Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B

Percentage Accurate: 99.8% → 99.8%

Time: 10.3s

Alternatives: 13

Speedup: 1.0×

• 26.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

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) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

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) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma x (+ (* 2.0 (+ y z)) t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return fma(x, ((2.0 * (y + z)) + t), (y * 5.0));
}

Julia

function code(x, y, z, t)
	return fma(x, Float64(Float64(2.0 * Float64(y + z)) + t), Float64(y * 5.0))
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Step-by-step derivation

   1. fma-define 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

   2. associate-+l+ 99.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

   3. +-commutative 99.9%

      \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

   4. count-2 99.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right) \]
6. Add Preprocessing

Alternative 2: 46.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-50}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-179}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-46}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+53}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+62}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* x 2.0))))
   (if (<= z -1.02e+136)
     t_1
     (if (<= z -9.5e-50)
       (* x t)
       (if (<= z -1.2e-179)
         (* y 5.0)
         (if (<= z 1.8e-46)
           (* x t)
           (if (<= z 3.8e+53) (* y 5.0) (if (<= z 1.85e+62) (* x t) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x * 2.0);
	double tmp;
	if (z <= -1.02e+136) {
		tmp = t_1;
	} else if (z <= -9.5e-50) {
		tmp = x * t;
	} else if (z <= -1.2e-179) {
		tmp = y * 5.0;
	} else if (z <= 1.8e-46) {
		tmp = x * t;
	} else if (z <= 3.8e+53) {
		tmp = y * 5.0;
	} else if (z <= 1.85e+62) {
		tmp = x * 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 = z * (x * 2.0d0)
    if (z <= (-1.02d+136)) then
        tmp = t_1
    else if (z <= (-9.5d-50)) then
        tmp = x * t
    else if (z <= (-1.2d-179)) then
        tmp = y * 5.0d0
    else if (z <= 1.8d-46) then
        tmp = x * t
    else if (z <= 3.8d+53) then
        tmp = y * 5.0d0
    else if (z <= 1.85d+62) then
        tmp = x * 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 = z * (x * 2.0);
	double tmp;
	if (z <= -1.02e+136) {
		tmp = t_1;
	} else if (z <= -9.5e-50) {
		tmp = x * t;
	} else if (z <= -1.2e-179) {
		tmp = y * 5.0;
	} else if (z <= 1.8e-46) {
		tmp = x * t;
	} else if (z <= 3.8e+53) {
		tmp = y * 5.0;
	} else if (z <= 1.85e+62) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x * 2.0)
	tmp = 0
	if z <= -1.02e+136:
		tmp = t_1
	elif z <= -9.5e-50:
		tmp = x * t
	elif z <= -1.2e-179:
		tmp = y * 5.0
	elif z <= 1.8e-46:
		tmp = x * t
	elif z <= 3.8e+53:
		tmp = y * 5.0
	elif z <= 1.85e+62:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x * 2.0))
	tmp = 0.0
	if (z <= -1.02e+136)
		tmp = t_1;
	elseif (z <= -9.5e-50)
		tmp = Float64(x * t);
	elseif (z <= -1.2e-179)
		tmp = Float64(y * 5.0);
	elseif (z <= 1.8e-46)
		tmp = Float64(x * t);
	elseif (z <= 3.8e+53)
		tmp = Float64(y * 5.0);
	elseif (z <= 1.85e+62)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x * 2.0);
	tmp = 0.0;
	if (z <= -1.02e+136)
		tmp = t_1;
	elseif (z <= -9.5e-50)
		tmp = x * t;
	elseif (z <= -1.2e-179)
		tmp = y * 5.0;
	elseif (z <= 1.8e-46)
		tmp = x * t;
	elseif (z <= 3.8e+53)
		tmp = y * 5.0;
	elseif (z <= 1.85e+62)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+136], t$95$1, If[LessEqual[z, -9.5e-50], N[(x * t), $MachinePrecision], If[LessEqual[z, -1.2e-179], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 1.8e-46], N[(x * t), $MachinePrecision], If[LessEqual[z, 3.8e+53], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 1.85e+62], N[(x * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.01999999999999996e136 or 1.85000000000000007e62 < z

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 74.2%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot z} \]

   if -1.01999999999999996e136 < z < -9.4999999999999993e-50 or -1.2e-179 < z < 1.8e-46 or 3.79999999999999997e53 < z < 1.85000000000000007e62

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 53.2%

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

   5. Simplified 53.2%

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

   if -9.4999999999999993e-50 < z < -1.2e-179 or 1.8e-46 < z < 3.79999999999999997e53

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 45.0%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+136}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-50}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-179}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-46}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+53}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+62}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-193}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-75}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (* 2.0 (+ y z)) t))))
   (if (<= x -7e-99)
     t_1
     (if (<= x 2.15e-193)
       (+ (* y 5.0) (* x t))
       (if (<= x 4.1e-75)
         (+ (* y 5.0) (* 2.0 (* x z)))
         (if (<= x 2.45e-45) (* t (+ x (* y (/ 5.0 t)))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((2.0 * (y + z)) + t);
	double tmp;
	if (x <= -7e-99) {
		tmp = t_1;
	} else if (x <= 2.15e-193) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 4.1e-75) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else if (x <= 2.45e-45) {
		tmp = t * (x + (y * (5.0 / 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 * ((2.0d0 * (y + z)) + t)
    if (x <= (-7d-99)) then
        tmp = t_1
    else if (x <= 2.15d-193) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 4.1d-75) then
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    else if (x <= 2.45d-45) then
        tmp = t * (x + (y * (5.0d0 / 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 * ((2.0 * (y + z)) + t);
	double tmp;
	if (x <= -7e-99) {
		tmp = t_1;
	} else if (x <= 2.15e-193) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 4.1e-75) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else if (x <= 2.45e-45) {
		tmp = t * (x + (y * (5.0 / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((2.0 * (y + z)) + t)
	tmp = 0
	if x <= -7e-99:
		tmp = t_1
	elif x <= 2.15e-193:
		tmp = (y * 5.0) + (x * t)
	elif x <= 4.1e-75:
		tmp = (y * 5.0) + (2.0 * (x * z))
	elif x <= 2.45e-45:
		tmp = t * (x + (y * (5.0 / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t))
	tmp = 0.0
	if (x <= -7e-99)
		tmp = t_1;
	elseif (x <= 2.15e-193)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 4.1e-75)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	elseif (x <= 2.45e-45)
		tmp = Float64(t * Float64(x + Float64(y * Float64(5.0 / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((2.0 * (y + z)) + t);
	tmp = 0.0;
	if (x <= -7e-99)
		tmp = t_1;
	elseif (x <= 2.15e-193)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 4.1e-75)
		tmp = (y * 5.0) + (2.0 * (x * z));
	elseif (x <= 2.45e-45)
		tmp = t * (x + (y * (5.0 / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e-99], t$95$1, If[LessEqual[x, 2.15e-193], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e-75], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.45e-45], N[(t * N[(x + N[(y * N[(5.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.9999999999999997e-99 or 2.4499999999999999e-45 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 95.4%

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot \left(y + z\right)\right)} \]

   if -6.9999999999999997e-99 < x < 2.1500000000000001e-193

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.9%

      \[\leadsto x \cdot \left(\color{blue}{2 \cdot z} + t\right) + y \cdot 5 \]

   4. Taylor expanded in z around 0 88.5%

      \[\leadsto \color{blue}{5 \cdot y + t \cdot x} \]

   if 2.1500000000000001e-193 < x < 4.10000000000000002e-75

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.9%

      \[\leadsto x \cdot \left(\color{blue}{2 \cdot z} + t\right) + y \cdot 5 \]

   4. Taylor expanded in t around 0 86.7%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right) + 5 \cdot y} \]

   if 4.10000000000000002e-75 < x < 2.4499999999999999e-45

   1. Initial program 99.6%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.6%

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot z\right) + y \cdot \left(5 + 2 \cdot x\right)} \]

   4. Taylor expanded in t around inf 99.4%

      \[\leadsto \color{blue}{t \cdot \left(x + \left(2 \cdot \frac{x \cdot z}{t} + \frac{y \cdot \left(5 + 2 \cdot x\right)}{t}\right)\right)} \]

   5. Taylor expanded in x around 0 87.4%

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

      1. associate-*r/ 87.2%

         \[\leadsto t \cdot \left(x + \color{blue}{\frac{5 \cdot y}{t}}\right) \]

      2. *-commutative 87.2%

         \[\leadsto t \cdot \left(x + \frac{\color{blue}{y \cdot 5}}{t}\right) \]

      3. associate-*r/ 87.6%

         \[\leadsto t \cdot \left(x + \color{blue}{y \cdot \frac{5}{t}}\right) \]

   7. Simplified 87.6%

      \[\leadsto t \cdot \left(x + \color{blue}{y \cdot \frac{5}{t}}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-193}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-75}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-86}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+66} \lor \neg \left(x \leq 1.1 \cdot 10^{+122}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* 2.0 (+ y z)))))
   (if (<= x -7.5e-101)
     t_1
     (if (<= x 5.6e-86)
       (* y 5.0)
       (if (or (<= x 1.7e+66) (not (<= x 1.1e+122))) t_1 (* x t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -7.5e-101) {
		tmp = t_1;
	} else if (x <= 5.6e-86) {
		tmp = y * 5.0;
	} else if ((x <= 1.7e+66) || !(x <= 1.1e+122)) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x * (2.0d0 * (y + z))
    if (x <= (-7.5d-101)) then
        tmp = t_1
    else if (x <= 5.6d-86) then
        tmp = y * 5.0d0
    else if ((x <= 1.7d+66) .or. (.not. (x <= 1.1d+122))) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -7.5e-101) {
		tmp = t_1;
	} else if (x <= 5.6e-86) {
		tmp = y * 5.0;
	} else if ((x <= 1.7e+66) || !(x <= 1.1e+122)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (2.0 * (y + z))
	tmp = 0
	if x <= -7.5e-101:
		tmp = t_1
	elif x <= 5.6e-86:
		tmp = y * 5.0
	elif (x <= 1.7e+66) or not (x <= 1.1e+122):
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(2.0 * Float64(y + z)))
	tmp = 0.0
	if (x <= -7.5e-101)
		tmp = t_1;
	elseif (x <= 5.6e-86)
		tmp = Float64(y * 5.0);
	elseif ((x <= 1.7e+66) || !(x <= 1.1e+122))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (2.0 * (y + z));
	tmp = 0.0;
	if (x <= -7.5e-101)
		tmp = t_1;
	elseif (x <= 5.6e-86)
		tmp = y * 5.0;
	elseif ((x <= 1.7e+66) || ~((x <= 1.1e+122)))
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e-101], t$95$1, If[LessEqual[x, 5.6e-86], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 1.7e+66], N[Not[LessEqual[x, 1.1e+122]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5000000000000001e-101 or 5.60000000000000019e-86 < x < 1.70000000000000015e66 or 1.1e122 < x

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.1%

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot z\right) + y \cdot \left(5 + 2 \cdot x\right)} \]

   4. Taylor expanded in x around inf 88.2%

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

      1. *-commutative 88.2%

         \[\leadsto x \cdot \left(t + 2 \cdot z\right) + \color{blue}{\left(x \cdot y\right) \cdot 2} \]

      2. *-commutative 88.2%

         \[\leadsto x \cdot \left(t + 2 \cdot z\right) + \color{blue}{\left(y \cdot x\right)} \cdot 2 \]

      3. associate-*r* 88.2%

         \[\leadsto x \cdot \left(t + 2 \cdot z\right) + \color{blue}{y \cdot \left(x \cdot 2\right)} \]

   6. Simplified 88.2%

      \[\leadsto x \cdot \left(t + 2 \cdot z\right) + \color{blue}{y \cdot \left(x \cdot 2\right)} \]

   7. Taylor expanded in t around 0 61.0%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right) + 2 \cdot \left(x \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 61.0%

         \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} + 2 \cdot \left(x \cdot z\right) \]

      2. associate-*r* 61.0%

         \[\leadsto \color{blue}{\left(2 \cdot y\right) \cdot x} + 2 \cdot \left(x \cdot z\right) \]

      3. *-commutative 61.0%

         \[\leadsto \left(2 \cdot y\right) \cdot x + 2 \cdot \color{blue}{\left(z \cdot x\right)} \]

      4. associate-*r* 61.0%

         \[\leadsto \left(2 \cdot y\right) \cdot x + \color{blue}{\left(2 \cdot z\right) \cdot x} \]

      5. distribute-rgt-in 65.3%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot y + 2 \cdot z\right)} \]

      6. +-commutative 65.3%

         \[\leadsto x \cdot \color{blue}{\left(2 \cdot z + 2 \cdot y\right)} \]

      7. distribute-lft-out 65.3%

         \[\leadsto x \cdot \color{blue}{\left(2 \cdot \left(z + y\right)\right)} \]

   9. Simplified 65.3%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \left(z + y\right)\right)} \]

   if -7.5000000000000001e-101 < x < 5.60000000000000019e-86

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 63.8%

      \[\leadsto \color{blue}{5 \cdot y} \]

   if 1.70000000000000015e66 < x < 1.1e122

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-86}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+66} \lor \neg \left(x \leq 1.1 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 1.18 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.5) (not (<= x 1.18e-20)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* x (+ t (* 2.0 z))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 1.18e-20)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (x * (t + (2.0 * z))) + (y * 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.5d0)) .or. (.not. (x <= 1.18d-20))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (x * (t + (2.0d0 * z))) + (y * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 1.18e-20)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (x * (t + (2.0 * z))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.5) or not (x <= 1.18e-20):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (x * (t + (2.0 * z))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.5) || !(x <= 1.18e-20))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(2.0 * z))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.5) || ~((x <= 1.18e-20)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (x * (t + (2.0 * z))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.5], N[Not[LessEqual[x, 1.18e-20]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5 or 1.1800000000000001e-20 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 98.8%

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot \left(y + z\right)\right)} \]

   if -2.5 < x < 1.1800000000000001e-20

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.5%

      \[\leadsto x \cdot \left(\color{blue}{2 \cdot z} + t\right) + y \cdot 5 \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 1.18 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(t + \left(t\_1 + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_1 + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= x -1.05e-12)
     (* x (+ t (+ t_1 (* 5.0 (/ y x)))))
     (if (<= x 1.18e-20)
       (+ (* x (+ t (* 2.0 z))) (* y 5.0))
       (* x (+ t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (x <= -1.05e-12) {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	} else if (x <= 1.18e-20) {
		tmp = (x * (t + (2.0 * z))) + (y * 5.0);
	} else {
		tmp = x * (t_1 + 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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    if (x <= (-1.05d-12)) then
        tmp = x * (t + (t_1 + (5.0d0 * (y / x))))
    else if (x <= 1.18d-20) then
        tmp = (x * (t + (2.0d0 * z))) + (y * 5.0d0)
    else
        tmp = x * (t_1 + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (x <= -1.05e-12) {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	} else if (x <= 1.18e-20) {
		tmp = (x * (t + (2.0 * z))) + (y * 5.0);
	} else {
		tmp = x * (t_1 + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if x <= -1.05e-12:
		tmp = x * (t + (t_1 + (5.0 * (y / x))))
	elif x <= 1.18e-20:
		tmp = (x * (t + (2.0 * z))) + (y * 5.0)
	else:
		tmp = x * (t_1 + t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (x <= -1.05e-12)
		tmp = Float64(x * Float64(t + Float64(t_1 + Float64(5.0 * Float64(y / x)))));
	elseif (x <= 1.18e-20)
		tmp = Float64(Float64(x * Float64(t + Float64(2.0 * z))) + Float64(y * 5.0));
	else
		tmp = Float64(x * Float64(t_1 + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (x <= -1.05e-12)
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	elseif (x <= 1.18e-20)
		tmp = (x * (t + (2.0 * z))) + (y * 5.0);
	else
		tmp = x * (t_1 + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e-12], N[(x * N[(t + N[(t$95$1 + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.18e-20], N[(N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.04999999999999997e-12

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)} \]

   if -1.04999999999999997e-12 < x < 1.1800000000000001e-20

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.9%

      \[\leadsto x \cdot \left(\color{blue}{2 \cdot z} + t\right) + y \cdot 5 \]

   if 1.1800000000000001e-20 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-99} \lor \neg \left(x \leq 1.05 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.7e-99) (not (<= x 1.05e-84)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.7e-99) || !(x <= 1.05e-84)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (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 ((x <= (-3.7d-99)) .or. (.not. (x <= 1.05d-84))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.7e-99) || !(x <= 1.05e-84)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.7e-99) or not (x <= 1.05e-84):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.7e-99) || !(x <= 1.05e-84))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.7e-99) || ~((x <= 1.05e-84)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.7e-99], N[Not[LessEqual[x, 1.05e-84]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7e-99 or 1.04999999999999999e-84 < x

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 93.5%

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot \left(y + z\right)\right)} \]

   if -3.7e-99 < x < 1.04999999999999999e-84

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.9%

      \[\leadsto x \cdot \left(\color{blue}{2 \cdot z} + t\right) + y \cdot 5 \]

   4. Taylor expanded in z around 0 84.9%

      \[\leadsto \color{blue}{5 \cdot y + t \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-99} \lor \neg \left(x \leq 1.05 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-183} \lor \neg \left(x \leq 1.15 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.4e-183) (not (<= x 1.15e-85)))
   (* x (+ t (* 2.0 z)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.4e-183) || !(x <= 1.15e-85)) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.4d-183)) .or. (.not. (x <= 1.15d-85))) then
        tmp = x * (t + (2.0d0 * z))
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.4e-183) || !(x <= 1.15e-85)) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.4e-183) or not (x <= 1.15e-85):
		tmp = x * (t + (2.0 * z))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.4e-183) || !(x <= 1.15e-85))
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.4e-183) || ~((x <= 1.15e-85)))
		tmp = x * (t + (2.0 * z));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.4e-183], N[Not[LessEqual[x, 1.15e-85]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999993e-183 or 1.15e-85 < x

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.1%

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot z\right)} \]

   if -2.39999999999999993e-183 < x < 1.15e-85

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 67.7%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-183} \lor \neg \left(x \leq 1.15 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+44} \lor \neg \left(y \leq 5.1 \cdot 10^{+90}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.05e+44) (not (<= y 5.1e+90)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e+44) || !(y <= 5.1e+90)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	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 <= (-1.05d+44)) .or. (.not. (y <= 5.1d+90))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (2.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e+44) || !(y <= 5.1e+90)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.05e+44) or not (y <= 5.1e+90):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.05e+44) || !(y <= 5.1e+90))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.05e+44) || ~((y <= 5.1e+90)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.05e+44], N[Not[LessEqual[y, 5.1e+90]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999993e44 or 5.09999999999999959e90 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 83.2%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   5. Simplified 83.2%

      \[\leadsto \color{blue}{y \cdot \left(5 + x \cdot 2\right)} \]

   if -1.04999999999999993e44 < y < 5.09999999999999959e90

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.4%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+44} \lor \neg \left(y \leq 5.1 \cdot 10^{+90}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 96.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(t + 2 \cdot z\right) + y \cdot \left(5 + x \cdot 2\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ t (* 2.0 z))) (* y (+ 5.0 (* x 2.0)))))

C

double code(double x, double y, double z, double t) {
	return (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)));
}

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 * (t + (2.0d0 * z))) + (y * (5.0d0 + (x * 2.0d0)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)));
}

Python

def code(x, y, z, t):
	return (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(t + Float64(2.0 * z))) + Float64(y * Float64(5.0 + Float64(x * 2.0))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Add Preprocessing

3. Taylor expanded in y around 0 96.8%

   \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot z\right) + y \cdot \left(5 + 2 \cdot x\right)} \]

4. Final simplification 96.8%

   \[\leadsto x \cdot \left(t + 2 \cdot z\right) + y \cdot \left(5 + x \cdot 2\right) \]
5. Add Preprocessing

Alternative 11: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ t (+ y (+ z (+ y z))))) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * (t + (y + (z + (y + z))))) + (y * 5.0);
}

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 * (t + (y + (z + (y + z))))) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * (t + (y + (z + (y + z))))) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * (t + (y + (z + (y + z))))) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(t + Float64(y + Float64(z + Float64(y + z))))) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (t + (y + (z + (y + z))))) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(t + N[(y + N[(z + N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) + y \cdot 5 \]
4. Add Preprocessing

Alternative 12: 47.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-8} \lor \neg \left(x \leq 1.4 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.5e-8) (not (<= x 1.4e-20))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.5e-8) || !(x <= 1.4e-20)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.5d-8)) .or. (.not. (x <= 1.4d-20))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.5e-8) || !(x <= 1.4e-20)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.5e-8) or not (x <= 1.4e-20):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.5e-8) || !(x <= 1.4e-20))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.5e-8) || ~((x <= 1.4e-20)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.5e-8], N[Not[LessEqual[x, 1.4e-20]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000003e-8 or 1.4000000000000001e-20 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 43.8%

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

   5. Simplified 43.8%

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

   if -5.5000000000000003e-8 < x < 1.4000000000000001e-20

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 54.5%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-8} \lor \neg \left(x \leq 1.4 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* y 5.0))

C

double code(double x, double y, double z, double t) {
	return y * 5.0;
}

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 = y * 5.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return y * 5.0;
}

Python

def code(x, y, z, t):
	return y * 5.0

Julia

function code(x, y, z, t)
	return Float64(y * 5.0)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = y * 5.0;
end

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Add Preprocessing

3. Taylor expanded in x around 0 25.8%

   \[\leadsto \color{blue}{5 \cdot y} \]

4. Final simplification 25.8%

   \[\leadsto y \cdot 5 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))