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

Percentage Accurate: 99.9% → 99.9%

Time: 11.0s

Alternatives: 14

Speedup: 1.0×

• 26.6% 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: 99.9% 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: 99.9% 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-def 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: 45.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -2.55 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(2 \cdot y\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-131}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-71}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-24} \lor \neg \left(x \leq 3.2 \cdot 10^{+189}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -2.55e+42)
     (* x (* 2.0 y))
     (if (<= x -1.4e-91)
       t_1
       (if (<= x -6e-131)
         (* y 5.0)
         (if (<= x -7e-176)
           t_1
           (if (<= x 1.15e-71)
             (* y 5.0)
             (if (or (<= x 2.8e-24) (not (<= x 3.2e+189))) t_1 (* x t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -2.55e+42) {
		tmp = x * (2.0 * y);
	} else if (x <= -1.4e-91) {
		tmp = t_1;
	} else if (x <= -6e-131) {
		tmp = y * 5.0;
	} else if (x <= -7e-176) {
		tmp = t_1;
	} else if (x <= 1.15e-71) {
		tmp = y * 5.0;
	} else if ((x <= 2.8e-24) || !(x <= 3.2e+189)) {
		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 = 2.0d0 * (x * z)
    if (x <= (-2.55d+42)) then
        tmp = x * (2.0d0 * y)
    else if (x <= (-1.4d-91)) then
        tmp = t_1
    else if (x <= (-6d-131)) then
        tmp = y * 5.0d0
    else if (x <= (-7d-176)) then
        tmp = t_1
    else if (x <= 1.15d-71) then
        tmp = y * 5.0d0
    else if ((x <= 2.8d-24) .or. (.not. (x <= 3.2d+189))) 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 = 2.0 * (x * z);
	double tmp;
	if (x <= -2.55e+42) {
		tmp = x * (2.0 * y);
	} else if (x <= -1.4e-91) {
		tmp = t_1;
	} else if (x <= -6e-131) {
		tmp = y * 5.0;
	} else if (x <= -7e-176) {
		tmp = t_1;
	} else if (x <= 1.15e-71) {
		tmp = y * 5.0;
	} else if ((x <= 2.8e-24) || !(x <= 3.2e+189)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -2.55e+42:
		tmp = x * (2.0 * y)
	elif x <= -1.4e-91:
		tmp = t_1
	elif x <= -6e-131:
		tmp = y * 5.0
	elif x <= -7e-176:
		tmp = t_1
	elif x <= 1.15e-71:
		tmp = y * 5.0
	elif (x <= 2.8e-24) or not (x <= 3.2e+189):
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -2.55e+42)
		tmp = Float64(x * Float64(2.0 * y));
	elseif (x <= -1.4e-91)
		tmp = t_1;
	elseif (x <= -6e-131)
		tmp = Float64(y * 5.0);
	elseif (x <= -7e-176)
		tmp = t_1;
	elseif (x <= 1.15e-71)
		tmp = Float64(y * 5.0);
	elseif ((x <= 2.8e-24) || !(x <= 3.2e+189))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -2.55e+42)
		tmp = x * (2.0 * y);
	elseif (x <= -1.4e-91)
		tmp = t_1;
	elseif (x <= -6e-131)
		tmp = y * 5.0;
	elseif (x <= -7e-176)
		tmp = t_1;
	elseif (x <= 1.15e-71)
		tmp = y * 5.0;
	elseif ((x <= 2.8e-24) || ~((x <= 3.2e+189)))
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.55e+42], N[(x * N[(2.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.4e-91], t$95$1, If[LessEqual[x, -6e-131], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, -7e-176], t$95$1, If[LessEqual[x, 1.15e-71], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 2.8e-24], N[Not[LessEqual[x, 3.2e+189]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.55e42

   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-def 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%

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

   6. Taylor expanded in y around inf 49.1%

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

      1. associate-*r* 49.1%

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

      2. *-commutative 49.1%

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

      3. associate-*r* 49.1%

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

   8. Simplified 49.1%

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

   if -2.55e42 < x < -1.4e-91 or -5.99999999999999992e-131 < x < -7e-176 or 1.1499999999999999e-71 < x < 2.8000000000000002e-24 or 3.2000000000000001e189 < 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 z around inf 59.4%

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

   if -1.4e-91 < x < -5.99999999999999992e-131 or -7e-176 < x < 1.1499999999999999e-71

   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 78.5%

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

   if 2.8000000000000002e-24 < x < 3.2000000000000001e189

   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 46.4%

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

   5. Simplified 46.4%

      \[\leadsto \color{blue}{x \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(2 \cdot y\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-91}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-131}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-176}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-71}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-24} \lor \neg \left(x \leq 3.2 \cdot 10^{+189}\right):\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-176}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-72}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-24} \lor \neg \left(x \leq 2.4 \cdot 10^{+26}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x (+ y z)))))
   (if (<= x -1.4e-91)
     t_1
     (if (<= x -6.8e-130)
       (* y 5.0)
       (if (<= x -7e-176)
         (* 2.0 (* x z))
         (if (<= x 8.5e-72)
           (* y 5.0)
           (if (or (<= x 4.1e-24) (not (<= x 2.4e+26))) t_1 (* x t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * (y + z));
	double tmp;
	if (x <= -1.4e-91) {
		tmp = t_1;
	} else if (x <= -6.8e-130) {
		tmp = y * 5.0;
	} else if (x <= -7e-176) {
		tmp = 2.0 * (x * z);
	} else if (x <= 8.5e-72) {
		tmp = y * 5.0;
	} else if ((x <= 4.1e-24) || !(x <= 2.4e+26)) {
		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 = 2.0d0 * (x * (y + z))
    if (x <= (-1.4d-91)) then
        tmp = t_1
    else if (x <= (-6.8d-130)) then
        tmp = y * 5.0d0
    else if (x <= (-7d-176)) then
        tmp = 2.0d0 * (x * z)
    else if (x <= 8.5d-72) then
        tmp = y * 5.0d0
    else if ((x <= 4.1d-24) .or. (.not. (x <= 2.4d+26))) 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 = 2.0 * (x * (y + z));
	double tmp;
	if (x <= -1.4e-91) {
		tmp = t_1;
	} else if (x <= -6.8e-130) {
		tmp = y * 5.0;
	} else if (x <= -7e-176) {
		tmp = 2.0 * (x * z);
	} else if (x <= 8.5e-72) {
		tmp = y * 5.0;
	} else if ((x <= 4.1e-24) || !(x <= 2.4e+26)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * (y + z))
	tmp = 0
	if x <= -1.4e-91:
		tmp = t_1
	elif x <= -6.8e-130:
		tmp = y * 5.0
	elif x <= -7e-176:
		tmp = 2.0 * (x * z)
	elif x <= 8.5e-72:
		tmp = y * 5.0
	elif (x <= 4.1e-24) or not (x <= 2.4e+26):
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * Float64(y + z)))
	tmp = 0.0
	if (x <= -1.4e-91)
		tmp = t_1;
	elseif (x <= -6.8e-130)
		tmp = Float64(y * 5.0);
	elseif (x <= -7e-176)
		tmp = Float64(2.0 * Float64(x * z));
	elseif (x <= 8.5e-72)
		tmp = Float64(y * 5.0);
	elseif ((x <= 4.1e-24) || !(x <= 2.4e+26))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * (y + z));
	tmp = 0.0;
	if (x <= -1.4e-91)
		tmp = t_1;
	elseif (x <= -6.8e-130)
		tmp = y * 5.0;
	elseif (x <= -7e-176)
		tmp = 2.0 * (x * z);
	elseif (x <= 8.5e-72)
		tmp = y * 5.0;
	elseif ((x <= 4.1e-24) || ~((x <= 2.4e+26)))
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e-91], t$95$1, If[LessEqual[x, -6.8e-130], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, -7e-176], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-72], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 4.1e-24], N[Not[LessEqual[x, 2.4e+26]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.4e-91 or 8.50000000000000008e-72 < x < 4.10000000000000015e-24 or 2.40000000000000005e26 < 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-def 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 96.8%

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

   6. Taylor expanded in t around 0 68.4%

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

      1. +-commutative 68.4%

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

   8. Simplified 68.4%

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

   if -1.4e-91 < x < -6.8000000000000001e-130 or -7e-176 < x < 8.50000000000000008e-72

   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 78.5%

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

   if -6.8000000000000001e-130 < x < -7e-176

   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 61.1%

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

   if 4.10000000000000015e-24 < x < 2.40000000000000005e26

   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 t around inf 51.6%

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

   5. Simplified 51.6%

      \[\leadsto \color{blue}{x \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-91}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-176}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-72}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-24} \lor \neg \left(x \leq 2.4 \cdot 10^{+26}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;x \leq -200000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-131}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-72}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-24}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))) (t_2 (* x (+ t (* 2.0 y)))))
   (if (<= x -200000.0)
     t_2
     (if (<= x -1.45e-92)
       t_1
       (if (<= x -6e-131)
         (* y 5.0)
         (if (<= x -7e-176)
           t_1
           (if (<= x 9.5e-72)
             (* y 5.0)
             (if (<= x 1.45e-24) (* 2.0 (* x (+ y z))) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -200000.0) {
		tmp = t_2;
	} else if (x <= -1.45e-92) {
		tmp = t_1;
	} else if (x <= -6e-131) {
		tmp = y * 5.0;
	} else if (x <= -7e-176) {
		tmp = t_1;
	} else if (x <= 9.5e-72) {
		tmp = y * 5.0;
	} else if (x <= 1.45e-24) {
		tmp = 2.0 * (x * (y + z));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    t_2 = x * (t + (2.0d0 * y))
    if (x <= (-200000.0d0)) then
        tmp = t_2
    else if (x <= (-1.45d-92)) then
        tmp = t_1
    else if (x <= (-6d-131)) then
        tmp = y * 5.0d0
    else if (x <= (-7d-176)) then
        tmp = t_1
    else if (x <= 9.5d-72) then
        tmp = y * 5.0d0
    else if (x <= 1.45d-24) then
        tmp = 2.0d0 * (x * (y + z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -200000.0) {
		tmp = t_2;
	} else if (x <= -1.45e-92) {
		tmp = t_1;
	} else if (x <= -6e-131) {
		tmp = y * 5.0;
	} else if (x <= -7e-176) {
		tmp = t_1;
	} else if (x <= 9.5e-72) {
		tmp = y * 5.0;
	} else if (x <= 1.45e-24) {
		tmp = 2.0 * (x * (y + z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	t_2 = x * (t + (2.0 * y))
	tmp = 0
	if x <= -200000.0:
		tmp = t_2
	elif x <= -1.45e-92:
		tmp = t_1
	elif x <= -6e-131:
		tmp = y * 5.0
	elif x <= -7e-176:
		tmp = t_1
	elif x <= 9.5e-72:
		tmp = y * 5.0
	elif x <= 1.45e-24:
		tmp = 2.0 * (x * (y + z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	t_2 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (x <= -200000.0)
		tmp = t_2;
	elseif (x <= -1.45e-92)
		tmp = t_1;
	elseif (x <= -6e-131)
		tmp = Float64(y * 5.0);
	elseif (x <= -7e-176)
		tmp = t_1;
	elseif (x <= 9.5e-72)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.45e-24)
		tmp = Float64(2.0 * Float64(x * Float64(y + z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	t_2 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (x <= -200000.0)
		tmp = t_2;
	elseif (x <= -1.45e-92)
		tmp = t_1;
	elseif (x <= -6e-131)
		tmp = y * 5.0;
	elseif (x <= -7e-176)
		tmp = t_1;
	elseif (x <= 9.5e-72)
		tmp = y * 5.0;
	elseif (x <= 1.45e-24)
		tmp = 2.0 * (x * (y + z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -200000.0], t$95$2, If[LessEqual[x, -1.45e-92], t$95$1, If[LessEqual[x, -6e-131], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, -7e-176], t$95$1, If[LessEqual[x, 9.5e-72], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.45e-24], N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2e5 or 1.4499999999999999e-24 < 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-def 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 96.0%

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

   6. Taylor expanded in z around 0 75.6%

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

   if -2e5 < x < -1.44999999999999992e-92 or -5.99999999999999992e-131 < x < -7e-176

   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 z around inf 65.9%

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

   if -1.44999999999999992e-92 < x < -5.99999999999999992e-131 or -7e-176 < x < 9.4999999999999998e-72

   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 78.5%

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

   if 9.4999999999999998e-72 < x < 1.4499999999999999e-24

   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-def 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 92.3%

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

   6. Taylor expanded in t around 0 76.0%

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

      1. +-commutative 76.0%

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

   8. Simplified 76.0%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(z + y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -200000:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-92}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-131}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-176}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-72}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-24}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-72}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-24} \lor \neg \left(x \leq 9.2 \cdot 10^{+187}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -1.2e-92)
     t_1
     (if (<= x -2e-130)
       (* y 5.0)
       (if (<= x -7e-176)
         t_1
         (if (<= x 4.9e-72)
           (* y 5.0)
           (if (or (<= x 2.35e-24) (not (<= x 9.2e+187))) t_1 (* x t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -1.2e-92) {
		tmp = t_1;
	} else if (x <= -2e-130) {
		tmp = y * 5.0;
	} else if (x <= -7e-176) {
		tmp = t_1;
	} else if (x <= 4.9e-72) {
		tmp = y * 5.0;
	} else if ((x <= 2.35e-24) || !(x <= 9.2e+187)) {
		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 = 2.0d0 * (x * z)
    if (x <= (-1.2d-92)) then
        tmp = t_1
    else if (x <= (-2d-130)) then
        tmp = y * 5.0d0
    else if (x <= (-7d-176)) then
        tmp = t_1
    else if (x <= 4.9d-72) then
        tmp = y * 5.0d0
    else if ((x <= 2.35d-24) .or. (.not. (x <= 9.2d+187))) 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 = 2.0 * (x * z);
	double tmp;
	if (x <= -1.2e-92) {
		tmp = t_1;
	} else if (x <= -2e-130) {
		tmp = y * 5.0;
	} else if (x <= -7e-176) {
		tmp = t_1;
	} else if (x <= 4.9e-72) {
		tmp = y * 5.0;
	} else if ((x <= 2.35e-24) || !(x <= 9.2e+187)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -1.2e-92:
		tmp = t_1
	elif x <= -2e-130:
		tmp = y * 5.0
	elif x <= -7e-176:
		tmp = t_1
	elif x <= 4.9e-72:
		tmp = y * 5.0
	elif (x <= 2.35e-24) or not (x <= 9.2e+187):
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -1.2e-92)
		tmp = t_1;
	elseif (x <= -2e-130)
		tmp = Float64(y * 5.0);
	elseif (x <= -7e-176)
		tmp = t_1;
	elseif (x <= 4.9e-72)
		tmp = Float64(y * 5.0);
	elseif ((x <= 2.35e-24) || !(x <= 9.2e+187))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -1.2e-92)
		tmp = t_1;
	elseif (x <= -2e-130)
		tmp = y * 5.0;
	elseif (x <= -7e-176)
		tmp = t_1;
	elseif (x <= 4.9e-72)
		tmp = y * 5.0;
	elseif ((x <= 2.35e-24) || ~((x <= 9.2e+187)))
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e-92], t$95$1, If[LessEqual[x, -2e-130], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, -7e-176], t$95$1, If[LessEqual[x, 4.9e-72], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 2.35e-24], N[Not[LessEqual[x, 9.2e+187]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2000000000000001e-92 or -2.0000000000000002e-130 < x < -7e-176 or 4.89999999999999991e-72 < x < 2.34999999999999996e-24 or 9.20000000000000015e187 < 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 z around inf 51.6%

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

   if -1.2000000000000001e-92 < x < -2.0000000000000002e-130 or -7e-176 < x < 4.89999999999999991e-72

   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 78.5%

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

   if 2.34999999999999996e-24 < x < 9.20000000000000015e187

   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 46.4%

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

   5. Simplified 46.4%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-92}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-176}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-72}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-24} \lor \neg \left(x \leq 9.2 \cdot 10^{+187}\right):\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ t_2 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;x \leq -2.65 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-132}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 z)))) (t_2 (* x (+ t (* 2.0 y)))))
   (if (<= x -2.65e+48)
     t_2
     (if (<= x -2.4e-187)
       t_1
       (if (<= x 6e-132) (* y 5.0) (if (<= x 3e+27) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -2.65e+48) {
		tmp = t_2;
	} else if (x <= -2.4e-187) {
		tmp = t_1;
	} else if (x <= 6e-132) {
		tmp = y * 5.0;
	} else if (x <= 3e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * z))
    t_2 = x * (t + (2.0d0 * y))
    if (x <= (-2.65d+48)) then
        tmp = t_2
    else if (x <= (-2.4d-187)) then
        tmp = t_1
    else if (x <= 6d-132) then
        tmp = y * 5.0d0
    else if (x <= 3d+27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -2.65e+48) {
		tmp = t_2;
	} else if (x <= -2.4e-187) {
		tmp = t_1;
	} else if (x <= 6e-132) {
		tmp = y * 5.0;
	} else if (x <= 3e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * z))
	t_2 = x * (t + (2.0 * y))
	tmp = 0
	if x <= -2.65e+48:
		tmp = t_2
	elif x <= -2.4e-187:
		tmp = t_1
	elif x <= 6e-132:
		tmp = y * 5.0
	elif x <= 3e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * z)))
	t_2 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (x <= -2.65e+48)
		tmp = t_2;
	elseif (x <= -2.4e-187)
		tmp = t_1;
	elseif (x <= 6e-132)
		tmp = Float64(y * 5.0);
	elseif (x <= 3e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * z));
	t_2 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (x <= -2.65e+48)
		tmp = t_2;
	elseif (x <= -2.4e-187)
		tmp = t_1;
	elseif (x <= 6e-132)
		tmp = y * 5.0;
	elseif (x <= 3e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.65e+48], t$95$2, If[LessEqual[x, -2.4e-187], t$95$1, If[LessEqual[x, 6e-132], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 3e+27], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.65e48 or 2.99999999999999976e27 < 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-def 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%

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

   6. Taylor expanded in z around 0 78.8%

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

   if -2.65e48 < x < -2.40000000000000013e-187 or 5.9999999999999999e-132 < x < 2.99999999999999976e27

   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 71.5%

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

   if -2.40000000000000013e-187 < x < 5.9999999999999999e-132

   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 86.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-132}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -28500 \lor \neg \left(x \leq 3.7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(x \cdot 2\right) + x \cdot t\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -28500.0) (not (<= x 3.7e-7)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (+ (* z (* x 2.0)) (* x t)) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -28500.0) || !(x <= 3.7e-7)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = ((z * (x * 2.0)) + (x * t)) + (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 <= (-28500.0d0)) .or. (.not. (x <= 3.7d-7))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = ((z * (x * 2.0d0)) + (x * t)) + (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 <= -28500.0) || !(x <= 3.7e-7)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = ((z * (x * 2.0)) + (x * t)) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -28500.0) or not (x <= 3.7e-7):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = ((z * (x * 2.0)) + (x * t)) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -28500.0) || !(x <= 3.7e-7))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(Float64(z * Float64(x * 2.0)) + Float64(x * t)) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -28500.0) || ~((x <= 3.7e-7)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = ((z * (x * 2.0)) + (x * t)) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -28500.0], N[Not[LessEqual[x, 3.7e-7]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -28500 or 3.70000000000000004e-7 < 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-def 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 99.2%

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

   if -28500 < x < 3.70000000000000004e-7

   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 99.6%

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

      1. distribute-rgt-in 99.6%

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

      2. *-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*l* 99.6%

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

   5. Applied egg-rr 99.6%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -28500 \lor \neg \left(x \leq 3.7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(x \cdot 2\right) + x \cdot t\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -28500 \lor \neg \left(x \leq 3.7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -28500.0) (not (<= x 3.7e-7)))
   (* 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 <= -28500.0) || !(x <= 3.7e-7)) {
		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 <= (-28500.0d0)) .or. (.not. (x <= 3.7d-7))) 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 <= -28500.0) || !(x <= 3.7e-7)) {
		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 <= -28500.0) or not (x <= 3.7e-7):
		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 <= -28500.0) || !(x <= 3.7e-7))
		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 <= -28500.0) || ~((x <= 3.7e-7)))
		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, -28500.0], N[Not[LessEqual[x, 3.7e-7]], $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 < -28500 or 3.70000000000000004e-7 < 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-def 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 99.2%

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

   if -28500 < x < 3.70000000000000004e-7

   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 99.6%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -28500 \lor \neg \left(x \leq 3.7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-187} \lor \neg \left(x \leq 7 \cdot 10^{-147}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.3e-187) (not (<= x 7e-147)))
   (* x (+ (* 2.0 (+ y z)) t))
   (* y (+ 5.0 (* x 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.3e-187) || !(x <= 7e-147)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = y * (5.0 + (x * 2.0));
	}
	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 <= (-2.3d-187)) .or. (.not. (x <= 7d-147))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = y * (5.0d0 + (x * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.3e-187) || !(x <= 7e-147)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = y * (5.0 + (x * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.3e-187) or not (x <= 7e-147):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = y * (5.0 + (x * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.3e-187) || !(x <= 7e-147))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.3e-187) || ~((x <= 7e-147)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = y * (5.0 + (x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.3e-187], N[Not[LessEqual[x, 7e-147]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.29999999999999998e-187 or 7.00000000000000007e-147 < 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-def 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+ 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 88.0%

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

   if -2.29999999999999998e-187 < x < 7.00000000000000007e-147

   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 y around inf 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-187} \lor \neg \left(x \leq 7 \cdot 10^{-147}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -28500 \lor \neg \left(x \leq 9.8 \cdot 10^{-126}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -28500.0) (not (<= x 9.8e-126)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* z (* x 2.0)) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -28500.0) || !(x <= 9.8e-126)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (z * (x * 2.0)) + (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 <= (-28500.0d0)) .or. (.not. (x <= 9.8d-126))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (z * (x * 2.0d0)) + (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 <= -28500.0) || !(x <= 9.8e-126)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (z * (x * 2.0)) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -28500.0) or not (x <= 9.8e-126):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (z * (x * 2.0)) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -28500.0) || !(x <= 9.8e-126))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(z * Float64(x * 2.0)) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -28500.0) || ~((x <= 9.8e-126)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (z * (x * 2.0)) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -28500.0], N[Not[LessEqual[x, 9.8e-126]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -28500 or 9.8000000000000002e-126 < 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-def 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. Taylor expanded in x around inf 93.5%

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

   if -28500 < x < 9.8000000000000002e-126

   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. Step-by-step derivation

      1. distribute-rgt-in 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. count-2 99.9%

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

      6. *-commutative 99.9%

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

      7. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf 93.7%

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

      1. associate-*r* 93.7%

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

      2. *-commutative 93.7%

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

   7. Simplified 93.7%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -28500 \lor \neg \left(x \leq 9.8 \cdot 10^{-126}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+26} \lor \neg \left(y \leq 10^{+42}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e+26) (not (<= y 1e+42)))
   (* 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 <= -1.9e+26) || !(y <= 1e+42)) {
		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 <= (-1.9d+26)) .or. (.not. (y <= 1d+42))) 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 <= -1.9e+26) || !(y <= 1e+42)) {
		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 <= -1.9e+26) or not (y <= 1e+42):
		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 <= -1.9e+26) || !(y <= 1e+42))
		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 <= -1.9e+26) || ~((y <= 1e+42)))
		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, -1.9e+26], N[Not[LessEqual[y, 1e+42]], $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 < -1.9000000000000001e26 or 1.00000000000000004e42 < 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 77.5%

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

   5. Simplified 77.5%

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

   if -1.9000000000000001e26 < y < 1.00000000000000004e42

   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 75.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+26} \lor \neg \left(y \leq 10^{+42}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.9% 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 13: 47.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-15} \lor \neg \left(x \leq 9.5 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9e-15) (not (<= x 9.5e-18))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e-15) || !(x <= 9.5e-18)) {
		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 <= (-9d-15)) .or. (.not. (x <= 9.5d-18))) 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 <= -9e-15) || !(x <= 9.5e-18)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9e-15) or not (x <= 9.5e-18):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9e-15) || !(x <= 9.5e-18))
		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 <= -9e-15) || ~((x <= 9.5e-18)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9e-15], N[Not[LessEqual[x, 9.5e-18]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.9999999999999995e-15 or 9.5000000000000003e-18 < 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 t around inf 39.2%

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

   5. Simplified 39.2%

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

   if -8.9999999999999995e-15 < x < 9.5000000000000003e-18

   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 61.0%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-15} \lor \neg \left(x \leq 9.5 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.1% 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 33.2%

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

4. Final simplification 33.2%

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

Reproduce

herbie shell --seed 2024036 
(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)))