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

Percentage Accurate: 99.9% → 99.9%

Time: 11.3s

Alternatives: 13

Speedup: 1.0×

• 27.3% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = 2.4103074879088003e-219
  2. y = 5.535291725253712e+178
  3. z = -1.7569520877276971e-62
  4. t = -5.581613478092196e-252

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

   3. flip-+ 58.9%

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

   4. associate-*r/ 56.6%

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

   5. fma-neg 59.6%

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

   6. associate-+l+ 59.6%

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

   7. +-commutative 59.6%

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

   8. count-2 59.6%

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

   9. associate-+l+ 59.6%

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

   10. +-commutative 59.6%

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

   11. count-2 59.6%

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

   12. fma-neg 56.6%

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

   13. associate-+l+ 56.6%

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

   14. +-commutative 56.6%

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

   15. count-2 56.6%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. fma-def 100.0%

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

   2. associate-+l+ 100.0%

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

   3. +-commutative 100.0%

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

   4. count-2 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 3: 46.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ t_2 := x \cdot \left(y \cdot 2\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{+20}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 500:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* x 2.0))) (t_2 (* x (* y 2.0))))
   (if (<= x -4.5e+183)
     t_1
     (if (<= x -5.6e+106)
       t_2
       (if (<= x -5.7e+20)
         (* x t)
         (if (<= x -9e-80)
           t_1
           (if (<= x 2.7e-29)
             (* y 5.0)
             (if (<= x 500.0) (* x t) (if (<= x 4.1e+80) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x * 2.0);
	double t_2 = x * (y * 2.0);
	double tmp;
	if (x <= -4.5e+183) {
		tmp = t_1;
	} else if (x <= -5.6e+106) {
		tmp = t_2;
	} else if (x <= -5.7e+20) {
		tmp = x * t;
	} else if (x <= -9e-80) {
		tmp = t_1;
	} else if (x <= 2.7e-29) {
		tmp = y * 5.0;
	} else if (x <= 500.0) {
		tmp = x * t;
	} else if (x <= 4.1e+80) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x * 2.0d0)
    t_2 = x * (y * 2.0d0)
    if (x <= (-4.5d+183)) then
        tmp = t_1
    else if (x <= (-5.6d+106)) then
        tmp = t_2
    else if (x <= (-5.7d+20)) then
        tmp = x * t
    else if (x <= (-9d-80)) then
        tmp = t_1
    else if (x <= 2.7d-29) then
        tmp = y * 5.0d0
    else if (x <= 500.0d0) then
        tmp = x * t
    else if (x <= 4.1d+80) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x * 2.0);
	double t_2 = x * (y * 2.0);
	double tmp;
	if (x <= -4.5e+183) {
		tmp = t_1;
	} else if (x <= -5.6e+106) {
		tmp = t_2;
	} else if (x <= -5.7e+20) {
		tmp = x * t;
	} else if (x <= -9e-80) {
		tmp = t_1;
	} else if (x <= 2.7e-29) {
		tmp = y * 5.0;
	} else if (x <= 500.0) {
		tmp = x * t;
	} else if (x <= 4.1e+80) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x * 2.0)
	t_2 = x * (y * 2.0)
	tmp = 0
	if x <= -4.5e+183:
		tmp = t_1
	elif x <= -5.6e+106:
		tmp = t_2
	elif x <= -5.7e+20:
		tmp = x * t
	elif x <= -9e-80:
		tmp = t_1
	elif x <= 2.7e-29:
		tmp = y * 5.0
	elif x <= 500.0:
		tmp = x * t
	elif x <= 4.1e+80:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x * 2.0))
	t_2 = Float64(x * Float64(y * 2.0))
	tmp = 0.0
	if (x <= -4.5e+183)
		tmp = t_1;
	elseif (x <= -5.6e+106)
		tmp = t_2;
	elseif (x <= -5.7e+20)
		tmp = Float64(x * t);
	elseif (x <= -9e-80)
		tmp = t_1;
	elseif (x <= 2.7e-29)
		tmp = Float64(y * 5.0);
	elseif (x <= 500.0)
		tmp = Float64(x * t);
	elseif (x <= 4.1e+80)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x * 2.0);
	t_2 = x * (y * 2.0);
	tmp = 0.0;
	if (x <= -4.5e+183)
		tmp = t_1;
	elseif (x <= -5.6e+106)
		tmp = t_2;
	elseif (x <= -5.7e+20)
		tmp = x * t;
	elseif (x <= -9e-80)
		tmp = t_1;
	elseif (x <= 2.7e-29)
		tmp = y * 5.0;
	elseif (x <= 500.0)
		tmp = x * t;
	elseif (x <= 4.1e+80)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+183], t$95$1, If[LessEqual[x, -5.6e+106], t$95$2, If[LessEqual[x, -5.7e+20], N[(x * t), $MachinePrecision], If[LessEqual[x, -9e-80], t$95$1, If[LessEqual[x, 2.7e-29], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 500.0], N[(x * t), $MachinePrecision], If[LessEqual[x, 4.1e+80], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.50000000000000017e183 or -5.7e20 < x < -9.0000000000000006e-80 or 4.10000000000000001e80 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 96.4%

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

   6. Taylor expanded in z around inf 52.2%

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

      1. associate-*r* 52.2%

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

   8. Simplified 52.2%

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

   if -4.50000000000000017e183 < x < -5.59999999999999986e106 or 500 < x < 4.10000000000000001e80

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 93.2%

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

   6. Taylor expanded in y around inf 52.1%

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

      1. associate-*r* 52.1%

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

      2. *-commutative 52.1%

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

      3. associate-*r* 52.1%

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

   8. Simplified 52.1%

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

   if -5.59999999999999986e106 < x < -5.7e20 or 2.70000000000000023e-29 < x < 500

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 92.7%

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

   6. Taylor expanded in t around inf 62.3%

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

      1. *-commutative 62.3%

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

   8. Simplified 62.3%

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

   if -9.0000000000000006e-80 < x < 2.70000000000000023e-29

   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 x around 0 60.8%

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

   5. Simplified 60.8%

      \[\leadsto \color{blue}{y \cdot 5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+183}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{+20}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-29}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 500:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 45.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot 2\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+143}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-87}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-40}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 500 \lor \neg \left(x \leq 3.5 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y 2.0))))
   (if (<= x -3.2e+143)
     (* x t)
     (if (<= x -5e+106)
       t_1
       (if (<= x -3.8e-87)
         (* x t)
         (if (<= x 1.4e-40)
           (* y 5.0)
           (if (or (<= x 500.0) (not (<= x 3.5e+101))) (* x t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * 2.0);
	double tmp;
	if (x <= -3.2e+143) {
		tmp = x * t;
	} else if (x <= -5e+106) {
		tmp = t_1;
	} else if (x <= -3.8e-87) {
		tmp = x * t;
	} else if (x <= 1.4e-40) {
		tmp = y * 5.0;
	} else if ((x <= 500.0) || !(x <= 3.5e+101)) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * 2.0d0)
    if (x <= (-3.2d+143)) then
        tmp = x * t
    else if (x <= (-5d+106)) then
        tmp = t_1
    else if (x <= (-3.8d-87)) then
        tmp = x * t
    else if (x <= 1.4d-40) then
        tmp = y * 5.0d0
    else if ((x <= 500.0d0) .or. (.not. (x <= 3.5d+101))) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y * 2.0);
	double tmp;
	if (x <= -3.2e+143) {
		tmp = x * t;
	} else if (x <= -5e+106) {
		tmp = t_1;
	} else if (x <= -3.8e-87) {
		tmp = x * t;
	} else if (x <= 1.4e-40) {
		tmp = y * 5.0;
	} else if ((x <= 500.0) || !(x <= 3.5e+101)) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * 2.0)
	tmp = 0
	if x <= -3.2e+143:
		tmp = x * t
	elif x <= -5e+106:
		tmp = t_1
	elif x <= -3.8e-87:
		tmp = x * t
	elif x <= 1.4e-40:
		tmp = y * 5.0
	elif (x <= 500.0) or not (x <= 3.5e+101):
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y * 2.0))
	tmp = 0.0
	if (x <= -3.2e+143)
		tmp = Float64(x * t);
	elseif (x <= -5e+106)
		tmp = t_1;
	elseif (x <= -3.8e-87)
		tmp = Float64(x * t);
	elseif (x <= 1.4e-40)
		tmp = Float64(y * 5.0);
	elseif ((x <= 500.0) || !(x <= 3.5e+101))
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y * 2.0);
	tmp = 0.0;
	if (x <= -3.2e+143)
		tmp = x * t;
	elseif (x <= -5e+106)
		tmp = t_1;
	elseif (x <= -3.8e-87)
		tmp = x * t;
	elseif (x <= 1.4e-40)
		tmp = y * 5.0;
	elseif ((x <= 500.0) || ~((x <= 3.5e+101)))
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+143], N[(x * t), $MachinePrecision], If[LessEqual[x, -5e+106], t$95$1, If[LessEqual[x, -3.8e-87], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.4e-40], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 500.0], N[Not[LessEqual[x, 3.5e+101]], $MachinePrecision]], N[(x * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.20000000000000016e143 or -4.9999999999999998e106 < x < -3.8e-87 or 1.4e-40 < x < 500 or 3.50000000000000023e101 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 95.1%

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

   6. Taylor expanded in t around inf 44.4%

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

      1. *-commutative 44.4%

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

   8. Simplified 44.4%

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

   if -3.20000000000000016e143 < x < -4.9999999999999998e106 or 500 < x < 3.50000000000000023e101

   1. Initial program 99.9%

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

      1. fma-def 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 91.1%

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

   6. Taylor expanded in y around inf 55.7%

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

      1. associate-*r* 55.7%

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

      2. *-commutative 55.7%

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

      3. associate-*r* 55.7%

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

   8. Simplified 55.7%

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

   if -3.8e-87 < x < 1.4e-40

   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 x around 0 61.0%

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

   5. Simplified 61.0%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+143}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-87}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-40}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 500 \lor \neg \left(x \leq 3.5 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-185} \lor \neg \left(x \leq 7.2 \cdot 10^{-238}\right) \land \left(x \leq 1.38 \cdot 10^{-188} \lor \neg \left(x \leq 1.35 \cdot 10^{-41}\right)\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6e-185)
         (and (not (<= x 7.2e-238))
              (or (<= x 1.38e-188) (not (<= x 1.35e-41)))))
   (* x (+ t (* z 2.0)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6e-185) || (!(x <= 7.2e-238) && ((x <= 1.38e-188) || !(x <= 1.35e-41)))) {
		tmp = x * (t + (z * 2.0));
	} 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 <= (-6d-185)) .or. (.not. (x <= 7.2d-238)) .and. (x <= 1.38d-188) .or. (.not. (x <= 1.35d-41))) then
        tmp = x * (t + (z * 2.0d0))
    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 <= -6e-185) || (!(x <= 7.2e-238) && ((x <= 1.38e-188) || !(x <= 1.35e-41)))) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6e-185) or (not (x <= 7.2e-238) and ((x <= 1.38e-188) or not (x <= 1.35e-41))):
		tmp = x * (t + (z * 2.0))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6e-185) || (!(x <= 7.2e-238) && ((x <= 1.38e-188) || !(x <= 1.35e-41))))
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6e-185) || (~((x <= 7.2e-238)) && ((x <= 1.38e-188) || ~((x <= 1.35e-41)))))
		tmp = x * (t + (z * 2.0));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6e-185], And[N[Not[LessEqual[x, 7.2e-238]], $MachinePrecision], Or[LessEqual[x, 1.38e-188], N[Not[LessEqual[x, 1.35e-41]], $MachinePrecision]]]], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.00000000000000061e-185 or 7.20000000000000021e-238 < x < 1.3800000000000001e-188 or 1.35e-41 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 88.5%

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

   6. Taylor expanded in y around 0 69.3%

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

   if -6.00000000000000061e-185 < x < 7.20000000000000021e-238 or 1.3800000000000001e-188 < x < 1.35e-41

   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 x around 0 69.0%

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

   5. Simplified 69.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-185} \lor \neg \left(x \leq 7.2 \cdot 10^{-238}\right) \land \left(x \leq 1.38 \cdot 10^{-188} \lor \neg \left(x \leq 1.35 \cdot 10^{-41}\right)\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-35}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* (+ y z) 2.0)))))
   (if (<= x -9.5e-74)
     t_1
     (if (<= x 1.2e-298)
       (+ (* y 5.0) (* x t))
       (if (<= x 9e-35) (+ (* 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 + ((y + z) * 2.0));
	double tmp;
	if (x <= -9.5e-74) {
		tmp = t_1;
	} else if (x <= 1.2e-298) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 9e-35) {
		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 + ((y + z) * 2.0d0))
    if (x <= (-9.5d-74)) then
        tmp = t_1
    else if (x <= 1.2d-298) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 9d-35) 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 + ((y + z) * 2.0));
	double tmp;
	if (x <= -9.5e-74) {
		tmp = t_1;
	} else if (x <= 1.2e-298) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 9e-35) {
		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 + ((y + z) * 2.0))
	tmp = 0
	if x <= -9.5e-74:
		tmp = t_1
	elif x <= 1.2e-298:
		tmp = (y * 5.0) + (x * t)
	elif x <= 9e-35:
		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(Float64(y + z) * 2.0)))
	tmp = 0.0
	if (x <= -9.5e-74)
		tmp = t_1;
	elseif (x <= 1.2e-298)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 9e-35)
		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 + ((y + z) * 2.0));
	tmp = 0.0;
	if (x <= -9.5e-74)
		tmp = t_1;
	elseif (x <= 1.2e-298)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 9e-35)
		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[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e-74], t$95$1, If[LessEqual[x, 1.2e-298], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-35], 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 < -9.5000000000000007e-74 or 9.0000000000000002e-35 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 95.0%

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

   if -9.5000000000000007e-74 < x < 1.19999999999999994e-298

   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 90.5%

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

   if 1.19999999999999994e-298 < x < 9.0000000000000002e-35

   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 86.8%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-35}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-74}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-36}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))))
   (if (<= x -8.6e+20)
     t_1
     (if (<= x -2.3e-74) (* z (* x 2.0)) (if (<= x 5.2e-36) (* y 5.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -8.6e+20) {
		tmp = t_1;
	} else if (x <= -2.3e-74) {
		tmp = z * (x * 2.0);
	} else if (x <= 5.2e-36) {
		tmp = y * 5.0;
	} 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 * (t + (y * 2.0d0))
    if (x <= (-8.6d+20)) then
        tmp = t_1
    else if (x <= (-2.3d-74)) then
        tmp = z * (x * 2.0d0)
    else if (x <= 5.2d-36) then
        tmp = y * 5.0d0
    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 * (t + (y * 2.0));
	double tmp;
	if (x <= -8.6e+20) {
		tmp = t_1;
	} else if (x <= -2.3e-74) {
		tmp = z * (x * 2.0);
	} else if (x <= 5.2e-36) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -8.6e+20:
		tmp = t_1
	elif x <= -2.3e-74:
		tmp = z * (x * 2.0)
	elif x <= 5.2e-36:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (x <= -8.6e+20)
		tmp = t_1;
	elseif (x <= -2.3e-74)
		tmp = Float64(z * Float64(x * 2.0));
	elseif (x <= 5.2e-36)
		tmp = Float64(y * 5.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y * 2.0));
	tmp = 0.0;
	if (x <= -8.6e+20)
		tmp = t_1;
	elseif (x <= -2.3e-74)
		tmp = z * (x * 2.0);
	elseif (x <= 5.2e-36)
		tmp = y * 5.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.6e+20], t$95$1, If[LessEqual[x, -2.3e-74], N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e-36], N[(y * 5.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.6e20 or 5.2000000000000001e-36 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 96.8%

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

   6. Taylor expanded in z around 0 66.6%

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

   if -8.6e20 < x < -2.2999999999999998e-74

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 81.5%

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

   6. Taylor expanded in z around inf 57.9%

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

      1. associate-*r* 57.9%

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

   8. Simplified 57.9%

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

   if -2.2999999999999998e-74 < x < 5.2000000000000001e-36

   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 x around 0 60.8%

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

   5. Simplified 60.8%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-74}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-36}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+94}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.4e+111)
     t_1
     (if (<= y 1.05e-63)
       (* x (+ t (* z 2.0)))
       (if (<= y 2.9e+94) (+ (* y 5.0) (* x t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.4e+111) {
		tmp = t_1;
	} else if (y <= 1.05e-63) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 2.9e+94) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.4d+111)) then
        tmp = t_1
    else if (y <= 1.05d-63) then
        tmp = x * (t + (z * 2.0d0))
    else if (y <= 2.9d+94) then
        tmp = (y * 5.0d0) + (x * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.4e+111) {
		tmp = t_1;
	} else if (y <= 1.05e-63) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 2.9e+94) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.4e+111:
		tmp = t_1
	elif y <= 1.05e-63:
		tmp = x * (t + (z * 2.0))
	elif y <= 2.9e+94:
		tmp = (y * 5.0) + (x * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.4e+111)
		tmp = t_1;
	elseif (y <= 1.05e-63)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (y <= 2.9e+94)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.4e+111)
		tmp = t_1;
	elseif (y <= 1.05e-63)
		tmp = x * (t + (z * 2.0));
	elseif (y <= 2.9e+94)
		tmp = (y * 5.0) + (x * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+111], t$95$1, If[LessEqual[y, 1.05e-63], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+94], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e111 or 2.8999999999999998e94 < y

   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 y around inf 89.2%

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

   if -1.4e111 < y < 1.05e-63

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 83.6%

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

   6. Taylor expanded in y around 0 80.1%

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

   if 1.05e-63 < y < 2.8999999999999998e94

   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 70.8%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+94}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-73} \lor \neg \left(x \leq 3.7 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.15e-73) (not (<= x 3.7e-38)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.15e-73) || !(x <= 3.7e-38)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.15d-73)) .or. (.not. (x <= 3.7d-38))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.15e-73) || !(x <= 3.7e-38)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.15e-73) or not (x <= 3.7e-38):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.15e-73) || !(x <= 3.7e-38))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.15e-73) || ~((x <= 3.7e-38)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.15e-73], N[Not[LessEqual[x, 3.7e-38]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.14999999999999994e-73 or 3.7e-38 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 95.0%

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

   if -1.14999999999999994e-73 < x < 3.7e-38

   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 79.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-73} \lor \neg \left(x \leq 3.7 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+111} \lor \neg \left(y \leq 6.1 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.35e+111) (not (<= y 6.1e-18)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.35e+111) || !(y <= 6.1e-18)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.35d+111)) .or. (.not. (y <= 6.1d-18))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.35e+111) || !(y <= 6.1e-18)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.35e+111) or not (y <= 6.1e-18):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.35e+111) || !(y <= 6.1e-18))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.35e+111) || ~((y <= 6.1e-18)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.35e+111], N[Not[LessEqual[y, 6.1e-18]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.35000000000000004e111 or 6.0999999999999999e-18 < y

   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 y around inf 82.9%

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

   if -2.35000000000000004e111 < y < 6.0999999999999999e-18

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 81.5%

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

   6. Taylor expanded in y around 0 78.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+111} \lor \neg \left(y \leq 6.1 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 12: 45.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-87} \lor \neg \left(x \leq 4 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9e-87) (not (<= x 4e-29))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e-87) || !(x <= 4e-29)) {
		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 <= (-9d-87)) .or. (.not. (x <= 4d-29))) 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 <= -9e-87) || !(x <= 4e-29)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9e-87) or not (x <= 4e-29):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9e-87) || !(x <= 4e-29))
		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 <= -9e-87) || ~((x <= 4e-29)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9e-87], N[Not[LessEqual[x, 4e-29]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999915e-87 or 3.99999999999999977e-29 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 94.4%

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

   6. Taylor expanded in t around inf 37.7%

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

      1. *-commutative 37.7%

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

   8. Simplified 37.7%

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

   if -8.99999999999999915e-87 < x < 3.99999999999999977e-29

   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 x around 0 61.0%

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

   5. Simplified 61.0%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-87} \lor \neg \left(x \leq 4 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.6% 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 100.0%

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

   1. fma-def 100.0%

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

   2. associate-+l+ 100.0%

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

   3. +-commutative 100.0%

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

   4. count-2 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around inf 70.6%

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

6. Taylor expanded in t around inf 30.0%

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

   1. *-commutative 30.0%

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

8. Simplified 30.0%

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

9. Final simplification 30.0%

   \[\leadsto x \cdot t \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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)))