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

Percentage Accurate: 92.5% → 98.1%

Time: 7.5s

Alternatives: 11

Speedup: 1.0×

• 24.6% 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: 92.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

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 92.5%

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

   1. associate-*l/ 98.4%

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

3. Simplified 98.4%

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

   1. *-commutative 98.4%

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

   2. clear-num 98.3%

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

   3. un-div-inv 98.5%

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

5. Applied egg-rr 98.5%

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

6. Final simplification 98.5%

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

Alternative 2: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+294}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.45e+294)
   x
   (if (<= x -3.8e+177)
     (* (/ x t) (- y))
     (if (<= x -5.4e+39) x (if (<= x 1.8e-13) (* z (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.45e+294) {
		tmp = x;
	} else if (x <= -3.8e+177) {
		tmp = (x / t) * -y;
	} else if (x <= -5.4e+39) {
		tmp = x;
	} else if (x <= 1.8e-13) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.45d+294)) then
        tmp = x
    else if (x <= (-3.8d+177)) then
        tmp = (x / t) * -y
    else if (x <= (-5.4d+39)) then
        tmp = x
    else if (x <= 1.8d-13) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.45e+294) {
		tmp = x;
	} else if (x <= -3.8e+177) {
		tmp = (x / t) * -y;
	} else if (x <= -5.4e+39) {
		tmp = x;
	} else if (x <= 1.8e-13) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.45e+294:
		tmp = x
	elif x <= -3.8e+177:
		tmp = (x / t) * -y
	elif x <= -5.4e+39:
		tmp = x
	elif x <= 1.8e-13:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.45e+294)
		tmp = x;
	elseif (x <= -3.8e+177)
		tmp = Float64(Float64(x / t) * Float64(-y));
	elseif (x <= -5.4e+39)
		tmp = x;
	elseif (x <= 1.8e-13)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.45e+294)
		tmp = x;
	elseif (x <= -3.8e+177)
		tmp = (x / t) * -y;
	elseif (x <= -5.4e+39)
		tmp = x;
	elseif (x <= 1.8e-13)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.45e+294], x, If[LessEqual[x, -3.8e+177], N[(N[(x / t), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[x, -5.4e+39], x, If[LessEqual[x, 1.8e-13], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4499999999999999e294 or -3.7999999999999998e177 < x < -5.40000000000000007e39 or 1.7999999999999999e-13 < x

   1. Initial program 93.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 62.4%

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

   if -2.4499999999999999e294 < x < -3.7999999999999998e177

   1. Initial program 92.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 63.1%

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

   5. Taylor expanded in z around 0 70.5%

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

      1. associate-*r/ 70.5%

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

      2. neg-mul-1 70.5%

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

   7. Simplified 70.5%

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

   if -5.40000000000000007e39 < x < 1.7999999999999999e-13

   1. Initial program 91.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 73.5%

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

   5. Taylor expanded in z around inf 59.7%

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

      1. clear-num 59.6%

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

      2. un-div-inv 59.9%

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

   7. Applied egg-rr 59.9%

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

      1. associate-/r/ 62.0%

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

   9. Applied egg-rr 62.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+294}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+293}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.2e+293)
   x
   (if (<= x -1.2e+177)
     (* x (/ (- y) t))
     (if (<= x -1.35e+40) x (if (<= x 9.4e-14) (* z (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2e+293) {
		tmp = x;
	} else if (x <= -1.2e+177) {
		tmp = x * (-y / t);
	} else if (x <= -1.35e+40) {
		tmp = x;
	} else if (x <= 9.4e-14) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.2d+293)) then
        tmp = x
    else if (x <= (-1.2d+177)) then
        tmp = x * (-y / t)
    else if (x <= (-1.35d+40)) then
        tmp = x
    else if (x <= 9.4d-14) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2e+293) {
		tmp = x;
	} else if (x <= -1.2e+177) {
		tmp = x * (-y / t);
	} else if (x <= -1.35e+40) {
		tmp = x;
	} else if (x <= 9.4e-14) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.2e+293:
		tmp = x
	elif x <= -1.2e+177:
		tmp = x * (-y / t)
	elif x <= -1.35e+40:
		tmp = x
	elif x <= 9.4e-14:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.2e+293)
		tmp = x;
	elseif (x <= -1.2e+177)
		tmp = Float64(x * Float64(Float64(-y) / t));
	elseif (x <= -1.35e+40)
		tmp = x;
	elseif (x <= 9.4e-14)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.2e+293)
		tmp = x;
	elseif (x <= -1.2e+177)
		tmp = x * (-y / t);
	elseif (x <= -1.35e+40)
		tmp = x;
	elseif (x <= 9.4e-14)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.2e+293], x, If[LessEqual[x, -1.2e+177], N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e+40], x, If[LessEqual[x, 9.4e-14], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.1999999999999998e293 or -1.2e177 < x < -1.35000000000000005e40 or 9.4000000000000003e-14 < x

   1. Initial program 93.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 62.4%

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

   if -6.1999999999999998e293 < x < -1.2e177

   1. Initial program 92.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 63.1%

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

   5. Taylor expanded in z around 0 70.5%

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

      1. associate-*r/ 70.5%

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

      2. neg-mul-1 70.5%

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

   7. Simplified 70.5%

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

      1. frac-2neg 70.5%

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

      2. remove-double-neg 70.5%

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

      3. associate-*r/ 70.6%

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

   9. Applied egg-rr 70.6%

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

       1. frac-2neg 70.6%

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

       2. *-commutative 70.6%

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

       3. distribute-lft-neg-in 70.6%

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

       4. remove-double-neg 70.6%

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

       5. associate-*r/ 70.7%

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

       6. *-commutative 70.7%

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

   11. Applied egg-rr 70.7%

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

   if -1.35000000000000005e40 < x < 9.4000000000000003e-14

   1. Initial program 91.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 73.5%

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

   5. Taylor expanded in z around inf 59.7%

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

      1. clear-num 59.6%

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

      2. un-div-inv 59.9%

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

   7. Applied egg-rr 59.9%

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

      1. associate-/r/ 62.0%

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

   9. Applied egg-rr 62.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+293}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-78} \lor \neg \left(y \leq 1.2 \cdot 10^{-82}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.2e-78) (not (<= y 1.2e-82))) (* y (/ (- z x) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-78) || !(y <= 1.2e-82)) {
		tmp = y * ((z - 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 <= (-3.2d-78)) .or. (.not. (y <= 1.2d-82))) then
        tmp = y * ((z - 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 <= -3.2e-78) || !(y <= 1.2e-82)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.2e-78) or not (y <= 1.2e-82):
		tmp = y * ((z - x) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.2e-78) || !(y <= 1.2e-82))
		tmp = Float64(y * Float64(Float64(z - x) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.2e-78) || ~((y <= 1.2e-82)))
		tmp = y * ((z - x) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.2e-78], N[Not[LessEqual[y, 1.2e-82]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e-78 or 1.20000000000000004e-82 < y

   1. Initial program 89.1%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around inf 75.2%

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

   5. Taylor expanded in z around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. sub-neg 75.2%

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

      4. div-sub 78.5%

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

   7. Simplified 78.5%

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

   if -3.2e-78 < y < 1.20000000000000004e-82

   1. Initial program 97.2%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around 0 70.2%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-78} \lor \neg \left(y \leq 1.2 \cdot 10^{-82}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-11} \lor \neg \left(y \leq 2.1 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.2e-11) (not (<= y 2.1e-34)))
   (* y (/ (- z x) t))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e-11) || !(y <= 2.1e-34)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7.2d-11)) .or. (.not. (y <= 2.1d-34))) then
        tmp = y * ((z - x) / t)
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e-11) || !(y <= 2.1e-34)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.2e-11) or not (y <= 2.1e-34):
		tmp = y * ((z - x) / t)
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.2e-11) || !(y <= 2.1e-34))
		tmp = Float64(y * Float64(Float64(z - x) / t));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.2e-11) || ~((y <= 2.1e-34)))
		tmp = y * ((z - x) / t);
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.2e-11], N[Not[LessEqual[y, 2.1e-34]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.19999999999999969e-11 or 2.1000000000000001e-34 < y

   1. Initial program 87.8%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 78.8%

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

   5. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. mul-1-neg 78.8%

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

      3. sub-neg 78.8%

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

      4. div-sub 81.9%

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

   7. Simplified 81.9%

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

   if -7.19999999999999969e-11 < y < 2.1000000000000001e-34

   1. Initial program 97.0%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around inf 87.3%

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

      1. associate-*l/ 86.7%

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

      2. *-commutative 86.7%

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

   6. Simplified 86.7%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-11} \lor \neg \left(y \leq 2.1 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-15} \lor \neg \left(y \leq 1.55 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e-15) (not (<= y 1.55e-34)))
   (* y (/ (- z x) t))
   (+ x (/ (* z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e-15) || !(y <= 1.55e-34)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.5d-15)) .or. (.not. (y <= 1.55d-34))) then
        tmp = y * ((z - x) / t)
    else
        tmp = x + ((z * y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e-15) || !(y <= 1.55e-34)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e-15) or not (y <= 1.55e-34):
		tmp = y * ((z - x) / t)
	else:
		tmp = x + ((z * y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e-15) || !(y <= 1.55e-34))
		tmp = Float64(y * Float64(Float64(z - x) / t));
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.5e-15) || ~((y <= 1.55e-34)))
		tmp = y * ((z - x) / t);
	else
		tmp = x + ((z * y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e-15], N[Not[LessEqual[y, 1.55e-34]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999991e-15 or 1.5499999999999999e-34 < y

   1. Initial program 87.8%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 78.8%

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

   5. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. mul-1-neg 78.8%

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

      3. sub-neg 78.8%

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

      4. div-sub 81.9%

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

   7. Simplified 81.9%

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

   if -6.49999999999999991e-15 < y < 1.5499999999999999e-34

   1. Initial program 97.0%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around inf 87.3%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-15} \lor \neg \left(y \leq 1.55 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]

Alternative 7: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+63} \lor \neg \left(x \leq 8 \cdot 10^{-12}\right):\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.2e+63) (not (<= x 8e-12)))
   (- x (* x (/ y t)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.2e+63) || !(x <= 8e-12)) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.2d+63)) .or. (.not. (x <= 8d-12))) then
        tmp = x - (x * (y / t))
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.2e+63) || !(x <= 8e-12)) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.2e+63) or not (x <= 8e-12):
		tmp = x - (x * (y / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.2e+63) || !(x <= 8e-12))
		tmp = Float64(x - Float64(x * Float64(y / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.2e+63) || ~((x <= 8e-12)))
		tmp = x - (x * (y / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.2e+63], N[Not[LessEqual[x, 8e-12]], $MachinePrecision]], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1999999999999999e63 or 7.99999999999999984e-12 < x

   1. Initial program 93.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 93.9%

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

      1. distribute-lft-in 93.9%

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

      2. mul-1-neg 93.9%

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

      3. distribute-rgt-neg-in 93.9%

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

      4. distribute-lft-neg-out 93.9%

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

      5. *-rgt-identity 93.9%

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

      6. neg-mul-1 93.9%

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

      7. associate-*r* 93.9%

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

      8. associate-*r/ 87.2%

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

      9. mul-1-neg 87.2%

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

      10. unsub-neg 87.2%

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

      11. associate-*r/ 93.9%

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

   6. Simplified 93.9%

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

   if -2.1999999999999999e63 < x < 7.99999999999999984e-12

   1. Initial program 91.6%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 77.5%

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

      1. associate-*l/ 82.8%

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

      2. *-commutative 82.8%

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

   6. Simplified 82.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+63} \lor \neg \left(x \leq 8 \cdot 10^{-12}\right):\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 8: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.1e+40) x (if (<= x 3.5e-14) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.1e+40) {
		tmp = x;
	} else if (x <= 3.5e-14) {
		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 (x <= (-2.1d+40)) then
        tmp = x
    else if (x <= 3.5d-14) 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 (x <= -2.1e+40) {
		tmp = x;
	} else if (x <= 3.5e-14) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.1e+40:
		tmp = x
	elif x <= 3.5e-14:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.1e+40)
		tmp = x;
	elseif (x <= 3.5e-14)
		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 (x <= -2.1e+40)
		tmp = x;
	elseif (x <= 3.5e-14)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.1e+40], x, If[LessEqual[x, 3.5e-14], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e40 or 3.5000000000000002e-14 < x

   1. Initial program 93.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 56.1%

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

   if -2.1000000000000001e40 < x < 3.5000000000000002e-14

   1. Initial program 91.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 73.5%

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

   5. Taylor expanded in z around inf 59.7%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.8e+40) x (if (<= x 5.4e-14) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8e+40) {
		tmp = x;
	} else if (x <= 5.4e-14) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.8d+40)) then
        tmp = x
    else if (x <= 5.4d-14) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8e+40) {
		tmp = x;
	} else if (x <= 5.4e-14) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.8e+40:
		tmp = x
	elif x <= 5.4e-14:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.8e+40)
		tmp = x;
	elseif (x <= 5.4e-14)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.8e+40)
		tmp = x;
	elseif (x <= 5.4e-14)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.8e+40], x, If[LessEqual[x, 5.4e-14], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000004e40 or 5.3999999999999997e-14 < x

   1. Initial program 93.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 56.1%

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

   if -3.80000000000000004e40 < x < 5.3999999999999997e-14

   1. Initial program 91.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 73.5%

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

   5. Taylor expanded in z around inf 59.7%

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

      1. clear-num 59.6%

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

      2. un-div-inv 59.9%

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

   7. Applied egg-rr 59.9%

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

      1. associate-/r/ 62.0%

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

   9. Applied egg-rr 62.0%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 97.9% 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 92.5%

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

   1. associate-*l/ 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 11: 38.3% 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. Step-by-step derivation

   1. associate-*l/ 98.4%

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

3. Simplified 98.4%

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

4. Taylor expanded in y around 0 41.0%

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

5. Final simplification 41.0%

   \[\leadsto x \]

Developer target: 91.1% 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 2023293 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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