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

Percentage Accurate: 99.8% → 99.8%

Time: 9.3s

Alternatives: 21

Speedup: 0.1×

• 26.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 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 99.9%

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

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

   3. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 99.8% 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 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
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. Final simplification 99.9%

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

Alternative 3: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 0.0062:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + \left(y + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.15e-60)
   (* x (+ t (* z 2.0)))
   (if (<= x 0.0062)
     (* y 5.0)
     (if (<= x 8.2e+21)
       (* x (+ t (* y 2.0)))
       (if (<= x 3.9e+184) (* x (* 2.0 (+ y z))) (* x (+ z (+ y t))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e-60) {
		tmp = x * (t + (z * 2.0));
	} else if (x <= 0.0062) {
		tmp = y * 5.0;
	} else if (x <= 8.2e+21) {
		tmp = x * (t + (y * 2.0));
	} else if (x <= 3.9e+184) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = x * (z + (y + 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 <= (-1.15d-60)) then
        tmp = x * (t + (z * 2.0d0))
    else if (x <= 0.0062d0) then
        tmp = y * 5.0d0
    else if (x <= 8.2d+21) then
        tmp = x * (t + (y * 2.0d0))
    else if (x <= 3.9d+184) then
        tmp = x * (2.0d0 * (y + z))
    else
        tmp = x * (z + (y + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e-60) {
		tmp = x * (t + (z * 2.0));
	} else if (x <= 0.0062) {
		tmp = y * 5.0;
	} else if (x <= 8.2e+21) {
		tmp = x * (t + (y * 2.0));
	} else if (x <= 3.9e+184) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = x * (z + (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.15e-60:
		tmp = x * (t + (z * 2.0))
	elif x <= 0.0062:
		tmp = y * 5.0
	elif x <= 8.2e+21:
		tmp = x * (t + (y * 2.0))
	elif x <= 3.9e+184:
		tmp = x * (2.0 * (y + z))
	else:
		tmp = x * (z + (y + t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.15e-60)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (x <= 0.0062)
		tmp = Float64(y * 5.0);
	elseif (x <= 8.2e+21)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	elseif (x <= 3.9e+184)
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	else
		tmp = Float64(x * Float64(z + Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.15e-60)
		tmp = x * (t + (z * 2.0));
	elseif (x <= 0.0062)
		tmp = y * 5.0;
	elseif (x <= 8.2e+21)
		tmp = x * (t + (y * 2.0));
	elseif (x <= 3.9e+184)
		tmp = x * (2.0 * (y + z));
	else
		tmp = x * (z + (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.15e-60], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0062], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 8.2e+21], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e+184], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.1500000000000001e-60

   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 92.0%

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

   6. Taylor expanded in x around inf 93.9%

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

      1. +-commutative 93.9%

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

   8. Simplified 93.9%

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

   9. Taylor expanded in z around inf 71.0%

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

   if -1.1500000000000001e-60 < x < 0.00619999999999999978

   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 66.9%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   if 0.00619999999999999978 < x < 8.2e21

   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 0 100.0%

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

   6. Taylor expanded in x around inf 89.6%

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

      1. +-commutative 89.6%

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

   8. Simplified 89.6%

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

   9. Taylor expanded in z around 0 89.6%

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

   if 8.2e21 < x < 3.89999999999999971e184

   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+ 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. Taylor expanded in x around inf 99.9%

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

      1. +-commutative 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in t around 0 82.9%

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

   if 3.89999999999999971e184 < 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%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in x around inf 87.2%

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

      1. +-commutative 87.2%

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

      2. +-commutative 87.2%

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

      3. associate-+l+ 87.2%

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

   10. Simplified 87.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 0.0062:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-13} \lor \neg \left(x \leq 2.5 \cdot 10^{-45}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right) + \left(y \cdot 5 + x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.3e-13) (not (<= x 2.5e-45)))
   (* x (+ t (+ (* 2.0 (+ y z)) (* 5.0 (/ y x)))))
   (+ (* z (* x 2.0)) (+ (* y 5.0) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e-13) || !(x <= 2.5e-45)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (z * (x * 2.0)) + ((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 <= (-4.3d-13)) .or. (.not. (x <= 2.5d-45))) then
        tmp = x * (t + ((2.0d0 * (y + z)) + (5.0d0 * (y / x))))
    else
        tmp = (z * (x * 2.0d0)) + ((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 <= -4.3e-13) || !(x <= 2.5e-45)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (z * (x * 2.0)) + ((y * 5.0) + (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.3e-13) or not (x <= 2.5e-45):
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))))
	else:
		tmp = (z * (x * 2.0)) + ((y * 5.0) + (x * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.3e-13) || !(x <= 2.5e-45))
		tmp = Float64(x * Float64(t + Float64(Float64(2.0 * Float64(y + z)) + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(Float64(z * Float64(x * 2.0)) + 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 <= -4.3e-13) || ~((x <= 2.5e-45)))
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	else
		tmp = (z * (x * 2.0)) + ((y * 5.0) + (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.3e-13], N[Not[LessEqual[x, 2.5e-45]], $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[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2999999999999999e-13 or 2.49999999999999988e-45 < 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 99.9%

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

   if -4.2999999999999999e-13 < x < 2.49999999999999988e-45

   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. Taylor expanded in y around 0 99.9%

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

      1. associate-*r* 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-13} \lor \neg \left(x \leq 2.5 \cdot 10^{-45}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right) + \left(y \cdot 5 + x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 0.0062:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 (+ y z))))))
   (if (<= x -1.4e-37)
     t_1
     (if (<= x 5.6e-127)
       (+ (* y 5.0) (* x t))
       (if (<= x 0.0062) (+ (* y 5.0) (* 2.0 (* x z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * (y + z)));
	double tmp;
	if (x <= -1.4e-37) {
		tmp = t_1;
	} else if (x <= 5.6e-127) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 0.0062) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * (y + z)))
    if (x <= (-1.4d-37)) then
        tmp = t_1
    else if (x <= 5.6d-127) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 0.0062d0) then
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * (y + z)));
	double tmp;
	if (x <= -1.4e-37) {
		tmp = t_1;
	} else if (x <= 5.6e-127) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 0.0062) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * (y + z)))
	tmp = 0
	if x <= -1.4e-37:
		tmp = t_1
	elif x <= 5.6e-127:
		tmp = (y * 5.0) + (x * t)
	elif x <= 0.0062:
		tmp = (y * 5.0) + (2.0 * (x * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))))
	tmp = 0.0
	if (x <= -1.4e-37)
		tmp = t_1;
	elseif (x <= 5.6e-127)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 0.0062)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * (y + z)));
	tmp = 0.0;
	if (x <= -1.4e-37)
		tmp = t_1;
	elseif (x <= 5.6e-127)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 0.0062)
		tmp = (y * 5.0) + (2.0 * (x * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e-37], t$95$1, If[LessEqual[x, 5.6e-127], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0062], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4000000000000001e-37 or 0.00619999999999999978 < 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 97.0%

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

   if -1.4000000000000001e-37 < x < 5.59999999999999999e-127

   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 87.4%

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

   5. Simplified 87.4%

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

   if 5.59999999999999999e-127 < x < 0.00619999999999999978

   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 84.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 0.0062:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.4% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 2.5)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (z * (x * 2.0)) + ((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 <= (-2.5d0)) .or. (.not. (x <= 2.5d0))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (z * (x * 2.0d0)) + ((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 <= -2.5) || !(x <= 2.5)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (z * (x * 2.0)) + ((y * 5.0) + (x * t));
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.5) || !(x <= 2.5))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(z * Float64(x * 2.0)) + 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 <= -2.5) || ~((x <= 2.5)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (z * (x * 2.0)) + ((y * 5.0) + (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -2.5 or 2.5 < 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 97.7%

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

   if -2.5 < x < 2.5

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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. Taylor expanded in y around 0 98.8%

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

      1. associate-*r* 98.8%

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

   8. Simplified 98.8%

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

4. Final simplification 98.3%

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

Alternative 7: 78.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-70}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -2e+111)
     t_1
     (if (<= y -9e-70)
       (+ (* y 5.0) (* x t))
       (if (<= y 8.2e+55) (* 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 <= -2e+111) {
		tmp = t_1;
	} else if (y <= -9e-70) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 8.2e+55) {
		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 <= (-2d+111)) then
        tmp = t_1
    else if (y <= (-9d-70)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 8.2d+55) 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 <= -2e+111) {
		tmp = t_1;
	} else if (y <= -9e-70) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 8.2e+55) {
		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 <= -2e+111:
		tmp = t_1
	elif y <= -9e-70:
		tmp = (y * 5.0) + (x * t)
	elif y <= 8.2e+55:
		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 <= -2e+111)
		tmp = t_1;
	elseif (y <= -9e-70)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 8.2e+55)
		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 <= -2e+111)
		tmp = t_1;
	elseif (y <= -9e-70)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 8.2e+55)
		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, -2e+111], t$95$1, If[LessEqual[y, -9e-70], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+55], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999991e111 or 8.19999999999999962e55 < y

   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 y around inf 91.8%

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

   if -1.99999999999999991e111 < y < -9.00000000000000044e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 73.3%

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

   5. Simplified 73.3%

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

   if -9.00000000000000044e-70 < y < 8.19999999999999962e55

   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 97.4%

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

   6. Taylor expanded in x around inf 89.3%

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

      1. +-commutative 89.3%

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

   8. Simplified 89.3%

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

   9. Taylor expanded in z around inf 86.9%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-70}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 0.0062:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3e-61)
   (* x (+ t (* z 2.0)))
   (if (<= x 0.0062)
     (* y 5.0)
     (if (<= x 8.5e+20) (* x (+ t (* y 2.0))) (* x (* 2.0 (+ y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3e-61) {
		tmp = x * (t + (z * 2.0));
	} else if (x <= 0.0062) {
		tmp = y * 5.0;
	} else if (x <= 8.5e+20) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = x * (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 <= (-3d-61)) then
        tmp = x * (t + (z * 2.0d0))
    else if (x <= 0.0062d0) then
        tmp = y * 5.0d0
    else if (x <= 8.5d+20) then
        tmp = x * (t + (y * 2.0d0))
    else
        tmp = x * (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 <= -3e-61) {
		tmp = x * (t + (z * 2.0));
	} else if (x <= 0.0062) {
		tmp = y * 5.0;
	} else if (x <= 8.5e+20) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = x * (2.0 * (y + z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3e-61:
		tmp = x * (t + (z * 2.0))
	elif x <= 0.0062:
		tmp = y * 5.0
	elif x <= 8.5e+20:
		tmp = x * (t + (y * 2.0))
	else:
		tmp = x * (2.0 * (y + z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3e-61)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (x <= 0.0062)
		tmp = Float64(y * 5.0);
	elseif (x <= 8.5e+20)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	else
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3e-61)
		tmp = x * (t + (z * 2.0));
	elseif (x <= 0.0062)
		tmp = y * 5.0;
	elseif (x <= 8.5e+20)
		tmp = x * (t + (y * 2.0));
	else
		tmp = x * (2.0 * (y + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3e-61], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0062], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 8.5e+20], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.00000000000000012e-61

   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 92.0%

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

   6. Taylor expanded in x around inf 93.9%

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

      1. +-commutative 93.9%

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

   8. Simplified 93.9%

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

   9. Taylor expanded in z around inf 71.0%

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

   if -3.00000000000000012e-61 < x < 0.00619999999999999978

   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 66.9%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   if 0.00619999999999999978 < x < 8.5e20

   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 0 100.0%

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

   6. Taylor expanded in x around inf 89.6%

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

      1. +-commutative 89.6%

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

   8. Simplified 89.6%

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

   9. Taylor expanded in z around 0 89.6%

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

   if 8.5e20 < 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+ 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 96.4%

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

   6. Taylor expanded in x around inf 99.9%

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

      1. +-commutative 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in t around 0 76.6%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 0.0062:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.0065:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* 2.0 (+ y z)))))
   (if (<= x -1.4e-58)
     t_1
     (if (<= x 0.0065)
       (* y 5.0)
       (if (<= x 1.85e+21) (* x (+ t (* y 2.0))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -1.4e-58) {
		tmp = t_1;
	} else if (x <= 0.0065) {
		tmp = y * 5.0;
	} else if (x <= 1.85e+21) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (2.0d0 * (y + z))
    if (x <= (-1.4d-58)) then
        tmp = t_1
    else if (x <= 0.0065d0) then
        tmp = y * 5.0d0
    else if (x <= 1.85d+21) then
        tmp = x * (t + (y * 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -1.4e-58) {
		tmp = t_1;
	} else if (x <= 0.0065) {
		tmp = y * 5.0;
	} else if (x <= 1.85e+21) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (2.0 * (y + z))
	tmp = 0
	if x <= -1.4e-58:
		tmp = t_1
	elif x <= 0.0065:
		tmp = y * 5.0
	elif x <= 1.85e+21:
		tmp = x * (t + (y * 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(2.0 * Float64(y + z)))
	tmp = 0.0
	if (x <= -1.4e-58)
		tmp = t_1;
	elseif (x <= 0.0065)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.85e+21)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (2.0 * (y + z));
	tmp = 0.0;
	if (x <= -1.4e-58)
		tmp = t_1;
	elseif (x <= 0.0065)
		tmp = y * 5.0;
	elseif (x <= 1.85e+21)
		tmp = x * (t + (y * 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e-58], t$95$1, If[LessEqual[x, 0.0065], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.85e+21], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4e-58 or 1.85e21 < 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 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. Taylor expanded in x around inf 96.8%

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

      1. +-commutative 96.8%

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

   8. Simplified 96.8%

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

   9. Taylor expanded in t around 0 70.4%

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

   if -1.4e-58 < x < 0.0064999999999999997

   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 66.9%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   if 0.0064999999999999997 < x < 1.85e21

   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 0 100.0%

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

   6. Taylor expanded in x around inf 89.6%

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

      1. +-commutative 89.6%

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

   8. Simplified 89.6%

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

   9. Taylor expanded in z around 0 89.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 0.0065:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.4% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 2.5)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (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 ((x <= (-2.5d0)) .or. (.not. (x <= 2.5d0))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (y * 5.0d0) + (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 ((x <= -2.5) || !(x <= 2.5)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.5) || !(x <= 2.5))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(y * 5.0) + 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 ((x <= -2.5) || ~((x <= 2.5)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -2.5 or 2.5 < 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 97.7%

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

   if -2.5 < x < 2.5

   1. Initial program 99.9%

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

   3. 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 98.3%

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

Alternative 11: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-70} \lor \neg \left(y \leq 2.2 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.18e-70) (not (<= y 2.2e+23)))
   (+ (* y 5.0) (* x (+ t (* y 2.0))))
   (* x (+ t (* 2.0 (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.18e-70) || !(y <= 2.2e+23)) {
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	} 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 ((y <= (-1.18d-70)) .or. (.not. (y <= 2.2d+23))) then
        tmp = (y * 5.0d0) + (x * (t + (y * 2.0d0)))
    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 ((y <= -1.18e-70) || !(y <= 2.2e+23)) {
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	} else {
		tmp = x * (t + (2.0 * (y + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.18e-70) or not (y <= 2.2e+23):
		tmp = (y * 5.0) + (x * (t + (y * 2.0)))
	else:
		tmp = x * (t + (2.0 * (y + z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.18e-70) || !(y <= 2.2e+23))
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y * 2.0))));
	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 ((y <= -1.18e-70) || ~((y <= 2.2e+23)))
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	else
		tmp = x * (t + (2.0 * (y + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.18e-70], N[Not[LessEqual[y, 2.2e+23]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $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 y < -1.18e-70 or 2.20000000000000008e23 < 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 91.5%

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

   if -1.18e-70 < y < 2.20000000000000008e23

   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 89.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-70} \lor \neg \left(y \leq 2.2 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.1% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.0)
   (* x (+ t (+ (* 2.0 (+ y z)) (* 5.0 (/ y x)))))
   (+ (* 2.0 (* x (+ y z))) (+ (* y 5.0) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.0) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (2.0 * (x * (y + z))) + ((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 <= (-5.0d0)) then
        tmp = x * (t + ((2.0d0 * (y + z)) + (5.0d0 * (y / x))))
    else
        tmp = (2.0d0 * (x * (y + z))) + ((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 <= -5.0) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.0)
		tmp = Float64(x * Float64(t + Float64(Float64(2.0 * Float64(y + z)) + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + 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 <= -5.0)
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	else
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -5

   1. Initial program 99.9%

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

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

   if -5 < 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 t around 0 98.9%

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

4. Final simplification 99.1%

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

Alternative 13: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-37} \lor \neg \left(x \leq 0.0062\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.5e-37) (not (<= x 0.0062)))
   (* 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 <= -1.5e-37) || !(x <= 0.0062)) {
		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 <= (-1.5d-37)) .or. (.not. (x <= 0.0062d0))) 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 <= -1.5e-37) || !(x <= 0.0062)) {
		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 <= -1.5e-37) or not (x <= 0.0062):
		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 <= -1.5e-37) || !(x <= 0.0062))
		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 <= -1.5e-37) || ~((x <= 0.0062)))
		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, -1.5e-37], N[Not[LessEqual[x, 0.0062]], $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 < -1.5e-37 or 0.00619999999999999978 < 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 97.0%

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

   if -1.5e-37 < x < 0.00619999999999999978

   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 83.5%

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

   5. Simplified 83.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-37} \lor \neg \left(x \leq 0.0062\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-69} \lor \neg \left(y \leq 8.5 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e-69) (not (<= y 8.5e+57)))
   (* 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 <= -5.2e-69) || !(y <= 8.5e+57)) {
		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 <= (-5.2d-69)) .or. (.not. (y <= 8.5d+57))) 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 <= -5.2e-69) || !(y <= 8.5e+57)) {
		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 <= -5.2e-69) or not (y <= 8.5e+57):
		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 <= -5.2e-69) || !(y <= 8.5e+57))
		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 <= -5.2e-69) || ~((y <= 8.5e+57)))
		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, -5.2e-69], N[Not[LessEqual[y, 8.5e+57]], $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 < -5.2000000000000004e-69 or 8.5000000000000001e57 < y

   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 inf 83.7%

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

   if -5.2000000000000004e-69 < y < 8.5000000000000001e57

   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 97.4%

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

   6. Taylor expanded in x around inf 89.3%

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

      1. +-commutative 89.3%

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

   8. Simplified 89.3%

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

   9. Taylor expanded in z around inf 86.9%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-69} \lor \neg \left(y \leq 8.5 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-58} \lor \neg \left(x \leq 0.0106\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.4e-58) (not (<= x 0.0106))) (* x (* 2.0 (+ y z))) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.4e-58) || !(x <= 0.0106)) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.4d-58)) .or. (.not. (x <= 0.0106d0))) then
        tmp = x * (2.0d0 * (y + z))
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.4e-58) || !(x <= 0.0106)) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.4e-58) or not (x <= 0.0106):
		tmp = x * (2.0 * (y + z))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.4e-58) || !(x <= 0.0106))
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.4e-58) || ~((x <= 0.0106)))
		tmp = x * (2.0 * (y + z));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.4e-58], N[Not[LessEqual[x, 0.0106]], $MachinePrecision]], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e-58 or 0.0106 < 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 94.4%

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

   6. Taylor expanded in x around inf 96.4%

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

      1. +-commutative 96.4%

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

   8. Simplified 96.4%

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

   9. Taylor expanded in t around 0 67.7%

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

   if -1.4e-58 < x < 0.0106

   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 66.9%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-58} \lor \neg \left(x \leq 0.0106\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-58} \lor \neg \left(x \leq 0.0062\right):\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.4e-58) (not (<= x 0.0062))) (* x (+ y t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.4e-58) || !(x <= 0.0062)) {
		tmp = x * (y + 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 <= (-1.4d-58)) .or. (.not. (x <= 0.0062d0))) then
        tmp = x * (y + 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 <= -1.4e-58) || !(x <= 0.0062)) {
		tmp = x * (y + t);
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.4e-58) or not (x <= 0.0062):
		tmp = x * (y + t)
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.4e-58) || !(x <= 0.0062))
		tmp = Float64(x * Float64(y + 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 <= -1.4e-58) || ~((x <= 0.0062)))
		tmp = x * (y + t);
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.4e-58], N[Not[LessEqual[x, 0.0062]], $MachinePrecision]], N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e-58 or 0.00619999999999999978 < 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%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in x around inf 65.9%

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

      1. +-commutative 65.9%

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

      2. +-commutative 65.9%

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

      3. associate-+l+ 65.9%

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

   10. Simplified 65.9%

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

   11. Taylor expanded in z around 0 53.2%

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

   if -1.4e-58 < x < 0.00619999999999999978

   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 66.9%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-58} \lor \neg \left(x \leq 0.0062\right):\\ \;\;\;\;x \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(z + t\right)\\ \mathbf{elif}\;x \leq 0.0062:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8e-59) (* x (+ z t)) (if (<= x 0.0062) (* y 5.0) (* x (+ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8e-59) {
		tmp = x * (z + t);
	} else if (x <= 0.0062) {
		tmp = y * 5.0;
	} else {
		tmp = x * (y + 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 <= (-8d-59)) then
        tmp = x * (z + t)
    else if (x <= 0.0062d0) then
        tmp = y * 5.0d0
    else
        tmp = x * (y + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8e-59) {
		tmp = x * (z + t);
	} else if (x <= 0.0062) {
		tmp = y * 5.0;
	} else {
		tmp = x * (y + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8e-59:
		tmp = x * (z + t)
	elif x <= 0.0062:
		tmp = y * 5.0
	else:
		tmp = x * (y + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8e-59)
		tmp = Float64(x * Float64(z + t));
	elseif (x <= 0.0062)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * Float64(y + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8e-59)
		tmp = x * (z + t);
	elseif (x <= 0.0062)
		tmp = y * 5.0;
	else
		tmp = x * (y + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8e-59], N[(x * N[(z + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0062], N[(y * 5.0), $MachinePrecision], N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.0000000000000002e-59

   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 100.0%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in y around 0 55.5%

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

      1. +-commutative 55.5%

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

   10. Simplified 55.5%

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

   if -8.0000000000000002e-59 < x < 0.00619999999999999978

   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 66.9%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   if 0.00619999999999999978 < 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%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. +-commutative 64.6%

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

      2. +-commutative 64.6%

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

      3. associate-+l+ 64.6%

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

   10. Simplified 64.6%

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

   11. Taylor expanded in z around 0 54.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(z + t\right)\\ \mathbf{elif}\;x \leq 0.0062:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (y * 5.0) + (x * (t + (y + (y + (z * 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 = (y * 5.0d0) + (x * (t + (y + (y + (z * 2.0d0)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.9%

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

Alternative 19: 48.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-59} \lor \neg \left(x \leq 0.0062\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.5e-59) (not (<= x 0.0062))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.5e-59) || !(x <= 0.0062)) {
		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 <= (-5.5d-59)) .or. (.not. (x <= 0.0062d0))) 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 <= -5.5e-59) || !(x <= 0.0062)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.5e-59) or not (x <= 0.0062):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.5e-59) || !(x <= 0.0062))
		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 <= -5.5e-59) || ~((x <= 0.0062)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.5e-59], N[Not[LessEqual[x, 0.0062]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000014e-59 or 0.00619999999999999978 < 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%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in y around 0 51.2%

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

      1. +-commutative 51.2%

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

   10. Simplified 51.2%

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

   11. Taylor expanded in z around 0 37.6%

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

       1. *-commutative 37.6%

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

   13. Simplified 37.6%

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

   if -5.50000000000000014e-59 < x < 0.00619999999999999978

   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 66.9%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-59} \lor \neg \left(x \leq 0.0062\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+113} \lor \neg \left(y \leq 2.2 \cdot 10^{+174}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e+113) (not (<= y 2.2e+174))) (* x y) (* x t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+113) || !(y <= 2.2e+174)) {
		tmp = x * y;
	} 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 ((y <= (-7.5d+113)) .or. (.not. (y <= 2.2d+174))) then
        tmp = x * y
    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 ((y <= -7.5e+113) || !(y <= 2.2e+174)) {
		tmp = x * y;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e+113) or not (y <= 2.2e+174):
		tmp = x * y
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e+113) || !(y <= 2.2e+174))
		tmp = Float64(x * y);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.5e+113) || ~((y <= 2.2e+174)))
		tmp = x * y;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e+113], N[Not[LessEqual[y, 2.2e+174]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(x * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000001e113 or 2.2000000000000002e174 < y

   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 x around inf 62.8%

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

   7. Simplified 46.0%

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

   8. Taylor expanded in x around inf 34.0%

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

      1. +-commutative 34.0%

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

      2. +-commutative 34.0%

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

      3. associate-+l+ 34.0%

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

   10. Simplified 34.0%

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

   11. Taylor expanded in y around inf 31.1%

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

   if -7.5000000000000001e113 < y < 2.2000000000000002e174

   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 95.5%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in y around 0 47.9%

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

      1. +-commutative 47.9%

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

   10. Simplified 47.9%

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

   11. Taylor expanded in z around 0 37.8%

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

       1. *-commutative 37.8%

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

   13. Simplified 37.8%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+113} \lor \neg \left(y \leq 2.2 \cdot 10^{+174}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.4% 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 x around inf 85.3%

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

7. Simplified 61.8%

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

8. Taylor expanded in y around 0 36.6%

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

   1. +-commutative 36.6%

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

10. Simplified 36.6%

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

11. Taylor expanded in z around 0 28.6%

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

    1. *-commutative 28.6%

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

13. Simplified 28.6%

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

Reproduce

herbie shell --seed 2024145 
(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)))