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

Percentage Accurate: 96.0% → 97.8%

Time: 12.6s

Alternatives: 14

Speedup: 0.4×

• 40.7% 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: 96.0% 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: 97.8% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* x y) (* z t))))))
   (if (<= t_1 INFINITY) t_1 (fma t z (* 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) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(t, z, (x * y));
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * z + N[(x * y), $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 22.2%

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

   4. Taylor expanded in a around 0 44.4%

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

      1. fma-def 66.7%

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

   6. Simplified 66.7%

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

4. Final simplification 98.8%

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

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-def 97.3%

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

   3. +-commutative 97.3%

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

   4. fma-def 98.0%

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

   5. fma-def 98.0%

      \[\leadsto \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)\right) \]

3. Simplified 98.0%

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

5. Final simplification 98.0%

   \[\leadsto \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right) \]
6. Add Preprocessing

Alternative 3: 66.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := x \cdot y + a \cdot b\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -2.9 \cdot 10^{+59}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -4 \cdot 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 2.6 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 4.8 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 6.8 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t)))
        (t_2 (+ (* x y) (* a b)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* c i) -2.9e+59)
     t_3
     (if (<= (* c i) -2e-18)
       t_1
       (if (<= (* c i) -4e-279)
         t_2
         (if (<= (* c i) 2.6e-227)
           t_1
           (if (<= (* c i) 4.8e-136)
             t_2
             (if (<= (* c i) 6.8e+68) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (a * b);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -2.9e+59) {
		tmp = t_3;
	} else if ((c * i) <= -2e-18) {
		tmp = t_1;
	} else if ((c * i) <= -4e-279) {
		tmp = t_2;
	} else if ((c * i) <= 2.6e-227) {
		tmp = t_1;
	} else if ((c * i) <= 4.8e-136) {
		tmp = t_2;
	} else if ((c * i) <= 6.8e+68) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 = (a * b) + (z * t)
    t_2 = (x * y) + (a * b)
    t_3 = (a * b) + (c * i)
    if ((c * i) <= (-2.9d+59)) then
        tmp = t_3
    else if ((c * i) <= (-2d-18)) then
        tmp = t_1
    else if ((c * i) <= (-4d-279)) then
        tmp = t_2
    else if ((c * i) <= 2.6d-227) then
        tmp = t_1
    else if ((c * i) <= 4.8d-136) then
        tmp = t_2
    else if ((c * i) <= 6.8d+68) then
        tmp = t_1
    else
        tmp = t_3
    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) + (z * t);
	double t_2 = (x * y) + (a * b);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -2.9e+59) {
		tmp = t_3;
	} else if ((c * i) <= -2e-18) {
		tmp = t_1;
	} else if ((c * i) <= -4e-279) {
		tmp = t_2;
	} else if ((c * i) <= 2.6e-227) {
		tmp = t_1;
	} else if ((c * i) <= 4.8e-136) {
		tmp = t_2;
	} else if ((c * i) <= 6.8e+68) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (x * y) + (a * b)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -2.9e+59:
		tmp = t_3
	elif (c * i) <= -2e-18:
		tmp = t_1
	elif (c * i) <= -4e-279:
		tmp = t_2
	elif (c * i) <= 2.6e-227:
		tmp = t_1
	elif (c * i) <= 4.8e-136:
		tmp = t_2
	elif (c * i) <= 6.8e+68:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(a * b))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -2.9e+59)
		tmp = t_3;
	elseif (Float64(c * i) <= -2e-18)
		tmp = t_1;
	elseif (Float64(c * i) <= -4e-279)
		tmp = t_2;
	elseif (Float64(c * i) <= 2.6e-227)
		tmp = t_1;
	elseif (Float64(c * i) <= 4.8e-136)
		tmp = t_2;
	elseif (Float64(c * i) <= 6.8e+68)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (x * y) + (a * b);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -2.9e+59)
		tmp = t_3;
	elseif ((c * i) <= -2e-18)
		tmp = t_1;
	elseif ((c * i) <= -4e-279)
		tmp = t_2;
	elseif ((c * i) <= 2.6e-227)
		tmp = t_1;
	elseif ((c * i) <= 4.8e-136)
		tmp = t_2;
	elseif ((c * i) <= 6.8e+68)
		tmp = t_1;
	else
		tmp = t_3;
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.9e+59], t$95$3, If[LessEqual[N[(c * i), $MachinePrecision], -2e-18], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -4e-279], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 2.6e-227], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 4.8e-136], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 6.8e+68], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.89999999999999991e59 or 6.8000000000000003e68 < (*.f64 c i)

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 84.2%

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

      1. fma-def 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in t around 0 75.9%

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

   if -2.89999999999999991e59 < (*.f64 c i) < -2.0000000000000001e-18 or -4.00000000000000022e-279 < (*.f64 c i) < 2.60000000000000011e-227 or 4.7999999999999997e-136 < (*.f64 c i) < 6.8000000000000003e68

   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 x around 0 81.4%

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

      1. fma-def 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in c around 0 80.7%

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

   if -2.0000000000000001e-18 < (*.f64 c i) < -4.00000000000000022e-279 or 2.60000000000000011e-227 < (*.f64 c i) < 4.7999999999999997e-136

   1. Initial program 96.7%

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

   3. Taylor expanded in c around 0 92.1%

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

   4. Taylor expanded in t around 0 74.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.9 \cdot 10^{+59}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{-18}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -4 \cdot 10^{-279}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.6 \cdot 10^{-227}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.8 \cdot 10^{-136}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 6.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := x \cdot y + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -2.1 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.1 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -9.5 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 3.2 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 6 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* x y) (* a b))))
   (if (<= (* c i) -2.1e+55)
     (+ (* x y) (* c i))
     (if (<= (* c i) -2.1e-18)
       t_1
       (if (<= (* c i) -9.5e-278)
         t_2
         (if (<= (* c i) 6.2e-226)
           t_1
           (if (<= (* c i) 3.2e-136)
             t_2
             (if (<= (* c i) 6e+69) t_1 (+ (* a b) (* c i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((c * i) <= -2.1e+55) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= -2.1e-18) {
		tmp = t_1;
	} else if ((c * i) <= -9.5e-278) {
		tmp = t_2;
	} else if ((c * i) <= 6.2e-226) {
		tmp = t_1;
	} else if ((c * i) <= 3.2e-136) {
		tmp = t_2;
	} else if ((c * i) <= 6e+69) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (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) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (x * y) + (a * b)
    if ((c * i) <= (-2.1d+55)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= (-2.1d-18)) then
        tmp = t_1
    else if ((c * i) <= (-9.5d-278)) then
        tmp = t_2
    else if ((c * i) <= 6.2d-226) then
        tmp = t_1
    else if ((c * i) <= 3.2d-136) then
        tmp = t_2
    else if ((c * i) <= 6d+69) then
        tmp = t_1
    else
        tmp = (a * b) + (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 = (a * b) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((c * i) <= -2.1e+55) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= -2.1e-18) {
		tmp = t_1;
	} else if ((c * i) <= -9.5e-278) {
		tmp = t_2;
	} else if ((c * i) <= 6.2e-226) {
		tmp = t_1;
	} else if ((c * i) <= 3.2e-136) {
		tmp = t_2;
	} else if ((c * i) <= 6e+69) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (x * y) + (a * b)
	tmp = 0
	if (c * i) <= -2.1e+55:
		tmp = (x * y) + (c * i)
	elif (c * i) <= -2.1e-18:
		tmp = t_1
	elif (c * i) <= -9.5e-278:
		tmp = t_2
	elif (c * i) <= 6.2e-226:
		tmp = t_1
	elif (c * i) <= 3.2e-136:
		tmp = t_2
	elif (c * i) <= 6e+69:
		tmp = t_1
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(c * i) <= -2.1e+55)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= -2.1e-18)
		tmp = t_1;
	elseif (Float64(c * i) <= -9.5e-278)
		tmp = t_2;
	elseif (Float64(c * i) <= 6.2e-226)
		tmp = t_1;
	elseif (Float64(c * i) <= 3.2e-136)
		tmp = t_2;
	elseif (Float64(c * i) <= 6e+69)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (x * y) + (a * b);
	tmp = 0.0;
	if ((c * i) <= -2.1e+55)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= -2.1e-18)
		tmp = t_1;
	elseif ((c * i) <= -9.5e-278)
		tmp = t_2;
	elseif ((c * i) <= 6.2e-226)
		tmp = t_1;
	elseif ((c * i) <= 3.2e-136)
		tmp = t_2;
	elseif ((c * i) <= 6e+69)
		tmp = t_1;
	else
		tmp = (a * b) + (c * i);
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.1e+55], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.1e-18], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -9.5e-278], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 6.2e-226], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 3.2e-136], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 6e+69], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -2.1000000000000001e55

   1. Initial program 96.6%

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

   3. Taylor expanded in a around 0 85.0%

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

      1. fma-def 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{c \cdot i + x \cdot y} \]

   if -2.1000000000000001e55 < (*.f64 c i) < -2.1e-18 or -9.49999999999999964e-278 < (*.f64 c i) < 6.19999999999999978e-226 or 3.19999999999999993e-136 < (*.f64 c i) < 5.99999999999999967e69

   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 x around 0 81.4%

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

      1. fma-def 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in c around 0 80.7%

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

   if -2.1e-18 < (*.f64 c i) < -9.49999999999999964e-278 or 6.19999999999999978e-226 < (*.f64 c i) < 3.19999999999999993e-136

   1. Initial program 96.7%

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

   3. Taylor expanded in c around 0 92.1%

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

   4. Taylor expanded in t around 0 74.2%

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

   if 5.99999999999999967e69 < (*.f64 c i)

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0 83.6%

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

      1. fma-def 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in t around 0 71.0%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.1 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.1 \cdot 10^{-18}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -9.5 \cdot 10^{-278}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-226}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.2 \cdot 10^{-136}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 6 \cdot 10^{+69}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -1.6 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -2.3 \cdot 10^{-162}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.4 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -1.6e+56)
     t_2
     (if (<= (* c i) -1.8e-101)
       t_1
       (if (<= (* c i) -2.3e-162)
         (* x y)
         (if (<= (* c i) 2.4e+69) 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 = (a * b) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.6e+56) {
		tmp = t_2;
	} else if ((c * i) <= -1.8e-101) {
		tmp = t_1;
	} else if ((c * i) <= -2.3e-162) {
		tmp = x * y;
	} else if ((c * i) <= 2.4e+69) {
		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 = (a * b) + (z * t)
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-1.6d+56)) then
        tmp = t_2
    else if ((c * i) <= (-1.8d-101)) then
        tmp = t_1
    else if ((c * i) <= (-2.3d-162)) then
        tmp = x * y
    else if ((c * i) <= 2.4d+69) 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 = (a * b) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.6e+56) {
		tmp = t_2;
	} else if ((c * i) <= -1.8e-101) {
		tmp = t_1;
	} else if ((c * i) <= -2.3e-162) {
		tmp = x * y;
	} else if ((c * i) <= 2.4e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -1.6e+56:
		tmp = t_2
	elif (c * i) <= -1.8e-101:
		tmp = t_1
	elif (c * i) <= -2.3e-162:
		tmp = x * y
	elif (c * i) <= 2.4e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -1.6e+56)
		tmp = t_2;
	elseif (Float64(c * i) <= -1.8e-101)
		tmp = t_1;
	elseif (Float64(c * i) <= -2.3e-162)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 2.4e+69)
		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 = (a * b) + (z * t);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -1.6e+56)
		tmp = t_2;
	elseif ((c * i) <= -1.8e-101)
		tmp = t_1;
	elseif ((c * i) <= -2.3e-162)
		tmp = x * y;
	elseif ((c * i) <= 2.4e+69)
		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[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.6e+56], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -1.8e-101], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -2.3e-162], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.4e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.60000000000000002e56 or 2.4000000000000002e69 < (*.f64 c i)

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 84.2%

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

      1. fma-def 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in t around 0 75.9%

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

   if -1.60000000000000002e56 < (*.f64 c i) < -1.8e-101 or -2.2999999999999998e-162 < (*.f64 c i) < 2.4000000000000002e69

   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 x around 0 74.3%

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

      1. fma-def 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in c around 0 72.6%

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

   if -1.8e-101 < (*.f64 c i) < -2.2999999999999998e-162

   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 x around inf 74.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.6 \cdot 10^{+56}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -2.3 \cdot 10^{-162}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.4 \cdot 10^{+69}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1.45 \cdot 10^{+57}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 1.75 \cdot 10^{-197}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* c i) -1.45e+57)
     (+ (* x y) (* c i))
     (if (<= (* c i) -2.2e-20)
       t_1
       (if (<= (* c i) 1.75e-197)
         (+ (* x y) (* z t))
         (if (<= (* c i) 7e+69) t_1 (+ (* a b) (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -1.45e+57) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= -2.2e-20) {
		tmp = t_1;
	} else if ((c * i) <= 1.75e-197) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 7e+69) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (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 = (a * b) + (z * t)
    if ((c * i) <= (-1.45d+57)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= (-2.2d-20)) then
        tmp = t_1
    else if ((c * i) <= 1.75d-197) then
        tmp = (x * y) + (z * t)
    else if ((c * i) <= 7d+69) then
        tmp = t_1
    else
        tmp = (a * b) + (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 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -1.45e+57) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= -2.2e-20) {
		tmp = t_1;
	} else if ((c * i) <= 1.75e-197) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 7e+69) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (c * i) <= -1.45e+57:
		tmp = (x * y) + (c * i)
	elif (c * i) <= -2.2e-20:
		tmp = t_1
	elif (c * i) <= 1.75e-197:
		tmp = (x * y) + (z * t)
	elif (c * i) <= 7e+69:
		tmp = t_1
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -1.45e+57)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= -2.2e-20)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.75e-197)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(c * i) <= 7e+69)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -1.45e+57)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= -2.2e-20)
		tmp = t_1;
	elseif ((c * i) <= 1.75e-197)
		tmp = (x * y) + (z * t);
	elseif ((c * i) <= 7e+69)
		tmp = t_1;
	else
		tmp = (a * b) + (c * i);
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.45e+57], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.2e-20], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.75e-197], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7e+69], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -1.4500000000000001e57

   1. Initial program 96.6%

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

   3. Taylor expanded in a around 0 85.0%

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

      1. fma-def 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{c \cdot i + x \cdot y} \]

   if -1.4500000000000001e57 < (*.f64 c i) < -2.19999999999999991e-20 or 1.7499999999999999e-197 < (*.f64 c i) < 6.99999999999999974e69

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 84.9%

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

      1. fma-def 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in c around 0 84.0%

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

   if -2.19999999999999991e-20 < (*.f64 c i) < 1.7499999999999999e-197

   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 c around 0 95.7%

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

   4. Taylor expanded in a around 0 73.5%

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

   if 6.99999999999999974e69 < (*.f64 c i)

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0 83.6%

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

      1. fma-def 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in t around 0 71.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.45 \cdot 10^{+57}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.2 \cdot 10^{-20}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.75 \cdot 10^{-197}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{+69}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.1% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* x y) (* z t))))))
   (if (<= t_1 INFINITY) 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) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	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 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)))
	tmp = 0
	if t_1 <= math.inf:
		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(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t))))
	tmp = 0.0
	if (t_1 <= Inf)
		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) + ((a * b) + ((x * y) + (z * t)));
	tmp = 0.0;
	if (t_1 <= Inf)
		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[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * y), $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 x around inf 55.9%

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

4. Final simplification 98.4%

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

Alternative 8: 42.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+80}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -3 \cdot 10^{-194}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{-54}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+176}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.15e+80)
   (* a b)
   (if (<= (* a b) -3e-194)
     (* z t)
     (if (<= (* a b) 2.3e-54)
       (* c i)
       (if (<= (* a b) 3.8e+176) (* x y) (* 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) <= -1.15e+80) {
		tmp = a * b;
	} else if ((a * b) <= -3e-194) {
		tmp = z * t;
	} else if ((a * b) <= 2.3e-54) {
		tmp = c * i;
	} else if ((a * b) <= 3.8e+176) {
		tmp = x * y;
	} 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) <= (-1.15d+80)) then
        tmp = a * b
    else if ((a * b) <= (-3d-194)) then
        tmp = z * t
    else if ((a * b) <= 2.3d-54) then
        tmp = c * i
    else if ((a * b) <= 3.8d+176) then
        tmp = x * y
    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) <= -1.15e+80) {
		tmp = a * b;
	} else if ((a * b) <= -3e-194) {
		tmp = z * t;
	} else if ((a * b) <= 2.3e-54) {
		tmp = c * i;
	} else if ((a * b) <= 3.8e+176) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.15e+80:
		tmp = a * b
	elif (a * b) <= -3e-194:
		tmp = z * t
	elif (a * b) <= 2.3e-54:
		tmp = c * i
	elif (a * b) <= 3.8e+176:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.15e+80)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -3e-194)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.3e-54)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 3.8e+176)
		tmp = Float64(x * y);
	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) <= -1.15e+80)
		tmp = a * b;
	elseif ((a * b) <= -3e-194)
		tmp = z * t;
	elseif ((a * b) <= 2.3e-54)
		tmp = c * i;
	elseif ((a * b) <= 3.8e+176)
		tmp = x * y;
	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], -1.15e+80], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -3e-194], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.3e-54], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.8e+176], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.15000000000000002e80 or 3.8000000000000003e176 < (*.f64 a b)

   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 a around inf 79.2%

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

   if -1.15000000000000002e80 < (*.f64 a b) < -3e-194

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 38.5%

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

   if -3e-194 < (*.f64 a b) < 2.2999999999999999e-54

   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 c around inf 46.0%

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

   if 2.2999999999999999e-54 < (*.f64 a b) < 3.8000000000000003e176

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf 43.3%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+80}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -3 \cdot 10^{-194}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{-54}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+176}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.5 \cdot 10^{+142} \lor \neg \left(c \cdot i \leq 2.5 \cdot 10^{+184}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.5e+142) (not (<= (* c i) 2.5e+184)))
   (+ (* a b) (* c i))
   (+ (* a b) (+ (* x y) (* z t)))))

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+142) || !((c * i) <= 2.5e+184)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	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+142)) .or. (.not. ((c * i) <= 2.5d+184))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (a * b) + ((x * y) + (z * t))
    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+142) || !((c * i) <= 2.5e+184)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -3.5e+142) or not ((c * i) <= 2.5e+184):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -3.5e+142) || !(Float64(c * i) <= 2.5e+184))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	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+142) || ~(((c * i) <= 2.5e+184)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.5e+142], N[Not[LessEqual[N[(c * i), $MachinePrecision], 2.5e+184]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.49999999999999997e142 or 2.4999999999999999e184 < (*.f64 c i)

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0 89.2%

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

      1. fma-def 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in t around 0 84.1%

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

   if -3.49999999999999997e142 < (*.f64 c i) < 2.4999999999999999e184

   1. Initial program 98.3%

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

   3. Taylor expanded in c around 0 90.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.5 \cdot 10^{+142} \lor \neg \left(c \cdot i \leq 2.5 \cdot 10^{+184}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+59} \lor \neg \left(c \cdot i \leq 5.8 \cdot 10^{+69}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.8e+59) (not (<= (* c i) 5.8e+69)))
   (+ (* c i) (+ (* x y) (* a b)))
   (+ (* a b) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.8e+59) || !((c * i) <= 5.8e+69)) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	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) <= (-3.8d+59)) .or. (.not. ((c * i) <= 5.8d+69))) then
        tmp = (c * i) + ((x * y) + (a * b))
    else
        tmp = (a * b) + ((x * y) + (z * t))
    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) <= -3.8e+59) || !((c * i) <= 5.8e+69)) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -3.8e+59) or not ((c * i) <= 5.8e+69):
		tmp = (c * i) + ((x * y) + (a * b))
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -3.8e+59) || !(Float64(c * i) <= 5.8e+69))
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -3.8e+59) || ~(((c * i) <= 5.8e+69)))
		tmp = (c * i) + ((x * y) + (a * b));
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.8e+59], N[Not[LessEqual[N[(c * i), $MachinePrecision], 5.8e+69]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.8000000000000001e59 or 5.7999999999999997e69 < (*.f64 c i)

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 87.4%

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

   if -3.8000000000000001e59 < (*.f64 c i) < 5.7999999999999997e69

   1. Initial program 98.7%

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

   3. Taylor expanded in c around 0 96.1%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+59} \lor \neg \left(c \cdot i \leq 5.8 \cdot 10^{+69}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.1 \cdot 10^{+81}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.3 \cdot 10^{-193}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.05 \cdot 10^{+93}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -2.1e+81)
   (* a b)
   (if (<= (* a b) -1.3e-193)
     (* z t)
     (if (<= (* a b) 1.05e+93) (* 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) <= -2.1e+81) {
		tmp = a * b;
	} else if ((a * b) <= -1.3e-193) {
		tmp = z * t;
	} else if ((a * b) <= 1.05e+93) {
		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) <= (-2.1d+81)) then
        tmp = a * b
    else if ((a * b) <= (-1.3d-193)) then
        tmp = z * t
    else if ((a * b) <= 1.05d+93) 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) <= -2.1e+81) {
		tmp = a * b;
	} else if ((a * b) <= -1.3e-193) {
		tmp = z * t;
	} else if ((a * b) <= 1.05e+93) {
		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) <= -2.1e+81:
		tmp = a * b
	elif (a * b) <= -1.3e-193:
		tmp = z * t
	elif (a * b) <= 1.05e+93:
		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) <= -2.1e+81)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.3e-193)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.05e+93)
		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) <= -2.1e+81)
		tmp = a * b;
	elseif ((a * b) <= -1.3e-193)
		tmp = z * t;
	elseif ((a * b) <= 1.05e+93)
		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], -2.1e+81], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.3e-193], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.05e+93], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0999999999999999e81 or 1.0499999999999999e93 < (*.f64 a b)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around inf 69.8%

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

   if -2.0999999999999999e81 < (*.f64 a b) < -1.30000000000000004e-193

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 38.5%

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

   if -1.30000000000000004e-193 < (*.f64 a b) < 1.0499999999999999e93

   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 c around inf 41.2%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.1 \cdot 10^{+81}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.3 \cdot 10^{-193}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.05 \cdot 10^{+93}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.1 \cdot 10^{+155} \lor \neg \left(x \cdot y \leq 2.7 \cdot 10^{+196}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -3.1e+155) (not (<= (* x y) 2.7e+196)))
   (* x y)
   (+ (* 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 (((x * y) <= -3.1e+155) || !((x * y) <= 2.7e+196)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (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) <= (-3.1d+155)) .or. (.not. ((x * y) <= 2.7d+196))) then
        tmp = x * y
    else
        tmp = (a * b) + (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) <= -3.1e+155) || !((x * y) <= 2.7e+196)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -3.1e+155) or not ((x * y) <= 2.7e+196):
		tmp = x * y
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -3.1e+155) || !(Float64(x * y) <= 2.7e+196))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + 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) <= -3.1e+155) || ~(((x * y) <= 2.7e+196)))
		tmp = x * y;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.1e+155], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.7e+196]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.09999999999999989e155 or 2.69999999999999995e196 < (*.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf 81.2%

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

   if -3.09999999999999989e155 < (*.f64 x y) < 2.69999999999999995e196

   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 x around 0 91.2%

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

      1. fma-def 91.2%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in t around 0 63.8%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.1 \cdot 10^{+155} \lor \neg \left(x \cdot y \leq 2.7 \cdot 10^{+196}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.6 \cdot 10^{+79} \lor \neg \left(a \cdot b \leq 8.5 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.6e+79) (not (<= (* a b) 8.5e+95))) (* 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 (((a * b) <= -1.6e+79) || !((a * b) <= 8.5e+95)) {
		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 (((a * b) <= (-1.6d+79)) .or. (.not. ((a * b) <= 8.5d+95))) 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 (((a * b) <= -1.6e+79) || !((a * b) <= 8.5e+95)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -1.6e+79) or not ((a * b) <= 8.5e+95):
		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(a * b) <= -1.6e+79) || !(Float64(a * b) <= 8.5e+95))
		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 (((a * b) <= -1.6e+79) || ~(((a * b) <= 8.5e+95)))
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.6e+79], N[Not[LessEqual[N[(a * b), $MachinePrecision], 8.5e+95]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.60000000000000001e79 or 8.5000000000000002e95 < (*.f64 a b)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around inf 69.8%

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

   if -1.60000000000000001e79 < (*.f64 a b) < 8.5000000000000002e95

   1. Initial program 97.0%

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

   3. Taylor expanded in c around inf 37.1%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.6 \cdot 10^{+79} \lor \neg \left(a \cdot b \leq 8.5 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.3% 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 28.0%

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

4. Final simplification 28.0%

   \[\leadsto a \cdot b \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(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)))