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

Percentage Accurate: 99.9% → 99.9%

Time: 9.7s

Alternatives: 13

Speedup: 1.0×

• 26.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. fma-def 99.5%

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

   2. associate-+l+ 99.5%

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

   3. +-commutative 99.5%

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

   4. count-2 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 2: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot y\right)\\ t_2 := x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 y)))) (t_2 (* x (* 2.0 (+ y z)))))
   (if (<= x -1e+91)
     t_2
     (if (<= x -1.3e-146)
       t_1
       (if (<= x 2.4e-24) (* y 5.0) (if (<= x 7e+91) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double t_2 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -1e+91) {
		tmp = t_2;
	} else if (x <= -1.3e-146) {
		tmp = t_1;
	} else if (x <= 2.4e-24) {
		tmp = y * 5.0;
	} else if (x <= 7e+91) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * y))
    t_2 = x * (2.0d0 * (y + z))
    if (x <= (-1d+91)) then
        tmp = t_2
    else if (x <= (-1.3d-146)) then
        tmp = t_1
    else if (x <= 2.4d-24) then
        tmp = y * 5.0d0
    else if (x <= 7d+91) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double t_2 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -1e+91) {
		tmp = t_2;
	} else if (x <= -1.3e-146) {
		tmp = t_1;
	} else if (x <= 2.4e-24) {
		tmp = y * 5.0;
	} else if (x <= 7e+91) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * y))
	t_2 = x * (2.0 * (y + z))
	tmp = 0
	if x <= -1e+91:
		tmp = t_2
	elif x <= -1.3e-146:
		tmp = t_1
	elif x <= 2.4e-24:
		tmp = y * 5.0
	elif x <= 7e+91:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * y)))
	t_2 = Float64(x * Float64(2.0 * Float64(y + z)))
	tmp = 0.0
	if (x <= -1e+91)
		tmp = t_2;
	elseif (x <= -1.3e-146)
		tmp = t_1;
	elseif (x <= 2.4e-24)
		tmp = Float64(y * 5.0);
	elseif (x <= 7e+91)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * y));
	t_2 = x * (2.0 * (y + z));
	tmp = 0.0;
	if (x <= -1e+91)
		tmp = t_2;
	elseif (x <= -1.3e-146)
		tmp = t_1;
	elseif (x <= 2.4e-24)
		tmp = y * 5.0;
	elseif (x <= 7e+91)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+91], t$95$2, If[LessEqual[x, -1.3e-146], t$95$1, If[LessEqual[x, 2.4e-24], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 7e+91], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.00000000000000008e91 or 2.3999999999999998e-24 < x < 7.00000000000000001e91

   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 0 84.1%

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

   4. Simplified 84.1%

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

      1. fma-udef 84.1%

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

      2. *-commutative 84.1%

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

   6. Applied egg-rr 84.1%

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

   7. Taylor expanded in x around inf 82.8%

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

      1. *-commutative 82.8%

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

      2. +-commutative 82.8%

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

      3. associate-*r* 82.8%

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

      4. *-commutative 82.8%

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

      5. +-commutative 82.8%

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

   9. Simplified 82.8%

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

   if -1.00000000000000008e91 < x < -1.29999999999999993e-146 or 7.00000000000000001e91 < x

   1. Initial program 98.9%

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

      1. fma-def 98.9%

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

      2. associate-+l+ 98.9%

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

      3. +-commutative 98.9%

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

      4. count-2 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in x around inf 88.3%

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

   5. Taylor expanded in z around 0 71.5%

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

      1. +-commutative 71.5%

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

      2. *-commutative 71.5%

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

   7. Simplified 71.5%

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

   if -1.29999999999999993e-146 < x < 2.3999999999999998e-24

   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 66.8%

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

   4. Simplified 66.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \end{array} \]

Alternative 3: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot y\right)\\ t_2 := x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 y)))) (t_2 (* x (* 2.0 (+ y z)))))
   (if (<= x -3e+90)
     t_2
     (if (<= x -1.3e-146)
       t_1
       (if (<= x 4.2e-25)
         (* y (+ 5.0 (* x 2.0)))
         (if (<= x 1.1e+90) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double t_2 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -3e+90) {
		tmp = t_2;
	} else if (x <= -1.3e-146) {
		tmp = t_1;
	} else if (x <= 4.2e-25) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (x <= 1.1e+90) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * y))
    t_2 = x * (2.0d0 * (y + z))
    if (x <= (-3d+90)) then
        tmp = t_2
    else if (x <= (-1.3d-146)) then
        tmp = t_1
    else if (x <= 4.2d-25) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else if (x <= 1.1d+90) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double t_2 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -3e+90) {
		tmp = t_2;
	} else if (x <= -1.3e-146) {
		tmp = t_1;
	} else if (x <= 4.2e-25) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (x <= 1.1e+90) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * y))
	t_2 = x * (2.0 * (y + z))
	tmp = 0
	if x <= -3e+90:
		tmp = t_2
	elif x <= -1.3e-146:
		tmp = t_1
	elif x <= 4.2e-25:
		tmp = y * (5.0 + (x * 2.0))
	elif x <= 1.1e+90:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * y)))
	t_2 = Float64(x * Float64(2.0 * Float64(y + z)))
	tmp = 0.0
	if (x <= -3e+90)
		tmp = t_2;
	elseif (x <= -1.3e-146)
		tmp = t_1;
	elseif (x <= 4.2e-25)
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	elseif (x <= 1.1e+90)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * y));
	t_2 = x * (2.0 * (y + z));
	tmp = 0.0;
	if (x <= -3e+90)
		tmp = t_2;
	elseif (x <= -1.3e-146)
		tmp = t_1;
	elseif (x <= 4.2e-25)
		tmp = y * (5.0 + (x * 2.0));
	elseif (x <= 1.1e+90)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+90], t$95$2, If[LessEqual[x, -1.3e-146], t$95$1, If[LessEqual[x, 4.2e-25], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+90], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.99999999999999979e90 or 4.20000000000000005e-25 < x < 1.09999999999999995e90

   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 0 84.1%

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

   4. Simplified 84.1%

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

      1. fma-udef 84.1%

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

      2. *-commutative 84.1%

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

   6. Applied egg-rr 84.1%

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

   7. Taylor expanded in x around inf 82.8%

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

      1. *-commutative 82.8%

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

      2. +-commutative 82.8%

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

      3. associate-*r* 82.8%

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

      4. *-commutative 82.8%

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

      5. +-commutative 82.8%

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

   9. Simplified 82.8%

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

   if -2.99999999999999979e90 < x < -1.29999999999999993e-146 or 1.09999999999999995e90 < x

   1. Initial program 98.9%

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

      1. fma-def 98.9%

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

      2. associate-+l+ 98.9%

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

      3. +-commutative 98.9%

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

      4. count-2 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in x around inf 88.3%

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

   5. Taylor expanded in z around 0 71.5%

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

      1. +-commutative 71.5%

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

      2. *-commutative 71.5%

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

   7. Simplified 71.5%

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

   if -1.29999999999999993e-146 < x < 4.20000000000000005e-25

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 66.8%

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

   4. Simplified 66.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \end{array} \]

Alternative 4: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot y\right)\\ t_2 := x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+21}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 y)))) (t_2 (* x (* 2.0 (+ y z)))))
   (if (<= x -4e+90)
     t_2
     (if (<= x -2.5)
       t_1
       (if (<= x 1.1e+21)
         (+ (* y 5.0) (* x t))
         (if (<= x 1.65e+91) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double t_2 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -4e+90) {
		tmp = t_2;
	} else if (x <= -2.5) {
		tmp = t_1;
	} else if (x <= 1.1e+21) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1.65e+91) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * y))
    t_2 = x * (2.0d0 * (y + z))
    if (x <= (-4d+90)) then
        tmp = t_2
    else if (x <= (-2.5d0)) then
        tmp = t_1
    else if (x <= 1.1d+21) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 1.65d+91) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double t_2 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -4e+90) {
		tmp = t_2;
	} else if (x <= -2.5) {
		tmp = t_1;
	} else if (x <= 1.1e+21) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1.65e+91) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * y))
	t_2 = x * (2.0 * (y + z))
	tmp = 0
	if x <= -4e+90:
		tmp = t_2
	elif x <= -2.5:
		tmp = t_1
	elif x <= 1.1e+21:
		tmp = (y * 5.0) + (x * t)
	elif x <= 1.65e+91:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * y)))
	t_2 = Float64(x * Float64(2.0 * Float64(y + z)))
	tmp = 0.0
	if (x <= -4e+90)
		tmp = t_2;
	elseif (x <= -2.5)
		tmp = t_1;
	elseif (x <= 1.1e+21)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 1.65e+91)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * y));
	t_2 = x * (2.0 * (y + z));
	tmp = 0.0;
	if (x <= -4e+90)
		tmp = t_2;
	elseif (x <= -2.5)
		tmp = t_1;
	elseif (x <= 1.1e+21)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 1.65e+91)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+90], t$95$2, If[LessEqual[x, -2.5], t$95$1, If[LessEqual[x, 1.1e+21], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e+91], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.99999999999999987e90 or 1.1e21 < x < 1.65000000000000009e91

   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 0 86.9%

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

   4. Simplified 86.9%

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

      1. fma-udef 86.9%

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

      2. *-commutative 86.9%

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

   6. Applied egg-rr 86.9%

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

   7. Taylor expanded in x around inf 86.9%

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

      1. *-commutative 86.9%

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

      2. +-commutative 86.9%

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

      3. associate-*r* 86.9%

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

      4. *-commutative 86.9%

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

      5. +-commutative 86.9%

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

   9. Simplified 86.9%

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

   if -3.99999999999999987e90 < x < -2.5 or 1.65000000000000009e91 < x

   1. Initial program 98.5%

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

      1. fma-def 98.5%

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

      2. associate-+l+ 98.5%

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

      3. +-commutative 98.5%

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

      4. count-2 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in x around inf 98.4%

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

   5. Taylor expanded in z around 0 82.7%

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

      1. +-commutative 82.7%

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

      2. *-commutative 82.7%

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

   7. Simplified 82.7%

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

   if -2.5 < x < 1.1e21

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 80.7%

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

   4. Simplified 80.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -2.5:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+21}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \end{array} \]

Alternative 5: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+62}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+131}:\\ \;\;\;\;y \cdot 5 + x \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t_1 + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= t -3.3e+62)
     (+ (* y 5.0) (* x t))
     (if (<= t 7.2e+131) (+ (* y 5.0) (* x t_1)) (* x (+ t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (t <= -3.3e+62) {
		tmp = (y * 5.0) + (x * t);
	} else if (t <= 7.2e+131) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = x * (t_1 + 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 * (y + z)
    if (t <= (-3.3d+62)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (t <= 7.2d+131) then
        tmp = (y * 5.0d0) + (x * t_1)
    else
        tmp = x * (t_1 + 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 * (y + z);
	double tmp;
	if (t <= -3.3e+62) {
		tmp = (y * 5.0) + (x * t);
	} else if (t <= 7.2e+131) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = x * (t_1 + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if t <= -3.3e+62:
		tmp = (y * 5.0) + (x * t)
	elif t <= 7.2e+131:
		tmp = (y * 5.0) + (x * t_1)
	else:
		tmp = x * (t_1 + t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (t <= -3.3e+62)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (t <= 7.2e+131)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t_1));
	else
		tmp = Float64(x * Float64(t_1 + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (t <= -3.3e+62)
		tmp = (y * 5.0) + (x * t);
	elseif (t <= 7.2e+131)
		tmp = (y * 5.0) + (x * t_1);
	else
		tmp = x * (t_1 + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+62], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+131], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3e62

   1. Initial program 98.2%

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

   2. Taylor expanded in t around inf 89.7%

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

   4. Simplified 89.7%

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

   if -3.3e62 < t < 7.20000000000000063e131

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 94.7%

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

   4. Simplified 94.7%

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

   if 7.20000000000000063e131 < t

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 86.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+62}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+131}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (x * (t + (y + (y + (2.0d0 * z)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + N[(y + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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 y around 0 99.5%

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

3. Final simplification 99.5%

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

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (x * (t + (y + (z + (y + z)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Final simplification 99.5%

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

Alternative 8: 46.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot z\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-146}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-24}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* 2.0 z))))
   (if (<= x -4e+86)
     t_1
     (if (<= x -1.15e-146)
       (* x t)
       (if (<= x 1.05e-24) (* y 5.0) (if (<= x 1.5e+99) t_1 (* x t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * z);
	double tmp;
	if (x <= -4e+86) {
		tmp = t_1;
	} else if (x <= -1.15e-146) {
		tmp = x * t;
	} else if (x <= 1.05e-24) {
		tmp = y * 5.0;
	} else if (x <= 1.5e+99) {
		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 * (2.0d0 * z)
    if (x <= (-4d+86)) then
        tmp = t_1
    else if (x <= (-1.15d-146)) then
        tmp = x * t
    else if (x <= 1.05d-24) then
        tmp = y * 5.0d0
    else if (x <= 1.5d+99) 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 * (2.0 * z);
	double tmp;
	if (x <= -4e+86) {
		tmp = t_1;
	} else if (x <= -1.15e-146) {
		tmp = x * t;
	} else if (x <= 1.05e-24) {
		tmp = y * 5.0;
	} else if (x <= 1.5e+99) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (2.0 * z)
	tmp = 0
	if x <= -4e+86:
		tmp = t_1
	elif x <= -1.15e-146:
		tmp = x * t
	elif x <= 1.05e-24:
		tmp = y * 5.0
	elif x <= 1.5e+99:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(2.0 * z))
	tmp = 0.0
	if (x <= -4e+86)
		tmp = t_1;
	elseif (x <= -1.15e-146)
		tmp = Float64(x * t);
	elseif (x <= 1.05e-24)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.5e+99)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (2.0 * z);
	tmp = 0.0;
	if (x <= -4e+86)
		tmp = t_1;
	elseif (x <= -1.15e-146)
		tmp = x * t;
	elseif (x <= 1.05e-24)
		tmp = y * 5.0;
	elseif (x <= 1.5e+99)
		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[(2.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+86], t$95$1, If[LessEqual[x, -1.15e-146], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.05e-24], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.5e+99], t$95$1, N[(x * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.0000000000000001e86 or 1.05e-24 < x < 1.50000000000000007e99

   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 91.3%

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

   4. Simplified 94.2%

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

   5. Taylor expanded in z around inf 49.6%

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

      1. associate-*r* 49.6%

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

      2. *-commutative 49.6%

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

      3. associate-*r* 49.6%

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

   7. Simplified 49.6%

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

   if -4.0000000000000001e86 < x < -1.15e-146 or 1.50000000000000007e99 < x

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 97.8%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 44.7%

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

      1. *-commutative 44.7%

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

   7. Simplified 44.7%

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

   if -1.15e-146 < x < 1.05e-24

   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 66.8%

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

   4. Simplified 66.8%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(2 \cdot z\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-146}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-24}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 9: 89.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.02 \lor \neg \left(x \leq 9 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.02) (not (<= x 9e-25)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.02) || !(x <= 9e-25)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} 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 <= (-0.02d0)) .or. (.not. (x <= 9d-25))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    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 <= -0.02) || !(x <= 9e-25)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.02) or not (x <= 9e-25):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.02) || !(x <= 9e-25))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	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 <= -0.02) || ~((x <= 9e-25)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.02], N[Not[LessEqual[x, 9e-25]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0200000000000000004 or 9.0000000000000002e-25 < x

   1. Initial program 99.2%

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

      1. fma-def 99.3%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. count-2 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 98.5%

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

   if -0.0200000000000000004 < x < 9.0000000000000002e-25

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 82.5%

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

   4. Simplified 82.5%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.02 \lor \neg \left(x \leq 9 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 10: 46.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(2 \cdot z\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.5:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.3e+88)
   (* x (* 2.0 z))
   (if (<= x -1.3e-146) (* x t) (if (<= x 2.5) (* y 5.0) (* y (* x 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.3e+88) {
		tmp = x * (2.0 * z);
	} else if (x <= -1.3e-146) {
		tmp = x * t;
	} else if (x <= 2.5) {
		tmp = y * 5.0;
	} else {
		tmp = y * (x * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.3d+88)) then
        tmp = x * (2.0d0 * z)
    else if (x <= (-1.3d-146)) then
        tmp = x * t
    else if (x <= 2.5d0) then
        tmp = y * 5.0d0
    else
        tmp = y * (x * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.3e+88) {
		tmp = x * (2.0 * z);
	} else if (x <= -1.3e-146) {
		tmp = x * t;
	} else if (x <= 2.5) {
		tmp = y * 5.0;
	} else {
		tmp = y * (x * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.3e+88:
		tmp = x * (2.0 * z)
	elif x <= -1.3e-146:
		tmp = x * t
	elif x <= 2.5:
		tmp = y * 5.0
	else:
		tmp = y * (x * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.3e+88)
		tmp = Float64(x * Float64(2.0 * z));
	elseif (x <= -1.3e-146)
		tmp = Float64(x * t);
	elseif (x <= 2.5)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(y * Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.3e+88)
		tmp = x * (2.0 * z);
	elseif (x <= -1.3e-146)
		tmp = x * t;
	elseif (x <= 2.5)
		tmp = y * 5.0;
	else
		tmp = y * (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.3e+88], N[(x * N[(2.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e-146], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.5], N[(y * 5.0), $MachinePrecision], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.29999999999999974e88

   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 87.7%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in z around inf 51.0%

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

      1. associate-*r* 51.0%

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

      2. *-commutative 51.0%

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

      3. associate-*r* 51.0%

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

   7. Simplified 51.0%

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

   if -4.29999999999999974e88 < x < -1.29999999999999993e-146

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 43.7%

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

      1. *-commutative 43.7%

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

   7. Simplified 43.7%

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

   if -1.29999999999999993e-146 < 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. Taylor expanded in x around 0 65.9%

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

   4. Simplified 65.9%

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

   if 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. Taylor expanded in y around inf 44.3%

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

   4. Simplified 44.3%

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

   5. Taylor expanded in x around inf 44.3%

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

      1. *-commutative 44.3%

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

      2. *-commutative 44.3%

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

      3. associate-*r* 44.3%

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

   7. Simplified 44.3%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(2 \cdot z\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.5:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]

Alternative 11: 63.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0165 \lor \neg \left(x \leq 5 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.0165) (not (<= x 5e-25))) (* x (* 2.0 (+ y z))) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.0165) || !(x <= 5e-25)) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-0.0165d0)) .or. (.not. (x <= 5d-25))) then
        tmp = x * (2.0d0 * (y + z))
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.0165) || !(x <= 5e-25)) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.0165) or not (x <= 5e-25):
		tmp = x * (2.0 * (y + z))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.0165) || !(x <= 5e-25))
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -0.0165) || ~((x <= 5e-25)))
		tmp = x * (2.0 * (y + z));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.0165], N[Not[LessEqual[x, 5e-25]], $MachinePrecision]], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.016500000000000001 or 4.99999999999999962e-25 < x

   1. Initial program 99.2%

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

   2. Taylor expanded in t around 0 73.0%

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

   4. Simplified 73.7%

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

      1. fma-udef 73.0%

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

      2. *-commutative 73.0%

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

   6. Applied egg-rr 73.0%

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

   7. Taylor expanded in x around inf 72.3%

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

      1. *-commutative 72.3%

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

      2. +-commutative 72.3%

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

      3. associate-*r* 72.3%

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

      4. *-commutative 72.3%

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

      5. +-commutative 72.3%

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

   9. Simplified 72.3%

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

   if -0.016500000000000001 < x < 4.99999999999999962e-25

   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 59.7%

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

   4. Simplified 59.7%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0165 \lor \neg \left(x \leq 5 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 12: 47.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-146} \lor \neg \left(x \leq 1720\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.3e-146) (not (<= x 1720.0))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.3e-146) || !(x <= 1720.0)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.3d-146)) .or. (.not. (x <= 1720.0d0))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.3e-146) || !(x <= 1720.0)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.3e-146) or not (x <= 1720.0):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.3e-146) || !(x <= 1720.0))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.3e-146) || ~((x <= 1720.0)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.3e-146], N[Not[LessEqual[x, 1720.0]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.29999999999999993e-146 or 1720 < x

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 94.9%

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

   4. Simplified 97.4%

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

   5. Taylor expanded in t around inf 37.1%

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

      1. *-commutative 37.1%

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

   7. Simplified 37.1%

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

   if -1.29999999999999993e-146 < x < 1720

   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 65.3%

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

   4. Simplified 65.3%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-146} \lor \neg \left(x \leq 1720\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 13: 31.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ x \cdot t \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 y around 0 96.8%

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

4. Simplified 98.4%

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

5. Taylor expanded in t around inf 30.3%

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

   1. *-commutative 30.3%

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

7. Simplified 30.3%

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

8. Final simplification 30.3%

   \[\leadsto x \cdot t \]

Reproduce

herbie shell --seed 2023336 
(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)))