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

Percentage Accurate: 99.8% → 99.8%

Time: 12.4s

Alternatives: 19

Speedup: 1.0×

• 26.7% 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 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. Final simplification 100.0%

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

Alternative 2: 56.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{if}\;t \leq -1.32 \cdot 10^{+100}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-207}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x (+ y z)))))
   (if (<= t -1.32e+100)
     (* x t)
     (if (<= t -1.5e+29)
       t_1
       (if (<= t -6e-207)
         (* y (+ x 5.0))
         (if (<= t 1.7e-199)
           t_1
           (if (<= t 4.5e-173) (* y 5.0) (if (<= t 3.4e+58) 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 (t <= -1.32e+100) {
		tmp = x * t;
	} else if (t <= -1.5e+29) {
		tmp = t_1;
	} else if (t <= -6e-207) {
		tmp = y * (x + 5.0);
	} else if (t <= 1.7e-199) {
		tmp = t_1;
	} else if (t <= 4.5e-173) {
		tmp = y * 5.0;
	} else if (t <= 3.4e+58) {
		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 (t <= (-1.32d+100)) then
        tmp = x * t
    else if (t <= (-1.5d+29)) then
        tmp = t_1
    else if (t <= (-6d-207)) then
        tmp = y * (x + 5.0d0)
    else if (t <= 1.7d-199) then
        tmp = t_1
    else if (t <= 4.5d-173) then
        tmp = y * 5.0d0
    else if (t <= 3.4d+58) 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 (t <= -1.32e+100) {
		tmp = x * t;
	} else if (t <= -1.5e+29) {
		tmp = t_1;
	} else if (t <= -6e-207) {
		tmp = y * (x + 5.0);
	} else if (t <= 1.7e-199) {
		tmp = t_1;
	} else if (t <= 4.5e-173) {
		tmp = y * 5.0;
	} else if (t <= 3.4e+58) {
		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 t <= -1.32e+100:
		tmp = x * t
	elif t <= -1.5e+29:
		tmp = t_1
	elif t <= -6e-207:
		tmp = y * (x + 5.0)
	elif t <= 1.7e-199:
		tmp = t_1
	elif t <= 4.5e-173:
		tmp = y * 5.0
	elif t <= 3.4e+58:
		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 (t <= -1.32e+100)
		tmp = Float64(x * t);
	elseif (t <= -1.5e+29)
		tmp = t_1;
	elseif (t <= -6e-207)
		tmp = Float64(y * Float64(x + 5.0));
	elseif (t <= 1.7e-199)
		tmp = t_1;
	elseif (t <= 4.5e-173)
		tmp = Float64(y * 5.0);
	elseif (t <= 3.4e+58)
		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 (t <= -1.32e+100)
		tmp = x * t;
	elseif (t <= -1.5e+29)
		tmp = t_1;
	elseif (t <= -6e-207)
		tmp = y * (x + 5.0);
	elseif (t <= 1.7e-199)
		tmp = t_1;
	elseif (t <= 4.5e-173)
		tmp = y * 5.0;
	elseif (t <= 3.4e+58)
		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[t, -1.32e+100], N[(x * t), $MachinePrecision], If[LessEqual[t, -1.5e+29], t$95$1, If[LessEqual[t, -6e-207], N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-199], t$95$1, If[LessEqual[t, 4.5e-173], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 3.4e+58], t$95$1, N[(x * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.32e100 or 3.4000000000000001e58 < t

   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 69.1%

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

   5. Simplified 69.1%

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

   if -1.32e100 < t < -1.5e29 or -5.9999999999999999e-207 < t < 1.70000000000000003e-199 or 4.50000000000000018e-173 < t < 3.4000000000000001e58

   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 97.9%

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

   4. Taylor expanded in x around inf 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in t around 0 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

      3. associate-*r* 66.8%

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

      4. *-commutative 66.8%

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

      5. associate-*r* 66.8%

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

      6. *-commutative 66.8%

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

      7. distribute-lft-out 67.9%

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

      8. associate-*r* 67.9%

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

      9. distribute-lft-out 67.9%

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

      10. *-commutative 67.9%

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

      11. distribute-lft-out 67.9%

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

      12. associate-*l* 67.9%

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

   9. Simplified 67.9%

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

   if -1.5e29 < t < -5.9999999999999999e-207

   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 93.4%

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

   4. Taylor expanded in y around inf 70.4%

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

   if 1.70000000000000003e-199 < t < 4.50000000000000018e-173

   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 78.0%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+100}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+29}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-207}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-199}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 44.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+39}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 10^{-301}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-140}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+57}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.2e+39)
   (* x t)
   (if (<= t 1e-301)
     (* y 5.0)
     (if (<= t 1.15e-259)
       (* y (* x 2.0))
       (if (<= t 1.15e-140)
         (* y 5.0)
         (if (<= t 4.7e+57) (* 2.0 (* x z)) (* x t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.2e+39) {
		tmp = x * t;
	} else if (t <= 1e-301) {
		tmp = y * 5.0;
	} else if (t <= 1.15e-259) {
		tmp = y * (x * 2.0);
	} else if (t <= 1.15e-140) {
		tmp = y * 5.0;
	} else if (t <= 4.7e+57) {
		tmp = 2.0 * (x * z);
	} 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) :: tmp
    if (t <= (-5.2d+39)) then
        tmp = x * t
    else if (t <= 1d-301) then
        tmp = y * 5.0d0
    else if (t <= 1.15d-259) then
        tmp = y * (x * 2.0d0)
    else if (t <= 1.15d-140) then
        tmp = y * 5.0d0
    else if (t <= 4.7d+57) then
        tmp = 2.0d0 * (x * z)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.2e+39) {
		tmp = x * t;
	} else if (t <= 1e-301) {
		tmp = y * 5.0;
	} else if (t <= 1.15e-259) {
		tmp = y * (x * 2.0);
	} else if (t <= 1.15e-140) {
		tmp = y * 5.0;
	} else if (t <= 4.7e+57) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.2e+39:
		tmp = x * t
	elif t <= 1e-301:
		tmp = y * 5.0
	elif t <= 1.15e-259:
		tmp = y * (x * 2.0)
	elif t <= 1.15e-140:
		tmp = y * 5.0
	elif t <= 4.7e+57:
		tmp = 2.0 * (x * z)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.2e+39)
		tmp = Float64(x * t);
	elseif (t <= 1e-301)
		tmp = Float64(y * 5.0);
	elseif (t <= 1.15e-259)
		tmp = Float64(y * Float64(x * 2.0));
	elseif (t <= 1.15e-140)
		tmp = Float64(y * 5.0);
	elseif (t <= 4.7e+57)
		tmp = Float64(2.0 * Float64(x * z));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.2e+39)
		tmp = x * t;
	elseif (t <= 1e-301)
		tmp = y * 5.0;
	elseif (t <= 1.15e-259)
		tmp = y * (x * 2.0);
	elseif (t <= 1.15e-140)
		tmp = y * 5.0;
	elseif (t <= 4.7e+57)
		tmp = 2.0 * (x * z);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.2e+39], N[(x * t), $MachinePrecision], If[LessEqual[t, 1e-301], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 1.15e-259], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-140], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 4.7e+57], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.2e39 or 4.7000000000000003e57 < t

   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 65.8%

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

   5. Simplified 65.8%

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

   if -5.2e39 < t < 1.00000000000000007e-301 or 1.15e-259 < t < 1.1500000000000001e-140

   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 47.3%

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

   if 1.00000000000000007e-301 < t < 1.15e-259

   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 inf 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in x around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. *-commutative 64.9%

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

      3. associate-*r* 64.9%

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

   8. Simplified 64.9%

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

   if 1.1500000000000001e-140 < t < 4.7000000000000003e57

   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 50.9%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+39}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 10^{-301}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-140}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+57}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-9} \lor \neg \left(x \leq 2.4 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + 2 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.65e-9) (not (<= x 2.4e-23)))
   (* x (+ t (+ (* 2.0 (+ y z)) (* 5.0 (/ y x)))))
   (+ (* y 5.0) (* x (+ t (+ y (* 2.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.65e-9) || !(x <= 2.4e-23)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (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 ((x <= (-1.65d-9)) .or. (.not. (x <= 2.4d-23))) then
        tmp = x * (t + ((2.0d0 * (y + z)) + (5.0d0 * (y / x))))
    else
        tmp = (y * 5.0d0) + (x * (t + (y + (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 ((x <= -1.65e-9) || !(x <= 2.4e-23)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.65e-9) or not (x <= 2.4e-23):
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))))
	else:
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.65e-9) || !(x <= 2.4e-23))
		tmp = Float64(x * Float64(t + Float64(Float64(2.0 * Float64(y + z)) + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + Float64(2.0 * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.65e-9) || ~((x <= 2.4e-23)))
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	else
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.65e-9], N[Not[LessEqual[x, 2.4e-23]], $MachinePrecision]], N[(x * N[(t + N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65000000000000009e-9 or 2.39999999999999996e-23 < 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 99.9%

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

   if -1.65000000000000009e-9 < x < 2.39999999999999996e-23

   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%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-9} \lor \neg \left(x \leq 2.4 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + 2 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -34000000000000 \lor \neg \left(x \leq 6.2 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + 2 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -34000000000000.0) (not (<= x 6.2e-6)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x (+ t (+ y (* 2.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -34000000000000.0) || !(x <= 6.2e-6)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (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 ((x <= (-34000000000000.0d0)) .or. (.not. (x <= 6.2d-6))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (x * (t + (y + (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 ((x <= -34000000000000.0) || !(x <= 6.2e-6)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -34000000000000.0) or not (x <= 6.2e-6):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -34000000000000.0) || !(x <= 6.2e-6))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + Float64(2.0 * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -34000000000000.0) || ~((x <= 6.2e-6)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -34000000000000.0], N[Not[LessEqual[x, 6.2e-6]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4e13 or 6.1999999999999999e-6 < 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 99.1%

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

   if -3.4e13 < x < 6.1999999999999999e-6

   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 99.1%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -34000000000000 \lor \neg \left(x \leq 6.2 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + 2 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7600000:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+122}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -8.5e+27)
     t_1
     (if (<= y 7600000.0)
       (* x (+ t (* 2.0 z)))
       (if (<= y 3.1e+122) (+ (* y 5.0) (* x t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -8.5e+27) {
		tmp = t_1;
	} else if (y <= 7600000.0) {
		tmp = x * (t + (2.0 * z));
	} else if (y <= 3.1e+122) {
		tmp = (y * 5.0) + (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 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-8.5d+27)) then
        tmp = t_1
    else if (y <= 7600000.0d0) then
        tmp = x * (t + (2.0d0 * z))
    else if (y <= 3.1d+122) then
        tmp = (y * 5.0d0) + (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 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -8.5e+27) {
		tmp = t_1;
	} else if (y <= 7600000.0) {
		tmp = x * (t + (2.0 * z));
	} else if (y <= 3.1e+122) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -8.5e+27:
		tmp = t_1
	elif y <= 7600000.0:
		tmp = x * (t + (2.0 * z))
	elif y <= 3.1e+122:
		tmp = (y * 5.0) + (x * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -8.5e+27)
		tmp = t_1;
	elseif (y <= 7600000.0)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	elseif (y <= 3.1e+122)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -8.5e+27)
		tmp = t_1;
	elseif (y <= 7600000.0)
		tmp = x * (t + (2.0 * z));
	elseif (y <= 3.1e+122)
		tmp = (y * 5.0) + (x * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+27], t$95$1, If[LessEqual[y, 7600000.0], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+122], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5e27 or 3.09999999999999999e122 < 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 87.1%

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

   5. Simplified 87.1%

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

   if -8.5e27 < y < 7.6e6

   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 83.0%

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

   if 7.6e6 < y < 3.09999999999999999e122

   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. Taylor expanded in x around inf 84.2%

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

   6. Taylor expanded in x around 0 66.0%

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

   7. Taylor expanded in x around 0 81.6%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 7600000:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+122}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-81} \lor \neg \left(y \leq 4200000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4e-81) (not (<= y 4200000.0)))
   (+ (* y (+ 5.0 (* x 2.0))) (* x t))
   (* x (+ (* 2.0 (+ y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e-81) || !(y <= 4200000.0)) {
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	} else {
		tmp = x * ((2.0 * (y + z)) + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.4d-81)) .or. (.not. (y <= 4200000.0d0))) then
        tmp = (y * (5.0d0 + (x * 2.0d0))) + (x * t)
    else
        tmp = x * ((2.0d0 * (y + z)) + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e-81) || !(y <= 4200000.0)) {
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	} else {
		tmp = x * ((2.0 * (y + z)) + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.4e-81) or not (y <= 4200000.0):
		tmp = (y * (5.0 + (x * 2.0))) + (x * t)
	else:
		tmp = x * ((2.0 * (y + z)) + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.4e-81) || !(y <= 4200000.0))
		tmp = Float64(Float64(y * Float64(5.0 + Float64(x * 2.0))) + Float64(x * t));
	else
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.4e-81) || ~((y <= 4200000.0)))
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	else
		tmp = x * ((2.0 * (y + z)) + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.4e-81], N[Not[LessEqual[y, 4200000.0]], $MachinePrecision]], N[(N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3999999999999999e-81 or 4.2e6 < 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 0 95.4%

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

   4. Taylor expanded in z around 0 90.7%

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

   if -3.3999999999999999e-81 < y < 4.2e6

   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 90.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-81} \lor \neg \left(y \leq 4200000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-81} \lor \neg \left(y \leq 180000000\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2e-81) (not (<= y 180000000.0)))
   (+ (* y 5.0) (* x (+ t (+ y y))))
   (* x (+ (* 2.0 (+ y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-81) || !(y <= 180000000.0)) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else {
		tmp = x * ((2.0 * (y + z)) + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2d-81)) .or. (.not. (y <= 180000000.0d0))) then
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    else
        tmp = x * ((2.0d0 * (y + z)) + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-81) || !(y <= 180000000.0)) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else {
		tmp = x * ((2.0 * (y + z)) + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2e-81) or not (y <= 180000000.0):
		tmp = (y * 5.0) + (x * (t + (y + y)))
	else:
		tmp = x * ((2.0 * (y + z)) + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2e-81) || !(y <= 180000000.0))
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	else
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2e-81) || ~((y <= 180000000.0)))
		tmp = (y * 5.0) + (x * (t + (y + y)));
	else
		tmp = x * ((2.0 * (y + z)) + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2e-81], N[Not[LessEqual[y, 180000000.0]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9999999999999999e-81 or 1.8e8 < 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 93.3%

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

   if -1.9999999999999999e-81 < y < 1.8e8

   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 90.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-81} \lor \neg \left(y \leq 180000000\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+92} \lor \neg \left(t \leq 1.45 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.5e+92) (not (<= t 1.45e+57)))
   (+ (* y 5.0) (* x (+ t (+ y y))))
   (+ (* y 5.0) (* (+ y z) (* x 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e+92) || !(t <= 1.45e+57)) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else {
		tmp = (y * 5.0) + ((y + z) * (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 ((t <= (-1.5d+92)) .or. (.not. (t <= 1.45d+57))) then
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    else
        tmp = (y * 5.0d0) + ((y + z) * (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 ((t <= -1.5e+92) || !(t <= 1.45e+57)) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else {
		tmp = (y * 5.0) + ((y + z) * (x * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.5e+92) or not (t <= 1.45e+57):
		tmp = (y * 5.0) + (x * (t + (y + y)))
	else:
		tmp = (y * 5.0) + ((y + z) * (x * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.5e+92) || !(t <= 1.45e+57))
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(Float64(y + z) * Float64(x * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.5e+92) || ~((t <= 1.45e+57)))
		tmp = (y * 5.0) + (x * (t + (y + y)));
	else
		tmp = (y * 5.0) + ((y + z) * (x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.5e+92], N[Not[LessEqual[t, 1.45e+57]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.50000000000000007e92 or 1.4500000000000001e57 < t

   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 91.9%

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

   if -1.50000000000000007e92 < t < 1.4500000000000001e57

   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 0 93.2%

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

   5. Simplified 93.2%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+92} \lor \neg \left(t \leq 1.45 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.4e+39)
   (* x t)
   (if (<= t 5.2e-145) (* y 5.0) (if (<= t 3.8e+53) (* 2.0 (* x z)) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.4e+39) {
		tmp = x * t;
	} else if (t <= 5.2e-145) {
		tmp = y * 5.0;
	} else if (t <= 3.8e+53) {
		tmp = 2.0 * (x * z);
	} 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) :: tmp
    if (t <= (-2.4d+39)) then
        tmp = x * t
    else if (t <= 5.2d-145) then
        tmp = y * 5.0d0
    else if (t <= 3.8d+53) then
        tmp = 2.0d0 * (x * z)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.4e+39) {
		tmp = x * t;
	} else if (t <= 5.2e-145) {
		tmp = y * 5.0;
	} else if (t <= 3.8e+53) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.4e+39:
		tmp = x * t
	elif t <= 5.2e-145:
		tmp = y * 5.0
	elif t <= 3.8e+53:
		tmp = 2.0 * (x * z)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.4e+39)
		tmp = Float64(x * t);
	elseif (t <= 5.2e-145)
		tmp = Float64(y * 5.0);
	elseif (t <= 3.8e+53)
		tmp = Float64(2.0 * Float64(x * z));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.4e+39)
		tmp = x * t;
	elseif (t <= 5.2e-145)
		tmp = y * 5.0;
	elseif (t <= 3.8e+53)
		tmp = 2.0 * (x * z);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.4e+39], N[(x * t), $MachinePrecision], If[LessEqual[t, 5.2e-145], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 3.8e+53], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4000000000000001e39 or 3.79999999999999997e53 < t

   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 65.8%

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

   5. Simplified 65.8%

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

   if -2.4000000000000001e39 < t < 5.1999999999999999e-145

   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 44.4%

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

   if 5.1999999999999999e-145 < t < 3.79999999999999997e53

   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 50.9%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.5e+30)
   (* x t)
   (if (<= t 1.75e-137)
     (* y (+ x 5.0))
     (if (<= t 4.5e+55) (* 2.0 (* x z)) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e+30) {
		tmp = x * t;
	} else if (t <= 1.75e-137) {
		tmp = y * (x + 5.0);
	} else if (t <= 4.5e+55) {
		tmp = 2.0 * (x * z);
	} 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) :: tmp
    if (t <= (-3.5d+30)) then
        tmp = x * t
    else if (t <= 1.75d-137) then
        tmp = y * (x + 5.0d0)
    else if (t <= 4.5d+55) then
        tmp = 2.0d0 * (x * z)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e+30) {
		tmp = x * t;
	} else if (t <= 1.75e-137) {
		tmp = y * (x + 5.0);
	} else if (t <= 4.5e+55) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.5e+30:
		tmp = x * t
	elif t <= 1.75e-137:
		tmp = y * (x + 5.0)
	elif t <= 4.5e+55:
		tmp = 2.0 * (x * z)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.5e+30)
		tmp = Float64(x * t);
	elseif (t <= 1.75e-137)
		tmp = Float64(y * Float64(x + 5.0));
	elseif (t <= 4.5e+55)
		tmp = Float64(2.0 * Float64(x * z));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.5e+30)
		tmp = x * t;
	elseif (t <= 1.75e-137)
		tmp = y * (x + 5.0);
	elseif (t <= 4.5e+55)
		tmp = 2.0 * (x * z);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.5e+30], N[(x * t), $MachinePrecision], If[LessEqual[t, 1.75e-137], N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+55], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.50000000000000021e30 or 4.49999999999999998e55 < t

   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 64.7%

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

   5. Simplified 64.7%

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

   if -3.50000000000000021e30 < t < 1.7500000000000001e-137

   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 86.0%

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

   4. Taylor expanded in y around inf 61.3%

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

   if 1.7500000000000001e-137 < t < 4.49999999999999998e55

   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 50.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-67} \lor \neg \left(x \leq 8.2 \cdot 10^{-82}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.18e-67) (not (<= x 8.2e-82)))
   (* 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 <= -1.18e-67) || !(x <= 8.2e-82)) {
		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 <= (-1.18d-67)) .or. (.not. (x <= 8.2d-82))) 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 <= -1.18e-67) || !(x <= 8.2e-82)) {
		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 <= -1.18e-67) or not (x <= 8.2e-82):
		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 <= -1.18e-67) || !(x <= 8.2e-82))
		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 <= -1.18e-67) || ~((x <= 8.2e-82)))
		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, -1.18e-67], N[Not[LessEqual[x, 8.2e-82]], $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 < -1.18e-67 or 8.19999999999999992e-82 < 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 93.8%

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

   if -1.18e-67 < x < 8.19999999999999992e-82

   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. Taylor expanded in x around inf 67.7%

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

   6. Taylor expanded in x around 0 54.1%

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

   7. Taylor expanded in x around 0 86.2%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-67} \lor \neg \left(x \leq 8.2 \cdot 10^{-82}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+63} \lor \neg \left(y \leq 1.1 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.35e+63) (not (<= y 1.1e+41)))
   (* y (+ x 5.0))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.35e+63) || !(y <= 1.1e+41)) {
		tmp = y * (x + 5.0);
	} 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 <= (-1.35d+63)) .or. (.not. (y <= 1.1d+41))) then
        tmp = y * (x + 5.0d0)
    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 <= -1.35e+63) || !(y <= 1.1e+41)) {
		tmp = y * (x + 5.0);
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.35e+63) or not (y <= 1.1e+41):
		tmp = y * (x + 5.0)
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.35e+63) || !(y <= 1.1e+41))
		tmp = Float64(y * Float64(x + 5.0));
	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 <= -1.35e+63) || ~((y <= 1.1e+41)))
		tmp = y * (x + 5.0);
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.35e+63], N[Not[LessEqual[y, 1.1e+41]], $MachinePrecision]], N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35000000000000009e63 or 1.09999999999999995e41 < 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 0 86.5%

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

   4. Taylor expanded in y around inf 74.2%

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

   if -1.35000000000000009e63 < y < 1.09999999999999995e41

   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 79.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+63} \lor \neg \left(y \leq 1.1 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+27} \lor \neg \left(y \leq 1.4 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.6e+27) (not (<= y 1.4e+41)))
   (* 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 <= -7.6e+27) || !(y <= 1.4e+41)) {
		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 <= (-7.6d+27)) .or. (.not. (y <= 1.4d+41))) 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 <= -7.6e+27) || !(y <= 1.4e+41)) {
		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 <= -7.6e+27) or not (y <= 1.4e+41):
		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 <= -7.6e+27) || !(y <= 1.4e+41))
		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 <= -7.6e+27) || ~((y <= 1.4e+41)))
		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, -7.6e+27], N[Not[LessEqual[y, 1.4e+41]], $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 < -7.60000000000000043e27 or 1.4e41 < 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 84.7%

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

   5. Simplified 84.7%

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

   if -7.60000000000000043e27 < y < 1.4e41

   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 81.3%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+27} \lor \neg \left(y \leq 1.4 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-84}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e-52)
   (* x (+ t (* 2.0 y)))
   (if (<= x 2.2e-84) (* y 5.0) (* 2.0 (* x (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-52) {
		tmp = x * (t + (2.0 * y));
	} else if (x <= 2.2e-84) {
		tmp = y * 5.0;
	} else {
		tmp = 2.0 * (x * (y + 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 (x <= (-2.6d-52)) then
        tmp = x * (t + (2.0d0 * y))
    else if (x <= 2.2d-84) then
        tmp = y * 5.0d0
    else
        tmp = 2.0d0 * (x * (y + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-52) {
		tmp = x * (t + (2.0 * y));
	} else if (x <= 2.2e-84) {
		tmp = y * 5.0;
	} else {
		tmp = 2.0 * (x * (y + z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.6e-52:
		tmp = x * (t + (2.0 * y))
	elif x <= 2.2e-84:
		tmp = y * 5.0
	else:
		tmp = 2.0 * (x * (y + z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e-52)
		tmp = Float64(x * Float64(t + Float64(2.0 * y)));
	elseif (x <= 2.2e-84)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(2.0 * Float64(x * Float64(y + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.6e-52)
		tmp = x * (t + (2.0 * y));
	elseif (x <= 2.2e-84)
		tmp = y * 5.0;
	else
		tmp = 2.0 * (x * (y + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e-52], N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-84], N[(y * 5.0), $MachinePrecision], N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5999999999999999e-52

   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 inf 75.5%

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

   4. Taylor expanded in x around inf 70.9%

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

   if -2.5999999999999999e-52 < x < 2.1999999999999999e-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 x around 0 63.4%

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

   if 2.1999999999999999e-84 < 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 y around 0 95.8%

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

   4. Taylor expanded in x around inf 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in t around 0 66.3%

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

      1. *-commutative 66.3%

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

      2. *-commutative 66.3%

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

      3. associate-*r* 66.3%

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

      4. *-commutative 66.3%

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

      5. associate-*r* 66.3%

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

      6. *-commutative 66.3%

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

      7. distribute-lft-out 67.7%

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

      8. associate-*r* 67.7%

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

      9. distribute-lft-out 67.7%

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

      10. *-commutative 67.7%

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

      11. distribute-lft-out 67.7%

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

      12. associate-*l* 67.7%

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

   9. Simplified 67.7%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-84}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 96.7% 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 97.2%

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

4. Final simplification 97.2%

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

Alternative 17: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (x * (t + (y + (z + (y + z)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + N[(z + N[(y + z), $MachinePrecision]), $MachinePrecision]), $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. Final simplification 99.9%

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

Alternative 18: 43.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+39} \lor \neg \left(t \leq 5.8 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.02e+39) (not (<= t 5.8e+26))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.02e+39) || !(t <= 5.8e+26)) {
		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 ((t <= (-1.02d+39)) .or. (.not. (t <= 5.8d+26))) 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 ((t <= -1.02e+39) || !(t <= 5.8e+26)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.02e+39) or not (t <= 5.8e+26):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.02e+39) || !(t <= 5.8e+26))
		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 ((t <= -1.02e+39) || ~((t <= 5.8e+26)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.02e+39], N[Not[LessEqual[t, 5.8e+26]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.02e39 or 5.8e26 < t

   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 64.5%

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

   5. Simplified 64.5%

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

   if -1.02e39 < t < 5.8e26

   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 39.4%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+39} \lor \neg \left(t \leq 5.8 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.1% 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 30.3%

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

4. Final simplification 30.3%

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

Reproduce

herbie shell --seed 2024054 
(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)))