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

Percentage Accurate: 99.9% → 99.9%

Time: 5.8s

Alternatives: 14

Speedup: 1.0×

• 27.3% 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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0 + N[(x * N[(N[(y + z), $MachinePrecision] * 2.0 + t), $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. 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-def 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. distribute-rgt-in 97.2%

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

   4. associate-+l+ 97.2%

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

   5. +-commutative 97.2%

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

   6. count-2 97.2%

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

   7. distribute-rgt-in 100.0%

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

   8. *-commutative 100.0%

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

   9. fma-def 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $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-def 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+192} \lor \neg \left(x \leq 2.85 \cdot 10^{+255}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ y z) (* x 2.0))))
   (if (<= x -2.9e-57)
     t_1
     (if (<= x 1.5e-19)
       (* y 5.0)
       (if (or (<= x 4e+192) (not (<= x 2.85e+255))) t_1 (* x t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y + z) * (x * 2.0);
	double tmp;
	if (x <= -2.9e-57) {
		tmp = t_1;
	} else if (x <= 1.5e-19) {
		tmp = y * 5.0;
	} else if ((x <= 4e+192) || !(x <= 2.85e+255)) {
		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 = (y + z) * (x * 2.0d0)
    if (x <= (-2.9d-57)) then
        tmp = t_1
    else if (x <= 1.5d-19) then
        tmp = y * 5.0d0
    else if ((x <= 4d+192) .or. (.not. (x <= 2.85d+255))) 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 = (y + z) * (x * 2.0);
	double tmp;
	if (x <= -2.9e-57) {
		tmp = t_1;
	} else if (x <= 1.5e-19) {
		tmp = y * 5.0;
	} else if ((x <= 4e+192) || !(x <= 2.85e+255)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y + z) * (x * 2.0)
	tmp = 0
	if x <= -2.9e-57:
		tmp = t_1
	elif x <= 1.5e-19:
		tmp = y * 5.0
	elif (x <= 4e+192) or not (x <= 2.85e+255):
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y + z) * Float64(x * 2.0))
	tmp = 0.0
	if (x <= -2.9e-57)
		tmp = t_1;
	elseif (x <= 1.5e-19)
		tmp = Float64(y * 5.0);
	elseif ((x <= 4e+192) || !(x <= 2.85e+255))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y + z) * (x * 2.0);
	tmp = 0.0;
	if (x <= -2.9e-57)
		tmp = t_1;
	elseif (x <= 1.5e-19)
		tmp = y * 5.0;
	elseif ((x <= 4e+192) || ~((x <= 2.85e+255)))
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e-57], t$95$1, If[LessEqual[x, 1.5e-19], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 4e+192], N[Not[LessEqual[x, 2.85e+255]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.90000000000000025e-57 or 1.49999999999999996e-19 < x < 4.00000000000000016e192 or 2.84999999999999994e255 < 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. +-commutative 100.0%

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

      2. fma-def 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. distribute-rgt-in 95.5%

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

      4. associate-+l+ 95.5%

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

      5. +-commutative 95.5%

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

      6. count-2 95.5%

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

      7. distribute-rgt-in 100.0%

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

      8. *-commutative 100.0%

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

      9. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around 0 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*r* 78.5%

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

      3. +-commutative 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in x around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-*r* 75.6%

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

      3. +-commutative 75.6%

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

   9. Simplified 75.6%

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

   if -2.90000000000000025e-57 < x < 1.49999999999999996e-19

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 60.2%

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

   if 4.00000000000000016e192 < x < 2.84999999999999994e255

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 100.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-57}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+192} \lor \neg \left(x \leq 2.85 \cdot 10^{+255}\right):\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 4: 62.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+192} \lor \neg \left(x \leq 3.2 \cdot 10^{+255}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ y z) (* x 2.0))))
   (if (<= x -2.4e-58)
     t_1
     (if (<= x 4.6e-16)
       (* y (+ 5.0 (* x 2.0)))
       (if (or (<= x 4e+192) (not (<= x 3.2e+255))) t_1 (* x t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y + z) * (x * 2.0);
	double tmp;
	if (x <= -2.4e-58) {
		tmp = t_1;
	} else if (x <= 4.6e-16) {
		tmp = y * (5.0 + (x * 2.0));
	} else if ((x <= 4e+192) || !(x <= 3.2e+255)) {
		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 = (y + z) * (x * 2.0d0)
    if (x <= (-2.4d-58)) then
        tmp = t_1
    else if (x <= 4.6d-16) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else if ((x <= 4d+192) .or. (.not. (x <= 3.2d+255))) 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 = (y + z) * (x * 2.0);
	double tmp;
	if (x <= -2.4e-58) {
		tmp = t_1;
	} else if (x <= 4.6e-16) {
		tmp = y * (5.0 + (x * 2.0));
	} else if ((x <= 4e+192) || !(x <= 3.2e+255)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y + z) * (x * 2.0)
	tmp = 0
	if x <= -2.4e-58:
		tmp = t_1
	elif x <= 4.6e-16:
		tmp = y * (5.0 + (x * 2.0))
	elif (x <= 4e+192) or not (x <= 3.2e+255):
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y + z) * Float64(x * 2.0))
	tmp = 0.0
	if (x <= -2.4e-58)
		tmp = t_1;
	elseif (x <= 4.6e-16)
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	elseif ((x <= 4e+192) || !(x <= 3.2e+255))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y + z) * (x * 2.0);
	tmp = 0.0;
	if (x <= -2.4e-58)
		tmp = t_1;
	elseif (x <= 4.6e-16)
		tmp = y * (5.0 + (x * 2.0));
	elseif ((x <= 4e+192) || ~((x <= 3.2e+255)))
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e-58], t$95$1, If[LessEqual[x, 4.6e-16], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 4e+192], N[Not[LessEqual[x, 3.2e+255]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4000000000000001e-58 or 4.5999999999999998e-16 < x < 4.00000000000000016e192 or 3.1999999999999998e255 < 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. +-commutative 100.0%

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

      2. fma-def 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. distribute-rgt-in 95.5%

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

      4. associate-+l+ 95.5%

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

      5. +-commutative 95.5%

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

      6. count-2 95.5%

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

      7. distribute-rgt-in 100.0%

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

      8. *-commutative 100.0%

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

      9. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around 0 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*r* 78.5%

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

      3. +-commutative 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in x around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-*r* 75.6%

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

      3. +-commutative 75.6%

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

   9. Simplified 75.6%

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

   if -2.4000000000000001e-58 < x < 4.5999999999999998e-16

   1. Initial program 99.8%

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

      1. fma-def 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 60.2%

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

   if 4.00000000000000016e192 < x < 3.1999999999999998e255

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 100.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-58}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+192} \lor \neg \left(x \leq 3.2 \cdot 10^{+255}\right):\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 5: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \lor \neg \left(y \leq 2.8 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.5) (not (<= y 2.8e+24)))
   (+ (* y 5.0) (* 2.0 (* x (+ y z))))
   (* x (+ t (* (+ y z) 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.5) || !(y <= 2.8e+24)) {
		tmp = (y * 5.0) + (2.0 * (x * (y + z)));
	} else {
		tmp = x * (t + ((y + 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 <= (-1.5d0)) .or. (.not. (y <= 2.8d+24))) then
        tmp = (y * 5.0d0) + (2.0d0 * (x * (y + z)))
    else
        tmp = x * (t + ((y + 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 <= -1.5) || !(y <= 2.8e+24)) {
		tmp = (y * 5.0) + (2.0 * (x * (y + z)));
	} else {
		tmp = x * (t + ((y + z) * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.5) or not (y <= 2.8e+24):
		tmp = (y * 5.0) + (2.0 * (x * (y + z)))
	else:
		tmp = x * (t + ((y + z) * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.5) || !(y <= 2.8e+24))
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * Float64(y + z))));
	else
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.5) || ~((y <= 2.8e+24)))
		tmp = (y * 5.0) + (2.0 * (x * (y + z)));
	else
		tmp = x * (t + ((y + z) * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.5], N[Not[LessEqual[y, 2.8e+24]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5 or 2.8000000000000002e24 < 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-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 93.8%

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

   if -1.5 < y < 2.8000000000000002e24

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 89.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \lor \neg \left(y \leq 2.8 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 6: 88.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+152} \lor \neg \left(t \leq 5.8 \cdot 10^{+111}\right):\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.1e+152) (not (<= t 5.8e+111)))
   (+ (* x (+ t (* y 2.0))) (* y 5.0))
   (+ (* y 5.0) (* 2.0 (* x (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e+152) || !(t <= 5.8e+111)) {
		tmp = (x * (t + (y * 2.0))) + (y * 5.0);
	} 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 ((t <= (-1.1d+152)) .or. (.not. (t <= 5.8d+111))) then
        tmp = (x * (t + (y * 2.0d0))) + (y * 5.0d0)
    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 ((t <= -1.1e+152) || !(t <= 5.8e+111)) {
		tmp = (x * (t + (y * 2.0))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (2.0 * (x * (y + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.1e+152) or not (t <= 5.8e+111):
		tmp = (x * (t + (y * 2.0))) + (y * 5.0)
	else:
		tmp = (y * 5.0) + (2.0 * (x * (y + z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.1e+152) || !(t <= 5.8e+111))
		tmp = Float64(Float64(x * Float64(t + Float64(y * 2.0))) + Float64(y * 5.0));
	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 ((t <= -1.1e+152) || ~((t <= 5.8e+111)))
		tmp = (x * (t + (y * 2.0))) + (y * 5.0);
	else
		tmp = (y * 5.0) + (2.0 * (x * (y + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.1e+152], N[Not[LessEqual[t, 5.8e+111]], $MachinePrecision]], N[(N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $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 t < -1.0999999999999999e152 or 5.7999999999999999e111 < 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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 94.9%

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

   if -1.0999999999999999e152 < t < 5.7999999999999999e111

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 92.7%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+152} \lor \neg \left(t \leq 5.8 \cdot 10^{+111}\right):\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \]

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (t + (y + (z + (y + z))))) + (y * 5.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

2. Final simplification 99.9%

   \[\leadsto x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) + y \cdot 5 \]

Alternative 8: 61.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ y z) (* x 2.0))))
   (if (<= z -1.15e-10)
     t_1
     (if (<= z -5.2e-185)
       (* y (+ 5.0 (* x 2.0)))
       (if (<= z 3.35e+21) (* x (+ t (* y 2.0))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y + z) * (x * 2.0);
	double tmp;
	if (z <= -1.15e-10) {
		tmp = t_1;
	} else if (z <= -5.2e-185) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (z <= 3.35e+21) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y + z) * (x * 2.0d0)
    if (z <= (-1.15d-10)) then
        tmp = t_1
    else if (z <= (-5.2d-185)) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else if (z <= 3.35d+21) then
        tmp = x * (t + (y * 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y + z) * (x * 2.0);
	double tmp;
	if (z <= -1.15e-10) {
		tmp = t_1;
	} else if (z <= -5.2e-185) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (z <= 3.35e+21) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y + z) * (x * 2.0)
	tmp = 0
	if z <= -1.15e-10:
		tmp = t_1
	elif z <= -5.2e-185:
		tmp = y * (5.0 + (x * 2.0))
	elif z <= 3.35e+21:
		tmp = x * (t + (y * 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y + z) * Float64(x * 2.0))
	tmp = 0.0
	if (z <= -1.15e-10)
		tmp = t_1;
	elseif (z <= -5.2e-185)
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	elseif (z <= 3.35e+21)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y + z) * (x * 2.0);
	tmp = 0.0;
	if (z <= -1.15e-10)
		tmp = t_1;
	elseif (z <= -5.2e-185)
		tmp = y * (5.0 + (x * 2.0));
	elseif (z <= 3.35e+21)
		tmp = x * (t + (y * 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e-10], t$95$1, If[LessEqual[z, -5.2e-185], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.35e+21], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000004e-10 or 3.35e21 < z

   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. +-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-def 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. distribute-rgt-in 96.3%

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

      4. associate-+l+ 96.3%

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

      5. +-commutative 96.3%

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

      6. count-2 96.3%

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

      7. distribute-rgt-in 100.0%

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

      8. *-commutative 100.0%

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

      9. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around 0 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*r* 87.3%

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

      3. +-commutative 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in x around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-*r* 68.7%

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

      3. +-commutative 68.7%

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

   9. Simplified 68.7%

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

   if -1.15000000000000004e-10 < z < -5.1999999999999997e-185

   1. Initial program 99.8%

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

      1. fma-def 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 77.5%

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

   if -5.1999999999999997e-185 < z < 3.35e21

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 98.3%

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

   5. Taylor expanded in x around inf 68.3%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \end{array} \]

Alternative 9: 82.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+93} \lor \neg \left(y \leq 1.85 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.8e+93) (not (<= y 1.85e+71)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* (+ y z) 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.8e+93) || !(y <= 1.85e+71)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + ((y + 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 <= (-5.8d+93)) .or. (.not. (y <= 1.85d+71))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + ((y + 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 <= -5.8e+93) || !(y <= 1.85e+71)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + ((y + z) * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.8e+93) or not (y <= 1.85e+71):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + ((y + z) * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.8e+93) || !(y <= 1.85e+71))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.8e+93) || ~((y <= 1.85e+71)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + ((y + z) * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.8e+93], N[Not[LessEqual[y, 1.85e+71]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999997e93 or 1.85e71 < 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-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 81.6%

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

   if -5.7999999999999997e93 < y < 1.85e71

   1. Initial program 99.9%

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

      1. fma-def 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. Taylor expanded in x around inf 87.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+93} \lor \neg \left(y \leq 1.85 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 10: 89.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-15} \lor \neg \left(x \leq 5.8 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.5e-15) (not (<= x 5.8e-16)))
   (* 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 <= -6.5e-15) || !(x <= 5.8e-16)) {
		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 <= (-6.5d-15)) .or. (.not. (x <= 5.8d-16))) 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 <= -6.5e-15) || !(x <= 5.8e-16)) {
		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 <= -6.5e-15) or not (x <= 5.8e-16):
		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 <= -6.5e-15) || !(x <= 5.8e-16))
		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 <= -6.5e-15) || ~((x <= 5.8e-16)))
		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, -6.5e-15], N[Not[LessEqual[x, 5.8e-16]], $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 < -6.49999999999999991e-15 or 5.7999999999999996e-16 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.8%

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

   if -6.49999999999999991e-15 < x < 5.7999999999999996e-16

   1. Initial program 99.8%

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

      1. fma-def 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 80.4%

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

   5. Taylor expanded in y around 0 80.4%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-15} \lor \neg \left(x \leq 5.8 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 11: 45.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-185}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= z -1.6e-8)
     t_1
     (if (<= z -2.55e-185) (* y 5.0) (if (<= z 2.5e+44) (* 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 (z <= -1.6e-8) {
		tmp = t_1;
	} else if (z <= -2.55e-185) {
		tmp = y * 5.0;
	} else if (z <= 2.5e+44) {
		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 (z <= (-1.6d-8)) then
        tmp = t_1
    else if (z <= (-2.55d-185)) then
        tmp = y * 5.0d0
    else if (z <= 2.5d+44) 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 (z <= -1.6e-8) {
		tmp = t_1;
	} else if (z <= -2.55e-185) {
		tmp = y * 5.0;
	} else if (z <= 2.5e+44) {
		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 z <= -1.6e-8:
		tmp = t_1
	elif z <= -2.55e-185:
		tmp = y * 5.0
	elif z <= 2.5e+44:
		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 (z <= -1.6e-8)
		tmp = t_1;
	elseif (z <= -2.55e-185)
		tmp = Float64(y * 5.0);
	elseif (z <= 2.5e+44)
		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 (z <= -1.6e-8)
		tmp = t_1;
	elseif (z <= -2.55e-185)
		tmp = y * 5.0;
	elseif (z <= 2.5e+44)
		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[z, -1.6e-8], t$95$1, If[LessEqual[z, -2.55e-185], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 2.5e+44], N[(x * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6000000000000001e-8 or 2.4999999999999998e44 < z

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in z around inf 63.5%

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

   if -1.6000000000000001e-8 < z < -2.5500000000000002e-185

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 53.1%

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

   if -2.5500000000000002e-185 < z < 2.4999999999999998e44

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 45.5%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-185}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 12: 79.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+44} \lor \neg \left(y \leq 3.7 \cdot 10^{+25}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e+44) (not (<= y 3.7e+25)))
   (* 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 <= -1.3e+44) || !(y <= 3.7e+25)) {
		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 <= (-1.3d+44)) .or. (.not. (y <= 3.7d+25))) 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 <= -1.3e+44) || !(y <= 3.7e+25)) {
		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 <= -1.3e+44) or not (y <= 3.7e+25):
		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 <= -1.3e+44) || !(y <= 3.7e+25))
		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 <= -1.3e+44) || ~((y <= 3.7e+25)))
		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, -1.3e+44], N[Not[LessEqual[y, 3.7e+25]], $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 < -1.3e44 or 3.6999999999999999e25 < 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-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 79.6%

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

   if -1.3e44 < y < 3.6999999999999999e25

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 84.0%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+44} \lor \neg \left(y \leq 3.7 \cdot 10^{+25}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 13: 46.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-121}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-20}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.1e-121) (* x t) (if (<= x 2.7e-20) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.1e-121) {
		tmp = x * t;
	} else if (x <= 2.7e-20) {
		tmp = y * 5.0;
	} 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 (x <= (-1.1d-121)) then
        tmp = x * t
    else if (x <= 2.7d-20) then
        tmp = y * 5.0d0
    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 (x <= -1.1e-121) {
		tmp = x * t;
	} else if (x <= 2.7e-20) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.1e-121:
		tmp = x * t
	elif x <= 2.7e-20:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.1e-121)
		tmp = Float64(x * t);
	elseif (x <= 2.7e-20)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.1e-121)
		tmp = x * t;
	elseif (x <= 2.7e-20)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.1e-121], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.7e-20], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.10000000000000011e-121 or 2.7e-20 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in t around inf 32.7%

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

   if -1.10000000000000011e-121 < x < 2.7e-20

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 62.6%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-121}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-20}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 14: 29.7% 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. Taylor expanded in x around 0 28.8%

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

3. Final simplification 28.8%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023240 
(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)))