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

Percentage Accurate: 93.1% → 98.5%

Time: 8.1s

Alternatives: 9

Speedup: 0.3×

• 24.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% 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: 98.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - x}{t}\\ t_2 := x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;x + y \cdot t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+279}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, t\_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- z x) t)) (t_2 (+ x (/ (* y (- z x)) t))))
   (if (<= t_2 (- INFINITY))
     (+ x (* y t_1))
     (if (<= t_2 2e+279) t_2 (fma y t_1 x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z - x) / t;
	double t_2 = x + ((y * (z - x)) / t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x + (y * t_1);
	} else if (t_2 <= 2e+279) {
		tmp = t_2;
	} else {
		tmp = fma(y, t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z - x) / t)
	t_2 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x + Float64(y * t_1));
	elseif (t_2 <= 2e+279)
		tmp = t_2;
	else
		tmp = fma(y, t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+279], t$95$2, N[(y * t$95$1 + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -inf.0

   1. Initial program 80.3%

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

      1. +-commutative 80.3%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 2.00000000000000012e279

   1. Initial program 99.8%

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

   if 2.00000000000000012e279 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-/l* 99.9%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 2 \cdot 10^{+279}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+279}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z x)) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+279)))
     (+ x (* y (/ (- z x) t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+279)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+279)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * (z - x)) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+279):
		tmp = x + (y * ((z - x) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+279))
		tmp = Float64(x + Float64(y * Float64(Float64(z - x) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * (z - x)) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+279)))
		tmp = x + (y * ((z - x) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+279]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -inf.0 or 2.00000000000000012e279 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 84.8%

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

      1. +-commutative 84.8%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 2.00000000000000012e279

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \leq 2 \cdot 10^{+279}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+279}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z x)) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+279)))
     (* y (/ (- z x) t))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+279)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+279)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * (z - x)) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+279):
		tmp = y * ((z - x) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+279))
		tmp = Float64(y * Float64(Float64(z - x) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * (z - x)) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+279)))
		tmp = y * ((z - x) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+279]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -inf.0 or 5.0000000000000002e279 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 84.6%

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

   3. Taylor expanded in y around -inf 84.6%

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

      1. associate-/l* 95.3%

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

      2. *-commutative 95.3%

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

   5. Applied egg-rr 95.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 5.0000000000000002e279

   1. Initial program 99.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \leq 5 \cdot 10^{+279}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-45} \lor \neg \left(z \leq 1.65 \cdot 10^{-13}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.15e-45) (not (<= z 1.65e-13)))
   (+ x (* z (/ y t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.15e-45) || !(z <= 1.65e-13)) {
		tmp = x + (z * (y / 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 ((z <= (-2.15d-45)) .or. (.not. (z <= 1.65d-13))) then
        tmp = x + (z * (y / 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 ((z <= -2.15e-45) || !(z <= 1.65e-13)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.15e-45) or not (z <= 1.65e-13):
		tmp = x + (z * (y / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.15e-45) || !(z <= 1.65e-13))
		tmp = Float64(x + Float64(z * Float64(y / 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 ((z <= -2.15e-45) || ~((z <= 1.65e-13)))
		tmp = x + (z * (y / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.15e-45], N[Not[LessEqual[z, 1.65e-13]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1499999999999999e-45 or 1.65e-13 < z

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-*r/ 92.2%

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

   5. Simplified 92.2%

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

   if -2.1499999999999999e-45 < z < 1.65e-13

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 89.1%

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

      1. mul-1-neg 89.1%

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

      2. unsub-neg 89.1%

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

   5. Simplified 89.1%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-45} \lor \neg \left(z \leq 1.65 \cdot 10^{-13}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-46} \lor \neg \left(z \leq 5.8 \cdot 10^{-18}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3e-46) (not (<= z 5.8e-18)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e-46) || !(z <= 5.8e-18)) {
		tmp = x + (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 ((z <= (-3d-46)) .or. (.not. (z <= 5.8d-18))) then
        tmp = x + (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 ((z <= -3e-46) || !(z <= 5.8e-18)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3e-46) or not (z <= 5.8e-18):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3e-46) || !(z <= 5.8e-18))
		tmp = Float64(x + Float64(y * Float64(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 ((z <= -3e-46) || ~((z <= 5.8e-18)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3e-46], N[Not[LessEqual[z, 5.8e-18]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999987e-46 or 5.8e-18 < z

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 88.6%

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

      1. associate-/l* 87.9%

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

   5. Simplified 87.9%

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

   if -2.99999999999999987e-46 < z < 5.8e-18

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 89.1%

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

      1. mul-1-neg 89.1%

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

      2. unsub-neg 89.1%

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

   5. Simplified 89.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-46} \lor \neg \left(z \leq 5.8 \cdot 10^{-18}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+103}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.65e+103)
   (/ z (/ t y))
   (if (<= z 3.7e+30) (* x (- 1.0 (/ y t))) (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+103) {
		tmp = z / (t / y);
	} else if (z <= 3.7e+30) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.65d+103)) then
        tmp = z / (t / y)
    else if (z <= 3.7d+30) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+103) {
		tmp = z / (t / y);
	} else if (z <= 3.7e+30) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.65e+103:
		tmp = z / (t / y)
	elif z <= 3.7e+30:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.65e+103)
		tmp = Float64(z / Float64(t / y));
	elseif (z <= 3.7e+30)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.65e+103)
		tmp = z / (t / y);
	elseif (z <= 3.7e+30)
		tmp = x * (1.0 - (y / t));
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.65e+103], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+30], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000004e103

   1. Initial program 94.3%

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

   3. Taylor expanded in y around -inf 74.6%

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

   4. Taylor expanded in z around inf 72.0%

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

      1. *-commutative 91.6%

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

      2. associate-*r/ 94.2%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in z around 0 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-*l/ 66.4%

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

      3. associate-/r/ 74.7%

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

   9. Simplified 74.7%

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

   if -1.65000000000000004e103 < z < 3.70000000000000016e30

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

   5. Simplified 84.5%

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

   if 3.70000000000000016e30 < z

   1. Initial program 92.4%

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

   3. Taylor expanded in y around -inf 77.0%

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

   4. Taylor expanded in z around inf 69.6%

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

      1. *-commutative 84.4%

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

      2. associate-*r/ 91.8%

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

   6. Simplified 77.0%

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

Alternative 7: 55.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+86}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.22e-21) x (if (<= t 2.15e+86) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.22e-21) {
		tmp = x;
	} else if (t <= 2.15e+86) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.22d-21)) then
        tmp = x
    else if (t <= 2.15d+86) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.22e-21) {
		tmp = x;
	} else if (t <= 2.15e+86) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.22e-21:
		tmp = x
	elif t <= 2.15e+86:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.22e-21)
		tmp = x;
	elseif (t <= 2.15e+86)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.22e-21)
		tmp = x;
	elseif (t <= 2.15e+86)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.22e-21], x, If[LessEqual[t, 2.15e+86], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.21999999999999991e-21 or 2.1500000000000001e86 < t

   1. Initial program 86.9%

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

   3. Taylor expanded in y around 0 72.2%

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

   if -1.21999999999999991e-21 < t < 2.1500000000000001e86

   1. Initial program 99.7%

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

   3. Taylor expanded in y around -inf 83.8%

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

   4. Taylor expanded in z around inf 52.3%

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

      1. *-commutative 66.6%

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

      2. associate-*r/ 70.2%

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

   6. Simplified 55.9%

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

Alternative 8: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.3e-22) x (if (<= t 8.5e+82) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.3e-22) {
		tmp = x;
	} else if (t <= 8.5e+82) {
		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 <= (-4.3d-22)) then
        tmp = x
    else if (t <= 8.5d+82) 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 <= -4.3e-22) {
		tmp = x;
	} else if (t <= 8.5e+82) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.3e-22:
		tmp = x
	elif t <= 8.5e+82:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.3e-22)
		tmp = x;
	elseif (t <= 8.5e+82)
		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 <= -4.3e-22)
		tmp = x;
	elseif (t <= 8.5e+82)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.3e-22], x, If[LessEqual[t, 8.5e+82], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -4.30000000000000037e-22 or 8.4999999999999995e82 < t

   1. Initial program 86.9%

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

   3. Taylor expanded in y around 0 72.2%

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

   if -4.30000000000000037e-22 < t < 8.4999999999999995e82

   1. Initial program 99.7%

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

   3. Taylor expanded in y around -inf 83.8%

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

   4. Taylor expanded in z around inf 52.3%

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

      1. associate-/l* 62.5%

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

   6. Simplified 48.6%

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

Alternative 9: 39.2% 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 94.7%

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

3. Taylor expanded in y around 0 38.6%

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

Developer target: 90.2% 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 2024084 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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