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

Percentage Accurate: 99.9% → 100.0%

Time: 11.5s

Alternatives: 15

Speedup: 1.0×

• 26.1% 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: 100.0% 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 96.9%

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

   4. associate-+l+ 96.9%

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

   5. +-commutative 96.9%

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

   6. count-2 96.9%

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

   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 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. Final simplification 100.0%

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

Alternative 3: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+45}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-23}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-94} \lor \neg \left(y \leq -2.4 \cdot 10^{-116}\right) \land y \leq 8 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.22e+143)
     t_2
     (if (<= y -2e+76)
       t_1
       (if (<= y -1.75e+45)
         (* y 5.0)
         (if (<= y -1.1e-23)
           (* (+ y z) (* x 2.0))
           (if (or (<= y -2.5e-94) (and (not (<= y -2.4e-116)) (<= y 8e+94)))
             t_1
             t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.22e+143) {
		tmp = t_2;
	} else if (y <= -2e+76) {
		tmp = t_1;
	} else if (y <= -1.75e+45) {
		tmp = y * 5.0;
	} else if (y <= -1.1e-23) {
		tmp = (y + z) * (x * 2.0);
	} else if ((y <= -2.5e-94) || (!(y <= -2.4e-116) && (y <= 8e+94))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.22d+143)) then
        tmp = t_2
    else if (y <= (-2d+76)) then
        tmp = t_1
    else if (y <= (-1.75d+45)) then
        tmp = y * 5.0d0
    else if (y <= (-1.1d-23)) then
        tmp = (y + z) * (x * 2.0d0)
    else if ((y <= (-2.5d-94)) .or. (.not. (y <= (-2.4d-116))) .and. (y <= 8d+94)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.22e+143) {
		tmp = t_2;
	} else if (y <= -2e+76) {
		tmp = t_1;
	} else if (y <= -1.75e+45) {
		tmp = y * 5.0;
	} else if (y <= -1.1e-23) {
		tmp = (y + z) * (x * 2.0);
	} else if ((y <= -2.5e-94) || (!(y <= -2.4e-116) && (y <= 8e+94))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.22e+143:
		tmp = t_2
	elif y <= -2e+76:
		tmp = t_1
	elif y <= -1.75e+45:
		tmp = y * 5.0
	elif y <= -1.1e-23:
		tmp = (y + z) * (x * 2.0)
	elif (y <= -2.5e-94) or (not (y <= -2.4e-116) and (y <= 8e+94)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.22e+143)
		tmp = t_2;
	elseif (y <= -2e+76)
		tmp = t_1;
	elseif (y <= -1.75e+45)
		tmp = Float64(y * 5.0);
	elseif (y <= -1.1e-23)
		tmp = Float64(Float64(y + z) * Float64(x * 2.0));
	elseif ((y <= -2.5e-94) || (!(y <= -2.4e-116) && (y <= 8e+94)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.22e+143)
		tmp = t_2;
	elseif (y <= -2e+76)
		tmp = t_1;
	elseif (y <= -1.75e+45)
		tmp = y * 5.0;
	elseif (y <= -1.1e-23)
		tmp = (y + z) * (x * 2.0);
	elseif ((y <= -2.5e-94) || (~((y <= -2.4e-116)) && (y <= 8e+94)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.22e+143], t$95$2, If[LessEqual[y, -2e+76], t$95$1, If[LessEqual[y, -1.75e+45], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, -1.1e-23], N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.5e-94], And[N[Not[LessEqual[y, -2.4e-116]], $MachinePrecision], LessEqual[y, 8e+94]]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.22000000000000004e143 or -2.4999999999999998e-94 < y < -2.39999999999999993e-116 or 8.0000000000000002e94 < 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 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 y around inf 90.2%

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

   if -1.22000000000000004e143 < y < -2.0000000000000001e76 or -1.1e-23 < y < -2.4999999999999998e-94 or -2.39999999999999993e-116 < y < 8.0000000000000002e94

   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 81.2%

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

   if -2.0000000000000001e76 < y < -1.75000000000000011e45

   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 58.7%

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

   if -1.75000000000000011e45 < y < -1.1e-23

   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 t around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. fma-def 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r* 91.8%

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

      3. +-commutative 91.8%

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

   9. Simplified 91.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+45}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-23}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-94} \lor \neg \left(y \leq -2.4 \cdot 10^{-116}\right) \land y \leq 8 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 4: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ t_3 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-250}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* 2.0 (* x z))))
        (t_2 (* x (+ t (* (+ y z) 2.0))))
        (t_3 (+ (* y 5.0) (* x t))))
   (if (<= x -5.2e-14)
     t_2
     (if (<= x -2.45e-86)
       t_1
       (if (<= x -5.8e-250)
         t_3
         (if (<= x 5.4e-157)
           t_1
           (if (<= x 2.5e-107) t_3 (if (<= x 3.8e-47) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (2.0 * (x * z));
	double t_2 = x * (t + ((y + z) * 2.0));
	double t_3 = (y * 5.0) + (x * t);
	double tmp;
	if (x <= -5.2e-14) {
		tmp = t_2;
	} else if (x <= -2.45e-86) {
		tmp = t_1;
	} else if (x <= -5.8e-250) {
		tmp = t_3;
	} else if (x <= 5.4e-157) {
		tmp = t_1;
	} else if (x <= 2.5e-107) {
		tmp = t_3;
	} else if (x <= 3.8e-47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * 5.0d0) + (2.0d0 * (x * z))
    t_2 = x * (t + ((y + z) * 2.0d0))
    t_3 = (y * 5.0d0) + (x * t)
    if (x <= (-5.2d-14)) then
        tmp = t_2
    else if (x <= (-2.45d-86)) then
        tmp = t_1
    else if (x <= (-5.8d-250)) then
        tmp = t_3
    else if (x <= 5.4d-157) then
        tmp = t_1
    else if (x <= 2.5d-107) then
        tmp = t_3
    else if (x <= 3.8d-47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (2.0 * (x * z));
	double t_2 = x * (t + ((y + z) * 2.0));
	double t_3 = (y * 5.0) + (x * t);
	double tmp;
	if (x <= -5.2e-14) {
		tmp = t_2;
	} else if (x <= -2.45e-86) {
		tmp = t_1;
	} else if (x <= -5.8e-250) {
		tmp = t_3;
	} else if (x <= 5.4e-157) {
		tmp = t_1;
	} else if (x <= 2.5e-107) {
		tmp = t_3;
	} else if (x <= 3.8e-47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (2.0 * (x * z))
	t_2 = x * (t + ((y + z) * 2.0))
	t_3 = (y * 5.0) + (x * t)
	tmp = 0
	if x <= -5.2e-14:
		tmp = t_2
	elif x <= -2.45e-86:
		tmp = t_1
	elif x <= -5.8e-250:
		tmp = t_3
	elif x <= 5.4e-157:
		tmp = t_1
	elif x <= 2.5e-107:
		tmp = t_3
	elif x <= 3.8e-47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)))
	t_2 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	t_3 = Float64(Float64(y * 5.0) + Float64(x * t))
	tmp = 0.0
	if (x <= -5.2e-14)
		tmp = t_2;
	elseif (x <= -2.45e-86)
		tmp = t_1;
	elseif (x <= -5.8e-250)
		tmp = t_3;
	elseif (x <= 5.4e-157)
		tmp = t_1;
	elseif (x <= 2.5e-107)
		tmp = t_3;
	elseif (x <= 3.8e-47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (2.0 * (x * z));
	t_2 = x * (t + ((y + z) * 2.0));
	t_3 = (y * 5.0) + (x * t);
	tmp = 0.0;
	if (x <= -5.2e-14)
		tmp = t_2;
	elseif (x <= -2.45e-86)
		tmp = t_1;
	elseif (x <= -5.8e-250)
		tmp = t_3;
	elseif (x <= 5.4e-157)
		tmp = t_1;
	elseif (x <= 2.5e-107)
		tmp = t_3;
	elseif (x <= 3.8e-47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e-14], t$95$2, If[LessEqual[x, -2.45e-86], t$95$1, If[LessEqual[x, -5.8e-250], t$95$3, If[LessEqual[x, 5.4e-157], t$95$1, If[LessEqual[x, 2.5e-107], t$95$3, If[LessEqual[x, 3.8e-47], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.19999999999999993e-14 or 3.80000000000000015e-47 < 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 98.6%

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

   if -5.19999999999999993e-14 < x < -2.44999999999999986e-86 or -5.8000000000000004e-250 < x < 5.4e-157 or 2.49999999999999985e-107 < x < 3.80000000000000015e-47

   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 88.6%

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

   5. Taylor expanded in y around 0 88.6%

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

   if -2.44999999999999986e-86 < x < -5.8000000000000004e-250 or 5.4e-157 < x < 2.49999999999999985e-107

   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 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. count-2 99.9%

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

      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 88.1%

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

      1. fma-udef 88.1%

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

      2. *-commutative 88.1%

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

   6. Applied egg-rr 88.1%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-86}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-250}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-157}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-47}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 5: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ t_2 := x \cdot \left(t + y \cdot 2\right)\\ t_3 := \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{+69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-276}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0))))
        (t_2 (* x (+ t (* y 2.0))))
        (t_3 (* (+ y z) (* x 2.0))))
   (if (<= z -5.7e+69)
     t_3
     (if (<= z -3e+20)
       t_1
       (if (<= z -1.3e-172)
         t_2
         (if (<= z -6.2e-246)
           t_1
           (if (<= z -3.8e-276) t_2 (if (<= z 4.2e+92) t_1 t_3))))))))

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 + (y * 2.0));
	double t_3 = (y + z) * (x * 2.0);
	double tmp;
	if (z <= -5.7e+69) {
		tmp = t_3;
	} else if (z <= -3e+20) {
		tmp = t_1;
	} else if (z <= -1.3e-172) {
		tmp = t_2;
	} else if (z <= -6.2e-246) {
		tmp = t_1;
	} else if (z <= -3.8e-276) {
		tmp = t_2;
	} else if (z <= 4.2e+92) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    t_2 = x * (t + (y * 2.0d0))
    t_3 = (y + z) * (x * 2.0d0)
    if (z <= (-5.7d+69)) then
        tmp = t_3
    else if (z <= (-3d+20)) then
        tmp = t_1
    else if (z <= (-1.3d-172)) then
        tmp = t_2
    else if (z <= (-6.2d-246)) then
        tmp = t_1
    else if (z <= (-3.8d-276)) then
        tmp = t_2
    else if (z <= 4.2d+92) then
        tmp = t_1
    else
        tmp = t_3
    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 + (y * 2.0));
	double t_3 = (y + z) * (x * 2.0);
	double tmp;
	if (z <= -5.7e+69) {
		tmp = t_3;
	} else if (z <= -3e+20) {
		tmp = t_1;
	} else if (z <= -1.3e-172) {
		tmp = t_2;
	} else if (z <= -6.2e-246) {
		tmp = t_1;
	} else if (z <= -3.8e-276) {
		tmp = t_2;
	} else if (z <= 4.2e+92) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	t_2 = x * (t + (y * 2.0))
	t_3 = (y + z) * (x * 2.0)
	tmp = 0
	if z <= -5.7e+69:
		tmp = t_3
	elif z <= -3e+20:
		tmp = t_1
	elif z <= -1.3e-172:
		tmp = t_2
	elif z <= -6.2e-246:
		tmp = t_1
	elif z <= -3.8e-276:
		tmp = t_2
	elif z <= 4.2e+92:
		tmp = t_1
	else:
		tmp = t_3
	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(y * 2.0)))
	t_3 = Float64(Float64(y + z) * Float64(x * 2.0))
	tmp = 0.0
	if (z <= -5.7e+69)
		tmp = t_3;
	elseif (z <= -3e+20)
		tmp = t_1;
	elseif (z <= -1.3e-172)
		tmp = t_2;
	elseif (z <= -6.2e-246)
		tmp = t_1;
	elseif (z <= -3.8e-276)
		tmp = t_2;
	elseif (z <= 4.2e+92)
		tmp = t_1;
	else
		tmp = t_3;
	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 + (y * 2.0));
	t_3 = (y + z) * (x * 2.0);
	tmp = 0.0;
	if (z <= -5.7e+69)
		tmp = t_3;
	elseif (z <= -3e+20)
		tmp = t_1;
	elseif (z <= -1.3e-172)
		tmp = t_2;
	elseif (z <= -6.2e-246)
		tmp = t_1;
	elseif (z <= -3.8e-276)
		tmp = t_2;
	elseif (z <= 4.2e+92)
		tmp = t_1;
	else
		tmp = t_3;
	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[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.7e+69], t$95$3, If[LessEqual[z, -3e+20], t$95$1, If[LessEqual[z, -1.3e-172], t$95$2, If[LessEqual[z, -6.2e-246], t$95$1, If[LessEqual[z, -3.8e-276], t$95$2, If[LessEqual[z, 4.2e+92], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.7e69 or 4.19999999999999972e92 < 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. 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 t around 0 91.1%

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

      1. associate-*r* 91.1%

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

      2. fma-def 91.1%

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

      3. *-commutative 91.1%

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

      4. *-commutative 91.1%

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

   6. Applied egg-rr 91.1%

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

   7. Taylor expanded in x around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-*r* 75.0%

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

      3. +-commutative 75.0%

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

   9. Simplified 75.0%

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

   if -5.7e69 < z < -3e20 or -1.2999999999999999e-172 < z < -6.2000000000000001e-246 or -3.8e-276 < z < 4.19999999999999972e92

   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 y around inf 65.4%

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

   if -3e20 < z < -1.2999999999999999e-172 or -6.2000000000000001e-246 < z < -3.8e-276

   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 90.2%

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

   5. Taylor expanded in x around inf 69.4%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+69}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-276}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \end{array} \]

Alternative 6: 75.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot t\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-31}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x t))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -9e+145)
     t_2
     (if (<= y -1.26e+45)
       t_1
       (if (<= y -1.05e-31)
         (* (+ y z) (* x 2.0))
         (if (<= y -2.4e-116)
           t_1
           (if (<= y 1.4e+94) (* x (+ t (* z 2.0))) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -9e+145) {
		tmp = t_2;
	} else if (y <= -1.26e+45) {
		tmp = t_1;
	} else if (y <= -1.05e-31) {
		tmp = (y + z) * (x * 2.0);
	} else if (y <= -2.4e-116) {
		tmp = t_1;
	} else if (y <= 1.4e+94) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * 5.0d0) + (x * t)
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-9d+145)) then
        tmp = t_2
    else if (y <= (-1.26d+45)) then
        tmp = t_1
    else if (y <= (-1.05d-31)) then
        tmp = (y + z) * (x * 2.0d0)
    else if (y <= (-2.4d-116)) then
        tmp = t_1
    else if (y <= 1.4d+94) then
        tmp = x * (t + (z * 2.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -9e+145) {
		tmp = t_2;
	} else if (y <= -1.26e+45) {
		tmp = t_1;
	} else if (y <= -1.05e-31) {
		tmp = (y + z) * (x * 2.0);
	} else if (y <= -2.4e-116) {
		tmp = t_1;
	} else if (y <= 1.4e+94) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (x * t)
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -9e+145:
		tmp = t_2
	elif y <= -1.26e+45:
		tmp = t_1
	elif y <= -1.05e-31:
		tmp = (y + z) * (x * 2.0)
	elif y <= -2.4e-116:
		tmp = t_1
	elif y <= 1.4e+94:
		tmp = x * (t + (z * 2.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(x * t))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -9e+145)
		tmp = t_2;
	elseif (y <= -1.26e+45)
		tmp = t_1;
	elseif (y <= -1.05e-31)
		tmp = Float64(Float64(y + z) * Float64(x * 2.0));
	elseif (y <= -2.4e-116)
		tmp = t_1;
	elseif (y <= 1.4e+94)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (x * t);
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -9e+145)
		tmp = t_2;
	elseif (y <= -1.26e+45)
		tmp = t_1;
	elseif (y <= -1.05e-31)
		tmp = (y + z) * (x * 2.0);
	elseif (y <= -2.4e-116)
		tmp = t_1;
	elseif (y <= 1.4e+94)
		tmp = x * (t + (z * 2.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+145], t$95$2, If[LessEqual[y, -1.26e+45], t$95$1, If[LessEqual[y, -1.05e-31], N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-116], t$95$1, If[LessEqual[y, 1.4e+94], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.9999999999999996e145 or 1.39999999999999999e94 < 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 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 y around inf 89.5%

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

   if -8.9999999999999996e145 < y < -1.26e45 or -1.04999999999999996e-31 < y < -2.39999999999999993e-116

   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. +-commutative 99.8%

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

      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 97.5%

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

      4. associate-+l+ 97.5%

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

      5. +-commutative 97.5%

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

      6. count-2 97.5%

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

      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 inf 76.2%

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

      1. fma-udef 76.1%

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

      2. *-commutative 76.1%

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

   6. Applied egg-rr 76.1%

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

   if -1.26e45 < y < -1.04999999999999996e-31

   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 t around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. fma-def 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-*r* 92.5%

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

      3. +-commutative 92.5%

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

   9. Simplified 92.5%

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

   if -2.39999999999999993e-116 < y < 1.39999999999999999e94

   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 83.1%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{+45}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-31}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-116}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 7: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+268}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.25 \cdot 10^{-13}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-36}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -1.15e+268)
     (* 2.0 (* y x))
     (if (<= x -1.6e+160)
       t_1
       (if (<= x -3.25e-13)
         (* x t)
         (if (<= x 3.8e-36) (* y 5.0) (if (<= x 6.6e+168) t_1 (* x t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -1.15e+268) {
		tmp = 2.0 * (y * x);
	} else if (x <= -1.6e+160) {
		tmp = t_1;
	} else if (x <= -3.25e-13) {
		tmp = x * t;
	} else if (x <= 3.8e-36) {
		tmp = y * 5.0;
	} else if (x <= 6.6e+168) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-1.15d+268)) then
        tmp = 2.0d0 * (y * x)
    else if (x <= (-1.6d+160)) then
        tmp = t_1
    else if (x <= (-3.25d-13)) then
        tmp = x * t
    else if (x <= 3.8d-36) then
        tmp = y * 5.0d0
    else if (x <= 6.6d+168) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -1.15e+268) {
		tmp = 2.0 * (y * x);
	} else if (x <= -1.6e+160) {
		tmp = t_1;
	} else if (x <= -3.25e-13) {
		tmp = x * t;
	} else if (x <= 3.8e-36) {
		tmp = y * 5.0;
	} else if (x <= 6.6e+168) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -1.15e+268:
		tmp = 2.0 * (y * x)
	elif x <= -1.6e+160:
		tmp = t_1
	elif x <= -3.25e-13:
		tmp = x * t
	elif x <= 3.8e-36:
		tmp = y * 5.0
	elif x <= 6.6e+168:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -1.15e+268)
		tmp = Float64(2.0 * Float64(y * x));
	elseif (x <= -1.6e+160)
		tmp = t_1;
	elseif (x <= -3.25e-13)
		tmp = Float64(x * t);
	elseif (x <= 3.8e-36)
		tmp = Float64(y * 5.0);
	elseif (x <= 6.6e+168)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -1.15e+268)
		tmp = 2.0 * (y * x);
	elseif (x <= -1.6e+160)
		tmp = t_1;
	elseif (x <= -3.25e-13)
		tmp = x * t;
	elseif (x <= 3.8e-36)
		tmp = y * 5.0;
	elseif (x <= 6.6e+168)
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+268], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e+160], t$95$1, If[LessEqual[x, -3.25e-13], N[(x * t), $MachinePrecision], If[LessEqual[x, 3.8e-36], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 6.6e+168], t$95$1, N[(x * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.15000000000000006e268

   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%

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

   5. Taylor expanded in y around inf 55.9%

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

   if -1.15000000000000006e268 < x < -1.5999999999999999e160 or 3.79999999999999971e-36 < x < 6.5999999999999997e168

   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 58.6%

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

   if -1.5999999999999999e160 < x < -3.24999999999999978e-13 or 6.5999999999999997e168 < 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 48.7%

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

   if -3.24999999999999978e-13 < x < 3.79999999999999971e-36

   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 57.0%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+268}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+160}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -3.25 \cdot 10^{-13}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-36}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+168}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 8: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;t \leq -3 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+94}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+137} \lor \neg \left(t \leq 1.2 \cdot 10^{+186}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x t))))
   (if (<= t -3e+72)
     t_1
     (if (<= t 3.3e+94)
       (+ (* y 5.0) (* 2.0 (* x (+ y z))))
       (if (or (<= t 8.8e+137) (not (<= t 1.2e+186)))
         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 * t);
	double tmp;
	if (t <= -3e+72) {
		tmp = t_1;
	} else if (t <= 3.3e+94) {
		tmp = (y * 5.0) + (2.0 * (x * (y + z)));
	} else if ((t <= 8.8e+137) || !(t <= 1.2e+186)) {
		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 * t)
    if (t <= (-3d+72)) then
        tmp = t_1
    else if (t <= 3.3d+94) then
        tmp = (y * 5.0d0) + (2.0d0 * (x * (y + z)))
    else if ((t <= 8.8d+137) .or. (.not. (t <= 1.2d+186))) 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 * t);
	double tmp;
	if (t <= -3e+72) {
		tmp = t_1;
	} else if (t <= 3.3e+94) {
		tmp = (y * 5.0) + (2.0 * (x * (y + z)));
	} else if ((t <= 8.8e+137) || !(t <= 1.2e+186)) {
		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 * t)
	tmp = 0
	if t <= -3e+72:
		tmp = t_1
	elif t <= 3.3e+94:
		tmp = (y * 5.0) + (2.0 * (x * (y + z)))
	elif (t <= 8.8e+137) or not (t <= 1.2e+186):
		tmp = t_1
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(x * t))
	tmp = 0.0
	if (t <= -3e+72)
		tmp = t_1;
	elseif (t <= 3.3e+94)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * Float64(y + z))));
	elseif ((t <= 8.8e+137) || !(t <= 1.2e+186))
		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 * t);
	tmp = 0.0;
	if (t <= -3e+72)
		tmp = t_1;
	elseif (t <= 3.3e+94)
		tmp = (y * 5.0) + (2.0 * (x * (y + z)));
	elseif ((t <= 8.8e+137) || ~((t <= 1.2e+186)))
		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[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+72], t$95$1, If[LessEqual[t, 3.3e+94], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 8.8e+137], N[Not[LessEqual[t, 1.2e+186]], $MachinePrecision]], t$95$1, N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.00000000000000003e72 or 3.3e94 < t < 8.80000000000000062e137 or 1.19999999999999998e186 < t

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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 92.3%

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

      4. associate-+l+ 92.3%

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

      5. +-commutative 92.3%

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

      6. count-2 92.3%

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

      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 inf 92.4%

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

      1. fma-udef 92.4%

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

      2. *-commutative 92.4%

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

   6. Applied egg-rr 92.4%

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

   if -3.00000000000000003e72 < t < 3.3e94

   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 t around 0 91.5%

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

   if 8.80000000000000062e137 < t < 1.19999999999999998e186

   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 0 100.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+72}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+94}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+137} \lor \neg \left(t \leq 1.2 \cdot 10^{+186}\right):\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 9: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-49}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-35}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ y z) (* x 2.0))))
   (if (<= x -4.1e+15)
     t_1
     (if (<= x -1.5e-30)
       (* x t)
       (if (<= x -5e-49)
         (* 2.0 (* x z))
         (if (<= x 1.05e-35) (* y 5.0) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y + z) * (x * 2.0);
	double tmp;
	if (x <= -4.1e+15) {
		tmp = t_1;
	} else if (x <= -1.5e-30) {
		tmp = x * t;
	} else if (x <= -5e-49) {
		tmp = 2.0 * (x * z);
	} else if (x <= 1.05e-35) {
		tmp = y * 5.0;
	} 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 (x <= (-4.1d+15)) then
        tmp = t_1
    else if (x <= (-1.5d-30)) then
        tmp = x * t
    else if (x <= (-5d-49)) then
        tmp = 2.0d0 * (x * z)
    else if (x <= 1.05d-35) then
        tmp = y * 5.0d0
    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 (x <= -4.1e+15) {
		tmp = t_1;
	} else if (x <= -1.5e-30) {
		tmp = x * t;
	} else if (x <= -5e-49) {
		tmp = 2.0 * (x * z);
	} else if (x <= 1.05e-35) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y + z) * (x * 2.0)
	tmp = 0
	if x <= -4.1e+15:
		tmp = t_1
	elif x <= -1.5e-30:
		tmp = x * t
	elif x <= -5e-49:
		tmp = 2.0 * (x * z)
	elif x <= 1.05e-35:
		tmp = y * 5.0
	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 (x <= -4.1e+15)
		tmp = t_1;
	elseif (x <= -1.5e-30)
		tmp = Float64(x * t);
	elseif (x <= -5e-49)
		tmp = Float64(2.0 * Float64(x * z));
	elseif (x <= 1.05e-35)
		tmp = Float64(y * 5.0);
	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 (x <= -4.1e+15)
		tmp = t_1;
	elseif (x <= -1.5e-30)
		tmp = x * t;
	elseif (x <= -5e-49)
		tmp = 2.0 * (x * z);
	elseif (x <= 1.05e-35)
		tmp = y * 5.0;
	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[x, -4.1e+15], t$95$1, If[LessEqual[x, -1.5e-30], N[(x * t), $MachinePrecision], If[LessEqual[x, -5e-49], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-35], N[(y * 5.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.1e15 or 1.05e-35 < 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 t around 0 72.8%

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

      1. associate-*r* 72.8%

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

      2. fma-def 72.8%

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

      3. *-commutative 72.8%

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

      4. *-commutative 72.8%

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

   6. Applied egg-rr 72.8%

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

   7. Taylor expanded in x around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*r* 72.1%

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

      3. +-commutative 72.1%

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

   9. Simplified 72.1%

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

   if -4.1e15 < x < -1.49999999999999995e-30

   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 72.5%

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

   if -1.49999999999999995e-30 < x < -4.9999999999999999e-49

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf 90.4%

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

   if -4.9999999999999999e-49 < x < 1.05e-35

   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 58.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+15}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-49}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-35}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \end{array} \]

Alternative 10: 88.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e+71)
   (* x (+ t (* (+ y z) 2.0)))
   (if (<= z 6.8e+83)
     (+ (* 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 (z <= -3.7e+71) {
		tmp = x * (t + ((y + z) * 2.0));
	} else if (z <= 6.8e+83) {
		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 (z <= (-3.7d+71)) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else if (z <= 6.8d+83) 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 (z <= -3.7e+71) {
		tmp = x * (t + ((y + z) * 2.0));
	} else if (z <= 6.8e+83) {
		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 z <= -3.7e+71:
		tmp = x * (t + ((y + z) * 2.0))
	elif z <= 6.8e+83:
		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 (z <= -3.7e+71)
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	elseif (z <= 6.8e+83)
		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 (z <= -3.7e+71)
		tmp = x * (t + ((y + z) * 2.0));
	elseif (z <= 6.8e+83)
		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[LessEqual[z, -3.7e+71], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+83], 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 3 regimes

2. if z < -3.7e71

   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 88.0%

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

   if -3.7e71 < z < 6.7999999999999996e83

   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 91.4%

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

   if 6.7999999999999996e83 < 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. 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 t around 0 97.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \]

Alternative 11: 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 12: 88.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-51} \lor \neg \left(x \leq 1.3 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.5e-51) (not (<= x 1.3e-35)))
   (* 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 <= -8.5e-51) || !(x <= 1.3e-35)) {
		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 <= (-8.5d-51)) .or. (.not. (x <= 1.3d-35))) 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 <= -8.5e-51) || !(x <= 1.3e-35)) {
		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 <= -8.5e-51) or not (x <= 1.3e-35):
		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 <= -8.5e-51) || !(x <= 1.3e-35))
		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 <= -8.5e-51) || ~((x <= 1.3e-35)))
		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, -8.5e-51], N[Not[LessEqual[x, 1.3e-35]], $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 < -8.50000000000000036e-51 or 1.30000000000000002e-35 < 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 97.7%

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

   if -8.50000000000000036e-51 < x < 1.30000000000000002e-35

   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 78.3%

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

      1. fma-udef 78.3%

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

      2. *-commutative 78.3%

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

   6. Applied egg-rr 78.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-51} \lor \neg \left(x \leq 1.3 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 13: 48.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-47}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5e-15) (* x t) (if (<= x 1.45e-47) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5e-15) {
		tmp = x * t;
	} else if (x <= 1.45e-47) {
		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 <= (-5d-15)) then
        tmp = x * t
    else if (x <= 1.45d-47) 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 <= -5e-15) {
		tmp = x * t;
	} else if (x <= 1.45e-47) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5e-15:
		tmp = x * t
	elif x <= 1.45e-47:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5e-15)
		tmp = Float64(x * t);
	elseif (x <= 1.45e-47)
		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 <= -5e-15)
		tmp = x * t;
	elseif (x <= 1.45e-47)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5e-15], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.45e-47], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.99999999999999999e-15 or 1.45e-47 < 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 38.8%

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

   if -4.99999999999999999e-15 < x < 1.45e-47

   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 57.5%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-47}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 14: 47.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -300000:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-50}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -300000.0) (* 2.0 (* y x)) (if (<= x 6e-50) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -300000.0) {
		tmp = 2.0 * (y * x);
	} else if (x <= 6e-50) {
		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 <= (-300000.0d0)) then
        tmp = 2.0d0 * (y * x)
    else if (x <= 6d-50) 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 <= -300000.0) {
		tmp = 2.0 * (y * x);
	} else if (x <= 6e-50) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -300000.0:
		tmp = 2.0 * (y * x)
	elif x <= 6e-50:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -300000.0)
		tmp = Float64(2.0 * Float64(y * x));
	elseif (x <= 6e-50)
		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 <= -300000.0)
		tmp = 2.0 * (y * x);
	elseif (x <= 6e-50)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -300000.0], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-50], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3e5

   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%

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

   5. Taylor expanded in y around inf 40.1%

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

   if -3e5 < x < 5.99999999999999981e-50

   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 56.2%

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

   if 5.99999999999999981e-50 < 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 41.9%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -300000:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-50}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 15: 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 30.5%

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

3. Final simplification 30.5%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023279 
(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)))