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

Percentage Accurate: 99.8% → 99.9%

Time: 9.5s

Alternatives: 16

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 100.0%

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

   3. flip-+ 60.4%

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

   4. associate-*r/ 56.7%

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

   5. fma-neg 57.7%

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

   6. associate-+l+ 57.7%

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

   7. +-commutative 57.7%

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

   8. count-2 57.7%

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

   9. associate-+l+ 57.7%

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

   10. +-commutative 57.7%

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

   11. count-2 57.7%

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

   12. fma-neg 56.7%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-def 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 47.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-102}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.16 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+253} \lor \neg \left(x \leq 4.6 \cdot 10^{+288}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -4.2e-42)
     t_1
     (if (<= x 2.9e-102)
       (* y 5.0)
       (if (<= x 4.2e-38)
         (* x t)
         (if (<= x 2.16e+102)
           t_1
           (if (or (<= x 1.65e+253) (not (<= x 4.6e+288)))
             (* x t)
             (* x (* y 2.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -4.2e-42) {
		tmp = t_1;
	} else if (x <= 2.9e-102) {
		tmp = y * 5.0;
	} else if (x <= 4.2e-38) {
		tmp = x * t;
	} else if (x <= 2.16e+102) {
		tmp = t_1;
	} else if ((x <= 1.65e+253) || !(x <= 4.6e+288)) {
		tmp = x * t;
	} else {
		tmp = x * (y * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-4.2d-42)) then
        tmp = t_1
    else if (x <= 2.9d-102) then
        tmp = y * 5.0d0
    else if (x <= 4.2d-38) then
        tmp = x * t
    else if (x <= 2.16d+102) then
        tmp = t_1
    else if ((x <= 1.65d+253) .or. (.not. (x <= 4.6d+288))) then
        tmp = x * t
    else
        tmp = x * (y * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -4.2e-42) {
		tmp = t_1;
	} else if (x <= 2.9e-102) {
		tmp = y * 5.0;
	} else if (x <= 4.2e-38) {
		tmp = x * t;
	} else if (x <= 2.16e+102) {
		tmp = t_1;
	} else if ((x <= 1.65e+253) || !(x <= 4.6e+288)) {
		tmp = x * t;
	} else {
		tmp = x * (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -4.2e-42:
		tmp = t_1
	elif x <= 2.9e-102:
		tmp = y * 5.0
	elif x <= 4.2e-38:
		tmp = x * t
	elif x <= 2.16e+102:
		tmp = t_1
	elif (x <= 1.65e+253) or not (x <= 4.6e+288):
		tmp = x * t
	else:
		tmp = x * (y * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -4.2e-42)
		tmp = t_1;
	elseif (x <= 2.9e-102)
		tmp = Float64(y * 5.0);
	elseif (x <= 4.2e-38)
		tmp = Float64(x * t);
	elseif (x <= 2.16e+102)
		tmp = t_1;
	elseif ((x <= 1.65e+253) || !(x <= 4.6e+288))
		tmp = Float64(x * t);
	else
		tmp = Float64(x * Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -4.2e-42)
		tmp = t_1;
	elseif (x <= 2.9e-102)
		tmp = y * 5.0;
	elseif (x <= 4.2e-38)
		tmp = x * t;
	elseif (x <= 2.16e+102)
		tmp = t_1;
	elseif ((x <= 1.65e+253) || ~((x <= 4.6e+288)))
		tmp = x * t;
	else
		tmp = x * (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e-42], t$95$1, If[LessEqual[x, 2.9e-102], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 4.2e-38], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.16e+102], t$95$1, If[Or[LessEqual[x, 1.65e+253], N[Not[LessEqual[x, 4.6e+288]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.20000000000000013e-42 or 4.20000000000000026e-38 < x < 2.16000000000000005e102

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 50.7%

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

   if -4.20000000000000013e-42 < x < 2.89999999999999986e-102

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 66.7%

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

   if 2.89999999999999986e-102 < x < 4.20000000000000026e-38 or 2.16000000000000005e102 < x < 1.65e253 or 4.59999999999999987e288 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 57.3%

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

   if 1.65e253 < x < 4.59999999999999987e288

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in y around inf 85.8%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-102}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.16 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+253} \lor \neg \left(x \leq 4.6 \cdot 10^{+288}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \]

Alternative 4: 87.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -5.9 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-287}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* 2.0 (* x z)))) (t_2 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -5.9e-33)
     t_2
     (if (<= x -1.65e-153)
       t_1
       (if (<= x -2e-287)
         (+ (* y 5.0) (* x t))
         (if (<= x 2.25e-101) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (2.0 * (x * z));
	double t_2 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -5.9e-33) {
		tmp = t_2;
	} else if (x <= -1.65e-153) {
		tmp = t_1;
	} else if (x <= -2e-287) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 2.25e-101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * 5.0d0) + (2.0d0 * (x * z))
    t_2 = x * (t + ((y + z) * 2.0d0))
    if (x <= (-5.9d-33)) then
        tmp = t_2
    else if (x <= (-1.65d-153)) then
        tmp = t_1
    else if (x <= (-2d-287)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 2.25d-101) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (2.0 * (x * z));
	double t_2 = x * (t + ((y + z) * 2.0));
	double tmp;
	if (x <= -5.9e-33) {
		tmp = t_2;
	} else if (x <= -1.65e-153) {
		tmp = t_1;
	} else if (x <= -2e-287) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 2.25e-101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (2.0 * (x * z))
	t_2 = x * (t + ((y + z) * 2.0))
	tmp = 0
	if x <= -5.9e-33:
		tmp = t_2
	elif x <= -1.65e-153:
		tmp = t_1
	elif x <= -2e-287:
		tmp = (y * 5.0) + (x * t)
	elif x <= 2.25e-101:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)))
	t_2 = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)))
	tmp = 0.0
	if (x <= -5.9e-33)
		tmp = t_2;
	elseif (x <= -1.65e-153)
		tmp = t_1;
	elseif (x <= -2e-287)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 2.25e-101)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (2.0 * (x * z));
	t_2 = x * (t + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -5.9e-33)
		tmp = t_2;
	elseif (x <= -1.65e-153)
		tmp = t_1;
	elseif (x <= -2e-287)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 2.25e-101)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.9e-33], t$95$2, If[LessEqual[x, -1.65e-153], t$95$1, If[LessEqual[x, -2e-287], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e-101], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.89999999999999985e-33 or 2.2499999999999999e-101 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 95.5%

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

   if -5.89999999999999985e-33 < x < -1.64999999999999994e-153 or -2.00000000000000004e-287 < x < 2.2499999999999999e-101

   1. Initial program 99.8%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 88.8%

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

   5. Taylor expanded in y around 0 88.8%

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

   if -1.64999999999999994e-153 < x < -2.00000000000000004e-287

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 100.0%

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

      3. flip-+ 36.5%

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

      4. associate-*r/ 36.4%

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

      5. fma-neg 36.8%

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

      6. associate-+l+ 36.8%

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

      7. +-commutative 36.8%

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

      8. count-2 36.8%

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

      9. associate-+l+ 36.8%

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

      10. +-commutative 36.8%

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

      11. count-2 36.8%

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

      12. fma-neg 36.4%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around inf 96.4%

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

      1. *-commutative 96.4%

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

   6. Simplified 96.4%

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

      1. fma-udef 96.4%

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

   8. Applied egg-rr 96.4%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-153}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-287}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 5: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-39} \lor \neg \left(x \leq 8 \cdot 10^{+108}\right):\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* (+ y z) 2.0))))
   (if (<= x -8e-42)
     t_1
     (if (<= x 2.1e-129)
       (* y 5.0)
       (if (or (<= x 4e-39) (not (<= x 8e+108))) (* x (+ t (* y 2.0))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -8e-42) {
		tmp = t_1;
	} else if (x <= 2.1e-129) {
		tmp = y * 5.0;
	} else if ((x <= 4e-39) || !(x <= 8e+108)) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + z) * 2.0d0)
    if (x <= (-8d-42)) then
        tmp = t_1
    else if (x <= 2.1d-129) then
        tmp = y * 5.0d0
    else if ((x <= 4d-39) .or. (.not. (x <= 8d+108))) then
        tmp = x * (t + (y * 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -8e-42) {
		tmp = t_1;
	} else if (x <= 2.1e-129) {
		tmp = y * 5.0;
	} else if ((x <= 4e-39) || !(x <= 8e+108)) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + z) * 2.0)
	tmp = 0
	if x <= -8e-42:
		tmp = t_1
	elif x <= 2.1e-129:
		tmp = y * 5.0
	elif (x <= 4e-39) or not (x <= 8e+108):
		tmp = x * (t + (y * 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + z) * 2.0))
	tmp = 0.0
	if (x <= -8e-42)
		tmp = t_1;
	elseif (x <= 2.1e-129)
		tmp = Float64(y * 5.0);
	elseif ((x <= 4e-39) || !(x <= 8e+108))
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + z) * 2.0);
	tmp = 0.0;
	if (x <= -8e-42)
		tmp = t_1;
	elseif (x <= 2.1e-129)
		tmp = y * 5.0;
	elseif ((x <= 4e-39) || ~((x <= 8e+108)))
		tmp = x * (t + (y * 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e-42], t$95$1, If[LessEqual[x, 2.1e-129], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 4e-39], N[Not[LessEqual[x, 8e+108]], $MachinePrecision]], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.0000000000000003e-42 or 3.99999999999999972e-39 < x < 8.0000000000000003e108

   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 94.8%

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

   5. Taylor expanded in t around 0 75.2%

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

   7. Simplified 75.2%

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

   if -8.0000000000000003e-42 < x < 2.1e-129

   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 67.7%

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

   if 2.1e-129 < x < 3.99999999999999972e-39 or 8.0000000000000003e108 < x

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 95.4%

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

   5. Taylor expanded in z around 0 72.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-39} \lor \neg \left(x \leq 8 \cdot 10^{+108}\right):\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 6: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.72 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))))
   (if (<= x -1.15e+36)
     (* x (* (+ y z) 2.0))
     (if (<= x -1.25e-42)
       t_1
       (if (<= x 1.72e-130)
         (* y 5.0)
         (if (<= x 6.5e+209) t_1 (* x (+ t (* y 2.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -1.15e+36) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= -1.25e-42) {
		tmp = t_1;
	} else if (x <= 1.72e-130) {
		tmp = y * 5.0;
	} else if (x <= 6.5e+209) {
		tmp = t_1;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    if (x <= (-1.15d+36)) then
        tmp = x * ((y + z) * 2.0d0)
    else if (x <= (-1.25d-42)) then
        tmp = t_1
    else if (x <= 1.72d-130) then
        tmp = y * 5.0d0
    else if (x <= 6.5d+209) then
        tmp = t_1
    else
        tmp = x * (t + (y * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -1.15e+36) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= -1.25e-42) {
		tmp = t_1;
	} else if (x <= 1.72e-130) {
		tmp = y * 5.0;
	} else if (x <= 6.5e+209) {
		tmp = t_1;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	tmp = 0
	if x <= -1.15e+36:
		tmp = x * ((y + z) * 2.0)
	elif x <= -1.25e-42:
		tmp = t_1
	elif x <= 1.72e-130:
		tmp = y * 5.0
	elif x <= 6.5e+209:
		tmp = t_1
	else:
		tmp = x * (t + (y * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	tmp = 0.0
	if (x <= -1.15e+36)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	elseif (x <= -1.25e-42)
		tmp = t_1;
	elseif (x <= 1.72e-130)
		tmp = Float64(y * 5.0);
	elseif (x <= 6.5e+209)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	tmp = 0.0;
	if (x <= -1.15e+36)
		tmp = x * ((y + z) * 2.0);
	elseif (x <= -1.25e-42)
		tmp = t_1;
	elseif (x <= 1.72e-130)
		tmp = y * 5.0;
	elseif (x <= 6.5e+209)
		tmp = t_1;
	else
		tmp = x * (t + (y * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+36], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.25e-42], t$95$1, If[LessEqual[x, 1.72e-130], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 6.5e+209], t$95$1, N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.14999999999999998e36

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in t around 0 80.6%

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

   7. Simplified 80.6%

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

   if -1.14999999999999998e36 < x < -1.25000000000000001e-42 or 1.72000000000000008e-130 < x < 6.49999999999999975e209

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.0%

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

   if -1.25000000000000001e-42 < x < 1.72000000000000008e-130

   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 67.7%

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

   if 6.49999999999999975e209 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in z around 0 94.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.72 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+209}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]

Alternative 7: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+71} \lor \neg \left(z \leq 8 \cdot 10^{-16}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e+71) (not (<= z 8e-16)))
   (+ (* 2.0 (* x (+ y z))) (* y 5.0))
   (+ (* y 5.0) (* x (+ t (+ y y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+71) || !(z <= 8e-16)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.9d+71)) .or. (.not. (z <= 8d-16))) then
        tmp = (2.0d0 * (x * (y + z))) + (y * 5.0d0)
    else
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+71) || !(z <= 8e-16)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9e+71) or not (z <= 8e-16):
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	else:
		tmp = (y * 5.0) + (x * (t + (y + y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9e+71) || !(z <= 8e-16))
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(y * 5.0));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.9e+71) || ~((z <= 8e-16)))
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	else
		tmp = (y * 5.0) + (x * (t + (y + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9e+71], N[Not[LessEqual[z, 8e-16]], $MachinePrecision]], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.90000000000000007e71 or 7.9999999999999998e-16 < z

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 89.1%

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

   if -2.90000000000000007e71 < z < 7.9999999999999998e-16

   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 95.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+71} \lor \neg \left(z \leq 8 \cdot 10^{-16}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \]

Alternative 8: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.8e-26)
   (* x (+ t (* (+ y z) 2.0)))
   (if (<= t 9.6e-23)
     (+ (* 2.0 (* x (+ y z))) (* y 5.0))
     (+ (* y 5.0) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e-26) {
		tmp = x * (t + ((y + z) * 2.0));
	} else if (t <= 9.6e-23) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.8d-26)) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else if (t <= 9.6d-23) then
        tmp = (2.0d0 * (x * (y + z))) + (y * 5.0d0)
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e-26) {
		tmp = x * (t + ((y + z) * 2.0));
	} else if (t <= 9.6e-23) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.8e-26:
		tmp = x * (t + ((y + z) * 2.0))
	elif t <= 9.6e-23:
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.8e-26)
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	elseif (t <= 9.6e-23)
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(y * 5.0));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.8e-26)
		tmp = x * (t + ((y + z) * 2.0));
	elseif (t <= 9.6e-23)
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.8e-26], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e-23], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8000000000000002e-26

   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 85.9%

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

   if -4.8000000000000002e-26 < t < 9.59999999999999986e-23

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 97.2%

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

   if 9.59999999999999986e-23 < t

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 100.0%

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

      3. flip-+ 50.1%

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

      4. associate-*r/ 46.7%

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

      5. fma-neg 49.1%

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

      6. associate-+l+ 49.1%

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

      7. +-commutative 49.1%

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

      8. count-2 49.1%

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

      9. associate-+l+ 49.1%

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

      10. +-commutative 49.1%

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

      11. count-2 49.1%

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

      12. fma-neg 46.7%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around inf 80.2%

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

      1. *-commutative 80.2%

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

   6. Simplified 80.2%

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

      1. fma-udef 80.2%

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

   8. Applied egg-rr 80.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 10: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-36} \lor \neg \left(x \leq 4.15 \cdot 10^{+102}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -2.1e-42)
     t_1
     (if (<= x 2.25e-101)
       (* y 5.0)
       (if (or (<= x 8e-36) (not (<= x 4.15e+102))) (* x t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -2.1e-42) {
		tmp = t_1;
	} else if (x <= 2.25e-101) {
		tmp = y * 5.0;
	} else if ((x <= 8e-36) || !(x <= 4.15e+102)) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-2.1d-42)) then
        tmp = t_1
    else if (x <= 2.25d-101) then
        tmp = y * 5.0d0
    else if ((x <= 8d-36) .or. (.not. (x <= 4.15d+102))) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -2.1e-42) {
		tmp = t_1;
	} else if (x <= 2.25e-101) {
		tmp = y * 5.0;
	} else if ((x <= 8e-36) || !(x <= 4.15e+102)) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -2.1e-42:
		tmp = t_1
	elif x <= 2.25e-101:
		tmp = y * 5.0
	elif (x <= 8e-36) or not (x <= 4.15e+102):
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -2.1e-42)
		tmp = t_1;
	elseif (x <= 2.25e-101)
		tmp = Float64(y * 5.0);
	elseif ((x <= 8e-36) || !(x <= 4.15e+102))
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -2.1e-42)
		tmp = t_1;
	elseif (x <= 2.25e-101)
		tmp = y * 5.0;
	elseif ((x <= 8e-36) || ~((x <= 4.15e+102)))
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e-42], t$95$1, If[LessEqual[x, 2.25e-101], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 8e-36], N[Not[LessEqual[x, 4.15e+102]], $MachinePrecision]], N[(x * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.10000000000000006e-42 or 7.9999999999999995e-36 < x < 4.1500000000000002e102

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 50.7%

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

   if -2.10000000000000006e-42 < x < 2.2499999999999999e-101

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 66.7%

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

   if 2.2499999999999999e-101 < x < 7.9999999999999995e-36 or 4.1500000000000002e102 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 52.3%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-42}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-36} \lor \neg \left(x \leq 4.15 \cdot 10^{+102}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 11: 62.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-105}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-37}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* (+ y z) 2.0))))
   (if (<= x -8e-42)
     t_1
     (if (<= x 5.8e-105) (* y 5.0) (if (<= x 7e-37) (* x t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -8e-42) {
		tmp = t_1;
	} else if (x <= 5.8e-105) {
		tmp = y * 5.0;
	} else if (x <= 7e-37) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + z) * 2.0d0)
    if (x <= (-8d-42)) then
        tmp = t_1
    else if (x <= 5.8d-105) then
        tmp = y * 5.0d0
    else if (x <= 7d-37) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -8e-42) {
		tmp = t_1;
	} else if (x <= 5.8e-105) {
		tmp = y * 5.0;
	} else if (x <= 7e-37) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + z) * 2.0)
	tmp = 0
	if x <= -8e-42:
		tmp = t_1
	elif x <= 5.8e-105:
		tmp = y * 5.0
	elif x <= 7e-37:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + z) * 2.0))
	tmp = 0.0
	if (x <= -8e-42)
		tmp = t_1;
	elseif (x <= 5.8e-105)
		tmp = Float64(y * 5.0);
	elseif (x <= 7e-37)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + z) * 2.0);
	tmp = 0.0;
	if (x <= -8e-42)
		tmp = t_1;
	elseif (x <= 5.8e-105)
		tmp = y * 5.0;
	elseif (x <= 7e-37)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e-42], t$95$1, If[LessEqual[x, 5.8e-105], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 7e-37], N[(x * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.0000000000000003e-42 or 7.0000000000000003e-37 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 96.3%

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

   5. Taylor expanded in t around 0 69.9%

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

   7. Simplified 69.9%

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

   if -8.0000000000000003e-42 < x < 5.80000000000000007e-105

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 66.7%

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

   if 5.80000000000000007e-105 < x < 7.0000000000000003e-37

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 65.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-105}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-37}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \end{array} \]

Alternative 12: 72.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+209}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.2e-11)
   (* x (* (+ y z) 2.0))
   (if (<= x 1.2e-129)
     (+ (* y 5.0) (* x t))
     (if (<= x 1.7e+209) (* x (+ t (* z 2.0))) (* x (+ t (* y 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e-11) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= 1.2e-129) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1.7e+209) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.2d-11)) then
        tmp = x * ((y + z) * 2.0d0)
    else if (x <= 1.2d-129) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 1.7d+209) then
        tmp = x * (t + (z * 2.0d0))
    else
        tmp = x * (t + (y * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e-11) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= 1.2e-129) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1.7e+209) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.2e-11:
		tmp = x * ((y + z) * 2.0)
	elif x <= 1.2e-129:
		tmp = (y * 5.0) + (x * t)
	elif x <= 1.7e+209:
		tmp = x * (t + (z * 2.0))
	else:
		tmp = x * (t + (y * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.2e-11)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	elseif (x <= 1.2e-129)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 1.7e+209)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.2e-11)
		tmp = x * ((y + z) * 2.0);
	elseif (x <= 1.2e-129)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 1.7e+209)
		tmp = x * (t + (z * 2.0));
	else
		tmp = x * (t + (y * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.2e-11], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e-129], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+209], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.1999999999999997e-11

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in t around 0 80.4%

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

   7. Simplified 80.4%

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

   if -4.1999999999999997e-11 < x < 1.19999999999999994e-129

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 100.0%

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

      3. flip-+ 46.3%

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

      4. associate-*r/ 46.2%

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

      5. fma-neg 46.5%

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

      6. associate-+l+ 46.5%

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

      7. +-commutative 46.5%

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

      8. count-2 46.5%

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

      9. associate-+l+ 46.5%

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

      10. +-commutative 46.5%

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

      11. count-2 46.5%

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

      12. fma-neg 46.2%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around inf 81.6%

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

      1. *-commutative 81.6%

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

   6. Simplified 81.6%

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

      1. fma-udef 81.5%

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

   8. Applied egg-rr 81.5%

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

   if 1.19999999999999994e-129 < x < 1.6999999999999998e209

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.8%

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

   if 1.6999999999999998e209 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in z around 0 94.9%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+209}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]

Alternative 13: 87.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-42} \lor \neg \left(x \leq 3.2 \cdot 10^{-129}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.4e-42) (not (<= x 3.2e-129)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.4e-42) || !(x <= 3.2e-129)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.4d-42)) .or. (.not. (x <= 3.2d-129))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.4e-42) || !(x <= 3.2e-129)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.4e-42) or not (x <= 3.2e-129):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.4e-42) || !(x <= 3.2e-129))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.4e-42) || ~((x <= 3.2e-129)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.4e-42], N[Not[LessEqual[x, 3.2e-129]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999999e-42 or 3.2000000000000003e-129 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 95.0%

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

   if -1.39999999999999999e-42 < x < 3.2000000000000003e-129

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 100.0%

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

      3. flip-+ 45.9%

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

      4. associate-*r/ 45.9%

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

      5. fma-neg 46.2%

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

      6. associate-+l+ 46.2%

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

      7. +-commutative 46.2%

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

      8. count-2 46.2%

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

      9. associate-+l+ 46.2%

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

      10. +-commutative 46.2%

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

      11. count-2 46.2%

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

      12. fma-neg 45.9%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around inf 82.6%

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

      1. *-commutative 82.6%

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

   6. Simplified 82.6%

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

      1. fma-udef 82.6%

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

   8. Applied egg-rr 82.6%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-42} \lor \neg \left(x \leq 3.2 \cdot 10^{-129}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 14: 78.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-33} \lor \neg \left(y \leq 3.4 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e-33) (not (<= y 3.4e+34)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e-33) || !(y <= 3.4e+34)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.2d-33)) .or. (.not. (y <= 3.4d+34))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e-33) || !(y <= 3.4e+34)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e-33) or not (y <= 3.4e+34):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e-33) || !(y <= 3.4e+34))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.2e-33) || ~((y <= 3.4e+34)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2e-33], N[Not[LessEqual[y, 3.4e+34]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e-33 or 3.3999999999999999e34 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 75.7%

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

   4. Simplified 75.7%

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

   if -4.2e-33 < y < 3.3999999999999999e34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-33} \lor \neg \left(y \leq 3.4 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 15: 47.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-32} \lor \neg \left(x \leq 2.25 \cdot 10^{-101}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3e-32) (not (<= x 2.25e-101))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3e-32) || !(x <= 2.25e-101)) {
		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 <= (-3d-32)) .or. (.not. (x <= 2.25d-101))) 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 <= -3e-32) || !(x <= 2.25e-101)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3e-32) or not (x <= 2.25e-101):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3e-32) || !(x <= 2.25e-101))
		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 <= -3e-32) || ~((x <= 2.25e-101)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3e-32], N[Not[LessEqual[x, 2.25e-101]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3e-32 or 2.2499999999999999e-101 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 35.1%

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

   if -3e-32 < x < 2.2499999999999999e-101

   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 66.1%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-32} \lor \neg \left(x \leq 2.25 \cdot 10^{-101}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 16: 30.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ y \cdot 5 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 29.9%

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

3. Final simplification 29.9%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023334 
(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)))