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

Percentage Accurate: 99.9% → 99.8%

Time: 10.4s

Alternatives: 15

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: 99.9% 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: 99.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -0.0035:\\ \;\;\;\;x \cdot \left(t + \left(t\_1 + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+143}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(y \cdot 5 + x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= x -0.0035)
     (* x (+ t (+ t_1 (* 5.0 (/ y x)))))
     (if (<= x 3e+143)
       (+ (* 2.0 (* x (+ y z))) (+ (* y 5.0) (* x t)))
       (* x (+ t t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (x <= -0.0035) {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	} else if (x <= 3e+143) {
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	} else {
		tmp = x * (t + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    if (x <= (-0.0035d0)) then
        tmp = x * (t + (t_1 + (5.0d0 * (y / x))))
    else if (x <= 3d+143) then
        tmp = (2.0d0 * (x * (y + z))) + ((y * 5.0d0) + (x * t))
    else
        tmp = x * (t + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (x <= -0.0035) {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	} else if (x <= 3e+143) {
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	} else {
		tmp = x * (t + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if x <= -0.0035:
		tmp = x * (t + (t_1 + (5.0 * (y / x))))
	elif x <= 3e+143:
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t))
	else:
		tmp = x * (t + t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (x <= -0.0035)
		tmp = Float64(x * Float64(t + Float64(t_1 + Float64(5.0 * Float64(y / x)))));
	elseif (x <= 3e+143)
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(Float64(y * 5.0) + Float64(x * t)));
	else
		tmp = Float64(x * Float64(t + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (x <= -0.0035)
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	elseif (x <= 3e+143)
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	else
		tmp = x * (t + t_1);
	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[x, -0.0035], N[(x * N[(t + N[(t$95$1 + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+143], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00350000000000000007

   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-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

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

   if -0.00350000000000000007 < x < 3.0000000000000001e143

   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-define 99.2%

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

      2. associate-+l+ 99.2%

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

      3. +-commutative 99.2%

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

      4. count-2 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 99.9%

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

   if 3.0000000000000001e143 < 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-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0035:\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+143}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(y \cdot 5 + x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y + N[(z + z), $MachinePrecision]), $MachinePrecision] + N[(y + t), $MachinePrecision]), $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-define 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+ 99.6%

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

   3. associate-+l+ 99.6%

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

3. Simplified 99.6%

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

Alternative 3: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $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-define 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. Add Preprocessing

5. Final simplification 99.5%

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

Alternative 4: 47.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-61}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+86}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+231}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -6e+92)
     t_1
     (if (<= x -1.4e-33)
       (* x t)
       (if (<= x 6.1e-61)
         (* y 5.0)
         (if (<= x 4.5e+86)
           (* x t)
           (if (<= x 3.8e+202)
             t_1
             (if (<= x 6.5e+231) (* y (* x 2.0)) (* x t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -6e+92) {
		tmp = t_1;
	} else if (x <= -1.4e-33) {
		tmp = x * t;
	} else if (x <= 6.1e-61) {
		tmp = y * 5.0;
	} else if (x <= 4.5e+86) {
		tmp = x * t;
	} else if (x <= 3.8e+202) {
		tmp = t_1;
	} else if (x <= 6.5e+231) {
		tmp = y * (x * 2.0);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-6d+92)) then
        tmp = t_1
    else if (x <= (-1.4d-33)) then
        tmp = x * t
    else if (x <= 6.1d-61) then
        tmp = y * 5.0d0
    else if (x <= 4.5d+86) then
        tmp = x * t
    else if (x <= 3.8d+202) then
        tmp = t_1
    else if (x <= 6.5d+231) then
        tmp = y * (x * 2.0d0)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -6e+92) {
		tmp = t_1;
	} else if (x <= -1.4e-33) {
		tmp = x * t;
	} else if (x <= 6.1e-61) {
		tmp = y * 5.0;
	} else if (x <= 4.5e+86) {
		tmp = x * t;
	} else if (x <= 3.8e+202) {
		tmp = t_1;
	} else if (x <= 6.5e+231) {
		tmp = y * (x * 2.0);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -6e+92:
		tmp = t_1
	elif x <= -1.4e-33:
		tmp = x * t
	elif x <= 6.1e-61:
		tmp = y * 5.0
	elif x <= 4.5e+86:
		tmp = x * t
	elif x <= 3.8e+202:
		tmp = t_1
	elif x <= 6.5e+231:
		tmp = y * (x * 2.0)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -6e+92)
		tmp = t_1;
	elseif (x <= -1.4e-33)
		tmp = Float64(x * t);
	elseif (x <= 6.1e-61)
		tmp = Float64(y * 5.0);
	elseif (x <= 4.5e+86)
		tmp = Float64(x * t);
	elseif (x <= 3.8e+202)
		tmp = t_1;
	elseif (x <= 6.5e+231)
		tmp = Float64(y * Float64(x * 2.0));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -6e+92)
		tmp = t_1;
	elseif (x <= -1.4e-33)
		tmp = x * t;
	elseif (x <= 6.1e-61)
		tmp = y * 5.0;
	elseif (x <= 4.5e+86)
		tmp = x * t;
	elseif (x <= 3.8e+202)
		tmp = t_1;
	elseif (x <= 6.5e+231)
		tmp = y * (x * 2.0);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+92], t$95$1, If[LessEqual[x, -1.4e-33], N[(x * t), $MachinePrecision], If[LessEqual[x, 6.1e-61], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 4.5e+86], N[(x * t), $MachinePrecision], If[LessEqual[x, 3.8e+202], t$95$1, If[LessEqual[x, 6.5e+231], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.00000000000000026e92 or 4.49999999999999993e86 < x < 3.8000000000000001e202

   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-define 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. Add Preprocessing

   5. Taylor expanded in t around 0 91.7%

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

   6. Taylor expanded in z around inf 53.3%

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

   if -6.00000000000000026e92 < x < -1.4e-33 or 6.1000000000000001e-61 < x < 4.49999999999999993e86 or 6.49999999999999933e231 < 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-define 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. Add Preprocessing

   5. Taylor expanded in t around 0 92.3%

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

   6. Taylor expanded in t around inf 53.0%

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

      1. *-commutative 53.0%

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

   8. Simplified 53.0%

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

   if -1.4e-33 < x < 6.1000000000000001e-61

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 66.1%

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

   5. Simplified 66.1%

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

   if 3.8000000000000001e202 < x < 6.49999999999999933e231

   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-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

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

   6. Taylor expanded in y around inf 80.7%

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

      1. associate-*r* 80.7%

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

      2. *-commutative 80.7%

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

      3. *-commutative 80.7%

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

   8. Simplified 80.7%

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

Alternative 5: 47.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-34}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-61}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+86} \lor \neg \left(x \leq 5 \cdot 10^{+171}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -5.6e+92)
     t_1
     (if (<= x -7.2e-34)
       (* x t)
       (if (<= x 6.2e-61)
         (* y 5.0)
         (if (or (<= x 3.5e+86) (not (<= x 5e+171))) (* 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 <= -5.6e+92) {
		tmp = t_1;
	} else if (x <= -7.2e-34) {
		tmp = x * t;
	} else if (x <= 6.2e-61) {
		tmp = y * 5.0;
	} else if ((x <= 3.5e+86) || !(x <= 5e+171)) {
		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 <= (-5.6d+92)) then
        tmp = t_1
    else if (x <= (-7.2d-34)) then
        tmp = x * t
    else if (x <= 6.2d-61) then
        tmp = y * 5.0d0
    else if ((x <= 3.5d+86) .or. (.not. (x <= 5d+171))) 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 <= -5.6e+92) {
		tmp = t_1;
	} else if (x <= -7.2e-34) {
		tmp = x * t;
	} else if (x <= 6.2e-61) {
		tmp = y * 5.0;
	} else if ((x <= 3.5e+86) || !(x <= 5e+171)) {
		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 <= -5.6e+92:
		tmp = t_1
	elif x <= -7.2e-34:
		tmp = x * t
	elif x <= 6.2e-61:
		tmp = y * 5.0
	elif (x <= 3.5e+86) or not (x <= 5e+171):
		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 <= -5.6e+92)
		tmp = t_1;
	elseif (x <= -7.2e-34)
		tmp = Float64(x * t);
	elseif (x <= 6.2e-61)
		tmp = Float64(y * 5.0);
	elseif ((x <= 3.5e+86) || !(x <= 5e+171))
		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 <= -5.6e+92)
		tmp = t_1;
	elseif (x <= -7.2e-34)
		tmp = x * t;
	elseif (x <= 6.2e-61)
		tmp = y * 5.0;
	elseif ((x <= 3.5e+86) || ~((x <= 5e+171)))
		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, -5.6e+92], t$95$1, If[LessEqual[x, -7.2e-34], N[(x * t), $MachinePrecision], If[LessEqual[x, 6.2e-61], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 3.5e+86], N[Not[LessEqual[x, 5e+171]], $MachinePrecision]], N[(x * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.60000000000000001e92 or 3.50000000000000019e86 < x < 5.0000000000000004e171

   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-define 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. Add Preprocessing

   5. Taylor expanded in t around 0 91.0%

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

   6. Taylor expanded in z around inf 54.2%

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

   if -5.60000000000000001e92 < x < -7.20000000000000016e-34 or 6.1999999999999999e-61 < x < 3.50000000000000019e86 or 5.0000000000000004e171 < 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-define 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. Add Preprocessing

   5. Taylor expanded in t around 0 93.5%

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

   6. Taylor expanded in t around inf 50.2%

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

      1. *-commutative 50.2%

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

   8. Simplified 50.2%

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

   if -7.20000000000000016e-34 < x < 6.1999999999999999e-61

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 66.1%

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

   5. Simplified 66.1%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+92}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-34}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-61}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+86} \lor \neg \left(x \leq 5 \cdot 10^{+171}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+127} \lor \neg \left(y \leq -2.8 \cdot 10^{+30} \lor \neg \left(y \leq -6.8 \cdot 10^{-51}\right) \land y \leq 1.3 \cdot 10^{+85}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.5e+127)
         (not (or (<= y -2.8e+30) (and (not (<= y -6.8e-51)) (<= y 1.3e+85)))))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e+127) || !((y <= -2.8e+30) || (!(y <= -6.8e-51) && (y <= 1.3e+85)))) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.5d+127)) .or. (.not. (y <= (-2.8d+30)) .or. (.not. (y <= (-6.8d-51))) .and. (y <= 1.3d+85))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e+127) || !((y <= -2.8e+30) || (!(y <= -6.8e-51) && (y <= 1.3e+85)))) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.5e+127) or not ((y <= -2.8e+30) or (not (y <= -6.8e-51) and (y <= 1.3e+85))):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.5e+127) || !((y <= -2.8e+30) || (!(y <= -6.8e-51) && (y <= 1.3e+85))))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.5e+127) || ~(((y <= -2.8e+30) || (~((y <= -6.8e-51)) && (y <= 1.3e+85)))))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.5e+127], N[Not[Or[LessEqual[y, -2.8e+30], And[N[Not[LessEqual[y, -6.8e-51]], $MachinePrecision], LessEqual[y, 1.3e+85]]]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5000000000000002e127 or -2.79999999999999983e30 < y < -6.80000000000000005e-51 or 1.30000000000000005e85 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 87.5%

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

   5. Simplified 87.5%

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

   if -2.5000000000000002e127 < y < -2.79999999999999983e30 or -6.80000000000000005e-51 < y < 1.30000000000000005e85

   1. Initial program 99.3%

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

      1. fma-define 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. Add Preprocessing

   5. Taylor expanded in t around 0 96.7%

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

   6. Taylor expanded in y around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. *-commutative 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*l* 81.0%

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

      5. *-commutative 81.0%

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

      6. distribute-lft-in 83.6%

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

   8. Simplified 83.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+127} \lor \neg \left(y \leq -2.8 \cdot 10^{+30} \lor \neg \left(y \leq -6.8 \cdot 10^{-51}\right) \land y \leq 1.3 \cdot 10^{+85}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-62}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+203} \lor \neg \left(x \leq 6.4 \cdot 10^{+274}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))))
   (if (<= x -6.2e-77)
     t_1
     (if (<= x 7.4e-62)
       (* y 5.0)
       (if (or (<= x 5.6e+203) (not (<= x 6.4e+274)))
         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 <= -6.2e-77) {
		tmp = t_1;
	} else if (x <= 7.4e-62) {
		tmp = y * 5.0;
	} else if ((x <= 5.6e+203) || !(x <= 6.4e+274)) {
		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 <= (-6.2d-77)) then
        tmp = t_1
    else if (x <= 7.4d-62) then
        tmp = y * 5.0d0
    else if ((x <= 5.6d+203) .or. (.not. (x <= 6.4d+274))) 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 <= -6.2e-77) {
		tmp = t_1;
	} else if (x <= 7.4e-62) {
		tmp = y * 5.0;
	} else if ((x <= 5.6e+203) || !(x <= 6.4e+274)) {
		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 <= -6.2e-77:
		tmp = t_1
	elif x <= 7.4e-62:
		tmp = y * 5.0
	elif (x <= 5.6e+203) or not (x <= 6.4e+274):
		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 <= -6.2e-77)
		tmp = t_1;
	elseif (x <= 7.4e-62)
		tmp = Float64(y * 5.0);
	elseif ((x <= 5.6e+203) || !(x <= 6.4e+274))
		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 <= -6.2e-77)
		tmp = t_1;
	elseif (x <= 7.4e-62)
		tmp = y * 5.0;
	elseif ((x <= 5.6e+203) || ~((x <= 6.4e+274)))
		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, -6.2e-77], t$95$1, If[LessEqual[x, 7.4e-62], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 5.6e+203], N[Not[LessEqual[x, 6.4e+274]], $MachinePrecision]], t$95$1, N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.20000000000000016e-77 or 7.3999999999999996e-62 < x < 5.5999999999999998e203 or 6.39999999999999965e274 < 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. Step-by-step derivation

      1. fma-define 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. Add Preprocessing

   5. Taylor expanded in t around 0 93.3%

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

   6. Taylor expanded in y around 0 69.9%

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

      1. +-commutative 69.9%

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

      2. *-commutative 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-*l* 69.3%

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

      5. *-commutative 69.3%

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

      6. distribute-lft-in 73.3%

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

   8. Simplified 73.3%

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

   if -6.20000000000000016e-77 < x < 7.3999999999999996e-62

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 68.2%

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

   5. Simplified 68.2%

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

   if 5.5999999999999998e203 < x < 6.39999999999999965e274

   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-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

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

   6. Taylor expanded in z around 0 85.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-62}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+203} \lor \neg \left(x \leq 6.4 \cdot 10^{+274}\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+95}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-35} \lor \neg \left(x \leq 3.3 \cdot 10^{-62}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))))
   (if (<= x -9.5e+114)
     t_1
     (if (<= x -1.6e+95)
       (* 2.0 (* x z))
       (if (or (<= x -2e-35) (not (<= x 3.3e-62))) t_1 (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -9.5e+114) {
		tmp = t_1;
	} else if (x <= -1.6e+95) {
		tmp = 2.0 * (x * z);
	} else if ((x <= -2e-35) || !(x <= 3.3e-62)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (y * 2.0d0))
    if (x <= (-9.5d+114)) then
        tmp = t_1
    else if (x <= (-1.6d+95)) then
        tmp = 2.0d0 * (x * z)
    else if ((x <= (-2d-35)) .or. (.not. (x <= 3.3d-62))) then
        tmp = t_1
    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 t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -9.5e+114) {
		tmp = t_1;
	} else if (x <= -1.6e+95) {
		tmp = 2.0 * (x * z);
	} else if ((x <= -2e-35) || !(x <= 3.3e-62)) {
		tmp = t_1;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -9.5e+114:
		tmp = t_1
	elif x <= -1.6e+95:
		tmp = 2.0 * (x * z)
	elif (x <= -2e-35) or not (x <= 3.3e-62):
		tmp = t_1
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (x <= -9.5e+114)
		tmp = t_1;
	elseif (x <= -1.6e+95)
		tmp = Float64(2.0 * Float64(x * z));
	elseif ((x <= -2e-35) || !(x <= 3.3e-62))
		tmp = t_1;
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y * 2.0));
	tmp = 0.0;
	if (x <= -9.5e+114)
		tmp = t_1;
	elseif (x <= -1.6e+95)
		tmp = 2.0 * (x * z);
	elseif ((x <= -2e-35) || ~((x <= 3.3e-62)))
		tmp = t_1;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+114], t$95$1, If[LessEqual[x, -1.6e+95], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -2e-35], N[Not[LessEqual[x, 3.3e-62]], $MachinePrecision]], t$95$1, N[(y * 5.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5000000000000001e114 or -1.6e95 < x < -2.00000000000000002e-35 or 3.30000000000000004e-62 < 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-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 95.6%

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

   6. Taylor expanded in z around 0 66.9%

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

   if -9.5000000000000001e114 < x < -1.6e95

   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-define 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 100.0%

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

   6. Taylor expanded in z around inf 80.4%

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

   if -2.00000000000000002e-35 < x < 3.30000000000000004e-62

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 66.1%

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

   5. Simplified 66.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+95}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-35} \lor \neg \left(x \leq 3.3 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -8.2e+205)
     t_1
     (if (<= y 5.2e+68)
       (* x (+ t (+ (* 2.0 (+ y z)) (* 5.0 (/ y x)))))
       (+ t_1 (* x t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -8.2e+205) {
		tmp = t_1;
	} else if (y <= 5.2e+68) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = t_1 + (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 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-8.2d+205)) then
        tmp = t_1
    else if (y <= 5.2d+68) then
        tmp = x * (t + ((2.0d0 * (y + z)) + (5.0d0 * (y / x))))
    else
        tmp = t_1 + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -8.2e+205) {
		tmp = t_1;
	} else if (y <= 5.2e+68) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = t_1 + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -8.2e+205:
		tmp = t_1
	elif y <= 5.2e+68:
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))))
	else:
		tmp = t_1 + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -8.2e+205)
		tmp = t_1;
	elseif (y <= 5.2e+68)
		tmp = Float64(x * Float64(t + Float64(Float64(2.0 * Float64(y + z)) + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(t_1 + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -8.2e+205)
		tmp = t_1;
	elseif (y <= 5.2e+68)
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	else
		tmp = t_1 + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+205], t$95$1, If[LessEqual[y, 5.2e+68], N[(x * N[(t + N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.2000000000000006e205

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.9%

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

   5. Simplified 99.9%

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

   if -8.2000000000000006e205 < y < 5.1999999999999996e68

   1. Initial program 99.4%

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

      1. fma-define 99.4%

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

      2. associate-+l+ 99.4%

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

      3. +-commutative 99.4%

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

      4. count-2 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 98.3%

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

   if 5.1999999999999996e68 < y

   1. Initial program 99.9%

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

      1. fma-define 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. Add Preprocessing

   5. Taylor expanded in t around 0 91.0%

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

   6. Taylor expanded in y around inf 89.6%

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

      1. associate-*r* 89.6%

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

      2. *-commutative 89.6%

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

      3. *-commutative 89.6%

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

   8. Simplified 89.6%

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

   9. Taylor expanded in y around 0 89.6%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-8} \lor \neg \left(x \leq 2.75 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 5 + x \cdot t\right) + y \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.65e-8) (not (<= x 2.75e-33)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (+ (* y 5.0) (* x t)) (* y (* x 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.65e-8) || !(x <= 2.75e-33)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = ((y * 5.0) + (x * t)) + (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 <= (-2.65d-8)) .or. (.not. (x <= 2.75d-33))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = ((y * 5.0d0) + (x * t)) + (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 <= -2.65e-8) || !(x <= 2.75e-33)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = ((y * 5.0) + (x * t)) + (y * (x * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.65e-8) or not (x <= 2.75e-33):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = ((y * 5.0) + (x * t)) + (y * (x * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.65e-8) || !(x <= 2.75e-33))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(Float64(y * 5.0) + Float64(x * t)) + Float64(y * Float64(x * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.65e-8) || ~((x <= 2.75e-33)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = ((y * 5.0) + (x * t)) + (y * (x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.65e-8], N[Not[LessEqual[x, 2.75e-33]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6499999999999999e-8 or 2.75e-33 < 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-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 98.7%

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

   if -2.6499999999999999e-8 < x < 2.75e-33

   1. Initial program 99.0%

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

      1. fma-define 99.0%

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

      2. associate-+l+ 99.0%

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

      3. +-commutative 99.0%

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

      4. count-2 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around 0 99.9%

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

   6. Taylor expanded in y around inf 84.0%

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

      1. associate-*r* 84.0%

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

      2. *-commutative 84.0%

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

      3. *-commutative 84.0%

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

   8. Simplified 84.0%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-8} \lor \neg \left(x \leq 2.75 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 5 + x \cdot t\right) + y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.2e+133)
     t_1
     (if (<= y -5e-57)
       (+ (* y 5.0) (* x t))
       (if (<= y 2.1e+85) (* x (+ t (* z 2.0))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.2e+133) {
		tmp = t_1;
	} else if (y <= -5e-57) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 2.1e+85) {
		tmp = x * (t + (z * 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 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.2d+133)) then
        tmp = t_1
    else if (y <= (-5d-57)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 2.1d+85) then
        tmp = x * (t + (z * 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 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.2e+133) {
		tmp = t_1;
	} else if (y <= -5e-57) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 2.1e+85) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.2e+133:
		tmp = t_1
	elif y <= -5e-57:
		tmp = (y * 5.0) + (x * t)
	elif y <= 2.1e+85:
		tmp = x * (t + (z * 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.2e+133)
		tmp = t_1;
	elseif (y <= -5e-57)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 2.1e+85)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.2e+133)
		tmp = t_1;
	elseif (y <= -5e-57)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 2.1e+85)
		tmp = x * (t + (z * 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+133], t$95$1, If[LessEqual[y, -5e-57], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+85], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1999999999999999e133 or 2.1000000000000001e85 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 90.8%

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

   5. Simplified 90.8%

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

   if -1.1999999999999999e133 < y < -5.0000000000000002e-57

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf 70.9%

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

   5. Simplified 70.9%

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

   if -5.0000000000000002e-57 < y < 2.1000000000000001e85

   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-define 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. Add Preprocessing

   5. Taylor expanded in t around 0 97.8%

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

   6. Taylor expanded in y around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. *-commutative 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-*l* 82.4%

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

      5. *-commutative 82.4%

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

      6. distribute-lft-in 84.6%

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

   8. Simplified 84.6%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-18} \lor \neg \left(x \leq 2.55 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e-18) (not (<= x 2.55e-37)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e-18) || !(x <= 2.55e-37)) {
		tmp = x * (t + (2.0 * (y + z)));
	} 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 <= (-1.6d-18)) .or. (.not. (x <= 2.55d-37))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    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 <= -1.6e-18) || !(x <= 2.55e-37)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.6e-18) or not (x <= 2.55e-37):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.6e-18) || !(x <= 2.55e-37))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	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 <= -1.6e-18) || ~((x <= 2.55e-37)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.6e-18], N[Not[LessEqual[x, 2.55e-37]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e-18 or 2.55e-37 < 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-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 98.0%

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

   if -1.6e-18 < x < 2.55e-37

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 84.6%

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

   5. Simplified 84.6%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-18} \lor \neg \left(x \leq 2.55 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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. Add Preprocessing

3. Final simplification 99.5%

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

Alternative 14: 47.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-34} \lor \neg \left(x \leq 6.4 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e-34) (not (<= x 6.4e-62))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e-34) || !(x <= 6.4e-62)) {
		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 <= (-1.6d-34)) .or. (.not. (x <= 6.4d-62))) 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 <= -1.6e-34) || !(x <= 6.4e-62)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.6e-34) or not (x <= 6.4e-62):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.6e-34) || !(x <= 6.4e-62))
		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 <= -1.6e-34) || ~((x <= 6.4e-62)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.6e-34], N[Not[LessEqual[x, 6.4e-62]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000001e-34 or 6.40000000000000043e-62 < 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-define 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. Add Preprocessing

   5. Taylor expanded in t around 0 92.5%

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

   6. Taylor expanded in t around inf 39.6%

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

      1. *-commutative 39.6%

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

   8. Simplified 39.6%

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

   if -1.60000000000000001e-34 < x < 6.40000000000000043e-62

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 66.1%

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

   5. Simplified 66.1%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-34} \lor \neg \left(x \leq 6.4 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.2% 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. Step-by-step derivation

   1. fma-define 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. Add Preprocessing

5. Taylor expanded in t around 0 95.2%

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

6. Taylor expanded in t around inf 32.1%

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

   1. *-commutative 32.1%

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

8. Simplified 32.1%

   \[\leadsto \color{blue}{x \cdot t} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024091 
(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)))