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

Percentage Accurate: 92.6% → 97.5%

Time: 10.7s

Alternatives: 13

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.6% 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: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

3. Taylor expanded in z around 0 87.2%

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

   1. mul-1-neg 87.2%

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

   2. associate-/l* 88.0%

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

   3. distribute-lft-neg-in 88.0%

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

   4. *-commutative 88.0%

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

   5. associate-*r/ 88.9%

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

   6. distribute-rgt-in 97.0%

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

   7. +-commutative 97.0%

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

   8. sub-neg 97.0%

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

5. Simplified 97.0%

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

Alternative 2: 52.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-287}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5e+51)
   x
   (if (<= t -2.2e-287)
     (/ (* y z) t)
     (if (<= t 1.25e+37) (/ x (/ (- t) y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e+51) {
		tmp = x;
	} else if (t <= -2.2e-287) {
		tmp = (y * z) / t;
	} else if (t <= 1.25e+37) {
		tmp = x / (-t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5d+51)) then
        tmp = x
    else if (t <= (-2.2d-287)) then
        tmp = (y * z) / t
    else if (t <= 1.25d+37) then
        tmp = x / (-t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e+51) {
		tmp = x;
	} else if (t <= -2.2e-287) {
		tmp = (y * z) / t;
	} else if (t <= 1.25e+37) {
		tmp = x / (-t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5e+51:
		tmp = x
	elif t <= -2.2e-287:
		tmp = (y * z) / t
	elif t <= 1.25e+37:
		tmp = x / (-t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5e+51)
		tmp = x;
	elseif (t <= -2.2e-287)
		tmp = Float64(Float64(y * z) / t);
	elseif (t <= 1.25e+37)
		tmp = Float64(x / Float64(Float64(-t) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5e+51)
		tmp = x;
	elseif (t <= -2.2e-287)
		tmp = (y * z) / t;
	elseif (t <= 1.25e+37)
		tmp = x / (-t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5e+51], x, If[LessEqual[t, -2.2e-287], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.25e+37], N[(x / N[((-t) / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if t < -5e51 or 1.24999999999999997e37 < t

   1. Initial program 80.3%

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

   3. Taylor expanded in y around 0 65.9%

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

   if -5e51 < t < -2.2e-287

   1. Initial program 99.7%

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

   3. Taylor expanded in y around -inf 86.1%

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

   4. Taylor expanded in z around inf 55.5%

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

   if -2.2e-287 < t < 1.24999999999999997e37

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in y around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. distribute-frac-neg 52.3%

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

   8. Simplified 52.3%

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

      1. distribute-frac-neg 52.3%

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

      2. distribute-rgt-neg-in 52.3%

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

      3. distribute-lft-neg-in 52.3%

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

      4. clear-num 52.3%

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

      5. un-div-inv 53.1%

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

   10. Applied egg-rr 53.1%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-287}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-289}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7.5e+52)
   x
   (if (<= t -3.2e-289)
     (/ (* y z) t)
     (if (<= t 2.55e+29) (* x (/ y (- t))) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.5e+52) {
		tmp = x;
	} else if (t <= -3.2e-289) {
		tmp = (y * z) / t;
	} else if (t <= 2.55e+29) {
		tmp = x * (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 (t <= (-7.5d+52)) then
        tmp = x
    else if (t <= (-3.2d-289)) then
        tmp = (y * z) / t
    else if (t <= 2.55d+29) then
        tmp = x * (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 (t <= -7.5e+52) {
		tmp = x;
	} else if (t <= -3.2e-289) {
		tmp = (y * z) / t;
	} else if (t <= 2.55e+29) {
		tmp = x * (y / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7.5e+52:
		tmp = x
	elif t <= -3.2e-289:
		tmp = (y * z) / t
	elif t <= 2.55e+29:
		tmp = x * (y / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7.5e+52)
		tmp = x;
	elseif (t <= -3.2e-289)
		tmp = Float64(Float64(y * z) / t);
	elseif (t <= 2.55e+29)
		tmp = Float64(x * Float64(y / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7.5e+52)
		tmp = x;
	elseif (t <= -3.2e-289)
		tmp = (y * z) / t;
	elseif (t <= 2.55e+29)
		tmp = x * (y / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7.5e+52], x, If[LessEqual[t, -3.2e-289], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.55e+29], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.49999999999999995e52 or 2.55e29 < t

   1. Initial program 80.3%

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

   3. Taylor expanded in y around 0 65.9%

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

   if -7.49999999999999995e52 < t < -3.2000000000000002e-289

   1. Initial program 99.7%

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

   3. Taylor expanded in y around -inf 86.1%

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

   4. Taylor expanded in z around inf 55.5%

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

   if -3.2000000000000002e-289 < t < 2.55e29

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in y around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. distribute-frac-neg 52.3%

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

   8. Simplified 52.3%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-289}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-21} \lor \neg \left(z \leq 7 \cdot 10^{-106}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4e-21) (not (<= z 7e-106)))
   (+ x (* (/ y t) z))
   (- x (* y (/ x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e-21) || !(z <= 7e-106)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x - (y * (x / 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 <= (-4d-21)) .or. (.not. (z <= 7d-106))) then
        tmp = x + ((y / t) * z)
    else
        tmp = x - (y * (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e-21) || !(z <= 7e-106)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x - (y * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4e-21) or not (z <= 7e-106):
		tmp = x + ((y / t) * z)
	else:
		tmp = x - (y * (x / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4e-21) || !(z <= 7e-106))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x - Float64(y * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4e-21) || ~((z <= 7e-106)))
		tmp = x + ((y / t) * z);
	else
		tmp = x - (y * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4e-21], N[Not[LessEqual[z, 7e-106]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999963e-21 or 7e-106 < z

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. associate-/l* 85.4%

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

      3. distribute-lft-neg-in 85.4%

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

      4. *-commutative 85.4%

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

      5. associate-*r/ 89.9%

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

      6. distribute-rgt-in 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 89.0%

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

   if -3.99999999999999963e-21 < z < 7e-106

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 80.7%

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

      1. associate-*r/ 80.7%

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

      2. mul-1-neg 80.7%

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

      3. distribute-lft-neg-out 80.7%

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

      4. *-commutative 80.7%

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

   5. Simplified 80.7%

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

      1. div-inv 80.7%

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

      2. *-commutative 80.7%

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

      3. add-sqr-sqrt 39.6%

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

      4. sqrt-unprod 46.9%

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

      5. sqr-neg 46.9%

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

      6. sqrt-unprod 15.4%

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

      7. add-sqr-sqrt 32.7%

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

      8. *-commutative 32.7%

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

      9. remove-double-neg 32.7%

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

      10. distribute-rgt-neg-out 32.7%

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

      11. cancel-sign-sub-inv 32.7%

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

      12. div-inv 32.7%

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

      13. associate-/l* 32.9%

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

      14. add-sqr-sqrt 17.3%

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

      15. sqrt-unprod 50.9%

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

      16. sqr-neg 50.9%

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

      17. sqrt-unprod 42.6%

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

      18. add-sqr-sqrt 87.1%

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

   7. Applied egg-rr 87.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-21} \lor \neg \left(z \leq 7 \cdot 10^{-106}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-20} \lor \neg \left(z \leq 155000\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.1e-20) (not (<= z 155000.0)))
   (+ x (* (/ y t) z))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e-20) || !(z <= 155000.0)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.1d-20)) .or. (.not. (z <= 155000.0d0))) then
        tmp = x + ((y / t) * z)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e-20) || !(z <= 155000.0)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.1e-20) or not (z <= 155000.0):
		tmp = x + ((y / t) * z)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.1e-20) || !(z <= 155000.0))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.1e-20) || ~((z <= 155000.0)))
		tmp = x + ((y / t) * z);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.1e-20], N[Not[LessEqual[z, 155000.0]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1000000000000001e-20 or 155000 < z

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. associate-/l* 84.0%

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

      3. distribute-lft-neg-in 84.0%

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

      4. *-commutative 84.0%

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

      5. associate-*r/ 89.4%

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

      6. distribute-rgt-in 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 91.8%

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

   if -4.1000000000000001e-20 < z < 155000

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-20} \lor \neg \left(z \leq 155000\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+25} \lor \neg \left(x \leq 4.1 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.6e+25) (not (<= x 4.1e-15)))
   (* x (- 1.0 (/ y t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.6e+25) || !(x <= 4.1e-15)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / 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 <= (-2.6d+25)) .or. (.not. (x <= 4.1d-15))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.6e+25) || !(x <= 4.1e-15)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.6e+25) or not (x <= 4.1e-15):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.6e+25) || !(x <= 4.1e-15))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.6e+25) || ~((x <= 4.1e-15)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.6e+25], N[Not[LessEqual[x, 4.1e-15]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999998e25 or 4.10000000000000036e-15 < x

   1. Initial program 87.5%

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

   3. Taylor expanded in x around inf 89.8%

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

      1. mul-1-neg 89.8%

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

      2. unsub-neg 89.8%

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

   5. Simplified 89.8%

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

   if -2.5999999999999998e25 < x < 4.10000000000000036e-15

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 81.8%

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

      1. associate-/l* 78.2%

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

   5. Simplified 78.2%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+25} \lor \neg \left(x \leq 4.1 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+89} \lor \neg \left(t \leq 3.2 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.35e+89) (not (<= t 3.2e-63)))
   (* x (- 1.0 (/ y t)))
   (* (/ y t) (- z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e+89) || !(t <= 3.2e-63)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.35d+89)) .or. (.not. (t <= 3.2d-63))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y / t) * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e+89) || !(t <= 3.2e-63)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.35e+89) or not (t <= 3.2e-63):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.35e+89) || !(t <= 3.2e-63))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.35e+89) || ~((t <= 3.2e-63)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.35e+89], N[Not[LessEqual[t, 3.2e-63]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e89 or 3.19999999999999989e-63 < t

   1. Initial program 82.8%

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

   3. Taylor expanded in x around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

   5. Simplified 80.9%

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

   if -1.35e89 < t < 3.19999999999999989e-63

   1. Initial program 98.3%

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

   3. Taylor expanded in y around -inf 85.7%

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

   4. Taylor expanded in z around 0 77.7%

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

      1. mul-1-neg 90.3%

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

      2. associate-/l* 84.2%

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

      3. distribute-lft-neg-in 84.2%

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

      4. *-commutative 84.2%

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

      5. associate-*r/ 81.4%

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

      6. distribute-rgt-in 94.9%

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

      7. +-commutative 94.9%

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

      8. sub-neg 94.9%

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

   6. Simplified 81.4%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+89} \lor \neg \left(t \leq 3.2 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-110} \lor \neg \left(x \leq 5.4 \cdot 10^{-76}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.2e-110) (not (<= x 5.4e-76)))
   (* x (- 1.0 (/ y t)))
   (/ (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.2e-110) || !(x <= 5.4e-76)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y * z) / 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 <= (-3.2d-110)) .or. (.not. (x <= 5.4d-76))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.2e-110) || !(x <= 5.4e-76)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.2e-110) or not (x <= 5.4e-76):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.2e-110) || !(x <= 5.4e-76))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.2e-110) || ~((x <= 5.4e-76)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.2e-110], N[Not[LessEqual[x, 5.4e-76]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.20000000000000028e-110 or 5.4000000000000001e-76 < x

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf 81.9%

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

      1. mul-1-neg 81.9%

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

      2. unsub-neg 81.9%

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

   5. Simplified 81.9%

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

   if -3.20000000000000028e-110 < x < 5.4000000000000001e-76

   1. Initial program 97.3%

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

   3. Taylor expanded in y around -inf 78.8%

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

   4. Taylor expanded in z around inf 68.5%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-110} \lor \neg \left(x \leq 5.4 \cdot 10^{-76}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-74}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.18e-107)
   (* x (/ (- t y) t))
   (if (<= x 3.05e-74) (/ (* y z) t) (* x (- 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.18e-107) {
		tmp = x * ((t - y) / t);
	} else if (x <= 3.05e-74) {
		tmp = (y * z) / t;
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.18d-107)) then
        tmp = x * ((t - y) / t)
    else if (x <= 3.05d-74) then
        tmp = (y * z) / t
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.18e-107) {
		tmp = x * ((t - y) / t);
	} else if (x <= 3.05e-74) {
		tmp = (y * z) / t;
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.18e-107:
		tmp = x * ((t - y) / t)
	elif x <= 3.05e-74:
		tmp = (y * z) / t
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.18e-107)
		tmp = Float64(x * Float64(Float64(t - y) / t));
	elseif (x <= 3.05e-74)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.18e-107)
		tmp = x * ((t - y) / t);
	elseif (x <= 3.05e-74)
		tmp = (y * z) / t;
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.18e-107], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.05e-74], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.17999999999999993e-107

   1. Initial program 87.6%

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

   3. Taylor expanded in x around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in t around 0 81.6%

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

   if -1.17999999999999993e-107 < x < 3.0499999999999999e-74

   1. Initial program 97.3%

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

   3. Taylor expanded in y around -inf 78.8%

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

   4. Taylor expanded in z around inf 68.5%

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

   if 3.0499999999999999e-74 < x

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf 82.2%

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

      1. mul-1-neg 82.2%

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

      2. unsub-neg 82.2%

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

   5. Simplified 82.2%

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

Alternative 10: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-63}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.2e+53) x (if (<= t 1.95e-63) (/ (* y z) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e+53) {
		tmp = x;
	} else if (t <= 1.95e-63) {
		tmp = (y * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.2d+53)) then
        tmp = x
    else if (t <= 1.95d-63) then
        tmp = (y * z) / t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e+53) {
		tmp = x;
	} else if (t <= 1.95e-63) {
		tmp = (y * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.2e+53:
		tmp = x
	elif t <= 1.95e-63:
		tmp = (y * z) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.2e+53)
		tmp = x;
	elseif (t <= 1.95e-63)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.2e+53)
		tmp = x;
	elseif (t <= 1.95e-63)
		tmp = (y * z) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.2e+53], x, If[LessEqual[t, 1.95e-63], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2e53 or 1.95000000000000011e-63 < t

   1. Initial program 83.0%

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

   3. Taylor expanded in y around 0 61.7%

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

   if -3.2e53 < t < 1.95000000000000011e-63

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 87.0%

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

   4. Taylor expanded in z around inf 52.9%

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

Alternative 11: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.65e+55) x (if (<= t 1.35e-64) (/ y (/ t z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.65e+55) {
		tmp = x;
	} else if (t <= 1.35e-64) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.65d+55)) then
        tmp = x
    else if (t <= 1.35d-64) then
        tmp = y / (t / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.65e+55) {
		tmp = x;
	} else if (t <= 1.35e-64) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.65e+55:
		tmp = x
	elif t <= 1.35e-64:
		tmp = y / (t / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.65e+55)
		tmp = x;
	elseif (t <= 1.35e-64)
		tmp = Float64(y / Float64(t / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.65e+55)
		tmp = x;
	elseif (t <= 1.35e-64)
		tmp = y / (t / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.65e+55], x, If[LessEqual[t, 1.35e-64], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65e55 or 1.34999999999999993e-64 < t

   1. Initial program 83.3%

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

   3. Taylor expanded in y around 0 60.7%

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

   if -1.65e55 < t < 1.34999999999999993e-64

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 86.8%

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

   4. Taylor expanded in z around inf 52.9%

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

      1. associate-/l* 55.6%

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

   6. Simplified 46.4%

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

      1. clear-num 46.4%

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

      2. un-div-inv 47.6%

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

   8. Applied egg-rr 47.6%

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

Alternative 12: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.6e+55) x (if (<= t 1.35e-64) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e+55) {
		tmp = x;
	} else if (t <= 1.35e-64) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.6d+55)) then
        tmp = x
    else if (t <= 1.35d-64) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e+55) {
		tmp = x;
	} else if (t <= 1.35e-64) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.6e+55:
		tmp = x
	elif t <= 1.35e-64:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.6e+55)
		tmp = x;
	elseif (t <= 1.35e-64)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.6e+55)
		tmp = x;
	elseif (t <= 1.35e-64)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.6e+55], x, If[LessEqual[t, 1.35e-64], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6000000000000001e55 or 1.34999999999999993e-64 < t

   1. Initial program 83.3%

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

   3. Taylor expanded in y around 0 60.7%

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

   if -1.6000000000000001e55 < t < 1.34999999999999993e-64

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 86.8%

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

   4. Taylor expanded in z around inf 52.9%

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

      1. associate-/l* 55.6%

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

   6. Simplified 46.4%

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

Alternative 13: 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 91.9%

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

3. Taylor expanded in y around 0 33.8%

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

Developer Target 1: 90.6% 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 2024132 
(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)))