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

Percentage Accurate: 92.9% → 99.0%

Time: 8.7s

Alternatives: 10

Speedup: 1.0×

• 25.5% 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: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;t\_1 \leq 10^{+294}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- z x) y) t))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ y (/ t (- z x))))
     (if (<= t_1 1e+294) t_1 (+ x (* y (/ (- z x) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) * y) / t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (y / (t / (z - x)));
	} else if (t_1 <= 1e+294) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z - x) / t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) * y) / t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (y / (t / (z - x)));
	} else if (t_1 <= 1e+294) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((z - x) * y) / t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (y / (t / (z - x)))
	elif t_1 <= 1e+294:
		tmp = t_1
	else:
		tmp = x + (y * ((z - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(z - x) * y) / t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - x))));
	elseif (t_1 <= 1e+294)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((z - x) * y) / t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (y / (t / (z - x)));
	elseif (t_1 <= 1e+294)
		tmp = t_1;
	else
		tmp = x + (y * ((z - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(y / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+294], t$95$1, N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 78.4%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - x}{t}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{t}{z - x}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{t}{z - x}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{t}{z - x}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{\left(z - x\right)}\right)\right)\right) \]

      6. --lowering--.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, \color{blue}{x}\right)\right)\right)\right) \]

   4. Applied egg-rr 100.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 1.00000000000000007e294

   1. Initial program 98.7%

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

   if 1.00000000000000007e294 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 80.9%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - x}{t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z - x}{t} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z - x}{t}\right), \color{blue}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - x\right), t\right), y\right)\right) \]

      5. --lowering--.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, x\right), t\right), y\right)\right) \]

   4. Applied egg-rr 100.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \leq 10^{+294}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-92}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-135}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.35e-92)
   (+ x (* y (/ (- z x) t)))
   (if (<= y 2.3e-135) (+ x (* z (/ y t))) (+ x (/ y (/ t (- z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.35e-92) {
		tmp = x + (y * ((z - x) / t));
	} else if (y <= 2.3e-135) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + (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 (y <= (-2.35d-92)) then
        tmp = x + (y * ((z - x) / t))
    else if (y <= 2.3d-135) then
        tmp = x + (z * (y / t))
    else
        tmp = x + (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 (y <= -2.35e-92) {
		tmp = x + (y * ((z - x) / t));
	} else if (y <= 2.3e-135) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + (y / (t / (z - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.35e-92:
		tmp = x + (y * ((z - x) / t))
	elif y <= 2.3e-135:
		tmp = x + (z * (y / t))
	else:
		tmp = x + (y / (t / (z - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.35e-92)
		tmp = Float64(x + Float64(y * Float64(Float64(z - x) / t)));
	elseif (y <= 2.3e-135)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.35e-92)
		tmp = x + (y * ((z - x) / t));
	elseif (y <= 2.3e-135)
		tmp = x + (z * (y / t));
	else
		tmp = x + (y / (t / (z - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.35e-92], N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-135], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.34999999999999996e-92

   1. Initial program 91.2%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - x}{t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z - x}{t} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z - x}{t}\right), \color{blue}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - x\right), t\right), y\right)\right) \]

      5. --lowering--.f64 99.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, x\right), t\right), y\right)\right) \]

   4. Applied egg-rr 99.4%

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

   if -2.34999999999999996e-92 < y < 2.2999999999999999e-135

   1. Initial program 98.8%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(z - x\right)}{t}\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(z - x\right) \cdot y}{t}\right), x\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - x\right) \cdot \frac{y}{t}\right), x\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(z - x\right), \left(\frac{y}{t}\right)\right), x\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, x\right), \left(\frac{y}{t}\right)\right), x\right) \]

      7. /-lowering-/.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, x\right), \mathsf{/.f64}\left(y, t\right)\right), x\right) \]

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(y, t\right)\right), x\right) \]
   6. Step-by-step derivation

   7. Simplified 96.4%

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

   if 2.2999999999999999e-135 < y

   1. Initial program 86.9%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - x}{t}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{t}{z - x}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{t}{z - x}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{t}{z - x}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{\left(z - x\right)}\right)\right)\right) \]

      6. --lowering--.f64 98.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, \color{blue}{x}\right)\right)\right)\right) \]

   4. Applied egg-rr 98.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-92}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-135}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - x}{t}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-155}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z x) t)))))
   (if (<= y -9.5e-93) t_1 (if (<= y 2e-155) (+ x (* z (/ y 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 (y <= -9.5e-93) {
		tmp = t_1;
	} else if (y <= 2e-155) {
		tmp = x + (z * (y / t));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - x) / t))
    if (y <= (-9.5d-93)) then
        tmp = t_1
    else if (y <= 2d-155) then
        tmp = x + (z * (y / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * ((z - x) / t));
	double tmp;
	if (y <= -9.5e-93) {
		tmp = t_1;
	} else if (y <= 2e-155) {
		tmp = x + (z * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * ((z - x) / t))
	tmp = 0
	if y <= -9.5e-93:
		tmp = t_1
	elif y <= 2e-155:
		tmp = x + (z * (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - x) / t)))
	tmp = 0.0
	if (y <= -9.5e-93)
		tmp = t_1;
	elseif (y <= 2e-155)
		tmp = Float64(x + Float64(z * Float64(y / 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 (y <= -9.5e-93)
		tmp = t_1;
	elseif (y <= 2e-155)
		tmp = x + (z * (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e-93], t$95$1, If[LessEqual[y, 2e-155], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000001e-93 or 2.00000000000000003e-155 < y

   1. Initial program 89.0%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z - x}{t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z - x}{t} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z - x}{t}\right), \color{blue}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - x\right), t\right), y\right)\right) \]

      5. --lowering--.f64 99.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, x\right), t\right), y\right)\right) \]

   4. Applied egg-rr 99.1%

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

   if -9.5000000000000001e-93 < y < 2.00000000000000003e-155

   1. Initial program 98.7%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(z - x\right)}{t}\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(z - x\right) \cdot y}{t}\right), x\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - x\right) \cdot \frac{y}{t}\right), x\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(z - x\right), \left(\frac{y}{t}\right)\right), x\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, x\right), \left(\frac{y}{t}\right)\right), x\right) \]

      7. /-lowering-/.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, x\right), \mathsf{/.f64}\left(y, t\right)\right), x\right) \]

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(y, t\right)\right), x\right) \]
   6. Step-by-step derivation

   7. Simplified 96.2%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-93}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-155}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+103}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))))
   (if (<= x -5.2e+220) t_1 (if (<= x 6.5e+103) (+ x (* z (/ y t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -5.2e+220) {
		tmp = t_1;
	} else if (x <= 6.5e+103) {
		tmp = x + (z * (y / t));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    if (x <= (-5.2d+220)) then
        tmp = t_1
    else if (x <= 6.5d+103) then
        tmp = x + (z * (y / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -5.2e+220) {
		tmp = t_1;
	} else if (x <= 6.5e+103) {
		tmp = x + (z * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -5.2e+220:
		tmp = t_1
	elif x <= 6.5e+103:
		tmp = x + (z * (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -5.2e+220)
		tmp = t_1;
	elseif (x <= 6.5e+103)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (x <= -5.2e+220)
		tmp = t_1;
	elseif (x <= 6.5e+103)
		tmp = x + (z * (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+220], t$95$1, If[LessEqual[x, 6.5e+103], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.19999999999999988e220 or 6.50000000000000001e103 < x

   1. Initial program 87.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{y}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 100.0%

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

   if -5.19999999999999988e220 < x < 6.50000000000000001e103

   1. Initial program 93.6%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(z - x\right)}{t}\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(z - x\right) \cdot y}{t}\right), x\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - x\right) \cdot \frac{y}{t}\right), x\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(z - x\right), \left(\frac{y}{t}\right)\right), x\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, x\right), \left(\frac{y}{t}\right)\right), x\right) \]

      7. /-lowering-/.f64 98.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, x\right), \mathsf{/.f64}\left(y, t\right)\right), x\right) \]

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(y, t\right)\right), x\right) \]
   6. Step-by-step derivation

   7. Simplified 91.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+220}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+103}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - x}{t}\\ \mathbf{if}\;y \leq -0.0033:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ (- z x) t))))
   (if (<= y -0.0033) t_1 (if (<= y 2.5e+53) (+ x (/ (* z y) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * ((z - x) / t);
	double tmp;
	if (y <= -0.0033) {
		tmp = t_1;
	} else if (y <= 2.5e+53) {
		tmp = x + ((z * y) / t);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - x) / t)
    if (y <= (-0.0033d0)) then
        tmp = t_1
    else if (y <= 2.5d+53) then
        tmp = x + ((z * y) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * ((z - x) / t);
	double tmp;
	if (y <= -0.0033) {
		tmp = t_1;
	} else if (y <= 2.5e+53) {
		tmp = x + ((z * y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * ((z - x) / t)
	tmp = 0
	if y <= -0.0033:
		tmp = t_1
	elif y <= 2.5e+53:
		tmp = x + ((z * y) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(Float64(z - x) / t))
	tmp = 0.0
	if (y <= -0.0033)
		tmp = t_1;
	elseif (y <= 2.5e+53)
		tmp = Float64(x + Float64(Float64(z * y) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * ((z - x) / t);
	tmp = 0.0;
	if (y <= -0.0033)
		tmp = t_1;
	elseif (y <= 2.5e+53)
		tmp = x + ((z * y) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0033], t$95$1, If[LessEqual[y, 2.5e+53], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0033 or 2.5000000000000002e53 < y

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(z - x\right)\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - x\right)\right), t\right) \]

      5. --lowering--.f64 77.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, x\right)\right), t\right) \]

   5. Simplified 77.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z - x}{t}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - x\right), t\right), y\right) \]

      5. --lowering--.f64 86.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, x\right), t\right), y\right) \]

   7. Applied egg-rr 86.9%

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

   if -0.0033 < y < 2.5000000000000002e53

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 93.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right) \]

   5. Simplified 93.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0033:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - x}{t}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ (- z x) t))))
   (if (<= z -3.2e+117) t_1 (if (<= z 4.2e+74) (* x (- 1.0 (/ y t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * ((z - x) / t);
	double tmp;
	if (z <= -3.2e+117) {
		tmp = t_1;
	} else if (z <= 4.2e+74) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - x) / t)
    if (z <= (-3.2d+117)) then
        tmp = t_1
    else if (z <= 4.2d+74) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * ((z - x) / t);
	double tmp;
	if (z <= -3.2e+117) {
		tmp = t_1;
	} else if (z <= 4.2e+74) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * ((z - x) / t)
	tmp = 0
	if z <= -3.2e+117:
		tmp = t_1
	elif z <= 4.2e+74:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(Float64(z - x) / t))
	tmp = 0.0
	if (z <= -3.2e+117)
		tmp = t_1;
	elseif (z <= 4.2e+74)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * ((z - x) / t);
	tmp = 0.0;
	if (z <= -3.2e+117)
		tmp = t_1;
	elseif (z <= 4.2e+74)
		tmp = x * (1.0 - (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+117], t$95$1, If[LessEqual[z, 4.2e+74], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000005e117 or 4.1999999999999998e74 < z

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(z - x\right)\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - x\right)\right), t\right) \]

      5. --lowering--.f64 68.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, x\right)\right), t\right) \]

   5. Simplified 68.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z - x}{t}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - x\right), t\right), y\right) \]

      5. --lowering--.f64 75.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, x\right), t\right), y\right) \]

   7. Applied egg-rr 75.5%

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

   if -3.20000000000000005e117 < z < 4.1999999999999998e74

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{y}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 82.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 82.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+117}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.85e+117)
   (* z (/ y t))
   (if (<= z 4.6e+91) (* x (- 1.0 (/ y t))) (/ z (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.85e+117) {
		tmp = z * (y / t);
	} else if (z <= 4.6e+91) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = 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 <= (-3.85d+117)) then
        tmp = z * (y / t)
    else if (z <= 4.6d+91) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = 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 <= -3.85e+117) {
		tmp = z * (y / t);
	} else if (z <= 4.6e+91) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.85e+117:
		tmp = z * (y / t)
	elif z <= 4.6e+91:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.85e+117)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 4.6e+91)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.85e+117)
		tmp = z * (y / t);
	elseif (z <= 4.6e+91)
		tmp = x * (1.0 - (y / t));
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.85e+117], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+91], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.84999999999999975e117

   1. Initial program 88.7%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 60.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right) \]

   5. Simplified 60.8%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{t}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 71.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right) \]

   7. Applied egg-rr 71.0%

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

   if -3.84999999999999975e117 < z < 4.59999999999999982e91

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{y}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 81.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 81.8%

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

   if 4.59999999999999982e91 < z

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 63.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right) \]

   5. Simplified 63.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-/r/ N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{t}{y}\right)}\right) \]

      5. /-lowering-/.f64 73.0%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 73.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+117}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.7e+51) x (if (<= t 1.15e+90) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e+51) {
		tmp = x;
	} else if (t <= 1.15e+90) {
		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 <= (-1.7d+51)) then
        tmp = x
    else if (t <= 1.15d+90) 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 <= -1.7e+51) {
		tmp = x;
	} else if (t <= 1.15e+90) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.7e+51:
		tmp = x
	elif t <= 1.15e+90:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.7e+51)
		tmp = x;
	elseif (t <= 1.15e+90)
		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 <= -1.7e+51)
		tmp = x;
	elseif (t <= 1.15e+90)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.7e+51], x, If[LessEqual[t, 1.15e+90], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.69999999999999992e51 or 1.15e90 < t

   1. Initial program 81.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 75.5%

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

   if -1.69999999999999992e51 < t < 1.15e90

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 56.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right) \]

   5. Simplified 56.5%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{t}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 59.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right) \]

   7. Applied egg-rr 59.6%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.6% 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 92.2%

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(z - x\right)}{t}\right), \color{blue}{x}\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(z - x\right) \cdot y}{t}\right), x\right) \]

   4. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(z - x\right) \cdot \frac{y}{t}\right), x\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(z - x\right), \left(\frac{y}{t}\right)\right), x\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, x\right), \left(\frac{y}{t}\right)\right), x\right) \]

   7. /-lowering-/.f64 99.0%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(z, x\right), \mathsf{/.f64}\left(y, t\right)\right), x\right) \]

4. Applied egg-rr 99.0%

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

5. Final simplification 99.0%

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

Alternative 10: 38.2% 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 92.2%

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

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 42.2%

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

Developer Target 1: 91.0% 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 2024161 
(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)))