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

Percentage Accurate: 93.6% → 97.6%

Time: 7.4s

Alternatives: 8

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: 93.6% 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: 97.6% 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 93.6%

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

   1. associate-*l/ 97.1%

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

3. Simplified 97.1%

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

   1. *-commutative 97.1%

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

   2. clear-num 96.9%

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

   3. un-div-inv 97.3%

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

5. Applied egg-rr 97.3%

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

6. Final simplification 97.3%

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

Alternative 2: 48.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-156} \lor \neg \left(t \leq 10^{-112}\right) \land t \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.4e-113)
   x
   (if (or (<= t 8.4e-156) (and (not (<= t 1e-112)) (<= t 2.8e-11)))
     (* y (/ x (- t)))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.4e-113) {
		tmp = x;
	} else if ((t <= 8.4e-156) || (!(t <= 1e-112) && (t <= 2.8e-11))) {
		tmp = y * (x / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.4d-113)) then
        tmp = x
    else if ((t <= 8.4d-156) .or. (.not. (t <= 1d-112)) .and. (t <= 2.8d-11)) then
        tmp = y * (x / -t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.4e-113) {
		tmp = x;
	} else if ((t <= 8.4e-156) || (!(t <= 1e-112) && (t <= 2.8e-11))) {
		tmp = y * (x / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.4e-113:
		tmp = x
	elif (t <= 8.4e-156) or (not (t <= 1e-112) and (t <= 2.8e-11)):
		tmp = y * (x / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.4e-113)
		tmp = x;
	elseif ((t <= 8.4e-156) || (!(t <= 1e-112) && (t <= 2.8e-11)))
		tmp = Float64(y * Float64(x / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.4e-113)
		tmp = x;
	elseif ((t <= 8.4e-156) || (~((t <= 1e-112)) && (t <= 2.8e-11)))
		tmp = y * (x / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.4e-113], x, If[Or[LessEqual[t, 8.4e-156], And[N[Not[LessEqual[t, 1e-112]], $MachinePrecision], LessEqual[t, 2.8e-11]]], N[(y * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -5.39999999999999991e-113 or 8.40000000000000049e-156 < t < 9.9999999999999995e-113 or 2.8e-11 < t

   1. Initial program 90.7%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in y around 0 53.6%

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

   if -5.39999999999999991e-113 < t < 8.40000000000000049e-156 or 9.9999999999999995e-113 < t < 2.8e-11

   1. Initial program 98.9%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. distribute-lft-in 63.4%

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

      3. *-rgt-identity 63.4%

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

      4. mul-1-neg 63.4%

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

      5. distribute-rgt-neg-in 63.4%

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

      6. unsub-neg 63.4%

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

   6. Simplified 63.4%

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

      1. clear-num 63.4%

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

      2. un-div-inv 64.3%

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

   8. Applied egg-rr 64.3%

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

   9. Taylor expanded in t around 0 51.7%

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

       1. associate-*r/ 51.7%

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

       2. associate-*l/ 51.6%

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

       3. metadata-eval 51.6%

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

       4. distribute-neg-frac 51.6%

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

       5. associate-*r* 51.7%

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

       6. distribute-neg-frac 51.7%

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

       7. metadata-eval 51.7%

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

       8. metadata-eval 51.7%

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

       9. associate-/r* 51.7%

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

       10. neg-mul-1 51.7%

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

       11. associate-/r/ 51.7%

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

       12. *-commutative 51.7%

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

       13. associate-*r/ 52.6%

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

       14. *-rgt-identity 52.6%

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

       15. associate-/r/ 47.7%

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

       16. *-commutative 47.7%

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

   11. Simplified 47.7%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-156} \lor \neg \left(t \leq 10^{-112}\right) \land t \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-156} \lor \neg \left(t \leq 8.5 \cdot 10^{-113}\right) \land t \leq 2.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.7e-105)
   x
   (if (or (<= t 8.8e-156) (and (not (<= t 8.5e-113)) (<= t 2.3e-12)))
     (* (/ y t) (- x))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.7e-105) {
		tmp = x;
	} else if ((t <= 8.8e-156) || (!(t <= 8.5e-113) && (t <= 2.3e-12))) {
		tmp = (y / t) * -x;
	} 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 <= (-2.7d-105)) then
        tmp = x
    else if ((t <= 8.8d-156) .or. (.not. (t <= 8.5d-113)) .and. (t <= 2.3d-12)) then
        tmp = (y / t) * -x
    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 <= -2.7e-105) {
		tmp = x;
	} else if ((t <= 8.8e-156) || (!(t <= 8.5e-113) && (t <= 2.3e-12))) {
		tmp = (y / t) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.7e-105:
		tmp = x
	elif (t <= 8.8e-156) or (not (t <= 8.5e-113) and (t <= 2.3e-12)):
		tmp = (y / t) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.7e-105)
		tmp = x;
	elseif ((t <= 8.8e-156) || (!(t <= 8.5e-113) && (t <= 2.3e-12)))
		tmp = Float64(Float64(y / t) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.7e-105)
		tmp = x;
	elseif ((t <= 8.8e-156) || (~((t <= 8.5e-113)) && (t <= 2.3e-12)))
		tmp = (y / t) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.7e-105], x, If[Or[LessEqual[t, 8.8e-156], And[N[Not[LessEqual[t, 8.5e-113]], $MachinePrecision], LessEqual[t, 2.3e-12]]], N[(N[(y / t), $MachinePrecision] * (-x)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.69999999999999993e-105 or 8.7999999999999996e-156 < t < 8.4999999999999995e-113 or 2.29999999999999989e-12 < t

   1. Initial program 90.7%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in y around 0 53.6%

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

   if -2.69999999999999993e-105 < t < 8.7999999999999996e-156 or 8.4999999999999995e-113 < t < 2.29999999999999989e-12

   1. Initial program 98.9%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. distribute-lft-in 63.4%

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

      3. *-rgt-identity 63.4%

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

      4. mul-1-neg 63.4%

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

      5. distribute-rgt-neg-in 63.4%

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

      6. unsub-neg 63.4%

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

   6. Simplified 63.4%

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

      1. clear-num 63.4%

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

      2. un-div-inv 64.3%

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

   8. Applied egg-rr 64.3%

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

   9. Taylor expanded in t around 0 51.7%

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

       1. mul-1-neg 51.7%

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

       2. associate-*l/ 51.7%

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

       3. distribute-rgt-neg-in 51.7%

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

   11. Simplified 51.7%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-156} \lor \neg \left(t \leq 8.5 \cdot 10^{-113}\right) \land t \leq 2.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-103}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-82}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e-103)
   (+ x (* z (/ y t)))
   (if (<= z 1.9e-82) (- x (* x (/ y t))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e-103) {
		tmp = x + (z * (y / t));
	} else if (z <= 1.9e-82) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	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 <= (-1.45d-103)) then
        tmp = x + (z * (y / t))
    else if (z <= 1.9d-82) then
        tmp = x - (x * (y / t))
    else
        tmp = x + (z / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e-103) {
		tmp = x + (z * (y / t));
	} else if (z <= 1.9e-82) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.45e-103:
		tmp = x + (z * (y / t))
	elif z <= 1.9e-82:
		tmp = x - (x * (y / t))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e-103)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (z <= 1.9e-82)
		tmp = Float64(x - Float64(x * Float64(y / t)));
	else
		tmp = Float64(x + Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.45e-103)
		tmp = x + (z * (y / t));
	elseif (z <= 1.9e-82)
		tmp = x - (x * (y / t));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e-103], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-82], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e-103

   1. Initial program 96.5%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 86.6%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -1.4499999999999999e-103 < z < 1.9000000000000001e-82

   1. Initial program 94.7%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 91.3%

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

      1. *-commutative 91.3%

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

      2. distribute-lft-in 91.3%

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

      3. *-rgt-identity 91.3%

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

      4. mul-1-neg 91.3%

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

      5. distribute-rgt-neg-in 91.3%

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

      6. unsub-neg 91.3%

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

   6. Simplified 91.3%

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

   if 1.9000000000000001e-82 < z

   1. Initial program 89.9%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

      1. *-commutative 97.7%

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

      2. clear-num 97.7%

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

      3. un-div-inv 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in z around inf 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-/l* 87.6%

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

   8. Simplified 87.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-103}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-82}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 5: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-103}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.3e-103)
   (+ x (* z (/ y t)))
   (if (<= z 1.6e-82) (- x (/ x (/ t y))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.3e-103) {
		tmp = x + (z * (y / t));
	} else if (z <= 1.6e-82) {
		tmp = x - (x / (t / y));
	} else {
		tmp = x + (z / (t / y));
	}
	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 <= (-5.3d-103)) then
        tmp = x + (z * (y / t))
    else if (z <= 1.6d-82) then
        tmp = x - (x / (t / y))
    else
        tmp = x + (z / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.3e-103) {
		tmp = x + (z * (y / t));
	} else if (z <= 1.6e-82) {
		tmp = x - (x / (t / y));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.3e-103:
		tmp = x + (z * (y / t))
	elif z <= 1.6e-82:
		tmp = x - (x / (t / y))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.3e-103)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (z <= 1.6e-82)
		tmp = Float64(x - Float64(x / Float64(t / y)));
	else
		tmp = Float64(x + Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.3e-103)
		tmp = x + (z * (y / t));
	elseif (z <= 1.6e-82)
		tmp = x - (x / (t / y));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.3e-103], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-82], N[(x - N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.30000000000000006e-103

   1. Initial program 96.5%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 86.6%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -5.30000000000000006e-103 < z < 1.6000000000000001e-82

   1. Initial program 94.7%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 91.3%

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

      1. *-commutative 91.3%

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

      2. distribute-lft-in 91.3%

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

      3. *-rgt-identity 91.3%

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

      4. mul-1-neg 91.3%

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

      5. distribute-rgt-neg-in 91.3%

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

      6. unsub-neg 91.3%

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

   6. Simplified 91.3%

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

      1. clear-num 91.3%

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

      2. un-div-inv 92.2%

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

   8. Applied egg-rr 92.2%

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

   if 1.6000000000000001e-82 < z

   1. Initial program 89.9%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

      1. *-commutative 97.7%

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

      2. clear-num 97.7%

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

      3. un-div-inv 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in z around inf 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-/l* 87.6%

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

   8. Simplified 87.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-103}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 6: 97.5% 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 93.6%

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

   1. associate-*l/ 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 7: 76.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + (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 + (z * (y / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. associate-*l/ 97.1%

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

3. Simplified 97.1%

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

4. Taylor expanded in z around inf 74.7%

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

   1. associate-*l/ 77.6%

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

   2. *-commutative 77.6%

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

6. Simplified 77.6%

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

7. Final simplification 77.6%

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

Alternative 8: 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 93.6%

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

   1. associate-*l/ 97.1%

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

3. Simplified 97.1%

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

4. Taylor expanded in y around 0 39.5%

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

5. Final simplification 39.5%

   \[\leadsto x \]

Developer target: 90.8% 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 2023221 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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