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

Percentage Accurate: 92.4% → 97.8%

Time: 10.4s

Alternatives: 13

Speedup: 1.0×

• 24.9% 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: 92.4% 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: 97.8% 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 91.3%

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

3. Taylor expanded in z around 0 87.4%

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

   1. mul-1-neg 87.4%

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

   2. associate-/l* 88.8%

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

   3. distribute-lft-neg-in 88.8%

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

   4. *-commutative 88.8%

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

   5. associate-*r/ 92.8%

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

   6. distribute-rgt-in 98.7%

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

   7. +-commutative 98.7%

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

   8. sub-neg 98.7%

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

5. Simplified 98.7%

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

   1. *-commutative 98.7%

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

   2. clear-num 98.7%

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

   3. un-div-inv 98.7%

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

7. Applied egg-rr 98.7%

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

Alternative 2: 47.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-294}:\\ \;\;\;\;\frac{y}{\frac{t}{-x}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e-23)
   (* y (/ z t))
   (if (<= z 3.2e-294) (/ y (/ t (- x))) (if (<= z 1.6e-9) x (/ (* z y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e-23) {
		tmp = y * (z / t);
	} else if (z <= 3.2e-294) {
		tmp = y / (t / -x);
	} else if (z <= 1.6e-9) {
		tmp = x;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.05d-23)) then
        tmp = y * (z / t)
    else if (z <= 3.2d-294) then
        tmp = y / (t / -x)
    else if (z <= 1.6d-9) then
        tmp = x
    else
        tmp = (z * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e-23) {
		tmp = y * (z / t);
	} else if (z <= 3.2e-294) {
		tmp = y / (t / -x);
	} else if (z <= 1.6e-9) {
		tmp = x;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e-23:
		tmp = y * (z / t)
	elif z <= 3.2e-294:
		tmp = y / (t / -x)
	elif z <= 1.6e-9:
		tmp = x
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e-23)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 3.2e-294)
		tmp = Float64(y / Float64(t / Float64(-x)));
	elseif (z <= 1.6e-9)
		tmp = x;
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05e-23)
		tmp = y * (z / t);
	elseif (z <= 3.2e-294)
		tmp = y / (t / -x);
	elseif (z <= 1.6e-9)
		tmp = x;
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e-23], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-294], N[(y / N[(t / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-9], x, N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05e-23

   1. Initial program 90.4%

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

   3. Taylor expanded in y around -inf 70.0%

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

   4. Taylor expanded in z around inf 64.3%

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

      1. associate-/l* 90.2%

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

   6. Simplified 69.8%

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

   if -1.05e-23 < z < 3.20000000000000019e-294

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in y around inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. distribute-frac-neg2 54.4%

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

   8. Simplified 54.4%

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

      1. *-commutative 54.4%

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

      2. associate-/r/ 54.5%

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

      3. frac-2neg 54.5%

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

      4. distribute-frac-neg 54.5%

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

      5. remove-double-neg 54.5%

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

   10. Applied egg-rr 54.5%

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

   if 3.20000000000000019e-294 < z < 1.60000000000000006e-9

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0 58.6%

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

   if 1.60000000000000006e-9 < z

   1. Initial program 90.2%

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

   3. Taylor expanded in y around -inf 75.1%

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

   4. Taylor expanded in z around inf 64.7%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-294}:\\ \;\;\;\;\frac{y}{\frac{t}{-x}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-294}:\\ \;\;\;\;y \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e-25)
   (* y (/ z t))
   (if (<= z 8e-294) (* y (/ x (- t))) (if (<= z 1.5e-9) x (/ (* z y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-25) {
		tmp = y * (z / t);
	} else if (z <= 8e-294) {
		tmp = y * (x / -t);
	} else if (z <= 1.5e-9) {
		tmp = x;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.8d-25)) then
        tmp = y * (z / t)
    else if (z <= 8d-294) then
        tmp = y * (x / -t)
    else if (z <= 1.5d-9) then
        tmp = x
    else
        tmp = (z * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-25) {
		tmp = y * (z / t);
	} else if (z <= 8e-294) {
		tmp = y * (x / -t);
	} else if (z <= 1.5e-9) {
		tmp = x;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e-25:
		tmp = y * (z / t)
	elif z <= 8e-294:
		tmp = y * (x / -t)
	elif z <= 1.5e-9:
		tmp = x
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e-25)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 8e-294)
		tmp = Float64(y * Float64(x / Float64(-t)));
	elseif (z <= 1.5e-9)
		tmp = x;
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e-25)
		tmp = y * (z / t);
	elseif (z <= 8e-294)
		tmp = y * (x / -t);
	elseif (z <= 1.5e-9)
		tmp = x;
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e-25], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-294], N[(y * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-9], x, N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e-25

   1. Initial program 90.4%

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

   3. Taylor expanded in y around -inf 70.0%

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

   4. Taylor expanded in z around inf 64.3%

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

      1. associate-/l* 90.2%

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

   6. Simplified 69.8%

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

   if -1.8e-25 < z < 8.00000000000000013e-294

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in y around inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. distribute-frac-neg2 54.4%

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

   8. Simplified 54.4%

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

   9. Taylor expanded in x around 0 47.7%

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

       1. mul-1-neg 47.7%

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

       2. associate-*l/ 54.4%

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

       3. distribute-rgt-neg-in 54.4%

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

   11. Simplified 54.4%

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

   if 8.00000000000000013e-294 < z < 1.49999999999999999e-9

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0 58.6%

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

   if 1.49999999999999999e-9 < z

   1. Initial program 90.2%

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

   3. Taylor expanded in y around -inf 75.1%

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

   4. Taylor expanded in z around inf 64.7%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-294}:\\ \;\;\;\;y \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-293}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.6e-24)
   (* y (/ z t))
   (if (<= z 3.5e-293) (* (/ y t) (- x)) (if (<= z 6.4e-9) x (/ (* z y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.6e-24) {
		tmp = y * (z / t);
	} else if (z <= 3.5e-293) {
		tmp = (y / t) * -x;
	} else if (z <= 6.4e-9) {
		tmp = x;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9.6d-24)) then
        tmp = y * (z / t)
    else if (z <= 3.5d-293) then
        tmp = (y / t) * -x
    else if (z <= 6.4d-9) then
        tmp = x
    else
        tmp = (z * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.6e-24) {
		tmp = y * (z / t);
	} else if (z <= 3.5e-293) {
		tmp = (y / t) * -x;
	} else if (z <= 6.4e-9) {
		tmp = x;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.6e-24:
		tmp = y * (z / t)
	elif z <= 3.5e-293:
		tmp = (y / t) * -x
	elif z <= 6.4e-9:
		tmp = x
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.6e-24)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 3.5e-293)
		tmp = Float64(Float64(y / t) * Float64(-x));
	elseif (z <= 6.4e-9)
		tmp = x;
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.6e-24)
		tmp = y * (z / t);
	elseif (z <= 3.5e-293)
		tmp = (y / t) * -x;
	elseif (z <= 6.4e-9)
		tmp = x;
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.6e-24], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-293], N[(N[(y / t), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, 6.4e-9], x, N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5999999999999993e-24

   1. Initial program 90.4%

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

   3. Taylor expanded in y around -inf 70.0%

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

   4. Taylor expanded in z around inf 64.3%

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

      1. associate-/l* 90.2%

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

   6. Simplified 69.8%

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

   if -9.5999999999999993e-24 < z < 3.5000000000000002e-293

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in y around inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. distribute-frac-neg2 54.4%

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

   8. Simplified 54.4%

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

   if 3.5000000000000002e-293 < z < 6.40000000000000023e-9

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0 58.6%

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

   if 6.40000000000000023e-9 < z

   1. Initial program 90.2%

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

   3. Taylor expanded in y around -inf 75.1%

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

   4. Taylor expanded in z around inf 64.7%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-293}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-22} \lor \neg \left(z \leq 1.12 \cdot 10^{-70}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e-22) (not (<= z 1.12e-70)))
   (+ x (* z (/ y t)))
   (* x (/ (- t y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-22) || !(z <= 1.12e-70)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * ((t - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d-22)) .or. (.not. (z <= 1.12d-70))) then
        tmp = x + (z * (y / t))
    else
        tmp = x * ((t - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-22) || !(z <= 1.12e-70)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * ((t - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e-22) or not (z <= 1.12e-70):
		tmp = x + (z * (y / t))
	else:
		tmp = x * ((t - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-22) || !(z <= 1.12e-70))
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x * Float64(Float64(t - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-22) || ~((z <= 1.12e-70)))
		tmp = x + (z * (y / t));
	else
		tmp = x * ((t - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e-22], N[Not[LessEqual[z, 1.12e-70]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999994e-22 or 1.12e-70 < z

   1. Initial program 90.2%

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

   3. Taylor expanded in z around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. associate-/l* 84.3%

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

      3. distribute-lft-neg-in 84.3%

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

      4. *-commutative 84.3%

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

      5. associate-*r/ 91.5%

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

      6. distribute-rgt-in 99.2%

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

      7. +-commutative 99.2%

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

      8. sub-neg 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in z around inf 89.3%

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

   if -1.59999999999999994e-22 < z < 1.12e-70

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in t around 0 90.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-22} \lor \neg \left(z \leq 1.12 \cdot 10^{-70}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-25} \lor \neg \left(z \leq 2.45 \cdot 10^{-69}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.05e-25) (not (<= z 2.45e-69)))
   (+ x (* y (/ z t)))
   (* x (/ (- t y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.05e-25) || !(z <= 2.45e-69)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * ((t - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.05d-25)) .or. (.not. (z <= 2.45d-69))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * ((t - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.05e-25) || !(z <= 2.45e-69)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * ((t - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.05e-25) or not (z <= 2.45e-69):
		tmp = x + (y * (z / t))
	else:
		tmp = x * ((t - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.05e-25) || !(z <= 2.45e-69))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(Float64(t - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.05e-25) || ~((z <= 2.45e-69)))
		tmp = x + (y * (z / t));
	else
		tmp = x * ((t - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.05e-25], N[Not[LessEqual[z, 2.45e-69]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.04999999999999994e-25 or 2.4499999999999999e-69 < z

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 82.6%

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

      1. associate-/l* 84.1%

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

   5. Simplified 84.1%

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

   if -2.04999999999999994e-25 < z < 2.4499999999999999e-69

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in t around 0 90.5%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-25} \lor \neg \left(z \leq 2.45 \cdot 10^{-69}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9e-23)
   (+ x (/ z (/ t y)))
   (if (<= z 1.06e-68) (* x (/ (- t y) t)) (+ x (* z (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e-23) {
		tmp = x + (z / (t / y));
	} else if (z <= 1.06e-68) {
		tmp = x * ((t - y) / t);
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9d-23)) then
        tmp = x + (z / (t / y))
    else if (z <= 1.06d-68) then
        tmp = x * ((t - y) / t)
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e-23) {
		tmp = x + (z / (t / y));
	} else if (z <= 1.06e-68) {
		tmp = x * ((t - y) / t);
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9e-23:
		tmp = x + (z / (t / y))
	elif z <= 1.06e-68:
		tmp = x * ((t - y) / t)
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9e-23)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (z <= 1.06e-68)
		tmp = Float64(x * Float64(Float64(t - 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 (z <= -9e-23)
		tmp = x + (z / (t / y));
	elseif (z <= 1.06e-68)
		tmp = x * ((t - y) / t);
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9e-23], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-68], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999995e-23

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. associate-/l* 87.4%

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

      3. distribute-lft-neg-in 87.4%

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

      4. *-commutative 87.4%

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

      5. associate-*r/ 95.4%

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

      6. distribute-rgt-in 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

   5. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in z around inf 92.8%

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

   if -8.9999999999999995e-23 < z < 1.06e-68

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in t around 0 90.5%

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

   if 1.06e-68 < z

   1. Initial program 90.0%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. mul-1-neg 83.1%

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

      2. associate-/l* 81.8%

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

      3. distribute-lft-neg-in 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-*r/ 88.5%

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

      6. distribute-rgt-in 98.7%

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

      7. +-commutative 98.7%

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

      8. sub-neg 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in z around inf 86.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e+17)
   (* y (/ z t))
   (if (<= z 1.35e+30) (* x (/ (- t y) t)) (/ (* z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+17) {
		tmp = y * (z / t);
	} else if (z <= 1.35e+30) {
		tmp = x * ((t - y) / t);
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.8d+17)) then
        tmp = y * (z / t)
    else if (z <= 1.35d+30) then
        tmp = x * ((t - y) / t)
    else
        tmp = (z * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+17) {
		tmp = y * (z / t);
	} else if (z <= 1.35e+30) {
		tmp = x * ((t - y) / t);
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e+17:
		tmp = y * (z / t)
	elif z <= 1.35e+30:
		tmp = x * ((t - y) / t)
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e+17)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 1.35e+30)
		tmp = Float64(x * Float64(Float64(t - y) / t));
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e+17)
		tmp = y * (z / t);
	elseif (z <= 1.35e+30)
		tmp = x * ((t - y) / t);
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e+17], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+30], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e17

   1. Initial program 89.8%

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

   3. Taylor expanded in y around -inf 71.2%

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

   4. Taylor expanded in z around inf 65.1%

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

      1. associate-/l* 89.6%

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

   6. Simplified 70.9%

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

   if -1.8e17 < z < 1.3499999999999999e30

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in t around 0 85.4%

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

   if 1.3499999999999999e30 < z

   1. Initial program 89.0%

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

   3. Taylor expanded in y around -inf 77.4%

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

   4. Taylor expanded in z around inf 67.3%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e+17)
   (* y (/ z t))
   (if (<= z 8.5e+30) (* x (- 1.0 (/ y t))) (/ (* z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+17) {
		tmp = y * (z / t);
	} else if (z <= 8.5e+30) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1d+17)) then
        tmp = y * (z / t)
    else if (z <= 8.5d+30) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (z * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+17) {
		tmp = y * (z / t);
	} else if (z <= 8.5e+30) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1e+17:
		tmp = y * (z / t)
	elif z <= 8.5e+30:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e+17)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 8.5e+30)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1e+17)
		tmp = y * (z / t);
	elseif (z <= 8.5e+30)
		tmp = x * (1.0 - (y / t));
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e+17], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+30], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e17

   1. Initial program 89.8%

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

   3. Taylor expanded in y around -inf 71.2%

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

   4. Taylor expanded in z around inf 65.1%

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

      1. associate-/l* 89.6%

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

   6. Simplified 70.9%

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

   if -1e17 < z < 8.4999999999999995e30

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

   5. Simplified 85.4%

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

   if 8.4999999999999995e30 < z

   1. Initial program 89.0%

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

   3. Taylor expanded in y around -inf 77.4%

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

   4. Taylor expanded in z around inf 67.3%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-48} \lor \neg \left(z \leq 1.85 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.4e-48) (not (<= z 1.85e-9))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e-48) || !(z <= 1.85e-9)) {
		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 ((z <= (-2.4d-48)) .or. (.not. (z <= 1.85d-9))) 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 ((z <= -2.4e-48) || !(z <= 1.85e-9)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.4e-48) or not (z <= 1.85e-9):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.4e-48) || !(z <= 1.85e-9))
		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 ((z <= -2.4e-48) || ~((z <= 1.85e-9)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.4e-48], N[Not[LessEqual[z, 1.85e-9]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e-48 or 1.85e-9 < z

   1. Initial program 90.7%

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

   3. Taylor expanded in y around -inf 73.9%

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

   4. Taylor expanded in z around inf 63.6%

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

      1. associate-/l* 82.4%

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

   6. Simplified 65.2%

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

   if -2.4e-48 < z < 1.85e-9

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 52.2%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-48} \lor \neg \left(z \leq 1.85 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.05e-48) (* y (/ z t)) (if (<= z 1.4e-9) x (/ (* z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.05e-48) {
		tmp = y * (z / t);
	} else if (z <= 1.4e-9) {
		tmp = x;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.05d-48)) then
        tmp = y * (z / t)
    else if (z <= 1.4d-9) then
        tmp = x
    else
        tmp = (z * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.05e-48) {
		tmp = y * (z / t);
	} else if (z <= 1.4e-9) {
		tmp = x;
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.05e-48:
		tmp = y * (z / t)
	elif z <= 1.4e-9:
		tmp = x
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.05e-48)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 1.4e-9)
		tmp = x;
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.05e-48)
		tmp = y * (z / t);
	elseif (z <= 1.4e-9)
		tmp = x;
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.05e-48], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-9], x, N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05000000000000007e-48

   1. Initial program 91.2%

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

   3. Taylor expanded in y around -inf 72.8%

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

   4. Taylor expanded in z around inf 62.5%

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

      1. associate-/l* 86.2%

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

   6. Simplified 67.5%

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

   if -2.05000000000000007e-48 < z < 1.39999999999999992e-9

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 52.2%

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

   if 1.39999999999999992e-9 < z

   1. Initial program 90.2%

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

   3. Taylor expanded in y around -inf 75.1%

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

   4. Taylor expanded in z around inf 64.7%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.3%

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

3. Taylor expanded in z around 0 87.4%

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

   1. mul-1-neg 87.4%

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

   2. associate-/l* 88.8%

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

   3. distribute-lft-neg-in 88.8%

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

   4. *-commutative 88.8%

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

   5. associate-*r/ 92.8%

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

   6. distribute-rgt-in 98.7%

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

   7. +-commutative 98.7%

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

   8. sub-neg 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 13: 39.0% 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 91.3%

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

3. Taylor expanded in y around 0 32.1%

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

Developer Target 1: 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 2024141 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (+ (* x (/ y t)) (* (- z) (/ y t)))))

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