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

Percentage Accurate: 99.9% → 99.9%

Time: 8.1s

Alternatives: 15

Speedup: 1.0×

• 26.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(5.0 * y + N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $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. 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 97.2%

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

   1. *-commutative 97.2%

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

   2. fma-define 97.2%

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

   3. *-commutative 97.2%

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

7. Applied egg-rr 97.2%

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

8. Taylor expanded in x around 0 99.9%

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

   1. fma-define 100.0%

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

10. Simplified 100.0%

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

Alternative 2: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-12} \lor \neg \left(x \leq 2.3 \cdot 10^{-103}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.2e-12) (not (<= x 2.3e-103)))
   (* x (+ t (+ (* 2.0 (+ y z)) (* 5.0 (/ y x)))))
   (+ (* 5.0 y) (* x (+ t (* 2.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e-12) || !(x <= 2.3e-103)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (5.0 * y) + (x * (t + (2.0 * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.2d-12)) .or. (.not. (x <= 2.3d-103))) then
        tmp = x * (t + ((2.0d0 * (y + z)) + (5.0d0 * (y / x))))
    else
        tmp = (5.0d0 * y) + (x * (t + (2.0d0 * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e-12) || !(x <= 2.3e-103)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (5.0 * y) + (x * (t + (2.0 * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.2e-12) or not (x <= 2.3e-103):
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))))
	else:
		tmp = (5.0 * y) + (x * (t + (2.0 * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.2e-12) || !(x <= 2.3e-103))
		tmp = Float64(x * Float64(t + Float64(Float64(2.0 * Float64(y + z)) + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(Float64(5.0 * y) + Float64(x * Float64(t + Float64(2.0 * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.2e-12) || ~((x <= 2.3e-103)))
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	else
		tmp = (5.0 * y) + (x * (t + (2.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.2e-12], N[Not[LessEqual[x, 2.3e-103]], $MachinePrecision]], 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[(N[(5.0 * y), $MachinePrecision] + N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2e-12 or 2.3000000000000001e-103 < 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 99.9%

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

   if -7.2e-12 < x < 2.3000000000000001e-103

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-12} \lor \neg \left(x \leq 2.3 \cdot 10^{-103}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-211} \lor \neg \left(x \leq 1.6 \cdot 10^{-156}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.1e+92)
   (* x (+ t (* y 2.0)))
   (if (or (<= x -1.4e-211) (not (<= x 1.6e-156)))
     (* x (+ t (* 2.0 z)))
     (* 5.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.1e+92) {
		tmp = x * (t + (y * 2.0));
	} else if ((x <= -1.4e-211) || !(x <= 1.6e-156)) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = 5.0 * 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 (x <= (-2.1d+92)) then
        tmp = x * (t + (y * 2.0d0))
    else if ((x <= (-1.4d-211)) .or. (.not. (x <= 1.6d-156))) then
        tmp = x * (t + (2.0d0 * z))
    else
        tmp = 5.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.1e+92) {
		tmp = x * (t + (y * 2.0));
	} else if ((x <= -1.4e-211) || !(x <= 1.6e-156)) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = 5.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.1e+92:
		tmp = x * (t + (y * 2.0))
	elif (x <= -1.4e-211) or not (x <= 1.6e-156):
		tmp = x * (t + (2.0 * z))
	else:
		tmp = 5.0 * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.1e+92)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	elseif ((x <= -1.4e-211) || !(x <= 1.6e-156))
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	else
		tmp = Float64(5.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.1e+92)
		tmp = x * (t + (y * 2.0));
	elseif ((x <= -1.4e-211) || ~((x <= 1.6e-156)))
		tmp = x * (t + (2.0 * z));
	else
		tmp = 5.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.1e+92], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.4e-211], N[Not[LessEqual[x, 1.6e-156]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(5.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.09999999999999986e92

   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 99.9%

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

   6. Taylor expanded in z around 0 80.8%

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

   if -2.09999999999999986e92 < x < -1.3999999999999999e-211 or 1.59999999999999991e-156 < 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 81.4%

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

   6. Taylor expanded in y around 0 71.4%

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

   if -1.3999999999999999e-211 < x < 1.59999999999999991e-156

   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 y around inf 66.4%

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

   7. Simplified 66.4%

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

   8. Taylor expanded in x around 0 66.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-211} \lor \neg \left(x \leq 1.6 \cdot 10^{-156}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 1.05 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.5) (not (<= x 1.05e-6)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (* 5.0 y) (* x (+ t (* 2.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 1.05e-6)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (5.0 * y) + (x * (t + (2.0 * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.5d0)) .or. (.not. (x <= 1.05d-6))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (5.0d0 * y) + (x * (t + (2.0d0 * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 1.05e-6)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (5.0 * y) + (x * (t + (2.0 * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.5) or not (x <= 1.05e-6):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = (5.0 * y) + (x * (t + (2.0 * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.5) || !(x <= 1.05e-6))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(5.0 * y) + Float64(x * Float64(t + Float64(2.0 * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.5) || ~((x <= 1.05e-6)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (5.0 * y) + (x * (t + (2.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.5], N[Not[LessEqual[x, 1.05e-6]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(5.0 * y), $MachinePrecision] + N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5 or 1.0499999999999999e-6 < 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 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 98.9%

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

   if -2.5 < x < 1.0499999999999999e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 98.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 1.05 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -390000000000:\\ \;\;\;\;5 \cdot y + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -390000000000.0)
   (+ (* 5.0 y) (* 2.0 (* x z)))
   (if (<= z 8.5e+127)
     (+ (* y (+ 5.0 (* x 2.0))) (* x t))
     (* x (+ t (* 2.0 (+ y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -390000000000.0) {
		tmp = (5.0 * y) + (2.0 * (x * z));
	} else if (z <= 8.5e+127) {
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	} else {
		tmp = x * (t + (2.0 * (y + z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-390000000000.0d0)) then
        tmp = (5.0d0 * y) + (2.0d0 * (x * z))
    else if (z <= 8.5d+127) then
        tmp = (y * (5.0d0 + (x * 2.0d0))) + (x * t)
    else
        tmp = x * (t + (2.0d0 * (y + z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -390000000000.0) {
		tmp = (5.0 * y) + (2.0 * (x * z));
	} else if (z <= 8.5e+127) {
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	} else {
		tmp = x * (t + (2.0 * (y + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -390000000000.0:
		tmp = (5.0 * y) + (2.0 * (x * z))
	elif z <= 8.5e+127:
		tmp = (y * (5.0 + (x * 2.0))) + (x * t)
	else:
		tmp = x * (t + (2.0 * (y + z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -390000000000.0)
		tmp = Float64(Float64(5.0 * y) + Float64(2.0 * Float64(x * z)));
	elseif (z <= 8.5e+127)
		tmp = Float64(Float64(y * Float64(5.0 + Float64(x * 2.0))) + Float64(x * t));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -390000000000.0)
		tmp = (5.0 * y) + (2.0 * (x * z));
	elseif (z <= 8.5e+127)
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	else
		tmp = x * (t + (2.0 * (y + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -390000000000.0], N[(N[(5.0 * y), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+127], N[(N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9e11

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 84.3%

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

   if -3.9e11 < z < 8.4999999999999997e127

   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 99.9%

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

      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 y around 0 99.9%

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

   6. Taylor expanded in t around inf 93.2%

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

      1. *-commutative 93.2%

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

   8. Simplified 93.2%

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

   if 8.4999999999999997e127 < z

   1. Initial program 100.0%

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

      1. fma-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 89.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -390000000000:\\ \;\;\;\;5 \cdot y + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 45.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-86}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.8e+24)
   (* x t)
   (if (<= t -1.95e-86)
     (* 5.0 y)
     (if (<= t 1.85e+96) (* x (* 2.0 z)) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e+24) {
		tmp = x * t;
	} else if (t <= -1.95e-86) {
		tmp = 5.0 * y;
	} else if (t <= 1.85e+96) {
		tmp = x * (2.0 * z);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.8d+24)) then
        tmp = x * t
    else if (t <= (-1.95d-86)) then
        tmp = 5.0d0 * y
    else if (t <= 1.85d+96) then
        tmp = x * (2.0d0 * z)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e+24) {
		tmp = x * t;
	} else if (t <= -1.95e-86) {
		tmp = 5.0 * y;
	} else if (t <= 1.85e+96) {
		tmp = x * (2.0 * z);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.8e+24:
		tmp = x * t
	elif t <= -1.95e-86:
		tmp = 5.0 * y
	elif t <= 1.85e+96:
		tmp = x * (2.0 * z)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.8e+24)
		tmp = Float64(x * t);
	elseif (t <= -1.95e-86)
		tmp = Float64(5.0 * y);
	elseif (t <= 1.85e+96)
		tmp = Float64(x * Float64(2.0 * z));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.8e+24)
		tmp = x * t;
	elseif (t <= -1.95e-86)
		tmp = 5.0 * y;
	elseif (t <= 1.85e+96)
		tmp = x * (2.0 * z);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.8e+24], N[(x * t), $MachinePrecision], If[LessEqual[t, -1.95e-86], N[(5.0 * y), $MachinePrecision], If[LessEqual[t, 1.85e+96], N[(x * N[(2.0 * z), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.80000000000000015e24 or 1.84999999999999996e96 < 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. 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 94.1%

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

      1. *-commutative 94.1%

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

      2. fma-define 94.1%

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

      3. *-commutative 94.1%

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

   7. Applied egg-rr 94.1%

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

   8. Taylor expanded in x around 0 99.9%

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

      1. fma-define 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in t around inf 58.3%

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

       1. *-commutative 58.3%

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

   13. Simplified 58.3%

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

   if -3.80000000000000015e24 < t < -1.9500000000000001e-86

   1. Initial program 99.6%

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

      1. fma-define 99.6%

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

      2. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. count-2 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 71.6%

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

   7. Simplified 54.2%

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

   8. Taylor expanded in x around 0 54.2%

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

   if -1.9500000000000001e-86 < t < 1.84999999999999996e96

   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 99.9%

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

      1. *-commutative 99.9%

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

      2. fma-define 99.9%

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

      3. *-commutative 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in z around inf 52.0%

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

      1. associate-*r* 52.0%

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

      2. *-commutative 52.0%

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

      3. associate-*l* 52.0%

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

   10. Simplified 52.0%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-86}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{+41}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(5 \cdot y + x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1e+41)
   (+ (* 2.0 (* x (+ y z))) (+ (* 5.0 y) (* x t)))
   (* x (+ t (* 2.0 (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1e+41) {
		tmp = (2.0 * (x * (y + z))) + ((5.0 * y) + (x * t));
	} else {
		tmp = x * (t + (2.0 * (y + z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 1d+41) then
        tmp = (2.0d0 * (x * (y + z))) + ((5.0d0 * y) + (x * t))
    else
        tmp = x * (t + (2.0d0 * (y + z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1e+41) {
		tmp = (2.0 * (x * (y + z))) + ((5.0 * y) + (x * t));
	} else {
		tmp = x * (t + (2.0 * (y + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1e+41:
		tmp = (2.0 * (x * (y + z))) + ((5.0 * y) + (x * t))
	else:
		tmp = x * (t + (2.0 * (y + z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1e+41)
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(Float64(5.0 * y) + Float64(x * t)));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 1e+41)
		tmp = (2.0 * (x * (y + z))) + ((5.0 * y) + (x * t));
	else
		tmp = x * (t + (2.0 * (y + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1e+41], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(5.0 * y), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000001e41

   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 98.9%

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

   if 1.00000000000000001e41 < 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 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+41}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(5 \cdot y + x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-18} \lor \neg \left(x \leq 1.7 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.02e-18) (not (<= x 1.7e-85)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (* 5.0 y) (* 2.0 (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.02e-18) || !(x <= 1.7e-85)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (5.0 * y) + (2.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.02d-18)) .or. (.not. (x <= 1.7d-85))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (5.0d0 * y) + (2.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.02e-18) || !(x <= 1.7e-85)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (5.0 * y) + (2.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.02e-18) or not (x <= 1.7e-85):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = (5.0 * y) + (2.0 * (x * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.02e-18) || !(x <= 1.7e-85))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(5.0 * y) + Float64(2.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.02e-18) || ~((x <= 1.7e-85)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (5.0 * y) + (2.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.02e-18], N[Not[LessEqual[x, 1.7e-85]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(5.0 * y), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e-18 or 1.7e-85 < 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 95.2%

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

   if -1.02e-18 < x < 1.7e-85

   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 z around inf 80.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-18} \lor \neg \left(x \leq 1.7 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-18} \lor \neg \left(x \leq 2.9 \cdot 10^{-146}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.5e-18) (not (<= x 2.9e-146)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (* 5.0 y) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.5e-18) || !(x <= 2.9e-146)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (5.0 * y) + (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 <= (-4.5d-18)) .or. (.not. (x <= 2.9d-146))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (5.0d0 * y) + (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 <= -4.5e-18) || !(x <= 2.9e-146)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (5.0 * y) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.5e-18) or not (x <= 2.9e-146):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = (5.0 * y) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.5e-18) || !(x <= 2.9e-146))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(5.0 * y) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.5e-18) || ~((x <= 2.9e-146)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (5.0 * y) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.5e-18], N[Not[LessEqual[x, 2.9e-146]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(5.0 * y), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999994e-18 or 2.90000000000000011e-146 < 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 92.5%

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

   if -4.49999999999999994e-18 < x < 2.90000000000000011e-146

   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 t around inf 80.5%

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

   5. Simplified 80.5%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-18} \lor \neg \left(x \leq 2.9 \cdot 10^{-146}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.16 \cdot 10^{+114} \lor \neg \left(y \leq 4.2 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.16e+114) (not (<= y 4.2e+32)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.16e+114) || !(y <= 4.2e+32)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.16d+114)) .or. (.not. (y <= 4.2d+32))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (2.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.16e+114) || !(y <= 4.2e+32)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.16e+114) or not (y <= 4.2e+32):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.16e+114) || !(y <= 4.2e+32))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.16e+114) || ~((y <= 4.2e+32)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.16e+114], N[Not[LessEqual[y, 4.2e+32]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.16000000000000009e114 or 4.2000000000000001e32 < 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 y around inf 80.5%

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

   if -2.16000000000000009e114 < y < 4.2000000000000001e32

   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 83.7%

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

   6. Taylor expanded in y around 0 80.6%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.16 \cdot 10^{+114} \lor \neg \left(y \leq 4.2 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -390000000000 \lor \neg \left(z \leq 1.9 \cdot 10^{+126}\right):\\ \;\;\;\;x \cdot \left(2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -390000000000.0) (not (<= z 1.9e+126)))
   (* x (* 2.0 z))
   (* x (+ t (* y 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -390000000000.0) || !(z <= 1.9e+126)) {
		tmp = x * (2.0 * z);
	} 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 ((z <= (-390000000000.0d0)) .or. (.not. (z <= 1.9d+126))) then
        tmp = x * (2.0d0 * z)
    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 ((z <= -390000000000.0) || !(z <= 1.9e+126)) {
		tmp = x * (2.0 * z);
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -390000000000.0) or not (z <= 1.9e+126):
		tmp = x * (2.0 * z)
	else:
		tmp = x * (t + (y * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -390000000000.0) || !(z <= 1.9e+126))
		tmp = Float64(x * Float64(2.0 * z));
	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 ((z <= -390000000000.0) || ~((z <= 1.9e+126)))
		tmp = x * (2.0 * z);
	else
		tmp = x * (t + (y * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -390000000000.0], N[Not[LessEqual[z, 1.9e+126]], $MachinePrecision]], N[(x * N[(2.0 * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e11 or 1.90000000000000008e126 < z

   1. Initial program 100.0%

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

      1. fma-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 93.9%

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

      1. *-commutative 93.9%

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

      2. fma-define 93.9%

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

      3. *-commutative 93.9%

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

   7. Applied egg-rr 93.9%

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

   8. Taylor expanded in z around inf 66.8%

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

      1. associate-*r* 66.8%

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

      2. *-commutative 66.8%

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

      3. associate-*l* 66.8%

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

   10. Simplified 66.8%

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

   if -3.9e11 < z < 1.90000000000000008e126

   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 99.9%

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

      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 67.2%

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

   6. Taylor expanded in z around 0 61.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -390000000000 \lor \neg \left(z \leq 1.9 \cdot 10^{+126}\right):\\ \;\;\;\;x \cdot \left(2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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))))) + (5.0d0 * y)
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (t + (y + (z + (y + z))))) + (5.0 * y);
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[(5.0 * y), $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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 13: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (2.0d0 * z))) + (y * (5.0d0 + (x * 2.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $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. 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 y around 0 97.6%

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

6. Final simplification 97.6%

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

Alternative 14: 44.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+25} \lor \neg \left(t \leq 1.8 \cdot 10^{+104}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.5e+25) (not (<= t 1.8e+104))) (* x t) (* 5.0 y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.5e+25) || !(t <= 1.8e+104)) {
		tmp = x * t;
	} else {
		tmp = 5.0 * 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 ((t <= (-7.5d+25)) .or. (.not. (t <= 1.8d+104))) then
        tmp = x * t
    else
        tmp = 5.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.5e+25) || !(t <= 1.8e+104)) {
		tmp = x * t;
	} else {
		tmp = 5.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7.5e+25) or not (t <= 1.8e+104):
		tmp = x * t
	else:
		tmp = 5.0 * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.5e+25) || !(t <= 1.8e+104))
		tmp = Float64(x * t);
	else
		tmp = Float64(5.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7.5e+25) || ~((t <= 1.8e+104)))
		tmp = x * t;
	else
		tmp = 5.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.5e+25], N[Not[LessEqual[t, 1.8e+104]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(5.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.49999999999999993e25 or 1.8e104 < 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. 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 94.0%

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

      1. *-commutative 94.0%

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

      2. fma-define 94.0%

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

      3. *-commutative 94.0%

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

   7. Applied egg-rr 94.0%

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

   8. Taylor expanded in x around 0 99.9%

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

      1. fma-define 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in t around inf 58.7%

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

       1. *-commutative 58.7%

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

   13. Simplified 58.7%

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

   if -7.49999999999999993e25 < t < 1.8e104

   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 y around inf 53.8%

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

   7. Simplified 33.6%

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

   8. Taylor expanded in x around 0 33.6%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+25} \lor \neg \left(t \leq 1.8 \cdot 10^{+104}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.3% 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 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
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 97.2%

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

   1. *-commutative 97.2%

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

   2. fma-define 97.2%

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

   3. *-commutative 97.2%

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

7. Applied egg-rr 97.2%

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

8. Taylor expanded in x around 0 99.9%

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

   1. fma-define 100.0%

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

10. Simplified 100.0%

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

11. Taylor expanded in t around inf 29.4%

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

    1. *-commutative 29.4%

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

13. Simplified 29.4%

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

Reproduce

herbie shell --seed 2024151 
(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)))