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

Percentage Accurate: 99.8% → 99.8%

Time: 9.0s

Alternatives: 11

Speedup: 1.0×

• 26.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 45.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y + y\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+144}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ y y))))
   (if (<= x -1.35e+83)
     t_1
     (if (<= x -2.2e-30)
       (* x t)
       (if (<= x 2.65e-145)
         (* y 5.0)
         (if (<= x 3.7e+144) (* x t) (if (<= x 7.2e+227) t_1 (* x t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y + y);
	double tmp;
	if (x <= -1.35e+83) {
		tmp = t_1;
	} else if (x <= -2.2e-30) {
		tmp = x * t;
	} else if (x <= 2.65e-145) {
		tmp = y * 5.0;
	} else if (x <= 3.7e+144) {
		tmp = x * t;
	} else if (x <= 7.2e+227) {
		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 = x * (y + y)
    if (x <= (-1.35d+83)) then
        tmp = t_1
    else if (x <= (-2.2d-30)) then
        tmp = x * t
    else if (x <= 2.65d-145) then
        tmp = y * 5.0d0
    else if (x <= 3.7d+144) then
        tmp = x * t
    else if (x <= 7.2d+227) 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 = x * (y + y);
	double tmp;
	if (x <= -1.35e+83) {
		tmp = t_1;
	} else if (x <= -2.2e-30) {
		tmp = x * t;
	} else if (x <= 2.65e-145) {
		tmp = y * 5.0;
	} else if (x <= 3.7e+144) {
		tmp = x * t;
	} else if (x <= 7.2e+227) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y + y)
	tmp = 0
	if x <= -1.35e+83:
		tmp = t_1
	elif x <= -2.2e-30:
		tmp = x * t
	elif x <= 2.65e-145:
		tmp = y * 5.0
	elif x <= 3.7e+144:
		tmp = x * t
	elif x <= 7.2e+227:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y + y))
	tmp = 0.0
	if (x <= -1.35e+83)
		tmp = t_1;
	elseif (x <= -2.2e-30)
		tmp = Float64(x * t);
	elseif (x <= 2.65e-145)
		tmp = Float64(y * 5.0);
	elseif (x <= 3.7e+144)
		tmp = Float64(x * t);
	elseif (x <= 7.2e+227)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y + y);
	tmp = 0.0;
	if (x <= -1.35e+83)
		tmp = t_1;
	elseif (x <= -2.2e-30)
		tmp = x * t;
	elseif (x <= 2.65e-145)
		tmp = y * 5.0;
	elseif (x <= 3.7e+144)
		tmp = x * t;
	elseif (x <= 7.2e+227)
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e+83], t$95$1, If[LessEqual[x, -2.2e-30], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.65e-145], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 3.7e+144], N[(x * t), $MachinePrecision], If[LessEqual[x, 7.2e+227], t$95$1, N[(x * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35000000000000003e83 or 3.6999999999999997e144 < x < 7.19999999999999983e227

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 55.2%

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

   if -1.35000000000000003e83 < x < -2.19999999999999983e-30 or 2.65e-145 < x < 3.6999999999999997e144 or 7.19999999999999983e227 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 51.9

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

   5. Applied rewrites 51.9%

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

   if -2.19999999999999983e-30 < x < 2.65e-145

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 68.7

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

   5. Applied rewrites 68.7%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(y + y\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+144}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+227}:\\ \;\;\;\;x \cdot \left(y + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \mathsf{fma}\left(x, 2, 5\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(x, t, y \cdot 5\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (fma x 2.0 5.0))))
   (if (<= y -1.3e+52)
     t_1
     (if (<= y -1.65e-51)
       (fma x t (* y 5.0))
       (if (<= y 3.3e+52) (* x (fma 2.0 z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * fma(x, 2.0, 5.0);
	double tmp;
	if (y <= -1.3e+52) {
		tmp = t_1;
	} else if (y <= -1.65e-51) {
		tmp = fma(x, t, (y * 5.0));
	} else if (y <= 3.3e+52) {
		tmp = x * fma(2.0, z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * fma(x, 2.0, 5.0))
	tmp = 0.0
	if (y <= -1.3e+52)
		tmp = t_1;
	elseif (y <= -1.65e-51)
		tmp = fma(x, t, Float64(y * 5.0));
	elseif (y <= 3.3e+52)
		tmp = Float64(x * fma(2.0, z, t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * 2.0 + 5.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+52], t$95$1, If[LessEqual[y, -1.65e-51], N[(x * t + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+52], N[(x * N[(2.0 * z + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e52 or 3.3e52 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. distribute-lft-neg-in N/A

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

      4. neg-sub0 N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(0 - -2 \cdot x\right)} + 5\right) \]

      5. associate--r- N/A

         \[\leadsto y \cdot \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \]

      6. neg-sub0 N/A

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

      7. lower-*.f64 N/A

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

      8. neg-sub0 N/A

         \[\leadsto y \cdot \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \]

      9. associate--r- N/A

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - -2 \cdot x\right) + 5\right)} \]

      10. neg-sub0 N/A

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

      11. distribute-lft-neg-in N/A

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

      12. metadata-eval N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 82.2

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

   5. Applied rewrites 82.2%

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

   if -1.3e52 < y < -1.64999999999999986e-51

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. flip-+ N/A

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

      11. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\frac{\color{blue}{0}}{\left(y + z\right) - \left(y + z\right)} + t\right)\right) \]

      12. +-inverses N/A

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

      13. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\frac{z \cdot z - z \cdot z}{\color{blue}{0}} + t\right)\right) \]

      14. +-inverses N/A

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

      15. flip-+ N/A

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

      16. lower-+.f64 89.9

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

   4. Applied rewrites 89.9%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{5 \cdot y + t \cdot x} \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 82.5

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

   7. Applied rewrites 82.5%

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

   if -1.64999999999999986e-51 < y < 3.3e52

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 80.6

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

   5. Applied rewrites 80.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(x, 2, 5\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(x, t, y \cdot 5\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(x, 2, 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-180}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (+ y y)))))
   (if (<= x -2.2e-30)
     t_1
     (if (<= x 7.5e-180)
       (* y 5.0)
       (if (<= x 1.4e+93) (* x (fma 2.0 z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y + y));
	double tmp;
	if (x <= -2.2e-30) {
		tmp = t_1;
	} else if (x <= 7.5e-180) {
		tmp = y * 5.0;
	} else if (x <= 1.4e+93) {
		tmp = x * fma(2.0, z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y + y)))
	tmp = 0.0
	if (x <= -2.2e-30)
		tmp = t_1;
	elseif (x <= 7.5e-180)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.4e+93)
		tmp = Float64(x * fma(2.0, z, t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e-30], t$95$1, If[LessEqual[x, 7.5e-180], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.4e+93], N[(x * N[(2.0 * z + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.19999999999999983e-30 or 1.39999999999999994e93 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 97.4

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 76.7%

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

   if -2.19999999999999983e-30 < x < 7.50000000000000015e-180

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 70.4

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

   5. Applied rewrites 70.4%

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

   if 7.50000000000000015e-180 < x < 1.39999999999999994e93

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 70.6

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

   5. Applied rewrites 70.6%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-180}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.5:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot \left(t + \left(z + z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (fma 2.0 (+ y z) t))))
   (if (<= x -9.2e+24)
     t_1
     (if (<= x 2.5) (fma y 5.0 (* x (+ t (+ z z)))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * fma(2.0, (y + z), t);
	double tmp;
	if (x <= -9.2e+24) {
		tmp = t_1;
	} else if (x <= 2.5) {
		tmp = fma(y, 5.0, (x * (t + (z + z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * fma(2.0, Float64(y + z), t))
	tmp = 0.0
	if (x <= -9.2e+24)
		tmp = t_1;
	elseif (x <= 2.5)
		tmp = fma(y, 5.0, Float64(x * Float64(t + Float64(z + z))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.2e+24], t$95$1, If[LessEqual[x, 2.5], N[(y * 5.0 + N[(x * N[(t + N[(z + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.1999999999999996e24 or 2.5 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -9.1999999999999996e24 < x < 2.5

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. flip-+ N/A

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

      11. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\frac{\color{blue}{0}}{\left(y + z\right) - \left(y + z\right)} + t\right)\right) \]

      12. +-inverses N/A

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

      13. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\frac{z \cdot z - z \cdot z}{\color{blue}{0}} + t\right)\right) \]

      14. +-inverses N/A

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

      15. flip-+ N/A

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

      16. lower-+.f64 98.5

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

   4. Applied rewrites 98.5%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \mathbf{elif}\;x \leq 2.5:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot \left(t + \left(z + z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-145}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot \left(z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (fma 2.0 (+ y z) t))))
   (if (<= x -2.2e-30)
     t_1
     (if (<= x 2.65e-145) (fma y 5.0 (* x (* z 2.0))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * fma(2.0, (y + z), t);
	double tmp;
	if (x <= -2.2e-30) {
		tmp = t_1;
	} else if (x <= 2.65e-145) {
		tmp = fma(y, 5.0, (x * (z * 2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * fma(2.0, Float64(y + z), t))
	tmp = 0.0
	if (x <= -2.2e-30)
		tmp = t_1;
	elseif (x <= 2.65e-145)
		tmp = fma(y, 5.0, Float64(x * Float64(z * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e-30], t$95$1, If[LessEqual[x, 2.65e-145], N[(y * 5.0 + N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.19999999999999983e-30 or 2.65e-145 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 93.4

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

   5. Applied rewrites 93.4%

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

   if -2.19999999999999983e-30 < x < 2.65e-145

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. flip-+ N/A

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

      11. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\frac{\color{blue}{0}}{\left(y + z\right) - \left(y + z\right)} + t\right)\right) \]

      12. +-inverses N/A

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

      13. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\frac{z \cdot z - z \cdot z}{\color{blue}{0}} + t\right)\right) \]

      14. +-inverses N/A

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

      15. flip-+ N/A

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

      16. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 86.6

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

   7. Applied rewrites 86.6%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-145}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot \left(z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \mathbf{if}\;x \leq -700000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-109}:\\ \;\;\;\;\mathsf{fma}\left(x, t, y \cdot 5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (fma 2.0 (+ y z) t))))
   (if (<= x -700000000.0) t_1 (if (<= x 1.45e-109) (fma x t (* y 5.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * fma(2.0, (y + z), t);
	double tmp;
	if (x <= -700000000.0) {
		tmp = t_1;
	} else if (x <= 1.45e-109) {
		tmp = fma(x, t, (y * 5.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * fma(2.0, Float64(y + z), t))
	tmp = 0.0
	if (x <= -700000000.0)
		tmp = t_1;
	elseif (x <= 1.45e-109)
		tmp = fma(x, t, Float64(y * 5.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -700000000.0], t$95$1, If[LessEqual[x, 1.45e-109], N[(x * t + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -7e8 or 1.45e-109 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 96.0

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

   5. Applied rewrites 96.0%

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

   if -7e8 < x < 1.45e-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. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. flip-+ N/A

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

      11. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\frac{\color{blue}{0}}{\left(y + z\right) - \left(y + z\right)} + t\right)\right) \]

      12. +-inverses N/A

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

      13. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\frac{z \cdot z - z \cdot z}{\color{blue}{0}} + t\right)\right) \]

      14. +-inverses N/A

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

      15. flip-+ N/A

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

      16. lower-+.f64 98.9

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

   4. Applied rewrites 98.9%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{5 \cdot y + t \cdot x} \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 82.8

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

   7. Applied rewrites 82.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -700000000:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-109}:\\ \;\;\;\;\mathsf{fma}\left(x, t, y \cdot 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, y + z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \mathsf{fma}\left(x, 2, 5\right)\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(2, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (fma x 2.0 5.0))))
   (if (<= y -1.12e+18) t_1 (if (<= y 3.3e+52) (* x (fma 2.0 z t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * fma(x, 2.0, 5.0);
	double tmp;
	if (y <= -1.12e+18) {
		tmp = t_1;
	} else if (y <= 3.3e+52) {
		tmp = x * fma(2.0, z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * fma(x, 2.0, 5.0))
	tmp = 0.0
	if (y <= -1.12e+18)
		tmp = t_1;
	elseif (y <= 3.3e+52)
		tmp = Float64(x * fma(2.0, z, t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * 2.0 + 5.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+18], t$95$1, If[LessEqual[y, 3.3e+52], N[(x * N[(2.0 * z + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.12e18 or 3.3e52 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. distribute-lft-neg-in N/A

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

      4. neg-sub0 N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(0 - -2 \cdot x\right)} + 5\right) \]

      5. associate--r- N/A

         \[\leadsto y \cdot \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \]

      6. neg-sub0 N/A

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

      7. lower-*.f64 N/A

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

      8. neg-sub0 N/A

         \[\leadsto y \cdot \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \]

      9. associate--r- N/A

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - -2 \cdot x\right) + 5\right)} \]

      10. neg-sub0 N/A

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

      11. distribute-lft-neg-in N/A

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

      12. metadata-eval N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 80.4

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

   5. Applied rewrites 80.4%

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

   if -1.12e18 < y < 3.3e52

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 77.6

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

   5. Applied rewrites 77.6%

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

Alternative 9: 61.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (+ y y)))))
   (if (<= x -2.2e-30) t_1 (if (<= x 2.65e-145) (* y 5.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y + y));
	double tmp;
	if (x <= -2.2e-30) {
		tmp = t_1;
	} else if (x <= 2.65e-145) {
		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 = x * (t + (y + y))
    if (x <= (-2.2d-30)) then
        tmp = t_1
    else if (x <= 2.65d-145) 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 = x * (t + (y + y));
	double tmp;
	if (x <= -2.2e-30) {
		tmp = t_1;
	} else if (x <= 2.65e-145) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y + y))
	tmp = 0
	if x <= -2.2e-30:
		tmp = t_1
	elif x <= 2.65e-145:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y + y)))
	tmp = 0.0
	if (x <= -2.2e-30)
		tmp = t_1;
	elseif (x <= 2.65e-145)
		tmp = Float64(y * 5.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y + y));
	tmp = 0.0;
	if (x <= -2.2e-30)
		tmp = t_1;
	elseif (x <= 2.65e-145)
		tmp = y * 5.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e-30], t$95$1, If[LessEqual[x, 2.65e-145], N[(y * 5.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.19999999999999983e-30 or 2.65e-145 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 93.4

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

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 69.6%

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

   if -2.19999999999999983e-30 < x < 2.65e-145

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 68.7

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

   5. Applied rewrites 68.7%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.2e-30) (* x t) (if (<= x 2.65e-145) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-30) {
		tmp = x * t;
	} else if (x <= 2.65e-145) {
		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 <= (-2.2d-30)) then
        tmp = x * t
    else if (x <= 2.65d-145) 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 <= -2.2e-30) {
		tmp = x * t;
	} else if (x <= 2.65e-145) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.2e-30:
		tmp = x * t
	elif x <= 2.65e-145:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.2e-30)
		tmp = Float64(x * t);
	elseif (x <= 2.65e-145)
		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 <= -2.2e-30)
		tmp = x * t;
	elseif (x <= 2.65e-145)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.2e-30], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.65e-145], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.19999999999999983e-30 or 2.65e-145 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 40.9

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

   5. Applied rewrites 40.9%

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

   if -2.19999999999999983e-30 < x < 2.65e-145

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 68.7

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

   5. Applied rewrites 68.7%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.0% accurate, 4.3× 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 100.0%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{5 \cdot y} \]
4. Step-by-step derivation

   1. lower-*.f64 30.1

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

5. Applied rewrites 30.1%

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

6. Final simplification 30.1%

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

Reproduce

herbie shell --seed 2024238 
(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)))