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

Percentage Accurate: 92.9% → 98.0%

Time: 6.6s

Alternatives: 7

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: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e+107) (fma y (/ (- z x) t) x) (+ x (* (- z x) (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e+107) {
		tmp = fma(y, ((z - x) / t), x);
	} else {
		tmp = x + ((z - x) * (y / t));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e+107)
		tmp = fma(y, Float64(Float64(z - x) / t), x);
	else
		tmp = Float64(x + Float64(Float64(z - x) * Float64(y / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1e+107], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.9999999999999997e106

   1. Initial program 79.0%

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

      1. +-commutative 79.0%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   if -9.9999999999999997e106 < y

   1. Initial program 94.0%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 2: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-73} \lor \neg \left(z \leq 5.8 \cdot 10^{-124}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e-73) (not (<= z 5.8e-124)))
   (+ x (* z (/ y t)))
   (- x (* y (/ x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e-73) || !(z <= 5.8e-124)) {
		tmp = x + (z * (y / t));
	} 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 <= (-6d-73)) .or. (.not. (z <= 5.8d-124))) then
        tmp = x + (z * (y / t))
    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 <= -6e-73) || !(z <= 5.8e-124)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x - (y * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e-73) or not (z <= 5.8e-124):
		tmp = x + (z * (y / t))
	else:
		tmp = x - (y * (x / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e-73) || !(z <= 5.8e-124))
		tmp = Float64(x + Float64(z * Float64(y / t)));
	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 <= -6e-73) || ~((z <= 5.8e-124)))
		tmp = x + (z * (y / t));
	else
		tmp = x - (y * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e-73], N[Not[LessEqual[z, 5.8e-124]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6e-73 or 5.8000000000000004e-124 < z

   1. Initial program 88.6%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around inf 79.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   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 -6e-73 < z < 5.8000000000000004e-124

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-*r/ 96.9%

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

      3. fma-def 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. mul-1-neg 85.1%

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

      3. unsub-neg 85.1%

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

      4. *-commutative 85.1%

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

      5. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

      1. associate-/r/ 89.0%

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

   8. Applied egg-rr 89.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-73} \lor \neg \left(z \leq 5.8 \cdot 10^{-124}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{t}\\ \end{array} \]

Alternative 3: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-69} \lor \neg \left(z \leq 3.4 \cdot 10^{-118}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e-69) (not (<= z 3.4e-118)))
   (+ x (* z (/ y t)))
   (- x (/ y (/ t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-69) || !(z <= 3.4e-118)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x - (y / (t / 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 <= (-5.2d-69)) .or. (.not. (z <= 3.4d-118))) then
        tmp = x + (z * (y / t))
    else
        tmp = x - (y / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-69) || !(z <= 3.4e-118)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x - (y / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e-69) or not (z <= 3.4e-118):
		tmp = x + (z * (y / t))
	else:
		tmp = x - (y / (t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e-69) || !(z <= 3.4e-118))
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x - Float64(y / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e-69) || ~((z <= 3.4e-118)))
		tmp = x + (z * (y / t));
	else
		tmp = x - (y / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e-69], N[Not[LessEqual[z, 3.4e-118]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000004e-69 or 3.39999999999999991e-118 < z

   1. Initial program 88.6%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around inf 79.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   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 -5.2000000000000004e-69 < z < 3.39999999999999991e-118

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-*r/ 96.9%

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

      3. fma-def 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. mul-1-neg 85.1%

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

      3. unsub-neg 85.1%

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

      4. *-commutative 85.1%

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

      5. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in x around 0 85.1%

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

      1. associate-/l* 90.0%

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

   9. Simplified 90.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-69} \lor \neg \left(z \leq 3.4 \cdot 10^{-118}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{x}}\\ \end{array} \]

Alternative 4: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e+125) (+ x (/ y (/ t (- z x)))) (+ x (* (- z x) (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e+125) {
		tmp = x + (y / (t / (z - x)));
	} else {
		tmp = x + ((z - x) * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3d+125)) then
        tmp = x + (y / (t / (z - x)))
    else
        tmp = x + ((z - x) * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e+125) {
		tmp = x + (y / (t / (z - x)));
	} else {
		tmp = x + ((z - x) * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e+125:
		tmp = x + (y / (t / (z - x)))
	else:
		tmp = x + ((z - x) * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e+125)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - x))));
	else
		tmp = Float64(x + Float64(Float64(z - x) * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3e+125)
		tmp = x + (y / (t / (z - x)));
	else
		tmp = x + ((z - x) * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e+125], N[(x + N[(y / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000015e125

   1. Initial program 78.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   if -3.00000000000000015e125 < y

   1. Initial program 93.7%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 5: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.3%

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

   1. associate-*l/ 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 6: 77.2% 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 90.3%

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

   1. associate-*l/ 96.9%

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

3. Simplified 96.9%

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

4. Taylor expanded in z around inf 67.7%

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

   1. associate-*l/ 73.5%

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

   2. *-commutative 73.5%

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

6. Simplified 73.5%

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

7. Final simplification 73.5%

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

Alternative 7: 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 90.3%

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

   1. +-commutative 90.3%

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

   2. associate-*r/ 95.0%

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

   3. fma-def 95.0%

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

3. Simplified 95.0%

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

4. Taylor expanded in y around 0 35.8%

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

5. Final simplification 35.8%

   \[\leadsto x \]

Developer target: 91.2% 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 2023238 
(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)))