Linear.V4:$cdot from linear-1.19.1.3, C

Percentage Accurate: 95.5% → 97.9%

Time: 11.3s

Alternatives: 13

Speedup: 0.4×

• 41.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((x * y) + (z * t)) + (a * b)) + (c * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((x * y) + (z * t)) + (a * b)) + (c * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((x * y) + (z * t)) + (a * b)) + (c * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((x * y) + (z * t)) + (a * b)) + (c * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((x * y) + (z * t)) + (a * b)) + (c * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((x * y) + (z * t)) + (a * b)) + (c * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + \frac{a}{\frac{x}{b}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
   (if (<= t_1 INFINITY) t_1 (* x (+ y (/ a (/ x b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((x * y) + (z * t)) + (a * b)) + (c * i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x * (y + (a / (x / b)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((x * y) + (z * t)) + (a * b)) + (c * i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x * (y + (a / (x / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (((x * y) + (z * t)) + (a * b)) + (c * i)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x * (y + (a / (x / b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y + Float64(a / Float64(x / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((x * y) + (z * t)) + (a * b)) + (c * i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x * (y + (a / (x / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(y + N[(a / N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 22.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 22.2%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 44.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   8. Simplified 44.4%

      \[\leadsto x \cdot y + \color{blue}{a \cdot b} \]
   9. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto x \cdot y + \left(a \cdot b\right) \cdot \color{blue}{1} \]

      2. lft-mult-inverse N/A

         \[\leadsto x \cdot y + \left(a \cdot b\right) \cdot \left(\frac{1}{x} \cdot \color{blue}{x}\right) \]

      3. associate-*l* N/A

         \[\leadsto x \cdot y + \left(\left(a \cdot b\right) \cdot \frac{1}{x}\right) \cdot \color{blue}{x} \]

      4. div-inv N/A

         \[\leadsto x \cdot y + \frac{a \cdot b}{x} \cdot x \]

      5. *-commutative N/A

         \[\leadsto x \cdot y + x \cdot \color{blue}{\frac{a \cdot b}{x}} \]

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y + \frac{a \cdot b}{x}\right), \color{blue}{x}\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\frac{a \cdot b}{x}\right)\right), x\right) \]

      10. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(a \cdot \frac{b}{x}\right)\right), x\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(a \cdot \frac{1}{\frac{x}{b}}\right)\right), x\right) \]

      12. un-div-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\frac{a}{\frac{x}{b}}\right)\right), x\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \mathsf{/.f64}\left(a, \left(\frac{x}{b}\right)\right)\right), x\right) \]

      14. /-lowering-/.f64 77.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(x, b\right)\right)\right), x\right) \]

   10. Applied egg-rr 77.8%

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

4. Final simplification 99.2%

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

Alternative 2: 65.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \left(y + \frac{a}{\frac{x}{b}}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-184}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-189}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-6}:\\ \;\;\;\;i \cdot \left(c + \frac{z \cdot t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+100)
   (* x (+ y (/ a (/ x b))))
   (if (<= (* x y) -5e-184)
     (+ (* c i) (* z t))
     (if (<= (* x y) 2e-189)
       (+ (* a b) (* c i))
       (if (<= (* x y) 2e-6) (* i (+ c (/ (* z t) i))) (+ (* x y) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2e+100) {
		tmp = x * (y + (a / (x / b)));
	} else if ((x * y) <= -5e-184) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 2e-189) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2e-6) {
		tmp = i * (c + ((z * t) / i));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-2d+100)) then
        tmp = x * (y + (a / (x / b)))
    else if ((x * y) <= (-5d-184)) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 2d-189) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 2d-6) then
        tmp = i * (c + ((z * t) / i))
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2e+100) {
		tmp = x * (y + (a / (x / b)));
	} else if ((x * y) <= -5e-184) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 2e-189) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2e-6) {
		tmp = i * (c + ((z * t) / i));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+100:
		tmp = x * (y + (a / (x / b)))
	elif (x * y) <= -5e-184:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 2e-189:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 2e-6:
		tmp = i * (c + ((z * t) / i))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+100)
		tmp = Float64(x * Float64(y + Float64(a / Float64(x / b))));
	elseif (Float64(x * y) <= -5e-184)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 2e-189)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 2e-6)
		tmp = Float64(i * Float64(c + Float64(Float64(z * t) / i)));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -2e+100)
		tmp = x * (y + (a / (x / b)));
	elseif ((x * y) <= -5e-184)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 2e-189)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 2e-6)
		tmp = i * (c + ((z * t) / i));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+100], N[(x * N[(y + N[(a / N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-184], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-189], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-6], N[(i * N[(c + N[(N[(z * t), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -2.00000000000000003e100

   1. Initial program 90.7%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 88.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 88.5%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 88.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   8. Simplified 88.5%

      \[\leadsto x \cdot y + \color{blue}{a \cdot b} \]
   9. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto x \cdot y + \left(a \cdot b\right) \cdot \color{blue}{1} \]

      2. lft-mult-inverse N/A

         \[\leadsto x \cdot y + \left(a \cdot b\right) \cdot \left(\frac{1}{x} \cdot \color{blue}{x}\right) \]

      3. associate-*l* N/A

         \[\leadsto x \cdot y + \left(\left(a \cdot b\right) \cdot \frac{1}{x}\right) \cdot \color{blue}{x} \]

      4. div-inv N/A

         \[\leadsto x \cdot y + \frac{a \cdot b}{x} \cdot x \]

      5. *-commutative N/A

         \[\leadsto x \cdot y + x \cdot \color{blue}{\frac{a \cdot b}{x}} \]

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y + \frac{a \cdot b}{x}\right), \color{blue}{x}\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\frac{a \cdot b}{x}\right)\right), x\right) \]

      10. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(a \cdot \frac{b}{x}\right)\right), x\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(a \cdot \frac{1}{\frac{x}{b}}\right)\right), x\right) \]

      12. un-div-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\frac{a}{\frac{x}{b}}\right)\right), x\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \mathsf{/.f64}\left(a, \left(\frac{x}{b}\right)\right)\right), x\right) \]

      14. /-lowering-/.f64 90.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(x, b\right)\right)\right), x\right) \]

   10. Applied egg-rr 90.8%

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

   if -2.00000000000000003e100 < (*.f64 x y) < -5.00000000000000003e-184

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 74.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 74.0%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -5.00000000000000003e-184 < (*.f64 x y) < 2.00000000000000014e-189

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 77.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 77.7%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]

   if 2.00000000000000014e-189 < (*.f64 x y) < 1.99999999999999991e-6

   1. Initial program 97.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 78.5%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(c + \frac{t \cdot z}{i}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{+.f64}\left(c, \color{blue}{\left(\frac{t \cdot z}{i}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{i}\right)\right)\right) \]

      4. *-lowering-*.f64 76.4%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), i\right)\right)\right) \]

   8. Simplified 76.4%

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

   if 1.99999999999999991e-6 < (*.f64 x y)

   1. Initial program 93.4%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 77.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 77.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \left(y + \frac{a}{\frac{x}{b}}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-184}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-189}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-6}:\\ \;\;\;\;i \cdot \left(c + \frac{z \cdot t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+89}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -1.75 \cdot 10^{-206}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.3 \cdot 10^{-189}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.4:\\ \;\;\;\;i \cdot \left(c + \frac{z \cdot t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1.45e+89)
   (+ (* x y) (* a b))
   (if (<= (* x y) -1.75e-206)
     (+ (* c i) (* z t))
     (if (<= (* x y) 3.3e-189)
       (+ (* a b) (* c i))
       (if (<= (* x y) 1.4) (* i (+ c (/ (* z t) i))) (+ (* x y) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.45e+89) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= -1.75e-206) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 3.3e-189) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.4) {
		tmp = i * (c + ((z * t) / i));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1.45d+89)) then
        tmp = (x * y) + (a * b)
    else if ((x * y) <= (-1.75d-206)) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 3.3d-189) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 1.4d0) then
        tmp = i * (c + ((z * t) / i))
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.45e+89) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= -1.75e-206) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 3.3e-189) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.4) {
		tmp = i * (c + ((z * t) / i));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1.45e+89:
		tmp = (x * y) + (a * b)
	elif (x * y) <= -1.75e-206:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 3.3e-189:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 1.4:
		tmp = i * (c + ((z * t) / i))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1.45e+89)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(x * y) <= -1.75e-206)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 3.3e-189)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 1.4)
		tmp = Float64(i * Float64(c + Float64(Float64(z * t) / i)));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1.45e+89)
		tmp = (x * y) + (a * b);
	elseif ((x * y) <= -1.75e-206)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 3.3e-189)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 1.4)
		tmp = i * (c + ((z * t) / i));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.45e+89], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.75e-206], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.3e-189], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.4], N[(i * N[(c + N[(N[(z * t), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.45000000000000013e89

   1. Initial program 90.7%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 88.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 88.5%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 88.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   8. Simplified 88.5%

      \[\leadsto x \cdot y + \color{blue}{a \cdot b} \]

   if -1.45000000000000013e89 < (*.f64 x y) < -1.74999999999999995e-206

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 74.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 74.0%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -1.74999999999999995e-206 < (*.f64 x y) < 3.3000000000000001e-189

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 77.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 77.7%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]

   if 3.3000000000000001e-189 < (*.f64 x y) < 1.3999999999999999

   1. Initial program 97.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 78.5%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(c + \frac{t \cdot z}{i}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{+.f64}\left(c, \color{blue}{\left(\frac{t \cdot z}{i}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{i}\right)\right)\right) \]

      4. *-lowering-*.f64 76.4%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), i\right)\right)\right) \]

   8. Simplified 76.4%

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

   if 1.3999999999999999 < (*.f64 x y)

   1. Initial program 93.4%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 77.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 77.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+89}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -1.75 \cdot 10^{-206}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.3 \cdot 10^{-189}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.4:\\ \;\;\;\;i \cdot \left(c + \frac{z \cdot t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 9 \cdot 10^{-165}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.02:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* x y) -4.5e+97)
     (+ (* x y) (* a b))
     (if (<= (* x y) -3.9e-208)
       t_1
       (if (<= (* x y) 9e-165)
         (+ (* a b) (* c i))
         (if (<= (* x y) 1.02) t_1 (+ (* x y) (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((x * y) <= -4.5e+97) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= -3.9e-208) {
		tmp = t_1;
	} else if ((x * y) <= 9e-165) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.02) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    if ((x * y) <= (-4.5d+97)) then
        tmp = (x * y) + (a * b)
    else if ((x * y) <= (-3.9d-208)) then
        tmp = t_1
    else if ((x * y) <= 9d-165) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 1.02d0) then
        tmp = t_1
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((x * y) <= -4.5e+97) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= -3.9e-208) {
		tmp = t_1;
	} else if ((x * y) <= 9e-165) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.02) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (x * y) <= -4.5e+97:
		tmp = (x * y) + (a * b)
	elif (x * y) <= -3.9e-208:
		tmp = t_1
	elif (x * y) <= 9e-165:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 1.02:
		tmp = t_1
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -4.5e+97)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(x * y) <= -3.9e-208)
		tmp = t_1;
	elseif (Float64(x * y) <= 9e-165)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 1.02)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -4.5e+97)
		tmp = (x * y) + (a * b);
	elseif ((x * y) <= -3.9e-208)
		tmp = t_1;
	elseif ((x * y) <= 9e-165)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 1.02)
		tmp = t_1;
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.5e+97], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.9e-208], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 9e-165], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.02], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.49999999999999976e97

   1. Initial program 90.7%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 88.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 88.5%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 88.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   8. Simplified 88.5%

      \[\leadsto x \cdot y + \color{blue}{a \cdot b} \]

   if -4.49999999999999976e97 < (*.f64 x y) < -3.90000000000000004e-208 or 8.99999999999999985e-165 < (*.f64 x y) < 1.02

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 76.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 76.9%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -3.90000000000000004e-208 < (*.f64 x y) < 8.99999999999999985e-165

   1. Initial program 98.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 76.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 76.5%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]

   if 1.02 < (*.f64 x y)

   1. Initial program 93.4%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 77.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 77.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{-208}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 9 \cdot 10^{-165}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.02:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := x \cdot y + a \cdot b\\ \mathbf{if}\;x \cdot y \leq -1.08 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1.25 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.75 \cdot 10^{-164}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* x y) (* a b))))
   (if (<= (* x y) -1.08e+99)
     t_2
     (if (<= (* x y) -1.25e-189)
       t_1
       (if (<= (* x y) 1.75e-164)
         (+ (* a b) (* c i))
         (if (<= (* x y) 3.6e+203) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -1.08e+99) {
		tmp = t_2;
	} else if ((x * y) <= -1.25e-189) {
		tmp = t_1;
	} else if ((x * y) <= 1.75e-164) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 3.6e+203) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (x * y) + (a * b)
    if ((x * y) <= (-1.08d+99)) then
        tmp = t_2
    else if ((x * y) <= (-1.25d-189)) then
        tmp = t_1
    else if ((x * y) <= 1.75d-164) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 3.6d+203) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -1.08e+99) {
		tmp = t_2;
	} else if ((x * y) <= -1.25e-189) {
		tmp = t_1;
	} else if ((x * y) <= 1.75e-164) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 3.6e+203) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (x * y) + (a * b)
	tmp = 0
	if (x * y) <= -1.08e+99:
		tmp = t_2
	elif (x * y) <= -1.25e-189:
		tmp = t_1
	elif (x * y) <= 1.75e-164:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 3.6e+203:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -1.08e+99)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.25e-189)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.75e-164)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 3.6e+203)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (x * y) + (a * b);
	tmp = 0.0;
	if ((x * y) <= -1.08e+99)
		tmp = t_2;
	elseif ((x * y) <= -1.25e-189)
		tmp = t_1;
	elseif ((x * y) <= 1.75e-164)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 3.6e+203)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.08e+99], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.25e-189], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.75e-164], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.6e+203], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.08e99 or 3.59999999999999982e203 < (*.f64 x y)

   1. Initial program 89.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 89.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 89.4%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 88.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   8. Simplified 88.2%

      \[\leadsto x \cdot y + \color{blue}{a \cdot b} \]

   if -1.08e99 < (*.f64 x y) < -1.2499999999999999e-189 or 1.75e-164 < (*.f64 x y) < 3.59999999999999982e203

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 71.9%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -1.2499999999999999e-189 < (*.f64 x y) < 1.75e-164

   1. Initial program 98.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 76.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 76.5%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.08 \cdot 10^{+99}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -1.25 \cdot 10^{-189}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.75 \cdot 10^{-164}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{+203}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -6.8 \cdot 10^{+109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.45 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5.6 \cdot 10^{-164}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.25 \cdot 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* x y) -6.8e+109)
     (* x y)
     (if (<= (* x y) -2.45e-198)
       t_1
       (if (<= (* x y) 5.6e-164)
         (+ (* a b) (* c i))
         (if (<= (* x y) 2.25e+206) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((x * y) <= -6.8e+109) {
		tmp = x * y;
	} else if ((x * y) <= -2.45e-198) {
		tmp = t_1;
	} else if ((x * y) <= 5.6e-164) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2.25e+206) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    if ((x * y) <= (-6.8d+109)) then
        tmp = x * y
    else if ((x * y) <= (-2.45d-198)) then
        tmp = t_1
    else if ((x * y) <= 5.6d-164) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 2.25d+206) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((x * y) <= -6.8e+109) {
		tmp = x * y;
	} else if ((x * y) <= -2.45e-198) {
		tmp = t_1;
	} else if ((x * y) <= 5.6e-164) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2.25e+206) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (x * y) <= -6.8e+109:
		tmp = x * y
	elif (x * y) <= -2.45e-198:
		tmp = t_1
	elif (x * y) <= 5.6e-164:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 2.25e+206:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -6.8e+109)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.45e-198)
		tmp = t_1;
	elseif (Float64(x * y) <= 5.6e-164)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 2.25e+206)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -6.8e+109)
		tmp = x * y;
	elseif ((x * y) <= -2.45e-198)
		tmp = t_1;
	elseif ((x * y) <= 5.6e-164)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 2.25e+206)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -6.8e+109], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.45e-198], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5.6e-164], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.25e+206], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.80000000000000013e109 or 2.25000000000000009e206 < (*.f64 x y)

   1. Initial program 89.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 79.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 79.8%

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

   if -6.80000000000000013e109 < (*.f64 x y) < -2.4500000000000001e-198 or 5.6000000000000002e-164 < (*.f64 x y) < 2.25000000000000009e206

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 70.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 70.7%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -2.4500000000000001e-198 < (*.f64 x y) < 5.6000000000000002e-164

   1. Initial program 98.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 76.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 76.5%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.8 \cdot 10^{+109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.45 \cdot 10^{-198}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.6 \cdot 10^{-164}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.25 \cdot 10^{+206}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.5 \cdot 10^{+150}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.2 \cdot 10^{-131}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{+64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.7 \cdot 10^{+127}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.5e+150)
   (* c i)
   (if (<= (* c i) -1.2e-131)
     (* a b)
     (if (<= (* c i) 2.5e+64)
       (* x y)
       (if (<= (* c i) 4.7e+127) (* z t) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.5e+150) {
		tmp = c * i;
	} else if ((c * i) <= -1.2e-131) {
		tmp = a * b;
	} else if ((c * i) <= 2.5e+64) {
		tmp = x * y;
	} else if ((c * i) <= 4.7e+127) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-3.5d+150)) then
        tmp = c * i
    else if ((c * i) <= (-1.2d-131)) then
        tmp = a * b
    else if ((c * i) <= 2.5d+64) then
        tmp = x * y
    else if ((c * i) <= 4.7d+127) then
        tmp = z * t
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.5e+150) {
		tmp = c * i;
	} else if ((c * i) <= -1.2e-131) {
		tmp = a * b;
	} else if ((c * i) <= 2.5e+64) {
		tmp = x * y;
	} else if ((c * i) <= 4.7e+127) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.5e+150:
		tmp = c * i
	elif (c * i) <= -1.2e-131:
		tmp = a * b
	elif (c * i) <= 2.5e+64:
		tmp = x * y
	elif (c * i) <= 4.7e+127:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.5e+150)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.2e-131)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 2.5e+64)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 4.7e+127)
		tmp = Float64(z * t);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.5e+150)
		tmp = c * i;
	elseif ((c * i) <= -1.2e-131)
		tmp = a * b;
	elseif ((c * i) <= 2.5e+64)
		tmp = x * y;
	elseif ((c * i) <= 4.7e+127)
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.5e+150], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.2e-131], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.5e+64], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.7e+127], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -3.49999999999999984e150 or 4.70000000000000035e127 < (*.f64 c i)

   1. Initial program 93.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 74.6%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 74.6%

      \[\leadsto \color{blue}{c \cdot i} \]

   if -3.49999999999999984e150 < (*.f64 c i) < -1.2e-131

   1. Initial program 97.8%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 46.8%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 46.8%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -1.2e-131 < (*.f64 c i) < 2.5e64

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 42.6%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 42.6%

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

   if 2.5e64 < (*.f64 c i) < 4.70000000000000035e127

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 67.6%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{z}\right) \]

   5. Simplified 67.6%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.5 \cdot 10^{+150}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.2 \cdot 10^{-131}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{+64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.7 \cdot 10^{+127}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+200}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{-176}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+121}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1.8e+200)
   (* x y)
   (if (<= (* x y) -1.5e-176)
     (+ (* a b) (* z t))
     (if (<= (* x y) 2.15e+121) (+ (* a b) (* c i)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.8e+200) {
		tmp = x * y;
	} else if ((x * y) <= -1.5e-176) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 2.15e+121) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1.8d+200)) then
        tmp = x * y
    else if ((x * y) <= (-1.5d-176)) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 2.15d+121) then
        tmp = (a * b) + (c * i)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.8e+200) {
		tmp = x * y;
	} else if ((x * y) <= -1.5e-176) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 2.15e+121) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1.8e+200:
		tmp = x * y
	elif (x * y) <= -1.5e-176:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 2.15e+121:
		tmp = (a * b) + (c * i)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1.8e+200)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.5e-176)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 2.15e+121)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1.8e+200)
		tmp = x * y;
	elseif ((x * y) <= -1.5e-176)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 2.15e+121)
		tmp = (a * b) + (c * i);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.8e+200], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.5e-176], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.15e+121], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.7999999999999999e200 or 2.1499999999999999e121 < (*.f64 x y)

   1. Initial program 89.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 79.3%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 79.3%

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

   if -1.7999999999999999e200 < (*.f64 x y) < -1.5e-176

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 76.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 76.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right) \]

      3. *-lowering-*.f64 63.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 63.6%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if -1.5e-176 < (*.f64 x y) < 2.1499999999999999e121

   1. Initial program 99.2%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 67.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 67.1%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+200}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{-176}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+121}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(c + \frac{z \cdot t}{i}\right)\\ \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{+56}:\\ \;\;\;\;x \cdot y + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (+ c (/ (* z t) i)))))
   (if (<= (* c i) -1e+164)
     t_1
     (if (<= (* c i) 4e+56) (+ (* x y) (+ (* a b) (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (c + ((z * t) / i));
	double tmp;
	if ((c * i) <= -1e+164) {
		tmp = t_1;
	} else if ((c * i) <= 4e+56) {
		tmp = (x * y) + ((a * b) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (c + ((z * t) / i))
    if ((c * i) <= (-1d+164)) then
        tmp = t_1
    else if ((c * i) <= 4d+56) then
        tmp = (x * y) + ((a * b) + (z * 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 a, double b, double c, double i) {
	double t_1 = i * (c + ((z * t) / i));
	double tmp;
	if ((c * i) <= -1e+164) {
		tmp = t_1;
	} else if ((c * i) <= 4e+56) {
		tmp = (x * y) + ((a * b) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i * (c + ((z * t) / i))
	tmp = 0
	if (c * i) <= -1e+164:
		tmp = t_1
	elif (c * i) <= 4e+56:
		tmp = (x * y) + ((a * b) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(c + Float64(Float64(z * t) / i)))
	tmp = 0.0
	if (Float64(c * i) <= -1e+164)
		tmp = t_1;
	elseif (Float64(c * i) <= 4e+56)
		tmp = Float64(Float64(x * y) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i * (c + ((z * t) / i));
	tmp = 0.0;
	if ((c * i) <= -1e+164)
		tmp = t_1;
	elseif ((c * i) <= 4e+56)
		tmp = (x * y) + ((a * b) + (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(c + N[(N[(z * t), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1e+164], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 4e+56], N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1e164 or 4.00000000000000037e56 < (*.f64 c i)

   1. Initial program 94.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 84.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 84.5%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(c + \frac{t \cdot z}{i}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{+.f64}\left(c, \color{blue}{\left(\frac{t \cdot z}{i}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{i}\right)\right)\right) \]

      4. *-lowering-*.f64 84.5%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), i\right)\right)\right) \]

   8. Simplified 84.5%

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

   if -1e164 < (*.f64 c i) < 4.00000000000000037e56

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(a \cdot b + t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{a \cdot b} + t \cdot z\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{t} \cdot z\right)\right)\right) \]

      7. *-lowering-*.f64 92.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 92.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+164}:\\ \;\;\;\;i \cdot \left(c + \frac{z \cdot t}{i}\right)\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{+56}:\\ \;\;\;\;x \cdot y + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(c + \frac{z \cdot t}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.5 \cdot 10^{+151}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.45 \cdot 10^{-95}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.3 \cdot 10^{+123}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.5e+151)
   (* c i)
   (if (<= (* c i) -1.45e-95)
     (* a b)
     (if (<= (* c i) 3.3e+123) (* z t) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.5e+151) {
		tmp = c * i;
	} else if ((c * i) <= -1.45e-95) {
		tmp = a * b;
	} else if ((c * i) <= 3.3e+123) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-2.5d+151)) then
        tmp = c * i
    else if ((c * i) <= (-1.45d-95)) then
        tmp = a * b
    else if ((c * i) <= 3.3d+123) then
        tmp = z * t
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.5e+151) {
		tmp = c * i;
	} else if ((c * i) <= -1.45e-95) {
		tmp = a * b;
	} else if ((c * i) <= 3.3e+123) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.5e+151:
		tmp = c * i
	elif (c * i) <= -1.45e-95:
		tmp = a * b
	elif (c * i) <= 3.3e+123:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2.5e+151)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.45e-95)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 3.3e+123)
		tmp = Float64(z * t);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -2.5e+151)
		tmp = c * i;
	elseif ((c * i) <= -1.45e-95)
		tmp = a * b;
	elseif ((c * i) <= 3.3e+123)
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2.5e+151], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.45e-95], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.3e+123], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.5000000000000001e151 or 3.30000000000000003e123 < (*.f64 c i)

   1. Initial program 93.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 74.6%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 74.6%

      \[\leadsto \color{blue}{c \cdot i} \]

   if -2.5000000000000001e151 < (*.f64 c i) < -1.45000000000000001e-95

   1. Initial program 97.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 46.4%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 46.4%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -1.45000000000000001e-95 < (*.f64 c i) < 3.30000000000000003e123

   1. Initial program 97.8%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 38.0%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{z}\right) \]

   5. Simplified 38.0%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.5 \cdot 10^{+151}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.45 \cdot 10^{-95}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.3 \cdot 10^{+123}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.5 \cdot 10^{+206}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{+123}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5.5e+206)
   (* x y)
   (if (<= (* x y) 7.6e+123) (+ (* a b) (* c i)) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5.5e+206) {
		tmp = x * y;
	} else if ((x * y) <= 7.6e+123) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-5.5d+206)) then
        tmp = x * y
    else if ((x * y) <= 7.6d+123) then
        tmp = (a * b) + (c * i)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5.5e+206) {
		tmp = x * y;
	} else if ((x * y) <= 7.6e+123) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5.5e+206:
		tmp = x * y
	elif (x * y) <= 7.6e+123:
		tmp = (a * b) + (c * i)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5.5e+206)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 7.6e+123)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -5.5e+206)
		tmp = x * y;
	elseif ((x * y) <= 7.6e+123)
		tmp = (a * b) + (c * i);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5.5e+206], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.6e+123], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.50000000000000021e206 or 7.59999999999999989e123 < (*.f64 x y)

   1. Initial program 90.4%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 80.1%

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

   if -5.50000000000000021e206 < (*.f64 x y) < 7.59999999999999989e123

   1. Initial program 98.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 61.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 61.9%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 42.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.7 \cdot 10^{+139}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{+50}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.7e+139) (* c i) (if (<= (* c i) 7e+50) (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.7e+139) {
		tmp = c * i;
	} else if ((c * i) <= 7e+50) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-2.7d+139)) then
        tmp = c * i
    else if ((c * i) <= 7d+50) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.7e+139) {
		tmp = c * i;
	} else if ((c * i) <= 7e+50) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.7e+139:
		tmp = c * i
	elif (c * i) <= 7e+50:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2.7e+139)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 7e+50)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -2.7e+139)
		tmp = c * i;
	elseif ((c * i) <= 7e+50)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2.7e+139], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7e+50], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.6999999999999998e139 or 7.00000000000000012e50 < (*.f64 c i)

   1. Initial program 94.8%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 64.8%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 64.8%

      \[\leadsto \color{blue}{c \cdot i} \]

   if -2.6999999999999998e139 < (*.f64 c i) < 7.00000000000000012e50

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 34.0%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 34.0%

      \[\leadsto \color{blue}{a \cdot b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 27.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (* a b))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a * b;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b, c, i):
	return a * b

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(a * b)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a * b;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a * b), $MachinePrecision]

Derivation

1. Initial program 96.5%

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot b} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 26.3%

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

5. Simplified 26.3%

   \[\leadsto \color{blue}{a \cdot b} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024185 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))