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

Percentage Accurate: 99.9% → 99.9%

Time: 10.4s

Alternatives: 13

Speedup: 1.2×

• 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: 99.9% 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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0 + N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. fma-define 100.0%

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

   3. +-commutative 100.0%

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

   4. associate-+l+ 100.0%

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

   5. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(t + \left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right)\right)\right) \]

   6. +-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(t + \left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right)\right)\right) \]

   7. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(t + \left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right)\right)\right) \]

   8. distribute-rgt-out 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(t + \color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)}\right)\right) \]

   9. metadata-eval 100.0%

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

4. Applied egg-rr 100.0%

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

Alternative 2: 62.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -0.00013:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-13}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+183} \lor \neg \left(x \leq 5.5 \cdot 10^{+192}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))) (t_2 (* x (+ t (* y 2.0)))))
   (if (<= x -0.00013)
     t_2
     (if (<= x 1.02e-101)
       (* y 5.0)
       (if (<= x 1.75e-39)
         t_1
         (if (<= x 2.05e-13)
           (* y 5.0)
           (if (or (<= x 3.5e+183) (not (<= x 5.5e+192))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double t_2 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -0.00013) {
		tmp = t_2;
	} else if (x <= 1.02e-101) {
		tmp = y * 5.0;
	} else if (x <= 1.75e-39) {
		tmp = t_1;
	} else if (x <= 2.05e-13) {
		tmp = y * 5.0;
	} else if ((x <= 3.5e+183) || !(x <= 5.5e+192)) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    t_2 = x * (t + (y * 2.0d0))
    if (x <= (-0.00013d0)) then
        tmp = t_2
    else if (x <= 1.02d-101) then
        tmp = y * 5.0d0
    else if (x <= 1.75d-39) then
        tmp = t_1
    else if (x <= 2.05d-13) then
        tmp = y * 5.0d0
    else if ((x <= 3.5d+183) .or. (.not. (x <= 5.5d+192))) then
        tmp = t_2
    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 = 2.0 * (x * z);
	double t_2 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -0.00013) {
		tmp = t_2;
	} else if (x <= 1.02e-101) {
		tmp = y * 5.0;
	} else if (x <= 1.75e-39) {
		tmp = t_1;
	} else if (x <= 2.05e-13) {
		tmp = y * 5.0;
	} else if ((x <= 3.5e+183) || !(x <= 5.5e+192)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	t_2 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -0.00013:
		tmp = t_2
	elif x <= 1.02e-101:
		tmp = y * 5.0
	elif x <= 1.75e-39:
		tmp = t_1
	elif x <= 2.05e-13:
		tmp = y * 5.0
	elif (x <= 3.5e+183) or not (x <= 5.5e+192):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	t_2 = Float64(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (x <= -0.00013)
		tmp = t_2;
	elseif (x <= 1.02e-101)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.75e-39)
		tmp = t_1;
	elseif (x <= 2.05e-13)
		tmp = Float64(y * 5.0);
	elseif ((x <= 3.5e+183) || !(x <= 5.5e+192))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	t_2 = x * (t + (y * 2.0));
	tmp = 0.0;
	if (x <= -0.00013)
		tmp = t_2;
	elseif (x <= 1.02e-101)
		tmp = y * 5.0;
	elseif (x <= 1.75e-39)
		tmp = t_1;
	elseif (x <= 2.05e-13)
		tmp = y * 5.0;
	elseif ((x <= 3.5e+183) || ~((x <= 5.5e+192)))
		tmp = t_2;
	else
		tmp = t_1;
	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[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.00013], t$95$2, If[LessEqual[x, 1.02e-101], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.75e-39], t$95$1, If[LessEqual[x, 2.05e-13], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 3.5e+183], N[Not[LessEqual[x, 5.5e+192]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.29999999999999989e-4 or 2.0500000000000001e-13 < x < 3.49999999999999987e183 or 5.49999999999999966e192 < 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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 98.3%

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

   6. Taylor expanded in y around inf 73.3%

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

   if -1.29999999999999989e-4 < x < 1.02e-101 or 1.75e-39 < x < 2.0500000000000001e-13

   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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 64.2%

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

   if 1.02e-101 < x < 1.75e-39 or 3.49999999999999987e183 < x < 5.49999999999999966e192

   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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 71.6%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00013:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-39}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-13}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+183} \lor \neg \left(x \leq 5.5 \cdot 10^{+192}\right):\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+97}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -8.2e-5)
     (* x t)
     (if (<= x 1.42e-101)
       (* y 5.0)
       (if (<= x 1.35e-42)
         t_1
         (if (<= x 1.8e-15) (* y 5.0) (if (<= x 9.2e+97) (* x t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -8.2e-5) {
		tmp = x * t;
	} else if (x <= 1.42e-101) {
		tmp = y * 5.0;
	} else if (x <= 1.35e-42) {
		tmp = t_1;
	} else if (x <= 1.8e-15) {
		tmp = y * 5.0;
	} else if (x <= 9.2e+97) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-8.2d-5)) then
        tmp = x * t
    else if (x <= 1.42d-101) then
        tmp = y * 5.0d0
    else if (x <= 1.35d-42) then
        tmp = t_1
    else if (x <= 1.8d-15) then
        tmp = y * 5.0d0
    else if (x <= 9.2d+97) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -8.2e-5) {
		tmp = x * t;
	} else if (x <= 1.42e-101) {
		tmp = y * 5.0;
	} else if (x <= 1.35e-42) {
		tmp = t_1;
	} else if (x <= 1.8e-15) {
		tmp = y * 5.0;
	} else if (x <= 9.2e+97) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -8.2e-5:
		tmp = x * t
	elif x <= 1.42e-101:
		tmp = y * 5.0
	elif x <= 1.35e-42:
		tmp = t_1
	elif x <= 1.8e-15:
		tmp = y * 5.0
	elif x <= 9.2e+97:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -8.2e-5)
		tmp = Float64(x * t);
	elseif (x <= 1.42e-101)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.35e-42)
		tmp = t_1;
	elseif (x <= 1.8e-15)
		tmp = Float64(y * 5.0);
	elseif (x <= 9.2e+97)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -8.2e-5)
		tmp = x * t;
	elseif (x <= 1.42e-101)
		tmp = y * 5.0;
	elseif (x <= 1.35e-42)
		tmp = t_1;
	elseif (x <= 1.8e-15)
		tmp = y * 5.0;
	elseif (x <= 9.2e+97)
		tmp = x * t;
	else
		tmp = t_1;
	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, -8.2e-5], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.42e-101], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.35e-42], t$95$1, If[LessEqual[x, 1.8e-15], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 9.2e+97], N[(x * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.20000000000000009e-5 or 1.8000000000000001e-15 < x < 9.20000000000000022e97

   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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 45.2%

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

   7. Simplified 45.2%

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

   if -8.20000000000000009e-5 < x < 1.4200000000000001e-101 or 1.35e-42 < x < 1.8000000000000001e-15

   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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 64.2%

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

   if 1.4200000000000001e-101 < x < 1.35e-42 or 9.20000000000000022e97 < 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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 49.1%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-42}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+97}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \left(x + 5 \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -6.4e+106)
     t_2
     (if (<= y -1.06e+18)
       t_1
       (if (<= y -4.4e-54)
         (* t (+ x (* 5.0 (/ y t))))
         (if (<= y 1.1e+74) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -6.4e+106) {
		tmp = t_2;
	} else if (y <= -1.06e+18) {
		tmp = t_1;
	} else if (y <= -4.4e-54) {
		tmp = t * (x + (5.0 * (y / t)));
	} else if (y <= 1.1e+74) {
		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 + ((y + z) * 2.0d0))
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-6.4d+106)) then
        tmp = t_2
    else if (y <= (-1.06d+18)) then
        tmp = t_1
    else if (y <= (-4.4d-54)) then
        tmp = t * (x + (5.0d0 * (y / t)))
    else if (y <= 1.1d+74) 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 + ((y + z) * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -6.4e+106) {
		tmp = t_2;
	} else if (y <= -1.06e+18) {
		tmp = t_1;
	} else if (y <= -4.4e-54) {
		tmp = t * (x + (5.0 * (y / t)));
	} else if (y <= 1.1e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((y + z) * 2.0))
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -6.4e+106:
		tmp = t_2
	elif y <= -1.06e+18:
		tmp = t_1
	elif y <= -4.4e-54:
		tmp = t * (x + (5.0 * (y / t)))
	elif y <= 1.1e+74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -6.4e+106)
		tmp = t_2;
	elseif (y <= -1.06e+18)
		tmp = t_1;
	elseif (y <= -4.4e-54)
		tmp = Float64(t * Float64(x + Float64(5.0 * Float64(y / t))));
	elseif (y <= 1.1e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + ((y + z) * 2.0));
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -6.4e+106)
		tmp = t_2;
	elseif (y <= -1.06e+18)
		tmp = t_1;
	elseif (y <= -4.4e-54)
		tmp = t * (x + (5.0 * (y / t)));
	elseif (y <= 1.1e+74)
		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[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+106], t$95$2, If[LessEqual[y, -1.06e+18], t$95$1, If[LessEqual[y, -4.4e-54], N[(t * N[(x + N[(5.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+74], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.3999999999999996e106 or 1.1000000000000001e74 < 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. 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%

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

      3. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 94.0%

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

   if -6.3999999999999996e106 < y < -1.06e18 or -4.3999999999999999e-54 < y < 1.1000000000000001e74

   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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 85.4%

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

      1. distribute-lft-out 85.4%

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

      2. *-commutative 85.4%

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

   7. Applied egg-rr 85.4%

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

   if -1.06e18 < y < -4.3999999999999999e-54

   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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-+r+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-in 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. *-un-lft-identity 99.9%

         \[\leadsto \left(y \cdot 5 + x \cdot \left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right)\right) + x \cdot t \]

      9. +-commutative 99.9%

         \[\leadsto \left(y \cdot 5 + x \cdot \left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right)\right) + x \cdot t \]

      10. *-un-lft-identity 99.9%

          \[\leadsto \left(y \cdot 5 + x \cdot \left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right)\right) + x \cdot t \]

      11. distribute-rgt-out 99.9%

          \[\leadsto \left(y \cdot 5 + x \cdot \color{blue}{\left(\left(y + z\right) \cdot \left(1 + 1\right)\right)}\right) + x \cdot t \]

      12. metadata-eval 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around inf 92.8%

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

   8. Taylor expanded in x around 0 80.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \left(x + 5 \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+106}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+216} \lor \neg \left(y \leq 2.2 \cdot 10^{+279}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.6e+106)
   (* y 5.0)
   (if (<= y 1.12e+69)
     (* x (+ t (* z 2.0)))
     (if (or (<= y 2.1e+216) (not (<= y 2.2e+279)))
       (* y 5.0)
       (* x (+ t (* y 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e+106) {
		tmp = y * 5.0;
	} else if (y <= 1.12e+69) {
		tmp = x * (t + (z * 2.0));
	} else if ((y <= 2.1e+216) || !(y <= 2.2e+279)) {
		tmp = y * 5.0;
	} else {
		tmp = x * (t + (y * 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 (y <= (-5.6d+106)) then
        tmp = y * 5.0d0
    else if (y <= 1.12d+69) then
        tmp = x * (t + (z * 2.0d0))
    else if ((y <= 2.1d+216) .or. (.not. (y <= 2.2d+279))) then
        tmp = y * 5.0d0
    else
        tmp = x * (t + (y * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e+106) {
		tmp = y * 5.0;
	} else if (y <= 1.12e+69) {
		tmp = x * (t + (z * 2.0));
	} else if ((y <= 2.1e+216) || !(y <= 2.2e+279)) {
		tmp = y * 5.0;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.6e+106:
		tmp = y * 5.0
	elif y <= 1.12e+69:
		tmp = x * (t + (z * 2.0))
	elif (y <= 2.1e+216) or not (y <= 2.2e+279):
		tmp = y * 5.0
	else:
		tmp = x * (t + (y * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.6e+106)
		tmp = Float64(y * 5.0);
	elseif (y <= 1.12e+69)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif ((y <= 2.1e+216) || !(y <= 2.2e+279))
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.6e+106)
		tmp = y * 5.0;
	elseif (y <= 1.12e+69)
		tmp = x * (t + (z * 2.0));
	elseif ((y <= 2.1e+216) || ~((y <= 2.2e+279)))
		tmp = y * 5.0;
	else
		tmp = x * (t + (y * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.6e+106], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, 1.12e+69], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.1e+216], N[Not[LessEqual[y, 2.2e+279]], $MachinePrecision]], N[(y * 5.0), $MachinePrecision], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.59999999999999986e106 or 1.12e69 < y < 2.10000000000000001e216 or 2.2e279 < 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. 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%

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

      3. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 62.6%

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

   if -5.59999999999999986e106 < y < 1.12e69

   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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 75.0%

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

   if 2.10000000000000001e216 < y < 2.2e279

   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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 74.3%

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

   6. Taylor expanded in y around inf 74.3%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+106}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+216} \lor \neg \left(y \leq 2.2 \cdot 10^{+279}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(x + 5 \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -2.8e+45)
     t_2
     (if (<= y -4.8e+17)
       t_1
       (if (<= y -1.7e-58)
         (* t (+ x (* 5.0 (/ y t))))
         (if (<= y 1.25e+72) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.8e+45) {
		tmp = t_2;
	} else if (y <= -4.8e+17) {
		tmp = t_1;
	} else if (y <= -1.7e-58) {
		tmp = t * (x + (5.0 * (y / t)));
	} else if (y <= 1.25e+72) {
		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 + (z * 2.0d0))
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-2.8d+45)) then
        tmp = t_2
    else if (y <= (-4.8d+17)) then
        tmp = t_1
    else if (y <= (-1.7d-58)) then
        tmp = t * (x + (5.0d0 * (y / t)))
    else if (y <= 1.25d+72) 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 + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.8e+45) {
		tmp = t_2;
	} else if (y <= -4.8e+17) {
		tmp = t_1;
	} else if (y <= -1.7e-58) {
		tmp = t * (x + (5.0 * (y / t)));
	} else if (y <= 1.25e+72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -2.8e+45:
		tmp = t_2
	elif y <= -4.8e+17:
		tmp = t_1
	elif y <= -1.7e-58:
		tmp = t * (x + (5.0 * (y / t)))
	elif y <= 1.25e+72:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -2.8e+45)
		tmp = t_2;
	elseif (y <= -4.8e+17)
		tmp = t_1;
	elseif (y <= -1.7e-58)
		tmp = Float64(t * Float64(x + Float64(5.0 * Float64(y / t))));
	elseif (y <= 1.25e+72)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -2.8e+45)
		tmp = t_2;
	elseif (y <= -4.8e+17)
		tmp = t_1;
	elseif (y <= -1.7e-58)
		tmp = t * (x + (5.0 * (y / t)));
	elseif (y <= 1.25e+72)
		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[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+45], t$95$2, If[LessEqual[y, -4.8e+17], t$95$1, If[LessEqual[y, -1.7e-58], N[(t * N[(x + N[(5.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+72], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999999e45 or 1.24999999999999998e72 < 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. 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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 89.8%

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

   if -2.7999999999999999e45 < y < -4.8e17 or -1.69999999999999987e-58 < y < 1.24999999999999998e72

   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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 81.0%

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

   if -4.8e17 < y < -1.69999999999999987e-58

   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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-+r+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-in 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. *-un-lft-identity 99.9%

         \[\leadsto \left(y \cdot 5 + x \cdot \left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right)\right) + x \cdot t \]

      9. +-commutative 99.9%

         \[\leadsto \left(y \cdot 5 + x \cdot \left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right)\right) + x \cdot t \]

      10. *-un-lft-identity 99.9%

          \[\leadsto \left(y \cdot 5 + x \cdot \left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right)\right) + x \cdot t \]

      11. distribute-rgt-out 99.9%

          \[\leadsto \left(y \cdot 5 + x \cdot \color{blue}{\left(\left(y + z\right) \cdot \left(1 + 1\right)\right)}\right) + x \cdot t \]

      12. metadata-eval 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around inf 92.8%

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

   8. Taylor expanded in x around 0 80.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(x + 5 \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1750000000 \lor \neg \left(x \leq 2.95 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z + y \cdot x\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1750000000.0) (not (<= x 2.95e-8)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* 2.0 (+ (* x z) (* y x))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1750000000.0) || !(x <= 2.95e-8)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (2.0 * ((x * z) + (y * x))) + (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 <= (-1750000000.0d0)) .or. (.not. (x <= 2.95d-8))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (2.0d0 * ((x * z) + (y * x))) + (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 <= -1750000000.0) || !(x <= 2.95e-8)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (2.0 * ((x * z) + (y * x))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1750000000.0) or not (x <= 2.95e-8):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (2.0 * ((x * z) + (y * x))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1750000000.0) || !(x <= 2.95e-8))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(2.0 * Float64(Float64(x * z) + Float64(y * x))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1750000000.0) || ~((x <= 2.95e-8)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (2.0 * ((x * z) + (y * x))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1750000000.0], N[Not[LessEqual[x, 2.95e-8]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(N[(x * z), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75e9 or 2.9499999999999999e-8 < 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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.5%

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

      1. distribute-lft-out 99.5%

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

      2. *-commutative 99.5%

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

   7. Applied egg-rr 99.5%

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

   if -1.75e9 < x < 2.9499999999999999e-8

   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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-+r+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-in 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. *-un-lft-identity 99.9%

         \[\leadsto \left(y \cdot 5 + x \cdot \left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right)\right) + x \cdot t \]

      9. +-commutative 99.9%

         \[\leadsto \left(y \cdot 5 + x \cdot \left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right)\right) + x \cdot t \]

      10. *-un-lft-identity 99.9%

          \[\leadsto \left(y \cdot 5 + x \cdot \left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right)\right) + x \cdot t \]

      11. distribute-rgt-out 99.9%

          \[\leadsto \left(y \cdot 5 + x \cdot \color{blue}{\left(\left(y + z\right) \cdot \left(1 + 1\right)\right)}\right) + x \cdot t \]

      12. metadata-eval 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 85.0%

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

      1. +-commutative 85.0%

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

      2. distribute-rgt-in 85.0%

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

   9. Applied egg-rr 85.0%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1750000000 \lor \neg \left(x \leq 2.95 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z + y \cdot x\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1900000000 \lor \neg \left(x \leq 1.75 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1900000000.0) (not (<= x 1.75e-12)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* 2.0 (* x (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1900000000.0) || !(x <= 1.75e-12)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (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 <= (-1900000000.0d0)) .or. (.not. (x <= 1.75d-12))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (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 <= -1900000000.0) || !(x <= 1.75e-12)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * (y + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1900000000.0) or not (x <= 1.75e-12):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (2.0 * (x * (y + z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1900000000.0) || !(x <= 1.75e-12))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + 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 <= -1900000000.0) || ~((x <= 1.75e-12)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (2.0 * (x * (y + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1900000000.0], N[Not[LessEqual[x, 1.75e-12]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e9 or 1.75e-12 < 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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.5%

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

      1. distribute-lft-out 99.5%

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

      2. *-commutative 99.5%

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

   7. Applied egg-rr 99.5%

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

   if -1.9e9 < x < 1.75e-12

   1. Initial program 99.9%

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

      1. fma-define 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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-+r+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-in 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. *-un-lft-identity 99.9%

         \[\leadsto \left(y \cdot 5 + x \cdot \left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right)\right) + x \cdot t \]

      9. +-commutative 99.9%

         \[\leadsto \left(y \cdot 5 + x \cdot \left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right)\right) + x \cdot t \]

      10. *-un-lft-identity 99.9%

          \[\leadsto \left(y \cdot 5 + x \cdot \left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right)\right) + x \cdot t \]

      11. distribute-rgt-out 99.9%

          \[\leadsto \left(y \cdot 5 + x \cdot \color{blue}{\left(\left(y + z\right) \cdot \left(1 + 1\right)\right)}\right) + x \cdot t \]

      12. metadata-eval 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 85.0%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1900000000 \lor \neg \left(x \leq 1.75 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-5} \lor \neg \left(x \leq 1.3 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.5e-5) (not (<= x 1.3e-7)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* 2.0 (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.5e-5) || !(x <= 1.3e-7)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * 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 <= (-8.5d-5)) .or. (.not. (x <= 1.3d-7))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.5e-5) || !(x <= 1.3e-7)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.5e-5) or not (x <= 1.3e-7):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (2.0 * (x * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.5e-5) || !(x <= 1.3e-7))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.5e-5) || ~((x <= 1.3e-7)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (2.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.5e-5], N[Not[LessEqual[x, 1.3e-7]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.500000000000001e-5 or 1.29999999999999999e-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-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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 98.4%

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

      1. distribute-lft-out 98.4%

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

      2. *-commutative 98.4%

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

   7. Applied egg-rr 98.4%

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

   if -8.500000000000001e-5 < x < 1.29999999999999999e-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. 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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-+r+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-in 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. *-un-lft-identity 99.9%

         \[\leadsto \left(y \cdot 5 + x \cdot \left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right)\right) + x \cdot t \]

      9. +-commutative 99.9%

         \[\leadsto \left(y \cdot 5 + x \cdot \left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right)\right) + x \cdot t \]

      10. *-un-lft-identity 99.9%

          \[\leadsto \left(y \cdot 5 + x \cdot \left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right)\right) + x \cdot t \]

      11. distribute-rgt-out 99.9%

          \[\leadsto \left(y \cdot 5 + x \cdot \color{blue}{\left(\left(y + z\right) \cdot \left(1 + 1\right)\right)}\right) + x \cdot t \]

      12. metadata-eval 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 85.3%

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

   8. Taylor expanded in y around 0 84.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-5} \lor \neg \left(x \leq 1.3 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+43} \lor \neg \left(y \leq 4.6 \cdot 10^{+73}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.85e+43) (not (<= y 4.6e+73)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e+43) || !(y <= 4.6e+73)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 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 ((y <= (-1.85d+43)) .or. (.not. (y <= 4.6d+73))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e+43) || !(y <= 4.6e+73)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.85e+43) or not (y <= 4.6e+73):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.85e+43) || !(y <= 4.6e+73))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.85e+43) || ~((y <= 4.6e+73)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.85e+43], N[Not[LessEqual[y, 4.6e+73]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e43 or 4.6e73 < 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. 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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 89.8%

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

   if -1.85e43 < y < 4.6e73

   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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 77.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+43} \lor \neg \left(y \leq 4.6 \cdot 10^{+73}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-5} \lor \neg \left(x \leq 1.35 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.2e-5) (not (<= x 1.35e-15))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.2e-5) || !(x <= 1.35e-15)) {
		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 <= (-8.2d-5)) .or. (.not. (x <= 1.35d-15))) 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 <= -8.2e-5) || !(x <= 1.35e-15)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.2e-5) or not (x <= 1.35e-15):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.2e-5) || !(x <= 1.35e-15))
		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 <= -8.2e-5) || ~((x <= 1.35e-15)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.2e-5], N[Not[LessEqual[x, 1.35e-15]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.20000000000000009e-5 or 1.35000000000000005e-15 < 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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 39.8%

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

   7. Simplified 39.8%

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

   if -8.20000000000000009e-5 < x < 1.35000000000000005e-15

   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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 60.6%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-5} \lor \neg \left(x \leq 1.35 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x * (t + ((y + z) * 2.0))) + (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) * 2.0d0))) + (y * 5.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   3. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

   1. fma-undefine 99.9%

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

   2. associate-+r+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l+ 99.9%

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

   7. *-un-lft-identity 99.9%

      \[\leadsto y \cdot 5 + x \cdot \left(t + \left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right)\right) \]

   8. +-commutative 99.9%

      \[\leadsto y \cdot 5 + x \cdot \left(t + \left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right)\right) \]

   9. *-un-lft-identity 99.9%

      \[\leadsto y \cdot 5 + x \cdot \left(t + \left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right)\right) \]

   10. distribute-rgt-out 99.9%

       \[\leadsto y \cdot 5 + x \cdot \left(t + \color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)}\right) \]

   11. metadata-eval 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

Alternative 13: 30.3% 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. 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%

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

   3. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around 0 31.7%

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

6. Final simplification 31.7%

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

Reproduce

herbie shell --seed 2024111 
(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)))