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

Percentage Accurate: 99.8% → 99.9%

Time: 8.2s

Alternatives: 16

Speedup: 1.0×

• 26.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% 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: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-113}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right) + y \cdot 5\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-122} \lor \neg \left(x \leq 4.8 \cdot 10^{-61}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -5.2e-11)
     t_1
     (if (<= x -2.35e-113)
       (+ (* 2.0 (* x z)) (* y 5.0))
       (if (<= x 2.6e-178)
         (+ (* y 5.0) (* x t))
         (if (or (<= x 1.45e-122) (not (<= x 4.8e-61)))
           t_1
           (+ (* x t) (* y (+ 5.0 (* x 2.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -5.2e-11) {
		tmp = t_1;
	} else if (x <= -2.35e-113) {
		tmp = (2.0 * (x * z)) + (y * 5.0);
	} else if (x <= 2.6e-178) {
		tmp = (y * 5.0) + (x * t);
	} else if ((x <= 1.45e-122) || !(x <= 4.8e-61)) {
		tmp = t_1;
	} else {
		tmp = (x * t) + (y * (5.0 + (x * 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + ((y + z) * 2.0d0))
    if (x <= (-5.2d-11)) then
        tmp = t_1
    else if (x <= (-2.35d-113)) then
        tmp = (2.0d0 * (x * z)) + (y * 5.0d0)
    else if (x <= 2.6d-178) then
        tmp = (y * 5.0d0) + (x * t)
    else if ((x <= 1.45d-122) .or. (.not. (x <= 4.8d-61))) then
        tmp = t_1
    else
        tmp = (x * t) + (y * (5.0d0 + (x * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -5.2e-11) {
		tmp = t_1;
	} else if (x <= -2.35e-113) {
		tmp = (2.0 * (x * z)) + (y * 5.0);
	} else if (x <= 2.6e-178) {
		tmp = (y * 5.0) + (x * t);
	} else if ((x <= 1.45e-122) || !(x <= 4.8e-61)) {
		tmp = t_1;
	} else {
		tmp = (x * t) + (y * (5.0 + (x * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((y + z) * 2.0))
	tmp = 0
	if x <= -5.2e-11:
		tmp = t_1
	elif x <= -2.35e-113:
		tmp = (2.0 * (x * z)) + (y * 5.0)
	elif x <= 2.6e-178:
		tmp = (y * 5.0) + (x * t)
	elif (x <= 1.45e-122) or not (x <= 4.8e-61):
		tmp = t_1
	else:
		tmp = (x * t) + (y * (5.0 + (x * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	tmp = 0.0
	if (x <= -5.2e-11)
		tmp = t_1;
	elseif (x <= -2.35e-113)
		tmp = Float64(Float64(2.0 * Float64(x * z)) + Float64(y * 5.0));
	elseif (x <= 2.6e-178)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif ((x <= 1.45e-122) || !(x <= 4.8e-61))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * t) + Float64(y * Float64(5.0 + Float64(x * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -5.2e-11)
		tmp = t_1;
	elseif (x <= -2.35e-113)
		tmp = (2.0 * (x * z)) + (y * 5.0);
	elseif (x <= 2.6e-178)
		tmp = (y * 5.0) + (x * t);
	elseif ((x <= 1.45e-122) || ~((x <= 4.8e-61)))
		tmp = t_1;
	else
		tmp = (x * t) + (y * (5.0 + (x * 2.0)));
	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]}, If[LessEqual[x, -5.2e-11], t$95$1, If[LessEqual[x, -2.35e-113], N[(N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e-178], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.45e-122], N[Not[LessEqual[x, 4.8e-61]], $MachinePrecision]], t$95$1, N[(N[(x * t), $MachinePrecision] + N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.2000000000000001e-11 or 2.59999999999999998e-178 < x < 1.4500000000000001e-122 or 4.8000000000000002e-61 < x

   1. Initial program 99.9%

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

      1. fma-def 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 96.2%

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

   if -5.2000000000000001e-11 < x < -2.3500000000000001e-113

   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 y around 0 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in t around 0 86.9%

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

   if -2.3500000000000001e-113 < x < 2.59999999999999998e-178

   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 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. count-2 100.0%

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

      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 inf 90.4%

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

      1. *-commutative 90.4%

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

   6. Simplified 90.4%

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

      1. fma-udef 90.4%

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

   8. Applied egg-rr 90.4%

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

   if 1.4500000000000001e-122 < x < 4.8000000000000002e-61

   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 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. count-2 100.0%

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

      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 y around 0 99.9%

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

      1. fma-def 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. fma-udef 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in z around 0 92.1%

      \[\leadsto \color{blue}{t \cdot x + y \cdot \left(5 + 2 \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-113}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right) + y \cdot 5\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-122} \lor \neg \left(x \leq 4.8 \cdot 10^{-61}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 4: 77.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ t_2 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+54}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))) (t_2 (* x (+ t (* z 2.0)))))
   (if (<= y -3.4e+131)
     t_1
     (if (<= y -4.5e+54)
       (* (+ y z) (* x 2.0))
       (if (<= y -2.6e-21)
         t_1
         (if (<= y 2.6e-7)
           t_2
           (if (<= y 2.8e+49)
             (+ (* y 5.0) (* x t))
             (if (<= y 3.5e+76) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double t_2 = x * (t + (z * 2.0));
	double tmp;
	if (y <= -3.4e+131) {
		tmp = t_1;
	} else if (y <= -4.5e+54) {
		tmp = (y + z) * (x * 2.0);
	} else if (y <= -2.6e-21) {
		tmp = t_1;
	} else if (y <= 2.6e-7) {
		tmp = t_2;
	} else if (y <= 2.8e+49) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 3.5e+76) {
		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 = y * (5.0d0 + (x * 2.0d0))
    t_2 = x * (t + (z * 2.0d0))
    if (y <= (-3.4d+131)) then
        tmp = t_1
    else if (y <= (-4.5d+54)) then
        tmp = (y + z) * (x * 2.0d0)
    else if (y <= (-2.6d-21)) then
        tmp = t_1
    else if (y <= 2.6d-7) then
        tmp = t_2
    else if (y <= 2.8d+49) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 3.5d+76) 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 = y * (5.0 + (x * 2.0));
	double t_2 = x * (t + (z * 2.0));
	double tmp;
	if (y <= -3.4e+131) {
		tmp = t_1;
	} else if (y <= -4.5e+54) {
		tmp = (y + z) * (x * 2.0);
	} else if (y <= -2.6e-21) {
		tmp = t_1;
	} else if (y <= 2.6e-7) {
		tmp = t_2;
	} else if (y <= 2.8e+49) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 3.5e+76) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	t_2 = x * (t + (z * 2.0))
	tmp = 0
	if y <= -3.4e+131:
		tmp = t_1
	elif y <= -4.5e+54:
		tmp = (y + z) * (x * 2.0)
	elif y <= -2.6e-21:
		tmp = t_1
	elif y <= 2.6e-7:
		tmp = t_2
	elif y <= 2.8e+49:
		tmp = (y * 5.0) + (x * t)
	elif y <= 3.5e+76:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	t_2 = Float64(x * Float64(t + Float64(z * 2.0)))
	tmp = 0.0
	if (y <= -3.4e+131)
		tmp = t_1;
	elseif (y <= -4.5e+54)
		tmp = Float64(Float64(y + z) * Float64(x * 2.0));
	elseif (y <= -2.6e-21)
		tmp = t_1;
	elseif (y <= 2.6e-7)
		tmp = t_2;
	elseif (y <= 2.8e+49)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 3.5e+76)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	t_2 = x * (t + (z * 2.0));
	tmp = 0.0;
	if (y <= -3.4e+131)
		tmp = t_1;
	elseif (y <= -4.5e+54)
		tmp = (y + z) * (x * 2.0);
	elseif (y <= -2.6e-21)
		tmp = t_1;
	elseif (y <= 2.6e-7)
		tmp = t_2;
	elseif (y <= 2.8e+49)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 3.5e+76)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+131], t$95$1, If[LessEqual[y, -4.5e+54], N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-21], t$95$1, If[LessEqual[y, 2.6e-7], t$95$2, If[LessEqual[y, 2.8e+49], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+76], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.39999999999999986e131 or -4.49999999999999984e54 < y < -2.60000000000000017e-21 or 3.5e76 < 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. Taylor expanded in y around inf 83.3%

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

   4. Simplified 83.3%

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

   if -3.39999999999999986e131 < y < -4.49999999999999984e54

   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 x around inf 89.3%

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

   5. Taylor expanded in t around 0 69.8%

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

      1. associate-*r* 69.8%

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

      2. *-commutative 69.8%

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

   7. Simplified 69.8%

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

   if -2.60000000000000017e-21 < y < 2.59999999999999999e-7 or 2.7999999999999998e49 < y < 3.5e76

   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 y around 0 84.7%

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

   if 2.59999999999999999e-7 < y < 2.7999999999999998e49

   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 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. count-2 100.0%

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

      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 inf 78.6%

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

      1. *-commutative 78.6%

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

   6. Simplified 78.6%

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

      1. fma-udef 78.5%

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

   8. Applied egg-rr 78.5%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+54}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 5: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-109}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right) + y \cdot 5\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-179} \lor \neg \left(x \leq 2.05 \cdot 10^{-123}\right) \land x \leq 7.8 \cdot 10^{-61}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -4.8e-9)
     t_1
     (if (<= x -1.25e-109)
       (+ (* 2.0 (* x z)) (* y 5.0))
       (if (or (<= x 5.8e-179) (and (not (<= x 2.05e-123)) (<= x 7.8e-61)))
         (+ (* y 5.0) (* x t))
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -4.8e-9) {
		tmp = t_1;
	} else if (x <= -1.25e-109) {
		tmp = (2.0 * (x * z)) + (y * 5.0);
	} else if ((x <= 5.8e-179) || (!(x <= 2.05e-123) && (x <= 7.8e-61))) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + ((y + z) * 2.0d0))
    if (x <= (-4.8d-9)) then
        tmp = t_1
    else if (x <= (-1.25d-109)) then
        tmp = (2.0d0 * (x * z)) + (y * 5.0d0)
    else if ((x <= 5.8d-179) .or. (.not. (x <= 2.05d-123)) .and. (x <= 7.8d-61)) then
        tmp = (y * 5.0d0) + (x * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -4.8e-9) {
		tmp = t_1;
	} else if (x <= -1.25e-109) {
		tmp = (2.0 * (x * z)) + (y * 5.0);
	} else if ((x <= 5.8e-179) || (!(x <= 2.05e-123) && (x <= 7.8e-61))) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((y + z) * 2.0))
	tmp = 0
	if x <= -4.8e-9:
		tmp = t_1
	elif x <= -1.25e-109:
		tmp = (2.0 * (x * z)) + (y * 5.0)
	elif (x <= 5.8e-179) or (not (x <= 2.05e-123) and (x <= 7.8e-61)):
		tmp = (y * 5.0) + (x * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	tmp = 0.0
	if (x <= -4.8e-9)
		tmp = t_1;
	elseif (x <= -1.25e-109)
		tmp = Float64(Float64(2.0 * Float64(x * z)) + Float64(y * 5.0));
	elseif ((x <= 5.8e-179) || (!(x <= 2.05e-123) && (x <= 7.8e-61)))
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -4.8e-9)
		tmp = t_1;
	elseif (x <= -1.25e-109)
		tmp = (2.0 * (x * z)) + (y * 5.0);
	elseif ((x <= 5.8e-179) || (~((x <= 2.05e-123)) && (x <= 7.8e-61)))
		tmp = (y * 5.0) + (x * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e-9], t$95$1, If[LessEqual[x, -1.25e-109], N[(N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.8e-179], And[N[Not[LessEqual[x, 2.05e-123]], $MachinePrecision], LessEqual[x, 7.8e-61]]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e-9 or 5.7999999999999998e-179 < x < 2.05e-123 or 7.80000000000000065e-61 < x

   1. Initial program 99.9%

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

      1. fma-def 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 96.2%

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

   if -4.8e-9 < x < -1.25000000000000005e-109

   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 y around 0 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in t around 0 86.9%

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

   if -1.25000000000000005e-109 < x < 5.7999999999999998e-179 or 2.05e-123 < x < 7.80000000000000065e-61

   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 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. count-2 100.0%

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

      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 inf 90.7%

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

      1. *-commutative 90.7%

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

   6. Simplified 90.7%

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

      1. fma-udef 90.6%

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

   8. Applied egg-rr 90.6%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-109}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right) + y \cdot 5\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-179} \lor \neg \left(x \leq 2.05 \cdot 10^{-123}\right) \land x \leq 7.8 \cdot 10^{-61}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 6: 44.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-140}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-33}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= z -2.3e+20)
     t_1
     (if (<= z -6e-140)
       (* x t)
       (if (<= z -2.8e-178)
         (* y 5.0)
         (if (<= z 5.5e-292)
           (* x t)
           (if (<= z 7e-33) (* y 5.0) (if (<= z 6e+52) (* 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 <= -2.3e+20) {
		tmp = t_1;
	} else if (z <= -6e-140) {
		tmp = x * t;
	} else if (z <= -2.8e-178) {
		tmp = y * 5.0;
	} else if (z <= 5.5e-292) {
		tmp = x * t;
	} else if (z <= 7e-33) {
		tmp = y * 5.0;
	} else if (z <= 6e+52) {
		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 <= (-2.3d+20)) then
        tmp = t_1
    else if (z <= (-6d-140)) then
        tmp = x * t
    else if (z <= (-2.8d-178)) then
        tmp = y * 5.0d0
    else if (z <= 5.5d-292) then
        tmp = x * t
    else if (z <= 7d-33) then
        tmp = y * 5.0d0
    else if (z <= 6d+52) 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 <= -2.3e+20) {
		tmp = t_1;
	} else if (z <= -6e-140) {
		tmp = x * t;
	} else if (z <= -2.8e-178) {
		tmp = y * 5.0;
	} else if (z <= 5.5e-292) {
		tmp = x * t;
	} else if (z <= 7e-33) {
		tmp = y * 5.0;
	} else if (z <= 6e+52) {
		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 <= -2.3e+20:
		tmp = t_1
	elif z <= -6e-140:
		tmp = x * t
	elif z <= -2.8e-178:
		tmp = y * 5.0
	elif z <= 5.5e-292:
		tmp = x * t
	elif z <= 7e-33:
		tmp = y * 5.0
	elif z <= 6e+52:
		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 <= -2.3e+20)
		tmp = t_1;
	elseif (z <= -6e-140)
		tmp = Float64(x * t);
	elseif (z <= -2.8e-178)
		tmp = Float64(y * 5.0);
	elseif (z <= 5.5e-292)
		tmp = Float64(x * t);
	elseif (z <= 7e-33)
		tmp = Float64(y * 5.0);
	elseif (z <= 6e+52)
		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 <= -2.3e+20)
		tmp = t_1;
	elseif (z <= -6e-140)
		tmp = x * t;
	elseif (z <= -2.8e-178)
		tmp = y * 5.0;
	elseif (z <= 5.5e-292)
		tmp = x * t;
	elseif (z <= 7e-33)
		tmp = y * 5.0;
	elseif (z <= 6e+52)
		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, -2.3e+20], t$95$1, If[LessEqual[z, -6e-140], N[(x * t), $MachinePrecision], If[LessEqual[z, -2.8e-178], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 5.5e-292], N[(x * t), $MachinePrecision], If[LessEqual[z, 7e-33], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 6e+52], N[(x * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e20 or 6e52 < 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. Taylor expanded in z around inf 61.4%

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

   if -2.3e20 < z < -6.00000000000000037e-140 or -2.80000000000000019e-178 < z < 5.50000000000000006e-292 or 6.9999999999999997e-33 < z < 6e52

   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 52.1%

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

   if -6.00000000000000037e-140 < z < -2.80000000000000019e-178 or 5.50000000000000006e-292 < z < 6.9999999999999997e-33

   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 x around 0 45.7%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-140}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-33}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 7: 87.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-27} \lor \neg \left(x \leq 2.6 \cdot 10^{-178} \lor \neg \left(x \leq 5.4 \cdot 10^{-123}\right) \land x \leq 1.45 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.7e-27)
         (not
          (or (<= x 2.6e-178) (and (not (<= x 5.4e-123)) (<= x 1.45e-62)))))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.7e-27) || !((x <= 2.6e-178) || (!(x <= 5.4e-123) && (x <= 1.45e-62)))) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.7d-27)) .or. (.not. (x <= 2.6d-178) .or. (.not. (x <= 5.4d-123)) .and. (x <= 1.45d-62))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.7e-27) || !((x <= 2.6e-178) || (!(x <= 5.4e-123) && (x <= 1.45e-62)))) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.7e-27) or not ((x <= 2.6e-178) or (not (x <= 5.4e-123) and (x <= 1.45e-62))):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.7e-27) || !((x <= 2.6e-178) || (!(x <= 5.4e-123) && (x <= 1.45e-62))))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.7e-27) || ~(((x <= 2.6e-178) || (~((x <= 5.4e-123)) && (x <= 1.45e-62)))))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.7e-27], N[Not[Or[LessEqual[x, 2.6e-178], And[N[Not[LessEqual[x, 5.4e-123]], $MachinePrecision], LessEqual[x, 1.45e-62]]]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.70000000000000029e-27 or 2.59999999999999998e-178 < x < 5.4000000000000002e-123 or 1.44999999999999993e-62 < x

   1. Initial program 99.9%

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

      1. fma-def 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 95.1%

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

   if -3.70000000000000029e-27 < x < 2.59999999999999998e-178 or 5.4000000000000002e-123 < x < 1.44999999999999993e-62

   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 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. count-2 100.0%

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

      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 inf 86.6%

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

      1. *-commutative 86.6%

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

   6. Simplified 86.6%

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

      1. fma-udef 86.6%

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

   8. Applied egg-rr 86.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-27} \lor \neg \left(x \leq 2.6 \cdot 10^{-178} \lor \neg \left(x \leq 5.4 \cdot 10^{-123}\right) \land x \leq 1.45 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 8: 77.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-21} \lor \neg \left(y \leq 3.6 \cdot 10^{+76}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -3.4e+131)
     t_1
     (if (<= y -5.2e+40)
       (* (+ y z) (* x 2.0))
       (if (or (<= y -2e-21) (not (<= y 3.6e+76)))
         t_1
         (* x (+ t (* z 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -3.4e+131) {
		tmp = t_1;
	} else if (y <= -5.2e+40) {
		tmp = (y + z) * (x * 2.0);
	} else if ((y <= -2e-21) || !(y <= 3.6e+76)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-3.4d+131)) then
        tmp = t_1
    else if (y <= (-5.2d+40)) then
        tmp = (y + z) * (x * 2.0d0)
    else if ((y <= (-2d-21)) .or. (.not. (y <= 3.6d+76))) then
        tmp = t_1
    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 t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -3.4e+131) {
		tmp = t_1;
	} else if (y <= -5.2e+40) {
		tmp = (y + z) * (x * 2.0);
	} else if ((y <= -2e-21) || !(y <= 3.6e+76)) {
		tmp = t_1;
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -3.4e+131:
		tmp = t_1
	elif y <= -5.2e+40:
		tmp = (y + z) * (x * 2.0)
	elif (y <= -2e-21) or not (y <= 3.6e+76):
		tmp = t_1
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -3.4e+131)
		tmp = t_1;
	elseif (y <= -5.2e+40)
		tmp = Float64(Float64(y + z) * Float64(x * 2.0));
	elseif ((y <= -2e-21) || !(y <= 3.6e+76))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -3.4e+131)
		tmp = t_1;
	elseif (y <= -5.2e+40)
		tmp = (y + z) * (x * 2.0);
	elseif ((y <= -2e-21) || ~((y <= 3.6e+76)))
		tmp = t_1;
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+131], t$95$1, If[LessEqual[y, -5.2e+40], N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2e-21], N[Not[LessEqual[y, 3.6e+76]], $MachinePrecision]], t$95$1, N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.39999999999999986e131 or -5.2000000000000001e40 < y < -1.99999999999999982e-21 or 3.6000000000000003e76 < 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. Taylor expanded in y around inf 83.3%

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

   4. Simplified 83.3%

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

   if -3.39999999999999986e131 < y < -5.2000000000000001e40

   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 x around inf 89.3%

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

   5. Taylor expanded in t around 0 69.8%

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

      1. associate-*r* 69.8%

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

      2. *-commutative 69.8%

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

   7. Simplified 69.8%

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

   if -1.99999999999999982e-21 < y < 3.6000000000000003e76

   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 y around 0 80.1%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-21} \lor \neg \left(y \leq 3.6 \cdot 10^{+76}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 9: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 1.7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(z + z\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.5) (not (<= x 1.7e-7)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* x (+ t (+ z z))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 1.7e-7)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (x * (t + (z + z))) + (y * 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.5d0)) .or. (.not. (x <= 1.7d-7))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (x * (t + (z + z))) + (y * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 1.7e-7)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (x * (t + (z + z))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.5) or not (x <= 1.7e-7):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (x * (t + (z + z))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.5) || !(x <= 1.7e-7))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(z + z))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.5) || ~((x <= 1.7e-7)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (x * (t + (z + z))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.5], N[Not[LessEqual[x, 1.7e-7]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(z + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5 or 1.69999999999999987e-7 < x

   1. Initial program 99.9%

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

      1. fma-def 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 99.1%

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

   if -2.5 < x < 1.69999999999999987e-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. Taylor expanded in y around 0 99.3%

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

   4. Simplified 99.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 1.7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(z + z\right)\right) + y \cdot 5\\ \end{array} \]

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 11: 65.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;x \leq -2.05 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))))
   (if (<= x -2.05e-71)
     t_1
     (if (<= x 2.6e-178)
       (* y 5.0)
       (if (<= x 3.2e+108) t_1 (* x (+ t (* y 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -2.05e-71) {
		tmp = t_1;
	} else if (x <= 2.6e-178) {
		tmp = y * 5.0;
	} else if (x <= 3.2e+108) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    if (x <= (-2.05d-71)) then
        tmp = t_1
    else if (x <= 2.6d-178) then
        tmp = y * 5.0d0
    else if (x <= 3.2d+108) then
        tmp = t_1
    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 t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -2.05e-71) {
		tmp = t_1;
	} else if (x <= 2.6e-178) {
		tmp = y * 5.0;
	} else if (x <= 3.2e+108) {
		tmp = t_1;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	tmp = 0
	if x <= -2.05e-71:
		tmp = t_1
	elif x <= 2.6e-178:
		tmp = y * 5.0
	elif x <= 3.2e+108:
		tmp = t_1
	else:
		tmp = x * (t + (y * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	tmp = 0.0
	if (x <= -2.05e-71)
		tmp = t_1;
	elseif (x <= 2.6e-178)
		tmp = Float64(y * 5.0);
	elseif (x <= 3.2e+108)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	tmp = 0.0;
	if (x <= -2.05e-71)
		tmp = t_1;
	elseif (x <= 2.6e-178)
		tmp = y * 5.0;
	elseif (x <= 3.2e+108)
		tmp = t_1;
	else
		tmp = x * (t + (y * 2.0));
	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]}, If[LessEqual[x, -2.05e-71], t$95$1, If[LessEqual[x, 2.6e-178], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 3.2e+108], t$95$1, N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.04999999999999997e-71 or 2.59999999999999998e-178 < x < 3.1999999999999999e108

   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 y around 0 66.8%

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

   if -2.04999999999999997e-71 < x < 2.59999999999999998e-178

   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 69.9%

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

   if 3.1999999999999999e108 < 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 100.0%

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

   5. Taylor expanded in z around 0 86.1%

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

      1. *-commutative 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]

Alternative 12: 48.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;x \leq -2.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-14}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+133}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* y x))))
   (if (<= x -2.5)
     t_1
     (if (<= x 1.7e-14) (* y 5.0) (if (<= x 3.3e+133) (* x t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y * x);
	double tmp;
	if (x <= -2.5) {
		tmp = t_1;
	} else if (x <= 1.7e-14) {
		tmp = y * 5.0;
	} else if (x <= 3.3e+133) {
		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 * (y * x)
    if (x <= (-2.5d0)) then
        tmp = t_1
    else if (x <= 1.7d-14) then
        tmp = y * 5.0d0
    else if (x <= 3.3d+133) 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 * (y * x);
	double tmp;
	if (x <= -2.5) {
		tmp = t_1;
	} else if (x <= 1.7e-14) {
		tmp = y * 5.0;
	} else if (x <= 3.3e+133) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y * x)
	tmp = 0
	if x <= -2.5:
		tmp = t_1
	elif x <= 1.7e-14:
		tmp = y * 5.0
	elif x <= 3.3e+133:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y * x))
	tmp = 0.0
	if (x <= -2.5)
		tmp = t_1;
	elseif (x <= 1.7e-14)
		tmp = Float64(y * 5.0);
	elseif (x <= 3.3e+133)
		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 * (y * x);
	tmp = 0.0;
	if (x <= -2.5)
		tmp = t_1;
	elseif (x <= 1.7e-14)
		tmp = y * 5.0;
	elseif (x <= 3.3e+133)
		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[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5], t$95$1, If[LessEqual[x, 1.7e-14], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 3.3e+133], N[(x * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5 or 3.3e133 < 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 99.4%

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

   5. Taylor expanded in z around 0 71.3%

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

      1. *-commutative 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in t around 0 44.7%

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

   if -2.5 < x < 1.70000000000000001e-14

   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 55.4%

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

   if 1.70000000000000001e-14 < x < 3.3e133

   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 t around inf 45.3%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-14}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+133}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 13: 65.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-68} \lor \neg \left(x \leq 3.9 \cdot 10^{-179}\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.2e-68) (not (<= x 3.9e-179)))
   (* x (+ t (* z 2.0)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.2e-68) || !(x <= 3.9e-179)) {
		tmp = x * (t + (z * 2.0));
	} 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 <= (-3.2d-68)) .or. (.not. (x <= 3.9d-179))) then
        tmp = x * (t + (z * 2.0d0))
    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 <= -3.2e-68) || !(x <= 3.9e-179)) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.2e-68) or not (x <= 3.9e-179):
		tmp = x * (t + (z * 2.0))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.2e-68) || !(x <= 3.9e-179))
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.2e-68) || ~((x <= 3.9e-179)))
		tmp = x * (t + (z * 2.0));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.2e-68], N[Not[LessEqual[x, 3.9e-179]], $MachinePrecision]], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1999999999999999e-68 or 3.9000000000000003e-179 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 65.9%

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

   if -3.1999999999999999e-68 < x < 3.9000000000000003e-179

   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 69.9%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-68} \lor \neg \left(x \leq 3.9 \cdot 10^{-179}\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 14: 78.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-21} \lor \neg \left(y \leq 1.66 \cdot 10^{+80}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e-21) (not (<= y 1.66e+80)))
   (* 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 <= -2.6e-21) || !(y <= 1.66e+80)) {
		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 <= (-2.6d-21)) .or. (.not. (y <= 1.66d+80))) 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 <= -2.6e-21) || !(y <= 1.66e+80)) {
		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 <= -2.6e-21) or not (y <= 1.66e+80):
		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 <= -2.6e-21) || !(y <= 1.66e+80))
		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 <= -2.6e-21) || ~((y <= 1.66e+80)))
		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, -2.6e-21], N[Not[LessEqual[y, 1.66e+80]], $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 < -2.60000000000000017e-21 or 1.6599999999999999e80 < 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. Taylor expanded in y around inf 77.9%

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

   4. Simplified 77.9%

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

   if -2.60000000000000017e-21 < y < 1.6599999999999999e80

   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 y around 0 80.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-21} \lor \neg \left(y \leq 1.66 \cdot 10^{+80}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 15: 47.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.55e-9) (* x t) (if (<= x 7.2e-20) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e-9) {
		tmp = x * t;
	} else if (x <= 7.2e-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 <= (-1.55d-9)) then
        tmp = x * t
    else if (x <= 7.2d-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 <= -1.55e-9) {
		tmp = x * t;
	} else if (x <= 7.2e-20) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.55e-9:
		tmp = x * t
	elif x <= 7.2e-20:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.55e-9)
		tmp = Float64(x * t);
	elseif (x <= 7.2e-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 <= -1.55e-9)
		tmp = x * t;
	elseif (x <= 7.2e-20)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.55e-9], N[(x * t), $MachinePrecision], If[LessEqual[x, 7.2e-20], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000002e-9 or 7.19999999999999948e-20 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 35.4%

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

   if -1.55000000000000002e-9 < x < 7.19999999999999948e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 57.1%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 16: 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 29.1%

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

3. Final simplification 29.1%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023271 
(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)))