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

Percentage Accurate: 99.9% → 100.0%

Time: 7.1s

Alternatives: 14

Speedup: 1.0×

• 26.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. fma-def 99.6%

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

   3. distribute-rgt-in 96.9%

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

   4. associate-+l+ 96.9%

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

   5. +-commutative 96.9%

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

   6. count-2 96.9%

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

   7. distribute-rgt-in 99.6%

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

   8. *-commutative 99.6%

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

   9. fma-def 99.6%

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

3. Applied egg-rr 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. fma-def 99.5%

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

   2. associate-+l+ 99.5%

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

   3. +-commutative 99.5%

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

   4. count-2 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 3: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+188}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+202}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.15e+129)
     t_2
     (if (<= y -2.45e+89)
       t_1
       (if (<= y -1.22e-17)
         t_2
         (if (<= y 6e+104)
           t_1
           (if (<= y 6.5e+178)
             t_2
             (if (<= y 1.85e+188)
               (* 2.0 (* x (+ y z)))
               (if (<= y 2.8e+202) (* x (+ t (* y 2.0))) t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.15e+129) {
		tmp = t_2;
	} else if (y <= -2.45e+89) {
		tmp = t_1;
	} else if (y <= -1.22e-17) {
		tmp = t_2;
	} else if (y <= 6e+104) {
		tmp = t_1;
	} else if (y <= 6.5e+178) {
		tmp = t_2;
	} else if (y <= 1.85e+188) {
		tmp = 2.0 * (x * (y + z));
	} else if (y <= 2.8e+202) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.15d+129)) then
        tmp = t_2
    else if (y <= (-2.45d+89)) then
        tmp = t_1
    else if (y <= (-1.22d-17)) then
        tmp = t_2
    else if (y <= 6d+104) then
        tmp = t_1
    else if (y <= 6.5d+178) then
        tmp = t_2
    else if (y <= 1.85d+188) then
        tmp = 2.0d0 * (x * (y + z))
    else if (y <= 2.8d+202) then
        tmp = x * (t + (y * 2.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.15e+129) {
		tmp = t_2;
	} else if (y <= -2.45e+89) {
		tmp = t_1;
	} else if (y <= -1.22e-17) {
		tmp = t_2;
	} else if (y <= 6e+104) {
		tmp = t_1;
	} else if (y <= 6.5e+178) {
		tmp = t_2;
	} else if (y <= 1.85e+188) {
		tmp = 2.0 * (x * (y + z));
	} else if (y <= 2.8e+202) {
		tmp = x * (t + (y * 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.15e+129:
		tmp = t_2
	elif y <= -2.45e+89:
		tmp = t_1
	elif y <= -1.22e-17:
		tmp = t_2
	elif y <= 6e+104:
		tmp = t_1
	elif y <= 6.5e+178:
		tmp = t_2
	elif y <= 1.85e+188:
		tmp = 2.0 * (x * (y + z))
	elif y <= 2.8e+202:
		tmp = x * (t + (y * 2.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.15e+129)
		tmp = t_2;
	elseif (y <= -2.45e+89)
		tmp = t_1;
	elseif (y <= -1.22e-17)
		tmp = t_2;
	elseif (y <= 6e+104)
		tmp = t_1;
	elseif (y <= 6.5e+178)
		tmp = t_2;
	elseif (y <= 1.85e+188)
		tmp = Float64(2.0 * Float64(x * Float64(y + z)));
	elseif (y <= 2.8e+202)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.15e+129)
		tmp = t_2;
	elseif (y <= -2.45e+89)
		tmp = t_1;
	elseif (y <= -1.22e-17)
		tmp = t_2;
	elseif (y <= 6e+104)
		tmp = t_1;
	elseif (y <= 6.5e+178)
		tmp = t_2;
	elseif (y <= 1.85e+188)
		tmp = 2.0 * (x * (y + z));
	elseif (y <= 2.8e+202)
		tmp = x * (t + (y * 2.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+129], t$95$2, If[LessEqual[y, -2.45e+89], t$95$1, If[LessEqual[y, -1.22e-17], t$95$2, If[LessEqual[y, 6e+104], t$95$1, If[LessEqual[y, 6.5e+178], t$95$2, If[LessEqual[y, 1.85e+188], N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+202], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.14999999999999995e129 or -2.44999999999999998e89 < y < -1.22e-17 or 5.99999999999999937e104 < y < 6.5000000000000005e178 or 2.80000000000000016e202 < y

   1. Initial program 98.7%

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

      1. fma-def 98.7%

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

      2. associate-+l+ 98.7%

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

      3. +-commutative 98.7%

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

      4. count-2 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around inf 80.5%

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

   if -1.14999999999999995e129 < y < -2.44999999999999998e89 or -1.22e-17 < y < 5.99999999999999937e104

   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. Taylor expanded in x around inf 83.5%

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

   5. Taylor expanded in y around 0 80.0%

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

   if 6.5000000000000005e178 < y < 1.85e188

   1. Initial program 99.6%

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

      1. fma-def 99.6%

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

      2. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. count-2 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 91.6%

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

   5. Taylor expanded in t around 0 89.1%

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

   if 1.85e188 < y < 2.80000000000000016e202

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+188}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+202}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 4: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+199}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+46}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-45}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+229}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* y x))))
   (if (<= x -6.2e+199)
     (* x t)
     (if (<= x -9e+156)
       t_1
       (if (<= x -1.12e+46)
         (* x t)
         (if (<= x -1.9e+14)
           t_1
           (if (<= x -2.45e-45)
             (* x t)
             (if (<= x 1.9e-9)
               (* y 5.0)
               (if (<= x 1.65e+229) (* x t) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y * x);
	double tmp;
	if (x <= -6.2e+199) {
		tmp = x * t;
	} else if (x <= -9e+156) {
		tmp = t_1;
	} else if (x <= -1.12e+46) {
		tmp = x * t;
	} else if (x <= -1.9e+14) {
		tmp = t_1;
	} else if (x <= -2.45e-45) {
		tmp = x * t;
	} else if (x <= 1.9e-9) {
		tmp = y * 5.0;
	} else if (x <= 1.65e+229) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y * x)
    if (x <= (-6.2d+199)) then
        tmp = x * t
    else if (x <= (-9d+156)) then
        tmp = t_1
    else if (x <= (-1.12d+46)) then
        tmp = x * t
    else if (x <= (-1.9d+14)) then
        tmp = t_1
    else if (x <= (-2.45d-45)) then
        tmp = x * t
    else if (x <= 1.9d-9) then
        tmp = y * 5.0d0
    else if (x <= 1.65d+229) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y * x);
	double tmp;
	if (x <= -6.2e+199) {
		tmp = x * t;
	} else if (x <= -9e+156) {
		tmp = t_1;
	} else if (x <= -1.12e+46) {
		tmp = x * t;
	} else if (x <= -1.9e+14) {
		tmp = t_1;
	} else if (x <= -2.45e-45) {
		tmp = x * t;
	} else if (x <= 1.9e-9) {
		tmp = y * 5.0;
	} else if (x <= 1.65e+229) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y * x)
	tmp = 0
	if x <= -6.2e+199:
		tmp = x * t
	elif x <= -9e+156:
		tmp = t_1
	elif x <= -1.12e+46:
		tmp = x * t
	elif x <= -1.9e+14:
		tmp = t_1
	elif x <= -2.45e-45:
		tmp = x * t
	elif x <= 1.9e-9:
		tmp = y * 5.0
	elif x <= 1.65e+229:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y * x))
	tmp = 0.0
	if (x <= -6.2e+199)
		tmp = Float64(x * t);
	elseif (x <= -9e+156)
		tmp = t_1;
	elseif (x <= -1.12e+46)
		tmp = Float64(x * t);
	elseif (x <= -1.9e+14)
		tmp = t_1;
	elseif (x <= -2.45e-45)
		tmp = Float64(x * t);
	elseif (x <= 1.9e-9)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.65e+229)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y * x);
	tmp = 0.0;
	if (x <= -6.2e+199)
		tmp = x * t;
	elseif (x <= -9e+156)
		tmp = t_1;
	elseif (x <= -1.12e+46)
		tmp = x * t;
	elseif (x <= -1.9e+14)
		tmp = t_1;
	elseif (x <= -2.45e-45)
		tmp = x * t;
	elseif (x <= 1.9e-9)
		tmp = y * 5.0;
	elseif (x <= 1.65e+229)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+199], N[(x * t), $MachinePrecision], If[LessEqual[x, -9e+156], t$95$1, If[LessEqual[x, -1.12e+46], N[(x * t), $MachinePrecision], If[LessEqual[x, -1.9e+14], t$95$1, If[LessEqual[x, -2.45e-45], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.9e-9], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.65e+229], N[(x * t), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.19999999999999971e199 or -9.00000000000000061e156 < x < -1.12e46 or -1.9e14 < x < -2.4499999999999999e-45 or 1.90000000000000006e-9 < x < 1.65e229

   1. Initial program 99.1%

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

      1. fma-def 99.1%

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

      2. associate-+l+ 99.1%

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

      3. +-commutative 99.1%

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

      4. count-2 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 98.0%

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

   5. Taylor expanded in t around inf 47.3%

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

      1. *-commutative 47.3%

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

   7. Simplified 47.3%

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

   if -6.19999999999999971e199 < x < -9.00000000000000061e156 or -1.12e46 < x < -1.9e14 or 1.65e229 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in y around inf 60.7%

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

   if -2.4499999999999999e-45 < x < 1.90000000000000006e-9

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 59.3%

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

   4. Simplified 59.3%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+199}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+156}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+46}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-45}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+229}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 5: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-97}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+180} \lor \neg \left(x \leq 4.3 \cdot 10^{+256}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))))
   (if (<= x -1.1e+259)
     (* x (* z 2.0))
     (if (<= x -2.45e-42)
       t_1
       (if (<= x 4.2e-97)
         (* y 5.0)
         (if (or (<= x 5.4e+180) (not (<= x 4.3e+256)))
           (* 2.0 (* x (+ y z)))
           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 <= -1.1e+259) {
		tmp = x * (z * 2.0);
	} else if (x <= -2.45e-42) {
		tmp = t_1;
	} else if (x <= 4.2e-97) {
		tmp = y * 5.0;
	} else if ((x <= 5.4e+180) || !(x <= 4.3e+256)) {
		tmp = 2.0 * (x * (y + 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 * 2.0d0))
    if (x <= (-1.1d+259)) then
        tmp = x * (z * 2.0d0)
    else if (x <= (-2.45d-42)) then
        tmp = t_1
    else if (x <= 4.2d-97) then
        tmp = y * 5.0d0
    else if ((x <= 5.4d+180) .or. (.not. (x <= 4.3d+256))) then
        tmp = 2.0d0 * (x * (y + 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 * 2.0));
	double tmp;
	if (x <= -1.1e+259) {
		tmp = x * (z * 2.0);
	} else if (x <= -2.45e-42) {
		tmp = t_1;
	} else if (x <= 4.2e-97) {
		tmp = y * 5.0;
	} else if ((x <= 5.4e+180) || !(x <= 4.3e+256)) {
		tmp = 2.0 * (x * (y + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -1.1e+259:
		tmp = x * (z * 2.0)
	elif x <= -2.45e-42:
		tmp = t_1
	elif x <= 4.2e-97:
		tmp = y * 5.0
	elif (x <= 5.4e+180) or not (x <= 4.3e+256):
		tmp = 2.0 * (x * (y + z))
	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 <= -1.1e+259)
		tmp = Float64(x * Float64(z * 2.0));
	elseif (x <= -2.45e-42)
		tmp = t_1;
	elseif (x <= 4.2e-97)
		tmp = Float64(y * 5.0);
	elseif ((x <= 5.4e+180) || !(x <= 4.3e+256))
		tmp = Float64(2.0 * Float64(x * Float64(y + z)));
	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 <= -1.1e+259)
		tmp = x * (z * 2.0);
	elseif (x <= -2.45e-42)
		tmp = t_1;
	elseif (x <= 4.2e-97)
		tmp = y * 5.0;
	elseif ((x <= 5.4e+180) || ~((x <= 4.3e+256)))
		tmp = 2.0 * (x * (y + 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[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+259], N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.45e-42], t$95$1, If[LessEqual[x, 4.2e-97], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 5.4e+180], N[Not[LessEqual[x, 4.3e+256]], $MachinePrecision]], N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.09999999999999996e259

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in z around inf 92.3%

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

      1. associate-*r* 92.3%

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

   7. Simplified 92.3%

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

   if -1.09999999999999996e259 < x < -2.45e-42 or 5.40000000000000033e180 < x < 4.29999999999999993e256

   1. Initial program 98.7%

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

      1. fma-def 98.7%

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

      2. associate-+l+ 98.7%

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

      3. +-commutative 98.7%

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

      4. count-2 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in x around inf 97.2%

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

   5. Taylor expanded in z around 0 75.1%

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

   if -2.45e-42 < x < 4.2000000000000002e-97

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 63.5%

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

   4. Simplified 63.5%

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

   if 4.2000000000000002e-97 < x < 5.40000000000000033e180 or 4.29999999999999993e256 < x

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 91.7%

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

   5. Taylor expanded in t around 0 66.8%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-97}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+180} \lor \neg \left(x \leq 4.3 \cdot 10^{+256}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]

Alternative 6: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+181} \lor \neg \left(x \leq 4.5 \cdot 10^{+259}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))))
   (if (<= x -1.1e+259)
     (* x (* z 2.0))
     (if (<= x -1.08e-43)
       t_1
       (if (<= x 3.3e-96)
         (* y (+ 5.0 (* x 2.0)))
         (if (or (<= x 1.7e+181) (not (<= x 4.5e+259)))
           (* 2.0 (* x (+ y z)))
           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 <= -1.1e+259) {
		tmp = x * (z * 2.0);
	} else if (x <= -1.08e-43) {
		tmp = t_1;
	} else if (x <= 3.3e-96) {
		tmp = y * (5.0 + (x * 2.0));
	} else if ((x <= 1.7e+181) || !(x <= 4.5e+259)) {
		tmp = 2.0 * (x * (y + 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 * 2.0d0))
    if (x <= (-1.1d+259)) then
        tmp = x * (z * 2.0d0)
    else if (x <= (-1.08d-43)) then
        tmp = t_1
    else if (x <= 3.3d-96) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else if ((x <= 1.7d+181) .or. (.not. (x <= 4.5d+259))) then
        tmp = 2.0d0 * (x * (y + 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 * 2.0));
	double tmp;
	if (x <= -1.1e+259) {
		tmp = x * (z * 2.0);
	} else if (x <= -1.08e-43) {
		tmp = t_1;
	} else if (x <= 3.3e-96) {
		tmp = y * (5.0 + (x * 2.0));
	} else if ((x <= 1.7e+181) || !(x <= 4.5e+259)) {
		tmp = 2.0 * (x * (y + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -1.1e+259:
		tmp = x * (z * 2.0)
	elif x <= -1.08e-43:
		tmp = t_1
	elif x <= 3.3e-96:
		tmp = y * (5.0 + (x * 2.0))
	elif (x <= 1.7e+181) or not (x <= 4.5e+259):
		tmp = 2.0 * (x * (y + z))
	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 <= -1.1e+259)
		tmp = Float64(x * Float64(z * 2.0));
	elseif (x <= -1.08e-43)
		tmp = t_1;
	elseif (x <= 3.3e-96)
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	elseif ((x <= 1.7e+181) || !(x <= 4.5e+259))
		tmp = Float64(2.0 * Float64(x * Float64(y + z)));
	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 <= -1.1e+259)
		tmp = x * (z * 2.0);
	elseif (x <= -1.08e-43)
		tmp = t_1;
	elseif (x <= 3.3e-96)
		tmp = y * (5.0 + (x * 2.0));
	elseif ((x <= 1.7e+181) || ~((x <= 4.5e+259)))
		tmp = 2.0 * (x * (y + 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[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+259], N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.08e-43], t$95$1, If[LessEqual[x, 3.3e-96], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.7e+181], N[Not[LessEqual[x, 4.5e+259]], $MachinePrecision]], N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.09999999999999996e259

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in z around inf 92.3%

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

      1. associate-*r* 92.3%

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

   7. Simplified 92.3%

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

   if -1.09999999999999996e259 < x < -1.08e-43 or 1.70000000000000015e181 < x < 4.4999999999999997e259

   1. Initial program 98.7%

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

      1. fma-def 98.7%

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

      2. associate-+l+ 98.7%

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

      3. +-commutative 98.7%

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

      4. count-2 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in x around inf 97.2%

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

   5. Taylor expanded in z around 0 75.1%

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

   if -1.08e-43 < x < 3.2999999999999999e-96

   1. Initial program 99.8%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 63.5%

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

   if 3.2999999999999999e-96 < x < 1.70000000000000015e181 or 4.4999999999999997e259 < x

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 91.7%

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

   5. Taylor expanded in t around 0 66.8%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+181} \lor \neg \left(x \leq 4.5 \cdot 10^{+259}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]

Alternative 7: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3500000000000:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-95}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))))
   (if (<= x -2.6e+207)
     t_1
     (if (<= x -4e+162)
       (* x (+ t (* y 2.0)))
       (if (<= x -2.65e+45)
         t_1
         (if (<= x -3500000000000.0)
           (* 2.0 (* x (+ y z)))
           (if (<= x 5.8e-95) (+ (* y 5.0) (* x t)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -2.6e+207) {
		tmp = t_1;
	} else if (x <= -4e+162) {
		tmp = x * (t + (y * 2.0));
	} else if (x <= -2.65e+45) {
		tmp = t_1;
	} else if (x <= -3500000000000.0) {
		tmp = 2.0 * (x * (y + z));
	} else if (x <= 5.8e-95) {
		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 = x * (t + (z * 2.0d0))
    if (x <= (-2.6d+207)) then
        tmp = t_1
    else if (x <= (-4d+162)) then
        tmp = x * (t + (y * 2.0d0))
    else if (x <= (-2.65d+45)) then
        tmp = t_1
    else if (x <= (-3500000000000.0d0)) then
        tmp = 2.0d0 * (x * (y + z))
    else if (x <= 5.8d-95) 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 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -2.6e+207) {
		tmp = t_1;
	} else if (x <= -4e+162) {
		tmp = x * (t + (y * 2.0));
	} else if (x <= -2.65e+45) {
		tmp = t_1;
	} else if (x <= -3500000000000.0) {
		tmp = 2.0 * (x * (y + z));
	} else if (x <= 5.8e-95) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	tmp = 0
	if x <= -2.6e+207:
		tmp = t_1
	elif x <= -4e+162:
		tmp = x * (t + (y * 2.0))
	elif x <= -2.65e+45:
		tmp = t_1
	elif x <= -3500000000000.0:
		tmp = 2.0 * (x * (y + z))
	elif x <= 5.8e-95:
		tmp = (y * 5.0) + (x * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	tmp = 0.0
	if (x <= -2.6e+207)
		tmp = t_1;
	elseif (x <= -4e+162)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	elseif (x <= -2.65e+45)
		tmp = t_1;
	elseif (x <= -3500000000000.0)
		tmp = Float64(2.0 * Float64(x * Float64(y + z)));
	elseif (x <= 5.8e-95)
		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 = x * (t + (z * 2.0));
	tmp = 0.0;
	if (x <= -2.6e+207)
		tmp = t_1;
	elseif (x <= -4e+162)
		tmp = x * (t + (y * 2.0));
	elseif (x <= -2.65e+45)
		tmp = t_1;
	elseif (x <= -3500000000000.0)
		tmp = 2.0 * (x * (y + z));
	elseif (x <= 5.8e-95)
		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[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+207], t$95$1, If[LessEqual[x, -4e+162], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.65e+45], t$95$1, If[LessEqual[x, -3500000000000.0], N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-95], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.5999999999999998e207 or -3.9999999999999998e162 < x < -2.64999999999999996e45 or 5.80000000000000004e-95 < x

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 95.6%

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

   5. Taylor expanded in y around 0 80.1%

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

   if -2.5999999999999998e207 < x < -3.9999999999999998e162

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

   if -2.64999999999999996e45 < x < -3.5e12

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in t around 0 98.6%

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

   if -3.5e12 < x < 5.80000000000000004e-95

   1. Initial program 98.9%

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

   2. Taylor expanded in t around inf 79.3%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+207}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq -3500000000000:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-95}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 8: 46.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot 2\right)\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{+46}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq -7.3 \cdot 10^{-40}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-95}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* z 2.0))))
   (if (<= x -8.6e+257)
     t_1
     (if (<= x -7.4e+46)
       (* x t)
       (if (<= x -4.5e+14)
         (* 2.0 (* y x))
         (if (<= x -7.3e-40) (* x t) (if (<= x 5.8e-95) (* y 5.0) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z * 2.0);
	double tmp;
	if (x <= -8.6e+257) {
		tmp = t_1;
	} else if (x <= -7.4e+46) {
		tmp = x * t;
	} else if (x <= -4.5e+14) {
		tmp = 2.0 * (y * x);
	} else if (x <= -7.3e-40) {
		tmp = x * t;
	} else if (x <= 5.8e-95) {
		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 * (z * 2.0d0)
    if (x <= (-8.6d+257)) then
        tmp = t_1
    else if (x <= (-7.4d+46)) then
        tmp = x * t
    else if (x <= (-4.5d+14)) then
        tmp = 2.0d0 * (y * x)
    else if (x <= (-7.3d-40)) then
        tmp = x * t
    else if (x <= 5.8d-95) 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 * (z * 2.0);
	double tmp;
	if (x <= -8.6e+257) {
		tmp = t_1;
	} else if (x <= -7.4e+46) {
		tmp = x * t;
	} else if (x <= -4.5e+14) {
		tmp = 2.0 * (y * x);
	} else if (x <= -7.3e-40) {
		tmp = x * t;
	} else if (x <= 5.8e-95) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z * 2.0)
	tmp = 0
	if x <= -8.6e+257:
		tmp = t_1
	elif x <= -7.4e+46:
		tmp = x * t
	elif x <= -4.5e+14:
		tmp = 2.0 * (y * x)
	elif x <= -7.3e-40:
		tmp = x * t
	elif x <= 5.8e-95:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z * 2.0))
	tmp = 0.0
	if (x <= -8.6e+257)
		tmp = t_1;
	elseif (x <= -7.4e+46)
		tmp = Float64(x * t);
	elseif (x <= -4.5e+14)
		tmp = Float64(2.0 * Float64(y * x));
	elseif (x <= -7.3e-40)
		tmp = Float64(x * t);
	elseif (x <= 5.8e-95)
		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 * (z * 2.0);
	tmp = 0.0;
	if (x <= -8.6e+257)
		tmp = t_1;
	elseif (x <= -7.4e+46)
		tmp = x * t;
	elseif (x <= -4.5e+14)
		tmp = 2.0 * (y * x);
	elseif (x <= -7.3e-40)
		tmp = x * t;
	elseif (x <= 5.8e-95)
		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[(z * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.6e+257], t$95$1, If[LessEqual[x, -7.4e+46], N[(x * t), $MachinePrecision], If[LessEqual[x, -4.5e+14], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.3e-40], N[(x * t), $MachinePrecision], If[LessEqual[x, 5.8e-95], N[(y * 5.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.5999999999999996e257 or 5.80000000000000004e-95 < x

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 94.3%

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

   5. Taylor expanded in z around inf 51.3%

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

      1. associate-*r* 51.3%

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

   7. Simplified 51.3%

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

   if -8.5999999999999996e257 < x < -7.3999999999999998e46 or -4.5e14 < x < -7.30000000000000005e-40

   1. Initial program 98.1%

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

      1. fma-def 98.1%

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

      2. associate-+l+ 98.1%

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

      3. +-commutative 98.1%

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

      4. count-2 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in x around inf 95.9%

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

   5. Taylor expanded in t around inf 53.4%

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

      1. *-commutative 53.4%

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

   7. Simplified 53.4%

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

   if -7.3999999999999998e46 < x < -4.5e14

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in y around inf 63.3%

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

   if -7.30000000000000005e-40 < x < 5.80000000000000004e-95

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 63.5%

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

   4. Simplified 63.5%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+257}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{+46}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq -7.3 \cdot 10^{-40}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-95}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 2\right)\\ \end{array} \]

Alternative 9: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+141}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-43}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x (+ y z)))))
   (if (<= t -4.8e+141)
     (* x t)
     (if (<= t -4.1e-22)
       t_1
       (if (<= t -7.8e-43) (* y 5.0) (if (<= t 6.2e+69) t_1 (* x t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * (y + z));
	double tmp;
	if (t <= -4.8e+141) {
		tmp = x * t;
	} else if (t <= -4.1e-22) {
		tmp = t_1;
	} else if (t <= -7.8e-43) {
		tmp = y * 5.0;
	} else if (t <= 6.2e+69) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * (y + z))
    if (t <= (-4.8d+141)) then
        tmp = x * t
    else if (t <= (-4.1d-22)) then
        tmp = t_1
    else if (t <= (-7.8d-43)) then
        tmp = y * 5.0d0
    else if (t <= 6.2d+69) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * (y + z));
	double tmp;
	if (t <= -4.8e+141) {
		tmp = x * t;
	} else if (t <= -4.1e-22) {
		tmp = t_1;
	} else if (t <= -7.8e-43) {
		tmp = y * 5.0;
	} else if (t <= 6.2e+69) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * (y + z))
	tmp = 0
	if t <= -4.8e+141:
		tmp = x * t
	elif t <= -4.1e-22:
		tmp = t_1
	elif t <= -7.8e-43:
		tmp = y * 5.0
	elif t <= 6.2e+69:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * Float64(y + z)))
	tmp = 0.0
	if (t <= -4.8e+141)
		tmp = Float64(x * t);
	elseif (t <= -4.1e-22)
		tmp = t_1;
	elseif (t <= -7.8e-43)
		tmp = Float64(y * 5.0);
	elseif (t <= 6.2e+69)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * (y + z));
	tmp = 0.0;
	if (t <= -4.8e+141)
		tmp = x * t;
	elseif (t <= -4.1e-22)
		tmp = t_1;
	elseif (t <= -7.8e-43)
		tmp = y * 5.0;
	elseif (t <= 6.2e+69)
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+141], N[(x * t), $MachinePrecision], If[LessEqual[t, -4.1e-22], t$95$1, If[LessEqual[t, -7.8e-43], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 6.2e+69], t$95$1, N[(x * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.79999999999999995e141 or 6.1999999999999997e69 < t

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 81.9%

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

   5. Taylor expanded in t around inf 67.1%

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

      1. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if -4.79999999999999995e141 < t < -4.0999999999999999e-22 or -7.80000000000000001e-43 < t < 6.1999999999999997e69

   1. Initial program 99.3%

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

      1. fma-def 99.3%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. count-2 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 72.2%

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

   5. Taylor expanded in t around 0 62.8%

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

   if -4.0999999999999999e-22 < t < -7.80000000000000001e-43

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 87.1%

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

   4. Simplified 87.1%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+141}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-22}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-43}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+69}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 10: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Final simplification 99.5%

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

Alternative 11: 88.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-31} \lor \neg \left(x \leq 3.4 \cdot 10^{-98}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.52e-31) (not (<= x 3.4e-98)))
   (* 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 <= -1.52e-31) || !(x <= 3.4e-98)) {
		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 <= (-1.52d-31)) .or. (.not. (x <= 3.4d-98))) 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 <= -1.52e-31) || !(x <= 3.4e-98)) {
		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 <= -1.52e-31) or not (x <= 3.4e-98):
		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 <= -1.52e-31) || !(x <= 3.4e-98))
		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 <= -1.52e-31) || ~((x <= 3.4e-98)))
		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, -1.52e-31], N[Not[LessEqual[x, 3.4e-98]], $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 < -1.52000000000000003e-31 or 3.4000000000000001e-98 < x

   1. Initial program 99.3%

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

      1. fma-def 99.3%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. count-2 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 95.0%

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

   if -1.52000000000000003e-31 < x < 3.4000000000000001e-98

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 81.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-31} \lor \neg \left(x \leq 3.4 \cdot 10^{-98}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 12: 88.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-45} \lor \neg \left(x \leq 9.5 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.8e-45) (not (<= x 9.5e-12)))
   (* x (+ t (* (+ y z) 2.0)))
   (+ (* y 5.0) (* 2.0 (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e-45) || !(x <= 9.5e-12)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.8d-45)) .or. (.not. (x <= 9.5d-12))) then
        tmp = x * (t + ((y + z) * 2.0d0))
    else
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e-45) || !(x <= 9.5e-12)) {
		tmp = x * (t + ((y + z) * 2.0));
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.8e-45) or not (x <= 9.5e-12):
		tmp = x * (t + ((y + z) * 2.0))
	else:
		tmp = (y * 5.0) + (2.0 * (x * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.8e-45) || !(x <= 9.5e-12))
		tmp = Float64(x * Float64(t + Float64(Float64(y + z) * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.8e-45) || ~((x <= 9.5e-12)))
		tmp = x * (t + ((y + z) * 2.0));
	else
		tmp = (y * 5.0) + (2.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.8e-45], N[Not[LessEqual[x, 9.5e-12]], $MachinePrecision]], N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.79999999999999997e-45 or 9.4999999999999995e-12 < x

   1. Initial program 99.3%

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

      1. fma-def 99.3%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. count-2 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 98.4%

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

   if -3.79999999999999997e-45 < x < 9.4999999999999995e-12

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 82.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-45} \lor \neg \left(x \leq 9.5 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 13: 46.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-43} \lor \neg \left(x \leq 5.6 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.36e-43) (not (<= x 5.6e-11))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.36e-43) || !(x <= 5.6e-11)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.36d-43)) .or. (.not. (x <= 5.6d-11))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.36e-43) || !(x <= 5.6e-11)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.36e-43) or not (x <= 5.6e-11):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.36e-43) || !(x <= 5.6e-11))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.36e-43) || ~((x <= 5.6e-11)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.36e-43], N[Not[LessEqual[x, 5.6e-11]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.36000000000000007e-43 or 5.6e-11 < x

   1. Initial program 99.3%

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

      1. fma-def 99.3%

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

      2. associate-+l+ 99.3%

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

      3. +-commutative 99.3%

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

      4. count-2 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 98.4%

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

   5. Taylor expanded in t around inf 40.7%

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

      1. *-commutative 40.7%

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

   7. Simplified 40.7%

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

   if -1.36000000000000007e-43 < x < 5.6e-11

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 59.3%

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

   4. Simplified 59.3%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-43} \lor \neg \left(x \leq 5.6 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 14: 29.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ x \cdot t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. fma-def 99.5%

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

   2. associate-+l+ 99.5%

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

   3. +-commutative 99.5%

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

   4. count-2 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around inf 73.9%

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

5. Taylor expanded in t around inf 31.4%

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

   1. *-commutative 31.4%

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

7. Simplified 31.4%

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

8. Final simplification 31.4%

   \[\leadsto x \cdot t \]

Reproduce

herbie shell --seed 2023230 
(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)))