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

Percentage Accurate: 92.8% → 97.3%

Time: 8.3s

Alternatives: 11

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.8% 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: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

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

3. Taylor expanded in z around 0 87.1%

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

   1. +-commutative 87.1%

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

   2. mul-1-neg 87.1%

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

   3. *-commutative 87.1%

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

   4. associate-*r/ 85.7%

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

   5. associate-/l* 90.0%

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

   6. distribute-lft-neg-in 90.0%

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

   7. distribute-rgt-in 97.9%

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

   8. sub-neg 97.9%

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

5. Simplified 97.9%

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

6. Final simplification 97.9%

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

Alternative 2: 54.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot z\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-204}:\\ \;\;\;\;\frac{y}{\frac{-t}{x}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y t) z)))
   (if (<= t -1.7e-91)
     x
     (if (<= t 1.95e-227)
       t_1
       (if (<= t 1.95e-204) (/ y (/ (- t) x)) (if (<= t 4.5e+97) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / t) * z;
	double tmp;
	if (t <= -1.7e-91) {
		tmp = x;
	} else if (t <= 1.95e-227) {
		tmp = t_1;
	} else if (t <= 1.95e-204) {
		tmp = y / (-t / x);
	} else if (t <= 4.5e+97) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / t) * z
    if (t <= (-1.7d-91)) then
        tmp = x
    else if (t <= 1.95d-227) then
        tmp = t_1
    else if (t <= 1.95d-204) then
        tmp = y / (-t / x)
    else if (t <= 4.5d+97) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / t) * z;
	double tmp;
	if (t <= -1.7e-91) {
		tmp = x;
	} else if (t <= 1.95e-227) {
		tmp = t_1;
	} else if (t <= 1.95e-204) {
		tmp = y / (-t / x);
	} else if (t <= 4.5e+97) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / t) * z
	tmp = 0
	if t <= -1.7e-91:
		tmp = x
	elif t <= 1.95e-227:
		tmp = t_1
	elif t <= 1.95e-204:
		tmp = y / (-t / x)
	elif t <= 4.5e+97:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / t) * z)
	tmp = 0.0
	if (t <= -1.7e-91)
		tmp = x;
	elseif (t <= 1.95e-227)
		tmp = t_1;
	elseif (t <= 1.95e-204)
		tmp = Float64(y / Float64(Float64(-t) / x));
	elseif (t <= 4.5e+97)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / t) * z;
	tmp = 0.0;
	if (t <= -1.7e-91)
		tmp = x;
	elseif (t <= 1.95e-227)
		tmp = t_1;
	elseif (t <= 1.95e-204)
		tmp = y / (-t / x);
	elseif (t <= 4.5e+97)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t, -1.7e-91], x, If[LessEqual[t, 1.95e-227], t$95$1, If[LessEqual[t, 1.95e-204], N[(y / N[((-t) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+97], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.70000000000000013e-91 or 4.49999999999999976e97 < t

   1. Initial program 85.8%

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

   3. Taylor expanded in y around 0 62.0%

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

   if -1.70000000000000013e-91 < t < 1.95e-227 or 1.95e-204 < t < 4.49999999999999976e97

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 76.6%

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

   4. Taylor expanded in z around inf 55.4%

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

      1. clear-num 55.4%

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

      2. un-div-inv 55.4%

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

   6. Applied egg-rr 55.4%

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

      1. associate-/r/ 66.3%

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

   8. Applied egg-rr 66.3%

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

   if 1.95e-227 < t < 1.95e-204

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 71.5%

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

   4. Taylor expanded in z around 0 81.5%

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

      1. associate-*r/ 81.5%

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

      2. neg-mul-1 81.5%

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

   6. Simplified 81.5%

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

      1. distribute-frac-neg 81.5%

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

      2. distribute-rgt-neg-out 81.5%

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

      3. add-sqr-sqrt 59.6%

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

      4. sqrt-unprod 60.4%

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

      5. sqr-neg 60.4%

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

      6. sqrt-unprod 0.5%

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

      7. add-sqr-sqrt 0.7%

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

      8. clear-num 0.7%

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

      9. un-div-inv 0.7%

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

      10. add-sqr-sqrt 0.5%

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

      11. sqrt-unprod 60.5%

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

      12. sqr-neg 60.5%

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

      13. sqrt-unprod 59.8%

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

      14. add-sqr-sqrt 81.6%

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

   8. Applied egg-rr 81.6%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-227}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-204}:\\ \;\;\;\;\frac{y}{\frac{-t}{x}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot z\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-162}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y t) z)))
   (if (<= t -3.7e-92)
     x
     (if (<= t 1.65e-227)
       t_1
       (if (<= t 1.9e-162) (/ (* x (- y)) t) (if (<= t 2.45e+86) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / t) * z;
	double tmp;
	if (t <= -3.7e-92) {
		tmp = x;
	} else if (t <= 1.65e-227) {
		tmp = t_1;
	} else if (t <= 1.9e-162) {
		tmp = (x * -y) / t;
	} else if (t <= 2.45e+86) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / t) * z
    if (t <= (-3.7d-92)) then
        tmp = x
    else if (t <= 1.65d-227) then
        tmp = t_1
    else if (t <= 1.9d-162) then
        tmp = (x * -y) / t
    else if (t <= 2.45d+86) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / t) * z;
	double tmp;
	if (t <= -3.7e-92) {
		tmp = x;
	} else if (t <= 1.65e-227) {
		tmp = t_1;
	} else if (t <= 1.9e-162) {
		tmp = (x * -y) / t;
	} else if (t <= 2.45e+86) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / t) * z
	tmp = 0
	if t <= -3.7e-92:
		tmp = x
	elif t <= 1.65e-227:
		tmp = t_1
	elif t <= 1.9e-162:
		tmp = (x * -y) / t
	elif t <= 2.45e+86:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / t) * z)
	tmp = 0.0
	if (t <= -3.7e-92)
		tmp = x;
	elseif (t <= 1.65e-227)
		tmp = t_1;
	elseif (t <= 1.9e-162)
		tmp = Float64(Float64(x * Float64(-y)) / t);
	elseif (t <= 2.45e+86)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / t) * z;
	tmp = 0.0;
	if (t <= -3.7e-92)
		tmp = x;
	elseif (t <= 1.65e-227)
		tmp = t_1;
	elseif (t <= 1.9e-162)
		tmp = (x * -y) / t;
	elseif (t <= 2.45e+86)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t, -3.7e-92], x, If[LessEqual[t, 1.65e-227], t$95$1, If[LessEqual[t, 1.9e-162], N[(N[(x * (-y)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.45e+86], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.69999999999999977e-92 or 2.45e86 < t

   1. Initial program 85.8%

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

   3. Taylor expanded in y around 0 62.0%

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

   if -3.69999999999999977e-92 < t < 1.65e-227 or 1.90000000000000002e-162 < t < 2.45e86

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf 76.9%

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

   4. Taylor expanded in z around inf 56.1%

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

      1. clear-num 56.1%

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

      2. un-div-inv 56.1%

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

   6. Applied egg-rr 56.1%

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

      1. associate-/r/ 67.7%

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

   8. Applied egg-rr 67.7%

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

   if 1.65e-227 < t < 1.90000000000000002e-162

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 83.1%

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

   4. Taylor expanded in z around 0 66.3%

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

      1. mul-1-neg 66.3%

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

      2. distribute-lft-neg-out 66.3%

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

      3. *-commutative 66.3%

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

   6. Simplified 66.3%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-227}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-162}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-46} \lor \neg \left(x \leq 5 \cdot 10^{-44}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.6e-46) (not (<= x 5e-44)))
   (* x (- 1.0 (/ y t)))
   (* (/ y t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-46) || !(x <= 5e-44)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.6d-46)) .or. (.not. (x <= 5d-44))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y / t) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-46) || !(x <= 5e-44)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.6e-46) or not (x <= 5e-44):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y / t) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.6e-46) || !(x <= 5e-44))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y / t) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.6e-46) || ~((x <= 5e-44)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y / t) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.6e-46], N[Not[LessEqual[x, 5e-44]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5999999999999993e-46 or 5.00000000000000039e-44 < x

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   5. Simplified 83.7%

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

   if -7.5999999999999993e-46 < x < 5.00000000000000039e-44

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf 76.5%

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

   4. Taylor expanded in z around inf 67.1%

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

      1. clear-num 67.0%

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

      2. un-div-inv 67.0%

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

   6. Applied egg-rr 67.0%

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

      1. associate-/r/ 69.1%

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

   8. Applied egg-rr 69.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-46} \lor \neg \left(x \leq 5 \cdot 10^{-44}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-102} \lor \neg \left(t \leq 1.6 \cdot 10^{+84}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.45e-102) (not (<= t 1.6e+84)))
   (* x (- 1.0 (/ y t)))
   (* (/ y t) (- z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e-102) || !(t <= 1.6e+84)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.45d-102)) .or. (.not. (t <= 1.6d+84))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y / t) * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e-102) || !(t <= 1.6e+84)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.45e-102) or not (t <= 1.6e+84):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.45e-102) || !(t <= 1.6e+84))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.45e-102) || ~((t <= 1.6e+84)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.45e-102], N[Not[LessEqual[t, 1.6e+84]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.44999999999999993e-102 or 1.60000000000000005e84 < t

   1. Initial program 86.1%

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

   3. Taylor expanded in x around inf 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

   5. Simplified 77.6%

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

   if -1.44999999999999993e-102 < t < 1.60000000000000005e84

   1. Initial program 98.5%

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

   3. Taylor expanded in y around -inf 88.3%

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

   4. Taylor expanded in z around 0 78.5%

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

      1. +-commutative 88.7%

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

      2. mul-1-neg 88.7%

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

      3. *-commutative 88.7%

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

      4. associate-*r/ 84.3%

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

      5. associate-/l* 81.9%

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

      6. distribute-lft-neg-in 81.9%

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

      7. distribute-rgt-in 97.1%

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

      8. sub-neg 97.1%

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

   6. Simplified 86.9%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-102} \lor \neg \left(t \leq 1.6 \cdot 10^{+84}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{-91} \lor \neg \left(t \leq 6.2 \cdot 10^{-21}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.65e-91) (not (<= t 6.2e-21)))
   (+ x (* y (/ z t)))
   (* (/ y t) (- z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.65e-91) || !(t <= 6.2e-21)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.65d-91)) .or. (.not. (t <= 6.2d-21))) then
        tmp = x + (y * (z / t))
    else
        tmp = (y / t) * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.65e-91) || !(t <= 6.2e-21)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.65e-91) or not (t <= 6.2e-21):
		tmp = x + (y * (z / t))
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.65e-91) || !(t <= 6.2e-21))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.65e-91) || ~((t <= 6.2e-21)))
		tmp = x + (y * (z / t));
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.65e-91], N[Not[LessEqual[t, 6.2e-21]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6500000000000001e-91 or 6.1999999999999997e-21 < t

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 83.7%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   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 -3.6500000000000001e-91 < t < 6.1999999999999997e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 91.3%

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

   4. Taylor expanded in z around 0 80.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{t} + \frac{y \cdot z}{t}} \]
   5. 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. mul-1-neg 88.5%

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

      3. *-commutative 88.5%

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

      4. associate-*r/ 82.6%

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

      5. associate-/l* 79.1%

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

      6. distribute-lft-neg-in 79.1%

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

      7. distribute-rgt-in 96.6%

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

      8. sub-neg 96.6%

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

   6. Simplified 88.2%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{-91} \lor \neg \left(t \leq 6.2 \cdot 10^{-21}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-46} \lor \neg \left(x \leq 3.5 \cdot 10^{+154}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9e-46) (not (<= x 3.5e+154)))
   (* x (- 1.0 (/ y t)))
   (+ x (* (/ y t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e-46) || !(x <= 3.5e+154)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-9d-46)) .or. (.not. (x <= 3.5d+154))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + ((y / t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e-46) || !(x <= 3.5e+154)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9e-46) or not (x <= 3.5e+154):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9e-46) || !(x <= 3.5e+154))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(y / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -9e-46) || ~((x <= 3.5e+154)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9e-46], N[Not[LessEqual[x, 3.5e+154]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.00000000000000001e-46 or 3.5000000000000002e154 < x

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 88.6%

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

      1. mul-1-neg 88.6%

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

      2. unsub-neg 88.6%

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

   5. Simplified 88.6%

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

   if -9.00000000000000001e-46 < x < 3.5000000000000002e154

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 93.7%

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

      1. +-commutative 93.7%

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

      2. mul-1-neg 93.7%

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

      3. *-commutative 93.7%

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

      4. associate-*r/ 91.3%

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

      5. associate-/l* 90.4%

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

      6. distribute-lft-neg-in 90.4%

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

      7. distribute-rgt-in 96.2%

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

      8. sub-neg 96.2%

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

   5. Simplified 96.2%

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

      1. *-commutative 96.2%

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

      2. clear-num 95.7%

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

      3. un-div-inv 96.1%

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

   7. Applied egg-rr 96.1%

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

   8. Taylor expanded in z around inf 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*r/ 86.2%

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

   10. Simplified 86.2%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-46} \lor \neg \left(x \leq 3.5 \cdot 10^{+154}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{-91}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-21}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.65e-91)
   (+ x (* y (/ z t)))
   (if (<= t 2.9e-21) (/ (* y (- z x)) t) (+ x (* (/ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.65e-91) {
		tmp = x + (y * (z / t));
	} else if (t <= 2.9e-21) {
		tmp = (y * (z - x)) / t;
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.65d-91)) then
        tmp = x + (y * (z / t))
    else if (t <= 2.9d-21) then
        tmp = (y * (z - x)) / t
    else
        tmp = x + ((y / t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.65e-91) {
		tmp = x + (y * (z / t));
	} else if (t <= 2.9e-21) {
		tmp = (y * (z - x)) / t;
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.65e-91:
		tmp = x + (y * (z / t))
	elif t <= 2.9e-21:
		tmp = (y * (z - x)) / t
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.65e-91)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 2.9e-21)
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	else
		tmp = Float64(x + Float64(Float64(y / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.65e-91)
		tmp = x + (y * (z / t));
	elseif (t <= 2.9e-21)
		tmp = (y * (z - x)) / t;
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.65e-91], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-21], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6500000000000001e-91

   1. Initial program 87.3%

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

   3. Taylor expanded in z around inf 79.1%

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

      1. associate-/l* 80.3%

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

   5. Simplified 80.3%

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

   if -3.6500000000000001e-91 < t < 2.9e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 91.3%

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

   if 2.9e-21 < t

   1. Initial program 85.8%

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

   3. Taylor expanded in z around 0 85.8%

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

      1. +-commutative 85.8%

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

      2. mul-1-neg 85.8%

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

      3. *-commutative 85.8%

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

      4. associate-*r/ 87.2%

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

      5. associate-/l* 98.5%

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

      6. distribute-lft-neg-in 98.5%

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

      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%

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

   5. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. clear-num 98.5%

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

      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. Taylor expanded in z around inf 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*r/ 91.6%

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

   10. Simplified 91.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{-91}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-21}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1e-91) x (if (<= t 1.45e+84) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1e-91) {
		tmp = x;
	} else if (t <= 1.45e+84) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1d-91)) then
        tmp = x
    else if (t <= 1.45d+84) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1e-91) {
		tmp = x;
	} else if (t <= 1.45e+84) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1e-91:
		tmp = x
	elif t <= 1.45e+84:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1e-91)
		tmp = x;
	elseif (t <= 1.45e+84)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1e-91)
		tmp = x;
	elseif (t <= 1.45e+84)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1e-91], x, If[LessEqual[t, 1.45e+84], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.00000000000000002e-91 or 1.44999999999999994e84 < t

   1. Initial program 85.8%

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

   3. Taylor expanded in y around 0 62.0%

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

   if -1.00000000000000002e-91 < t < 1.44999999999999994e84

   1. Initial program 98.5%

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

   3. Taylor expanded in y around inf 76.2%

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

   4. Taylor expanded in z around inf 52.3%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.75e-91) x (if (<= t 2.4e+86) (* (/ y t) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.75e-91) {
		tmp = x;
	} else if (t <= 2.4e+86) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.75d-91)) then
        tmp = x
    else if (t <= 2.4d+86) then
        tmp = (y / t) * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.75e-91) {
		tmp = x;
	} else if (t <= 2.4e+86) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.75e-91:
		tmp = x
	elif t <= 2.4e+86:
		tmp = (y / t) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.75e-91)
		tmp = x;
	elseif (t <= 2.4e+86)
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.75e-91)
		tmp = x;
	elseif (t <= 2.4e+86)
		tmp = (y / t) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.75e-91], x, If[LessEqual[t, 2.4e+86], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7499999999999999e-91 or 2.4e86 < t

   1. Initial program 85.8%

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

   3. Taylor expanded in y around 0 62.0%

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

   if -1.7499999999999999e-91 < t < 2.4e86

   1. Initial program 98.5%

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

   3. Taylor expanded in y around inf 76.2%

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

   4. Taylor expanded in z around inf 52.3%

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

      1. clear-num 52.2%

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

      2. un-div-inv 52.2%

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

   6. Applied egg-rr 52.2%

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

      1. associate-/r/ 62.3%

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

   8. Applied egg-rr 62.3%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.6% 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 92.5%

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

3. Taylor expanded in y around 0 35.6%

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

4. Final simplification 35.6%

   \[\leadsto x \]
5. 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 2024115 
(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)))