.2e-21) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / t)
	t_2 = z * (y / t)
	tmp = 0
	if x <= -2.6e-28:
		tmp = t_1
	elif x <= -1.12e-151:
		tmp = t_2
	elif x <= -1.32e-186:
		tmp = x
	elif x <= 1.2e-21:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / t))
	t_2 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (x <= -2.6e-28)
		tmp = t_1;
	elseif (x <= -1.12e-151)
		tmp = t_2;
	elseif (x <= -1.32e-186)
		tmp = x;
	elseif (x <= 1.2e-21)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / t);
	t_2 = z * (y / t);
	tmp = 0.0;
	if (x <= -2.6e-28)
		tmp = t_1;
	elseif (x <= -1.12e-151)
		tmp = t_2;
	elseif (x <= -1.32e-186)
		tmp = x;
	elseif (x <= 1.2e-21)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e-28], t$95$1, If[LessEqual[x, -1.12e-151], t$95$2, If[LessEqual[x, -1.32e-186], x, If[LessEqual[x, 1.2e-21], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6e-28 or 1.2e-21 < x

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0 80.1%

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

   4. Taylor expanded in t around inf 35.4%

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

      1. *-commutative 35.4%

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

   6. Simplified 35.4%

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

      1. *-commutative 35.4%

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

      2. associate-/l* 60.0%

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

   8. Applied egg-rr 60.0%

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

   if -2.6e-28 < x < -1.11999999999999994e-151 or -1.32e-186 < x < 1.2e-21

   1. Initial program 95.7%

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

   3. Taylor expanded in y around -inf 78.3%

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

   4. Taylor expanded in z around inf 64.6%

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

      1. associate-/l* 79.7%

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

   6. Simplified 62.9%

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

      1. clear-num 62.0%

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

      2. un-div-inv 62.5%

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

   8. Applied egg-rr 62.5%

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

      1. associate-/r/ 66.4%

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

   10. Applied egg-rr 66.4%

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

   if -1.11999999999999994e-151 < x < -1.32e-186

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.6%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-151}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{t}\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-186}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x t))) (t_2 (* y (/ z t))))
   (if (<= x -4.4e-31)
     t_1
     (if (<= x -1.35e-153)
       t_2
       (if (<= x -1.32e-186) x (if (<= x 2.5e-22) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / t);
	double t_2 = y * (z / t);
	double tmp;
	if (x <= -4.4e-31) {
		tmp = t_1;
	} else if (x <= -1.35e-153) {
		tmp = t_2;
	} else if (x <= -1.32e-186) {
		tmp = x;
	} else if (x <= 2.5e-22) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t * (x / t)
    t_2 = y * (z / t)
    if (x <= (-4.4d-31)) then
        tmp = t_1
    else if (x <= (-1.35d-153)) then
        tmp = t_2
    else if (x <= (-1.32d-186)) then
        tmp = x
    else if (x <= 2.5d-22) then
        tmp = t_2
    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 = t * (x / t);
	double t_2 = y * (z / t);
	double tmp;
	if (x <= -4.4e-31) {
		tmp = t_1;
	} else if (x <= -1.35e-153) {
		tmp = t_2;
	} else if (x <= -1.32e-186) {
		tmp = x;
	} else if (x <= 2.5e-22) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / t)
	t_2 = y * (z / t)
	tmp = 0
	if x <= -4.4e-31:
		tmp = t_1
	elif x <= -1.35e-153:
		tmp = t_2
	elif x <= -1.32e-186:
		tmp = x
	elif x <= 2.5e-22:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / t))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (x <= -4.4e-31)
		tmp = t_1;
	elseif (x <= -1.35e-153)
		tmp = t_2;
	elseif (x <= -1.32e-186)
		tmp = x;
	elseif (x <= 2.5e-22)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / t);
	t_2 = y * (z / t);
	tmp = 0.0;
	if (x <= -4.4e-31)
		tmp = t_1;
	elseif (x <= -1.35e-153)
		tmp = t_2;
	elseif (x <= -1.32e-186)
		tmp = x;
	elseif (x <= 2.5e-22)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.4e-31], t$95$1, If[LessEqual[x, -1.35e-153], t$95$2, If[LessEqual[x, -1.32e-186], x, If[LessEqual[x, 2.5e-22], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.40000000000000019e-31 or 2.49999999999999977e-22 < x

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0 80.1%

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

   4. Taylor expanded in t around inf 35.4%

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

      1. *-commutative 35.4%

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

   6. Simplified 35.4%

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

      1. *-commutative 35.4%

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

      2. associate-/l* 60.0%

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

   8. Applied egg-rr 60.0%

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

   if -4.40000000000000019e-31 < x < -1.35000000000000005e-153 or -1.32e-186 < x < 2.49999999999999977e-22

   1. Initial program 95.7%

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

   3. Taylor expanded in y around -inf 78.3%

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

   4. Taylor expanded in z around inf 64.6%

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

      1. associate-/l* 79.7%

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

   6. Simplified 62.9%

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

   if -1.35000000000000005e-153 < x < -1.32e-186

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.6%

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

Alternative 6: 83.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-66} \lor \neg \left(z \leq 3.3 \cdot 10^{-128}\right):\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-66) (not (<= z 3.3e-128)))
   (+ x (/ (* z y) t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-66) || !(z <= 3.3e-128)) {
		tmp = x + ((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 <= (-7.2d-66)) .or. (.not. (z <= 3.3d-128))) then
        tmp = x + ((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 <= -7.2e-66) || !(z <= 3.3e-128)) {
		tmp = x + ((z * y) / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e-66) or not (z <= 3.3e-128):
		tmp = x + ((z * y) / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e-66) || !(z <= 3.3e-128))
		tmp = Float64(x + Float64(Float64(z * 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 <= -7.2e-66) || ~((z <= 3.3e-128)))
		tmp = x + ((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, -7.2e-66], N[Not[LessEqual[z, 3.3e-128]], $MachinePrecision]], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.20000000000000025e-66 or 3.3e-128 < z

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 88.5%

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

      1. +-commutative 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*r/ 89.7%

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

      4. mul-1-neg 89.7%

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

      5. associate-/l* 87.6%

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

      6. distribute-lft-neg-in 87.6%

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

      7. distribute-rgt-in 98.1%

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

      8. sub-neg 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in z around inf 89.4%

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

   if -7.20000000000000025e-66 < z < 3.3e-128

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-66} \lor \neg \left(z \leq 3.3 \cdot 10^{-128}\right):\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-67} \lor \neg \left(z \leq 6.6 \cdot 10^{-131}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-67) (not (<= z 6.6e-131)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-67) || !(z <= 6.6e-131)) {
		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 <= (-7.2d-67)) .or. (.not. (z <= 6.6d-131))) 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 <= -7.2e-67) || !(z <= 6.6e-131)) {
		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 <= -7.2e-67) or not (z <= 6.6e-131):
		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 <= -7.2e-67) || !(z <= 6.6e-131))
		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 <= -7.2e-67) || ~((z <= 6.6e-131)))
		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, -7.2e-67], N[Not[LessEqual[z, 6.6e-131]], $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 < -7.19999999999999998e-67 or 6.6000000000000004e-131 < 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 89.4%

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

      1. associate-/l* 85.6%

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

   5. Simplified 85.6%

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

   if -7.19999999999999998e-67 < z < 6.6000000000000004e-131

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-67} \lor \neg \left(z \leq 6.6 \cdot 10^{-131}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.4e+114)
   (* z (/ y t))
   (if (<= z 5e+113) (* x (- 1.0 (/ y t))) (/ (* z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.4e+114) {
		tmp = z * (y / t);
	} else if (z <= 5e+113) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (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 <= (-6.4d+114)) then
        tmp = z * (y / t)
    else if (z <= 5d+113) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (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 <= -6.4e+114) {
		tmp = z * (y / t);
	} else if (z <= 5e+113) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.4e+114:
		tmp = z * (y / t)
	elif z <= 5e+113:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.4e+114)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 5e+113)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.4e+114)
		tmp = z * (y / t);
	elseif (z <= 5e+113)
		tmp = x * (1.0 - (y / t));
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.4e+114], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+113], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4e114

   1. Initial program 89.2%

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

   3. Taylor expanded in y around -inf 73.5%

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

   4. Taylor expanded in z around inf 73.0%

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

      1. associate-/l* 88.9%

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

   6. Simplified 70.7%

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

      1. clear-num 70.7%

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

      2. un-div-inv 70.8%

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

   8. Applied egg-rr 70.8%

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

      1. associate-/r/ 79.5%

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

   10. Applied egg-rr 79.5%

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

   if -6.4e114 < z < 5e113

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. unsub-neg 77.3%

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

   5. Simplified 77.3%

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

   if 5e113 < z

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0 90.5%

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

   4. Taylor expanded in x around 0 76.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00045 \lor \neg \left(y \leq 3.2 \cdot 10^{+111}\right):\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.00045) (not (<= y 3.2e+111))) (* t (/ x t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.00045) || !(y <= 3.2e+111)) {
		tmp = t * (x / 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 <= (-0.00045d0)) .or. (.not. (y <= 3.2d+111))) then
        tmp = t * (x / 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 <= -0.00045) || !(y <= 3.2e+111)) {
		tmp = t * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.00045) or not (y <= 3.2e+111):
		tmp = t * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.00045) || !(y <= 3.2e+111))
		tmp = Float64(t * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.00045) || ~((y <= 3.2e+111)))
		tmp = t * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.00045], N[Not[LessEqual[y, 3.2e+111]], $MachinePrecision]], N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999999e-4 or 3.2000000000000001e111 < y

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0 86.1%

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

   4. Taylor expanded in t around inf 5.4%

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

      1. *-commutative 5.4%

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

   6. Simplified 5.4%

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

      1. *-commutative 5.4%

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

      2. associate-/l* 23.3%

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

   8. Applied egg-rr 23.3%

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

   if -4.4999999999999999e-4 < y < 3.2000000000000001e111

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 57.6%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00045 \lor \neg \left(y \leq 3.2 \cdot 10^{+111}\right):\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% 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 95.4%

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

3. Taylor expanded in z around 0 91.9%

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

   1. +-commutative 91.9%

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

   2. *-commutative 91.9%

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

   3. associate-*r/ 90.0%

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

   4. mul-1-neg 90.0%

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

   5. associate-/l* 89.5%

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

   6. distribute-lft-neg-in 89.5%

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

   7. distribute-rgt-in 97.3%

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

   8. sub-neg 97.3%

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

5. Simplified 97.3%

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

6. Final simplification 97.3%

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

Alternative 11: 38.8% 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 95.4%

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

3. Taylor expanded in y around 0 38.6%

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

Developer target: 90.9% 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 2024100 
(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)))