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

Percentage Accurate: 95.7% → 97.7%

Time: 13.8s

Alternatives: 11

Speedup: 0.4×

• 41.2% 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: 95.7% 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: 97.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(t + N[(N[(c * i), $MachinePrecision] / z), $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 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 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in z around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 77.9%

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

   8. Simplified 77.9%

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

4. Final simplification 99.2%

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

Alternative 2: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(a + \frac{c \cdot i}{b}\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-321}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* x y) (* z t))))
   (if (<= (* a b) -1e+153)
     (* b (+ a (/ (* c i) b)))
     (if (<= (* a b) -1e-26)
       t_2
       (if (<= (* a b) -1e-96)
         t_1
         (if (<= (* a b) 2e-321)
           t_2
           (if (<= (* a b) 4e+129) t_1 (+ (* x y) (* a b)))))))))

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) + (z * t);
	double tmp;
	if ((a * b) <= -1e+153) {
		tmp = b * (a + ((c * i) / b));
	} else if ((a * b) <= -1e-26) {
		tmp = t_2;
	} else if ((a * b) <= -1e-96) {
		tmp = t_1;
	} else if ((a * b) <= 2e-321) {
		tmp = t_2;
	} else if ((a * b) <= 4e+129) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (a * b);
	}
	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) + (z * t)
    if ((a * b) <= (-1d+153)) then
        tmp = b * (a + ((c * i) / b))
    else if ((a * b) <= (-1d-26)) then
        tmp = t_2
    else if ((a * b) <= (-1d-96)) then
        tmp = t_1
    else if ((a * b) <= 2d-321) then
        tmp = t_2
    else if ((a * b) <= 4d+129) then
        tmp = t_1
    else
        tmp = (x * y) + (a * b)
    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) + (z * t);
	double tmp;
	if ((a * b) <= -1e+153) {
		tmp = b * (a + ((c * i) / b));
	} else if ((a * b) <= -1e-26) {
		tmp = t_2;
	} else if ((a * b) <= -1e-96) {
		tmp = t_1;
	} else if ((a * b) <= 2e-321) {
		tmp = t_2;
	} else if ((a * b) <= 4e+129) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (a * b) <= -1e+153:
		tmp = b * (a + ((c * i) / b))
	elif (a * b) <= -1e-26:
		tmp = t_2
	elif (a * b) <= -1e-96:
		tmp = t_1
	elif (a * b) <= 2e-321:
		tmp = t_2
	elif (a * b) <= 4e+129:
		tmp = t_1
	else:
		tmp = (x * y) + (a * b)
	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(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -1e+153)
		tmp = Float64(b * Float64(a + Float64(Float64(c * i) / b)));
	elseif (Float64(a * b) <= -1e-26)
		tmp = t_2;
	elseif (Float64(a * b) <= -1e-96)
		tmp = t_1;
	elseif (Float64(a * b) <= 2e-321)
		tmp = t_2;
	elseif (Float64(a * b) <= 4e+129)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(a * b));
	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) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -1e+153)
		tmp = b * (a + ((c * i) / b));
	elseif ((a * b) <= -1e-26)
		tmp = t_2;
	elseif ((a * b) <= -1e-96)
		tmp = t_1;
	elseif ((a * b) <= 2e-321)
		tmp = t_2;
	elseif ((a * b) <= 4e+129)
		tmp = t_1;
	else
		tmp = (x * y) + (a * b);
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+153], N[(b * N[(a + N[(N[(c * i), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e-26], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1e-96], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2e-321], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 4e+129], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1e153

   1. Initial program 93.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   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 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 85.4%

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

   8. Simplified 85.4%

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

   if -1e153 < (*.f64 a b) < -1e-26 or -9.9999999999999991e-97 < (*.f64 a b) < 2.00097e-321

   1. Initial program 97.9%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - c \cdot i}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) \cdot \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - \left(c \cdot i\right) \cdot \left(c \cdot i\right)}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) \cdot \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - \left(c \cdot i\right) \cdot \left(c \cdot i\right)}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - c \cdot i}}}\right)\right) \]

      5. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + \color{blue}{c \cdot i}}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \color{blue}{\left(\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\right)}\right)\right) \]

      7. associate-+l+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \left(\left(x \cdot y + \left(z \cdot t + a \cdot b\right)\right) + \color{blue}{c} \cdot i\right)\right)\right) \]

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \color{blue}{\left(c \cdot i\right)}\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 92.7%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(c, \color{blue}{i}\right)\right)\right)\right)\right) \]

   7. Simplified 92.7%

      \[\leadsto \frac{1}{\frac{1}{x \cdot y + \left(z \cdot t + \color{blue}{c \cdot i}\right)}} \]

   8. Taylor expanded in c around 0

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

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

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

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

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

      3. *-lowering-*.f64 73.2%

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

   10. Simplified 73.2%

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

   if -1e-26 < (*.f64 a b) < -9.9999999999999991e-97 or 2.00097e-321 < (*.f64 a b) < 4e129

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 82.6%

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

   5. Simplified 82.6%

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

   if 4e129 < (*.f64 a b)

   1. Initial program 90.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   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 83.6%

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

   5. Simplified 83.6%

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

   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 83.6%

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

   8. Simplified 83.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(a + \frac{c \cdot i}{b}\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-26}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-96}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-321}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+129}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := c \cdot i + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -2.4 \cdot 10^{+147}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -1.16 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1.45 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-321}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1.3 \cdot 10^{+132}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* c i) (* z t))))
   (if (<= (* a b) -2.4e+147)
     (+ (* a b) (* c i))
     (if (<= (* a b) -1.16e-28)
       t_1
       (if (<= (* a b) -1.45e-97)
         t_2
         (if (<= (* a b) 2e-321)
           t_1
           (if (<= (* a b) 1.3e+132) t_2 (+ (* x y) (* a 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);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if ((a * b) <= -2.4e+147) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -1.16e-28) {
		tmp = t_1;
	} else if ((a * b) <= -1.45e-97) {
		tmp = t_2;
	} else if ((a * b) <= 2e-321) {
		tmp = t_1;
	} else if ((a * b) <= 1.3e+132) {
		tmp = t_2;
	} else {
		tmp = (x * y) + (a * b);
	}
	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 = (x * y) + (z * t)
    t_2 = (c * i) + (z * t)
    if ((a * b) <= (-2.4d+147)) then
        tmp = (a * b) + (c * i)
    else if ((a * b) <= (-1.16d-28)) then
        tmp = t_1
    else if ((a * b) <= (-1.45d-97)) then
        tmp = t_2
    else if ((a * b) <= 2d-321) then
        tmp = t_1
    else if ((a * b) <= 1.3d+132) then
        tmp = t_2
    else
        tmp = (x * y) + (a * b)
    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 = (x * y) + (z * t);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if ((a * b) <= -2.4e+147) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -1.16e-28) {
		tmp = t_1;
	} else if ((a * b) <= -1.45e-97) {
		tmp = t_2;
	} else if ((a * b) <= 2e-321) {
		tmp = t_1;
	} else if ((a * b) <= 1.3e+132) {
		tmp = t_2;
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (c * i) + (z * t)
	tmp = 0
	if (a * b) <= -2.4e+147:
		tmp = (a * b) + (c * i)
	elif (a * b) <= -1.16e-28:
		tmp = t_1
	elif (a * b) <= -1.45e-97:
		tmp = t_2
	elif (a * b) <= 2e-321:
		tmp = t_1
	elif (a * b) <= 1.3e+132:
		tmp = t_2
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -2.4e+147)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(a * b) <= -1.16e-28)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.45e-97)
		tmp = t_2;
	elseif (Float64(a * b) <= 2e-321)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.3e+132)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * y) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = (c * i) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -2.4e+147)
		tmp = (a * b) + (c * i);
	elseif ((a * b) <= -1.16e-28)
		tmp = t_1;
	elseif ((a * b) <= -1.45e-97)
		tmp = t_2;
	elseif ((a * b) <= 2e-321)
		tmp = t_1;
	elseif ((a * b) <= 1.3e+132)
		tmp = t_2;
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2.4e+147], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.16e-28], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.45e-97], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 2e-321], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.3e+132], t$95$2, N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -2.40000000000000002e147

   1. Initial program 93.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   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 85.4%

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

   5. Simplified 85.4%

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

   if -2.40000000000000002e147 < (*.f64 a b) < -1.1600000000000001e-28 or -1.45e-97 < (*.f64 a b) < 2.00097e-321

   1. Initial program 97.9%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - c \cdot i}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) \cdot \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - \left(c \cdot i\right) \cdot \left(c \cdot i\right)}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) \cdot \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - \left(c \cdot i\right) \cdot \left(c \cdot i\right)}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - c \cdot i}}}\right)\right) \]

      5. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + \color{blue}{c \cdot i}}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \color{blue}{\left(\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\right)}\right)\right) \]

      7. associate-+l+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \left(\left(x \cdot y + \left(z \cdot t + a \cdot b\right)\right) + \color{blue}{c} \cdot i\right)\right)\right) \]

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \color{blue}{\left(c \cdot i\right)}\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 92.7%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(c, \color{blue}{i}\right)\right)\right)\right)\right) \]

   7. Simplified 92.7%

      \[\leadsto \frac{1}{\frac{1}{x \cdot y + \left(z \cdot t + \color{blue}{c \cdot i}\right)}} \]

   8. Taylor expanded in c around 0

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

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

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

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

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

      3. *-lowering-*.f64 73.2%

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

   10. Simplified 73.2%

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

   if -1.1600000000000001e-28 < (*.f64 a b) < -1.45e-97 or 2.00097e-321 < (*.f64 a b) < 1.3e132

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 82.6%

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

   5. Simplified 82.6%

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

   if 1.3e132 < (*.f64 a b)

   1. Initial program 90.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   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 83.6%

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

   5. Simplified 83.6%

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

   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 83.6%

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

   8. Simplified 83.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.4 \cdot 10^{+147}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -1.16 \cdot 10^{-28}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.45 \cdot 10^{-97}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-321}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.3 \cdot 10^{+132}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ t_3 := c \cdot i + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -9.6 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -6.5 \cdot 10^{-97}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-321}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1.55 \cdot 10^{+128}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t)))
        (t_2 (+ (* a b) (* c i)))
        (t_3 (+ (* c i) (* z t))))
   (if (<= (* a b) -9.6e+151)
     t_2
     (if (<= (* a b) -3.4e-27)
       t_1
       (if (<= (* a b) -6.5e-97)
         t_3
         (if (<= (* a b) 2e-321) t_1 (if (<= (* a b) 1.55e+128) t_3 t_2)))))))

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);
	double t_2 = (a * b) + (c * i);
	double t_3 = (c * i) + (z * t);
	double tmp;
	if ((a * b) <= -9.6e+151) {
		tmp = t_2;
	} else if ((a * b) <= -3.4e-27) {
		tmp = t_1;
	} else if ((a * b) <= -6.5e-97) {
		tmp = t_3;
	} else if ((a * b) <= 2e-321) {
		tmp = t_1;
	} else if ((a * b) <= 1.55e+128) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = (a * b) + (c * i)
    t_3 = (c * i) + (z * t)
    if ((a * b) <= (-9.6d+151)) then
        tmp = t_2
    else if ((a * b) <= (-3.4d-27)) then
        tmp = t_1
    else if ((a * b) <= (-6.5d-97)) then
        tmp = t_3
    else if ((a * b) <= 2d-321) then
        tmp = t_1
    else if ((a * b) <= 1.55d+128) then
        tmp = t_3
    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 = (x * y) + (z * t);
	double t_2 = (a * b) + (c * i);
	double t_3 = (c * i) + (z * t);
	double tmp;
	if ((a * b) <= -9.6e+151) {
		tmp = t_2;
	} else if ((a * b) <= -3.4e-27) {
		tmp = t_1;
	} else if ((a * b) <= -6.5e-97) {
		tmp = t_3;
	} else if ((a * b) <= 2e-321) {
		tmp = t_1;
	} else if ((a * b) <= 1.55e+128) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + (c * i)
	t_3 = (c * i) + (z * t)
	tmp = 0
	if (a * b) <= -9.6e+151:
		tmp = t_2
	elif (a * b) <= -3.4e-27:
		tmp = t_1
	elif (a * b) <= -6.5e-97:
		tmp = t_3
	elif (a * b) <= 2e-321:
		tmp = t_1
	elif (a * b) <= 1.55e+128:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	t_3 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -9.6e+151)
		tmp = t_2;
	elseif (Float64(a * b) <= -3.4e-27)
		tmp = t_1;
	elseif (Float64(a * b) <= -6.5e-97)
		tmp = t_3;
	elseif (Float64(a * b) <= 2e-321)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.55e+128)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = (a * b) + (c * i);
	t_3 = (c * i) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -9.6e+151)
		tmp = t_2;
	elseif ((a * b) <= -3.4e-27)
		tmp = t_1;
	elseif ((a * b) <= -6.5e-97)
		tmp = t_3;
	elseif ((a * b) <= 2e-321)
		tmp = t_1;
	elseif ((a * b) <= 1.55e+128)
		tmp = t_3;
	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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -9.6e+151], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -3.4e-27], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -6.5e-97], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 2e-321], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.55e+128], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.6000000000000004e151 or 1.55000000000000002e128 < (*.f64 a b)

   1. Initial program 92.1%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   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 80.4%

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

   5. Simplified 80.4%

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

   if -9.6000000000000004e151 < (*.f64 a b) < -3.3999999999999997e-27 or -6.5000000000000004e-97 < (*.f64 a b) < 2.00097e-321

   1. Initial program 97.9%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - c \cdot i}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) \cdot \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - \left(c \cdot i\right) \cdot \left(c \cdot i\right)}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) \cdot \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - \left(c \cdot i\right) \cdot \left(c \cdot i\right)}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) - c \cdot i}}}\right)\right) \]

      5. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + \color{blue}{c \cdot i}}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \color{blue}{\left(\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\right)}\right)\right) \]

      7. associate-+l+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \left(\left(x \cdot y + \left(z \cdot t + a \cdot b\right)\right) + \color{blue}{c} \cdot i\right)\right)\right) \]

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \color{blue}{\left(c \cdot i\right)}\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 92.7%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(c, \color{blue}{i}\right)\right)\right)\right)\right) \]

   7. Simplified 92.7%

      \[\leadsto \frac{1}{\frac{1}{x \cdot y + \left(z \cdot t + \color{blue}{c \cdot i}\right)}} \]

   8. Taylor expanded in c around 0

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

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

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

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

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

      3. *-lowering-*.f64 73.2%

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

   10. Simplified 73.2%

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

   if -3.3999999999999997e-27 < (*.f64 a b) < -6.5000000000000004e-97 or 2.00097e-321 < (*.f64 a b) < 1.55000000000000002e128

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.6 \cdot 10^{+151}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -6.5 \cdot 10^{-97}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-321}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.55 \cdot 10^{+128}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.18 \cdot 10^{+107}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{+40}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -7 \cdot 10^{-226}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.35 \cdot 10^{-228}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.25 \cdot 10^{+149}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.18e+107)
   (* c i)
   (if (<= (* c i) -5e+40)
     (* x y)
     (if (<= (* c i) -7e-226)
       (* z t)
       (if (<= (* c i) 2.35e-228)
         (* a b)
         (if (<= (* c i) 3.25e+149) (* 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 ((c * i) <= -1.18e+107) {
		tmp = c * i;
	} else if ((c * i) <= -5e+40) {
		tmp = x * y;
	} else if ((c * i) <= -7e-226) {
		tmp = z * t;
	} else if ((c * i) <= 2.35e-228) {
		tmp = a * b;
	} else if ((c * i) <= 3.25e+149) {
		tmp = x * y;
	} 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) <= (-1.18d+107)) then
        tmp = c * i
    else if ((c * i) <= (-5d+40)) then
        tmp = x * y
    else if ((c * i) <= (-7d-226)) then
        tmp = z * t
    else if ((c * i) <= 2.35d-228) then
        tmp = a * b
    else if ((c * i) <= 3.25d+149) then
        tmp = x * y
    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) <= -1.18e+107) {
		tmp = c * i;
	} else if ((c * i) <= -5e+40) {
		tmp = x * y;
	} else if ((c * i) <= -7e-226) {
		tmp = z * t;
	} else if ((c * i) <= 2.35e-228) {
		tmp = a * b;
	} else if ((c * i) <= 3.25e+149) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.18e+107:
		tmp = c * i
	elif (c * i) <= -5e+40:
		tmp = x * y
	elif (c * i) <= -7e-226:
		tmp = z * t
	elif (c * i) <= 2.35e-228:
		tmp = a * b
	elif (c * i) <= 3.25e+149:
		tmp = x * y
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.18e+107)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -5e+40)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -7e-226)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 2.35e-228)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 3.25e+149)
		tmp = Float64(x * y);
	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) <= -1.18e+107)
		tmp = c * i;
	elseif ((c * i) <= -5e+40)
		tmp = x * y;
	elseif ((c * i) <= -7e-226)
		tmp = z * t;
	elseif ((c * i) <= 2.35e-228)
		tmp = a * b;
	elseif ((c * i) <= 3.25e+149)
		tmp = x * y;
	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], -1.18e+107], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -5e+40], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -7e-226], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.35e-228], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.25e+149], N[(x * y), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -1.18000000000000005e107 or 3.25000000000000007e149 < (*.f64 c i)

   1. Initial program 94.0%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 71.7%

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

   5. Simplified 71.7%

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

   if -1.18000000000000005e107 < (*.f64 c i) < -5.00000000000000003e40 or 2.3500000000000001e-228 < (*.f64 c i) < 3.25000000000000007e149

   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 40.9%

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

   5. Simplified 40.9%

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

   if -5.00000000000000003e40 < (*.f64 c i) < -7e-226

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 51.8%

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

   5. Simplified 51.8%

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

   if -7e-226 < (*.f64 c i) < 2.3500000000000001e-228

   1. Initial program 98.1%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 49.5%

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

   5. Simplified 49.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.18 \cdot 10^{+107}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{+40}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -7 \cdot 10^{-226}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.35 \cdot 10^{-228}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.25 \cdot 10^{+149}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+98}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.46 \cdot 10^{-210}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.9 \cdot 10^{-114}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{+137}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4e+98)
   (* c i)
   (if (<= (* c i) -1.46e-210)
     (* z t)
     (if (<= (* c i) 2.9e-114)
       (* a b)
       (if (<= (* c i) 2.7e+137) (* 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) <= -4e+98) {
		tmp = c * i;
	} else if ((c * i) <= -1.46e-210) {
		tmp = z * t;
	} else if ((c * i) <= 2.9e-114) {
		tmp = a * b;
	} else if ((c * i) <= 2.7e+137) {
		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) <= (-4d+98)) then
        tmp = c * i
    else if ((c * i) <= (-1.46d-210)) then
        tmp = z * t
    else if ((c * i) <= 2.9d-114) then
        tmp = a * b
    else if ((c * i) <= 2.7d+137) 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) <= -4e+98) {
		tmp = c * i;
	} else if ((c * i) <= -1.46e-210) {
		tmp = z * t;
	} else if ((c * i) <= 2.9e-114) {
		tmp = a * b;
	} else if ((c * i) <= 2.7e+137) {
		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) <= -4e+98:
		tmp = c * i
	elif (c * i) <= -1.46e-210:
		tmp = z * t
	elif (c * i) <= 2.9e-114:
		tmp = a * b
	elif (c * i) <= 2.7e+137:
		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) <= -4e+98)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.46e-210)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 2.9e-114)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 2.7e+137)
		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) <= -4e+98)
		tmp = c * i;
	elseif ((c * i) <= -1.46e-210)
		tmp = z * t;
	elseif ((c * i) <= 2.9e-114)
		tmp = a * b;
	elseif ((c * i) <= 2.7e+137)
		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], -4e+98], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.46e-210], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.9e-114], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.7e+137], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.99999999999999999e98 or 2.70000000000000017e137 < (*.f64 c i)

   1. Initial program 94.3%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 68.2%

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

   5. Simplified 68.2%

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

   if -3.99999999999999999e98 < (*.f64 c i) < -1.45999999999999994e-210 or 2.89999999999999997e-114 < (*.f64 c i) < 2.70000000000000017e137

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 41.1%

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

   5. Simplified 41.1%

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

   if -1.45999999999999994e-210 < (*.f64 c i) < 2.89999999999999997e-114

   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

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

      1. *-lowering-*.f64 45.0%

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

   5. Simplified 45.0%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+98}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.46 \cdot 10^{-210}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.9 \cdot 10^{-114}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{+137}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -3.4 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 7.4 \cdot 10^{+149}:\\ \;\;\;\;x \cdot y + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* c i) -3.4e+176)
     t_1
     (if (<= (* c i) 7.4e+149) (+ (* 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 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -3.4e+176) {
		tmp = t_1;
	} else if ((c * i) <= 7.4e+149) {
		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 = (c * i) + (z * t)
    if ((c * i) <= (-3.4d+176)) then
        tmp = t_1
    else if ((c * i) <= 7.4d+149) 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 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -3.4e+176) {
		tmp = t_1;
	} else if ((c * i) <= 7.4e+149) {
		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 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -3.4e+176:
		tmp = t_1
	elif (c * i) <= 7.4e+149:
		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(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -3.4e+176)
		tmp = t_1;
	elseif (Float64(c * i) <= 7.4e+149)
		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 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -3.4e+176)
		tmp = t_1;
	elseif ((c * i) <= 7.4e+149)
		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[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.4e+176], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 7.4e+149], 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) < -3.40000000000000014e176 or 7.39999999999999957e149 < (*.f64 c i)

   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 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 85.4%

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

   5. Simplified 85.4%

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

   if -3.40000000000000014e176 < (*.f64 c i) < 7.39999999999999957e149

   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 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 90.3%

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

   5. Simplified 90.3%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.4 \cdot 10^{+176}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7.4 \cdot 10^{+149}:\\ \;\;\;\;x \cdot y + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -3.6 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 9.2 \cdot 10^{+126}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* a b) -3.6e+95)
     t_1
     (if (<= (* a b) 9.2e+126) (+ (* c i) (* 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 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -3.6e+95) {
		tmp = t_1;
	} else if ((a * b) <= 9.2e+126) {
		tmp = (c * i) + (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 = (a * b) + (c * i)
    if ((a * b) <= (-3.6d+95)) then
        tmp = t_1
    else if ((a * b) <= 9.2d+126) then
        tmp = (c * i) + (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 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -3.6e+95) {
		tmp = t_1;
	} else if ((a * b) <= 9.2e+126) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -3.6e+95:
		tmp = t_1
	elif (a * b) <= 9.2e+126:
		tmp = (c * i) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -3.6e+95)
		tmp = t_1;
	elseif (Float64(a * b) <= 9.2e+126)
		tmp = Float64(Float64(c * i) + 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 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -3.6e+95)
		tmp = t_1;
	elseif ((a * b) <= 9.2e+126)
		tmp = (c * i) + (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[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -3.6e+95], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 9.2e+126], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -3.59999999999999978e95 or 9.2000000000000002e126 < (*.f64 a b)

   1. Initial program 92.8%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 77.4%

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

   5. Simplified 77.4%

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

   if -3.59999999999999978e95 < (*.f64 a b) < 9.2000000000000002e126

   1. Initial program 98.2%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   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 70.2%

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

   5. Simplified 70.2%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.6 \cdot 10^{+95}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 9.2 \cdot 10^{+126}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+142}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+247}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5e+142)
   (* x y)
   (if (<= (* x y) 4e+247) (+ (* 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) <= -5e+142) {
		tmp = x * y;
	} else if ((x * y) <= 4e+247) {
		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) <= (-5d+142)) then
        tmp = x * y
    else if ((x * y) <= 4d+247) 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) <= -5e+142) {
		tmp = x * y;
	} else if ((x * y) <= 4e+247) {
		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) <= -5e+142:
		tmp = x * y
	elif (x * y) <= 4e+247:
		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) <= -5e+142)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 4e+247)
		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) <= -5e+142)
		tmp = x * y;
	elseif ((x * y) <= 4e+247)
		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], -5e+142], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+247], 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) < -5.0000000000000001e142 or 3.99999999999999981e247 < (*.f64 x y)

   1. Initial program 88.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 76.1%

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

   5. Simplified 76.1%

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

   if -5.0000000000000001e142 < (*.f64 x y) < 3.99999999999999981e247

   1. Initial program 99.4%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   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 61.3%

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

   5. Simplified 61.3%

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

Alternative 10: 43.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.4 \cdot 10^{+54}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 3.4 \cdot 10^{+130}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -9.4e+54) (* a b) (if (<= (* a b) 3.4e+130) (* c i) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -9.4e+54) {
		tmp = a * b;
	} else if ((a * b) <= 3.4e+130) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	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 ((a * b) <= (-9.4d+54)) then
        tmp = a * b
    else if ((a * b) <= 3.4d+130) then
        tmp = c * i
    else
        tmp = a * b
    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 ((a * b) <= -9.4e+54) {
		tmp = a * b;
	} else if ((a * b) <= 3.4e+130) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -9.4e+54:
		tmp = a * b
	elif (a * b) <= 3.4e+130:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -9.4e+54)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 3.4e+130)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -9.4e+54)
		tmp = a * b;
	elseif ((a * b) <= 3.4e+130)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -9.4e+54], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.4e+130], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.39999999999999985e54 or 3.4000000000000001e130 < (*.f64 a b)

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 63.4%

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

   5. Simplified 63.4%

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

   if -9.39999999999999985e54 < (*.f64 a b) < 3.4000000000000001e130

   1. Initial program 98.2%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 36.6%

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

   5. Simplified 36.6%

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

Alternative 11: 26.9% 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 25.4%

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

5. Simplified 25.4%

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

Reproduce

herbie shell --seed 2024192 
(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)))