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

Percentage Accurate: 95.8% → 98.5%

Time: 12.5s

Alternatives: 13

Speedup: 0.4×

• 41.9% 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: 95.8% 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: 98.5% accurate, 0.4× speedup

Math

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

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 (+ (* a (/ b z)) (* 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 + ((a * (b / z)) + (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 + ((a * (b / z)) + (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 + ((a * (b / z)) + (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(a * Float64(b / z)) + Float64(c * Float64(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 + ((a * (b / z)) + (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[(a * N[(b / z), $MachinePrecision]), $MachinePrecision] + N[(c * N[(i / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 38.5%

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

   4. Taylor expanded in z around inf 61.5%

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

      1. associate-/l* 61.5%

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

      2. associate-/l* 84.6%

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

   6. Simplified 84.6%

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

4. Final simplification 99.2%

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

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-define 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-define 97.6%

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

   5. fma-define 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 62.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ t_3 := x \cdot y + c \cdot i\\ t_4 := z \cdot \left(t + \frac{a \cdot b}{z}\right)\\ \mathbf{if}\;a \cdot b \leq -2.45 \cdot 10^{+120}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-76}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1.35 \cdot 10^{-153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 3.9 \cdot 10^{-95}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 3.5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t)))
        (t_2 (* z (+ t (/ (* x y) z))))
        (t_3 (+ (* x y) (* c i)))
        (t_4 (* z (+ t (/ (* a b) z)))))
   (if (<= (* a b) -2.45e+120)
     t_4
     (if (<= (* a b) -1e-76)
       t_3
       (if (<= (* a b) 6.2e-232)
         t_1
         (if (<= (* a b) 1.35e-153)
           t_2
           (if (<= (* a b) 3.9e-95)
             t_3
             (if (<= (* a b) 1.7e-33)
               t_2
               (if (<= (* a b) 3.5e+100) t_1 t_4)))))))))

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 = z * (t + ((x * y) / z));
	double t_3 = (x * y) + (c * i);
	double t_4 = z * (t + ((a * b) / z));
	double tmp;
	if ((a * b) <= -2.45e+120) {
		tmp = t_4;
	} else if ((a * b) <= -1e-76) {
		tmp = t_3;
	} else if ((a * b) <= 6.2e-232) {
		tmp = t_1;
	} else if ((a * b) <= 1.35e-153) {
		tmp = t_2;
	} else if ((a * b) <= 3.9e-95) {
		tmp = t_3;
	} else if ((a * b) <= 1.7e-33) {
		tmp = t_2;
	} else if ((a * b) <= 3.5e+100) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = z * (t + ((x * y) / z))
    t_3 = (x * y) + (c * i)
    t_4 = z * (t + ((a * b) / z))
    if ((a * b) <= (-2.45d+120)) then
        tmp = t_4
    else if ((a * b) <= (-1d-76)) then
        tmp = t_3
    else if ((a * b) <= 6.2d-232) then
        tmp = t_1
    else if ((a * b) <= 1.35d-153) then
        tmp = t_2
    else if ((a * b) <= 3.9d-95) then
        tmp = t_3
    else if ((a * b) <= 1.7d-33) then
        tmp = t_2
    else if ((a * b) <= 3.5d+100) then
        tmp = t_1
    else
        tmp = t_4
    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 = z * (t + ((x * y) / z));
	double t_3 = (x * y) + (c * i);
	double t_4 = z * (t + ((a * b) / z));
	double tmp;
	if ((a * b) <= -2.45e+120) {
		tmp = t_4;
	} else if ((a * b) <= -1e-76) {
		tmp = t_3;
	} else if ((a * b) <= 6.2e-232) {
		tmp = t_1;
	} else if ((a * b) <= 1.35e-153) {
		tmp = t_2;
	} else if ((a * b) <= 3.9e-95) {
		tmp = t_3;
	} else if ((a * b) <= 1.7e-33) {
		tmp = t_2;
	} else if ((a * b) <= 3.5e+100) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = z * (t + ((x * y) / z))
	t_3 = (x * y) + (c * i)
	t_4 = z * (t + ((a * b) / z))
	tmp = 0
	if (a * b) <= -2.45e+120:
		tmp = t_4
	elif (a * b) <= -1e-76:
		tmp = t_3
	elif (a * b) <= 6.2e-232:
		tmp = t_1
	elif (a * b) <= 1.35e-153:
		tmp = t_2
	elif (a * b) <= 3.9e-95:
		tmp = t_3
	elif (a * b) <= 1.7e-33:
		tmp = t_2
	elif (a * b) <= 3.5e+100:
		tmp = t_1
	else:
		tmp = t_4
	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(z * Float64(t + Float64(Float64(x * y) / z)))
	t_3 = Float64(Float64(x * y) + Float64(c * i))
	t_4 = Float64(z * Float64(t + Float64(Float64(a * b) / z)))
	tmp = 0.0
	if (Float64(a * b) <= -2.45e+120)
		tmp = t_4;
	elseif (Float64(a * b) <= -1e-76)
		tmp = t_3;
	elseif (Float64(a * b) <= 6.2e-232)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.35e-153)
		tmp = t_2;
	elseif (Float64(a * b) <= 3.9e-95)
		tmp = t_3;
	elseif (Float64(a * b) <= 1.7e-33)
		tmp = t_2;
	elseif (Float64(a * b) <= 3.5e+100)
		tmp = t_1;
	else
		tmp = t_4;
	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 = z * (t + ((x * y) / z));
	t_3 = (x * y) + (c * i);
	t_4 = z * (t + ((a * b) / z));
	tmp = 0.0;
	if ((a * b) <= -2.45e+120)
		tmp = t_4;
	elseif ((a * b) <= -1e-76)
		tmp = t_3;
	elseif ((a * b) <= 6.2e-232)
		tmp = t_1;
	elseif ((a * b) <= 1.35e-153)
		tmp = t_2;
	elseif ((a * b) <= 3.9e-95)
		tmp = t_3;
	elseif ((a * b) <= 1.7e-33)
		tmp = t_2;
	elseif ((a * b) <= 3.5e+100)
		tmp = t_1;
	else
		tmp = t_4;
	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[(z * N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t + N[(N[(a * b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2.45e+120], t$95$4, If[LessEqual[N[(a * b), $MachinePrecision], -1e-76], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 6.2e-232], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.35e-153], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 3.9e-95], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 1.7e-33], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 3.5e+100], t$95$1, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -2.45000000000000005e120 or 3.49999999999999976e100 < (*.f64 a b)

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0 84.3%

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

   4. Taylor expanded in z around inf 77.9%

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

   5. Taylor expanded in c around 0 80.7%

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

   if -2.45000000000000005e120 < (*.f64 a b) < -9.99999999999999927e-77 or 1.35000000000000005e-153 < (*.f64 a b) < 3.9e-95

   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 78.6%

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

   if -9.99999999999999927e-77 < (*.f64 a b) < 6.1999999999999998e-232 or 1.7e-33 < (*.f64 a b) < 3.49999999999999976e100

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 74.2%

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

   if 6.1999999999999998e-232 < (*.f64 a b) < 1.35000000000000005e-153 or 3.9e-95 < (*.f64 a b) < 1.7e-33

   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 z around inf 90.2%

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

   4. Taylor expanded in a around 0 90.2%

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

   5. Taylor expanded in c around 0 82.2%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.45 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \left(t + \frac{a \cdot b}{z}\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-76}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.35 \cdot 10^{-153}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \mathbf{elif}\;a \cdot b \leq 3.9 \cdot 10^{-95}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \mathbf{elif}\;a \cdot b \leq 3.5 \cdot 10^{+100}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \frac{a \cdot b}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := x \cdot y + c \cdot i\\ t_3 := z \cdot \left(t + \frac{a \cdot b}{z}\right)\\ \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+120}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq -7 \cdot 10^{-89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 1.08 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 3.9 \cdot 10^{-73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t)))
        (t_2 (+ (* x y) (* c i)))
        (t_3 (* z (+ t (/ (* a b) z)))))
   (if (<= (* a b) -3e+120)
     t_3
     (if (<= (* a b) -7e-89)
       t_2
       (if (<= (* a b) 1.08e-215)
         t_1
         (if (<= (* a b) 3.9e-73) t_2 (if (<= (* a b) 2.5e+101) 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 = (c * i) + (z * t);
	double t_2 = (x * y) + (c * i);
	double t_3 = z * (t + ((a * b) / z));
	double tmp;
	if ((a * b) <= -3e+120) {
		tmp = t_3;
	} else if ((a * b) <= -7e-89) {
		tmp = t_2;
	} else if ((a * b) <= 1.08e-215) {
		tmp = t_1;
	} else if ((a * b) <= 3.9e-73) {
		tmp = t_2;
	} else if ((a * b) <= 2.5e+101) {
		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 = (c * i) + (z * t)
    t_2 = (x * y) + (c * i)
    t_3 = z * (t + ((a * b) / z))
    if ((a * b) <= (-3d+120)) then
        tmp = t_3
    else if ((a * b) <= (-7d-89)) then
        tmp = t_2
    else if ((a * b) <= 1.08d-215) then
        tmp = t_1
    else if ((a * b) <= 3.9d-73) then
        tmp = t_2
    else if ((a * b) <= 2.5d+101) 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 = (c * i) + (z * t);
	double t_2 = (x * y) + (c * i);
	double t_3 = z * (t + ((a * b) / z));
	double tmp;
	if ((a * b) <= -3e+120) {
		tmp = t_3;
	} else if ((a * b) <= -7e-89) {
		tmp = t_2;
	} else if ((a * b) <= 1.08e-215) {
		tmp = t_1;
	} else if ((a * b) <= 3.9e-73) {
		tmp = t_2;
	} else if ((a * b) <= 2.5e+101) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (x * y) + (c * i)
	t_3 = z * (t + ((a * b) / z))
	tmp = 0
	if (a * b) <= -3e+120:
		tmp = t_3
	elif (a * b) <= -7e-89:
		tmp = t_2
	elif (a * b) <= 1.08e-215:
		tmp = t_1
	elif (a * b) <= 3.9e-73:
		tmp = t_2
	elif (a * b) <= 2.5e+101:
		tmp = t_1
	else:
		tmp = t_3
	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(c * i))
	t_3 = Float64(z * Float64(t + Float64(Float64(a * b) / z)))
	tmp = 0.0
	if (Float64(a * b) <= -3e+120)
		tmp = t_3;
	elseif (Float64(a * b) <= -7e-89)
		tmp = t_2;
	elseif (Float64(a * b) <= 1.08e-215)
		tmp = t_1;
	elseif (Float64(a * b) <= 3.9e-73)
		tmp = t_2;
	elseif (Float64(a * b) <= 2.5e+101)
		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 = (c * i) + (z * t);
	t_2 = (x * y) + (c * i);
	t_3 = z * (t + ((a * b) / z));
	tmp = 0.0;
	if ((a * b) <= -3e+120)
		tmp = t_3;
	elseif ((a * b) <= -7e-89)
		tmp = t_2;
	elseif ((a * b) <= 1.08e-215)
		tmp = t_1;
	elseif ((a * b) <= 3.9e-73)
		tmp = t_2;
	elseif ((a * b) <= 2.5e+101)
		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[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t + N[(N[(a * b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -3e+120], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -7e-89], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 1.08e-215], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 3.9e-73], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 2.5e+101], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3e120 or 2.49999999999999994e101 < (*.f64 a b)

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0 84.3%

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

   4. Taylor expanded in z around inf 77.9%

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

   5. Taylor expanded in c around 0 80.7%

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

   if -3e120 < (*.f64 a b) < -6.9999999999999994e-89 or 1.08e-215 < (*.f64 a b) < 3.89999999999999982e-73

   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 75.0%

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

   if -6.9999999999999994e-89 < (*.f64 a b) < 1.08e-215 or 3.89999999999999982e-73 < (*.f64 a b) < 2.49999999999999994e101

   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 z around inf 74.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \left(t + \frac{a \cdot b}{z}\right)\\ \mathbf{elif}\;a \cdot b \leq -7 \cdot 10^{-89}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.08 \cdot 10^{-215}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.9 \cdot 10^{-73}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \frac{a \cdot b}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c \cdot i\\ t_2 := c \cdot i + z \cdot t\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -2.55 \cdot 10^{+120}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq -5.5 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 3.2 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 5.8 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1.4 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* c i)))
        (t_2 (+ (* c i) (* z t)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* a b) -2.55e+120)
     t_3
     (if (<= (* a b) -5.5e-77)
       t_1
       (if (<= (* a b) 3.2e-209)
         t_2
         (if (<= (* a b) 5.8e-72) t_1 (if (<= (* a b) 1.4e+130) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double t_2 = (c * i) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -2.55e+120) {
		tmp = t_3;
	} else if ((a * b) <= -5.5e-77) {
		tmp = t_1;
	} else if ((a * b) <= 3.2e-209) {
		tmp = t_2;
	} else if ((a * b) <= 5.8e-72) {
		tmp = t_1;
	} else if ((a * b) <= 1.4e+130) {
		tmp = t_2;
	} 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 = (x * y) + (c * i)
    t_2 = (c * i) + (z * t)
    t_3 = (a * b) + (c * i)
    if ((a * b) <= (-2.55d+120)) then
        tmp = t_3
    else if ((a * b) <= (-5.5d-77)) then
        tmp = t_1
    else if ((a * b) <= 3.2d-209) then
        tmp = t_2
    else if ((a * b) <= 5.8d-72) then
        tmp = t_1
    else if ((a * b) <= 1.4d+130) then
        tmp = t_2
    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 = (x * y) + (c * i);
	double t_2 = (c * i) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -2.55e+120) {
		tmp = t_3;
	} else if ((a * b) <= -5.5e-77) {
		tmp = t_1;
	} else if ((a * b) <= 3.2e-209) {
		tmp = t_2;
	} else if ((a * b) <= 5.8e-72) {
		tmp = t_1;
	} else if ((a * b) <= 1.4e+130) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (c * i)
	t_2 = (c * i) + (z * t)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -2.55e+120:
		tmp = t_3
	elif (a * b) <= -5.5e-77:
		tmp = t_1
	elif (a * b) <= 3.2e-209:
		tmp = t_2
	elif (a * b) <= 5.8e-72:
		tmp = t_1
	elif (a * b) <= 1.4e+130:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(c * i))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -2.55e+120)
		tmp = t_3;
	elseif (Float64(a * b) <= -5.5e-77)
		tmp = t_1;
	elseif (Float64(a * b) <= 3.2e-209)
		tmp = t_2;
	elseif (Float64(a * b) <= 5.8e-72)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.4e+130)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (c * i);
	t_2 = (c * i) + (z * t);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -2.55e+120)
		tmp = t_3;
	elseif ((a * b) <= -5.5e-77)
		tmp = t_1;
	elseif ((a * b) <= 3.2e-209)
		tmp = t_2;
	elseif ((a * b) <= 5.8e-72)
		tmp = t_1;
	elseif ((a * b) <= 1.4e+130)
		tmp = t_2;
	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[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2.55e+120], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -5.5e-77], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 3.2e-209], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 5.8e-72], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.4e+130], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.55000000000000014e120 or 1.3999999999999999e130 < (*.f64 a b)

   1. Initial program 85.9%

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

   3. Taylor expanded in a around inf 78.1%

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

   if -2.55000000000000014e120 < (*.f64 a b) < -5.49999999999999998e-77 or 3.2000000000000001e-209 < (*.f64 a b) < 5.79999999999999995e-72

   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 75.0%

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

   if -5.49999999999999998e-77 < (*.f64 a b) < 3.2000000000000001e-209 or 5.79999999999999995e-72 < (*.f64 a b) < 1.3999999999999999e130

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 73.7%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.55 \cdot 10^{+120}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -5.5 \cdot 10^{-77}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.2 \cdot 10^{-209}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.8 \cdot 10^{-72}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.4 \cdot 10^{+130}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+89}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 10^{-94}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1e+89)
   (* c i)
   (if (<= (* c i) -5e-38)
     (* x y)
     (if (<= (* c i) 1e-94) (* z t) (if (<= (* c i) 5e-7) (* 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) <= -1e+89) {
		tmp = c * i;
	} else if ((c * i) <= -5e-38) {
		tmp = x * y;
	} else if ((c * i) <= 1e-94) {
		tmp = z * t;
	} else if ((c * i) <= 5e-7) {
		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) <= (-1d+89)) then
        tmp = c * i
    else if ((c * i) <= (-5d-38)) then
        tmp = x * y
    else if ((c * i) <= 1d-94) then
        tmp = z * t
    else if ((c * i) <= 5d-7) 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) <= -1e+89) {
		tmp = c * i;
	} else if ((c * i) <= -5e-38) {
		tmp = x * y;
	} else if ((c * i) <= 1e-94) {
		tmp = z * t;
	} else if ((c * i) <= 5e-7) {
		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) <= -1e+89:
		tmp = c * i
	elif (c * i) <= -5e-38:
		tmp = x * y
	elif (c * i) <= 1e-94:
		tmp = z * t
	elif (c * i) <= 5e-7:
		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) <= -1e+89)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -5e-38)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 1e-94)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 5e-7)
		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) <= -1e+89)
		tmp = c * i;
	elseif ((c * i) <= -5e-38)
		tmp = x * y;
	elseif ((c * i) <= 1e-94)
		tmp = z * t;
	elseif ((c * i) <= 5e-7)
		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], -1e+89], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -5e-38], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e-94], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e-7], N[(x * y), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -9.99999999999999995e88 or 4.99999999999999977e-7 < (*.f64 c i)

   1. Initial program 93.3%

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

   3. Taylor expanded in c around inf 56.6%

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

   if -9.99999999999999995e88 < (*.f64 c i) < -5.00000000000000033e-38 or 9.9999999999999996e-95 < (*.f64 c i) < 4.99999999999999977e-7

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 87.7%

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

   4. Taylor expanded in a around 0 76.0%

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

   5. Taylor expanded in x around inf 49.3%

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

   if -5.00000000000000033e-38 < (*.f64 c i) < 9.9999999999999996e-95

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 86.8%

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

   4. Taylor expanded in a around 0 66.2%

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

   5. Taylor expanded in z around inf 45.7%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+89}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 10^{-94}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{+239}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= z -3.05e+239)
     (* z t)
     (if (<= z -5.5e-17)
       t_1
       (if (<= z -4.5e-36) (* x y) (if (<= z 8.8e-51) t_1 (* z t)))))))

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 (z <= -3.05e+239) {
		tmp = z * t;
	} else if (z <= -5.5e-17) {
		tmp = t_1;
	} else if (z <= -4.5e-36) {
		tmp = x * y;
	} else if (z <= 8.8e-51) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if (z <= (-3.05d+239)) then
        tmp = z * t
    else if (z <= (-5.5d-17)) then
        tmp = t_1
    else if (z <= (-4.5d-36)) then
        tmp = x * y
    else if (z <= 8.8d-51) then
        tmp = t_1
    else
        tmp = 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 t_1 = (a * b) + (c * i);
	double tmp;
	if (z <= -3.05e+239) {
		tmp = z * t;
	} else if (z <= -5.5e-17) {
		tmp = t_1;
	} else if (z <= -4.5e-36) {
		tmp = x * y;
	} else if (z <= 8.8e-51) {
		tmp = t_1;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if z <= -3.05e+239:
		tmp = z * t
	elif z <= -5.5e-17:
		tmp = t_1
	elif z <= -4.5e-36:
		tmp = x * y
	elif z <= 8.8e-51:
		tmp = t_1
	else:
		tmp = z * t
	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 (z <= -3.05e+239)
		tmp = Float64(z * t);
	elseif (z <= -5.5e-17)
		tmp = t_1;
	elseif (z <= -4.5e-36)
		tmp = Float64(x * y);
	elseif (z <= 8.8e-51)
		tmp = t_1;
	else
		tmp = Float64(z * t);
	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 (z <= -3.05e+239)
		tmp = z * t;
	elseif (z <= -5.5e-17)
		tmp = t_1;
	elseif (z <= -4.5e-36)
		tmp = x * y;
	elseif (z <= 8.8e-51)
		tmp = t_1;
	else
		tmp = z * t;
	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[z, -3.05e+239], N[(z * t), $MachinePrecision], If[LessEqual[z, -5.5e-17], t$95$1, If[LessEqual[z, -4.5e-36], N[(x * y), $MachinePrecision], If[LessEqual[z, 8.8e-51], t$95$1, N[(z * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0500000000000002e239 or 8.8000000000000001e-51 < z

   1. Initial program 93.6%

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

   3. Taylor expanded in z around inf 91.5%

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

   4. Taylor expanded in a around 0 78.7%

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

   5. Taylor expanded in z around inf 51.1%

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

   if -3.0500000000000002e239 < z < -5.50000000000000001e-17 or -4.50000000000000024e-36 < z < 8.8000000000000001e-51

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf 54.1%

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

   if -5.50000000000000001e-17 < z < -4.50000000000000024e-36

   1. Initial program 83.3%

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

   3. Taylor expanded in z around inf 67.8%

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

   4. Taylor expanded in a around 0 67.8%

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

   5. Taylor expanded in x around inf 66.8%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+239}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-17}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-51}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+223} \lor \neg \left(x \cdot y \leq 1.8 \cdot 10^{+177}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -4.8e+223) (not (<= (* x y) 1.8e+177)))
   (+ (* x y) (* c i))
   (+ (* c i) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -4.8e+223) || !((x * y) <= 1.8e+177)) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = (c * i) + ((a * b) + (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 (((x * y) <= (-4.8d+223)) .or. (.not. ((x * y) <= 1.8d+177))) then
        tmp = (x * y) + (c * i)
    else
        tmp = (c * i) + ((a * b) + (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 (((x * y) <= -4.8e+223) || !((x * y) <= 1.8e+177)) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -4.8e+223) or not ((x * y) <= 1.8e+177):
		tmp = (x * y) + (c * i)
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -4.8e+223) || !(Float64(x * y) <= 1.8e+177))
		tmp = Float64(Float64(x * y) + Float64(c * i));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -4.8e+223) || ~(((x * y) <= 1.8e+177)))
		tmp = (x * y) + (c * i);
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -4.8e+223], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.8e+177]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.80000000000000022e223 or 1.80000000000000001e177 < (*.f64 x y)

   1. Initial program 89.8%

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

   3. Taylor expanded in x around inf 83.5%

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

   if -4.80000000000000022e223 < (*.f64 x y) < 1.80000000000000001e177

   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 x around 0 84.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+223} \lor \neg \left(x \cdot y \leq 1.8 \cdot 10^{+177}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+121} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+136}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1e+121) (not (<= (* a b) 2e+136)))
   (+ (* c i) (+ (* a b) (* z t)))
   (+ (* c i) (+ (* 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 (((a * b) <= -1e+121) || !((a * b) <= 2e+136)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((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 (((a * b) <= (-1d+121)) .or. (.not. ((a * b) <= 2d+136))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((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 (((a * b) <= -1e+121) || !((a * b) <= 2e+136)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -1e+121) or not ((a * b) <= 2e+136):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -1e+121) || !(Float64(a * b) <= 2e+136))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + 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 (((a * b) <= -1e+121) || ~(((a * b) <= 2e+136)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e+121], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+136]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.00000000000000004e121 or 2.00000000000000012e136 < (*.f64 a b)

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0 85.5%

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

   if -1.00000000000000004e121 < (*.f64 a b) < 2.00000000000000012e136

   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. Taylor expanded in a around 0 92.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+121} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+136}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.6 \cdot 10^{+185} \lor \neg \left(a \cdot b \leq 4.5 \cdot 10^{+130}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.6e+185) (not (<= (* a b) 4.5e+130)))
   (+ (* a b) (* c i))
   (+ (* c i) (* z t))))

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+185) || !((a * b) <= 4.5e+130)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (c * i) + (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 (((a * b) <= (-1.6d+185)) .or. (.not. ((a * b) <= 4.5d+130))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (c * i) + (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 (((a * b) <= -1.6e+185) || !((a * b) <= 4.5e+130)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -1.6e+185) or not ((a * b) <= 4.5e+130):
		tmp = (a * b) + (c * i)
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -1.6e+185) || !(Float64(a * b) <= 4.5e+130))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	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+185) || ~(((a * b) <= 4.5e+130)))
		tmp = (a * b) + (c * i);
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.6e+185], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.5e+130]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.60000000000000003e185 or 4.50000000000000039e130 < (*.f64 a b)

   1. Initial program 86.4%

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

   3. Taylor expanded in a around inf 82.7%

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

   if -1.60000000000000003e185 < (*.f64 a b) < 4.50000000000000039e130

   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 65.4%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.6 \cdot 10^{+185} \lor \neg \left(a \cdot b \leq 4.5 \cdot 10^{+130}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -31000000:\\ \;\;\;\;z \cdot \left(t + \frac{a \cdot b}{z}\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+79}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= t -31000000.0)
   (* z (+ t (/ (* a b) z)))
   (if (<= t 1.65e+79)
     (+ (* c i) (+ (* a b) (* x y)))
     (+ (* c i) (+ (* a b) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (t <= -31000000.0) {
		tmp = z * (t + ((a * b) / z));
	} else if (t <= 1.65e+79) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (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 (t <= (-31000000.0d0)) then
        tmp = z * (t + ((a * b) / z))
    else if (t <= 1.65d+79) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (c * i) + ((a * b) + (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 (t <= -31000000.0) {
		tmp = z * (t + ((a * b) / z));
	} else if (t <= 1.65e+79) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if t <= -31000000.0:
		tmp = z * (t + ((a * b) / z))
	elif t <= 1.65e+79:
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (t <= -31000000.0)
		tmp = Float64(z * Float64(t + Float64(Float64(a * b) / z)));
	elseif (t <= 1.65e+79)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (t <= -31000000.0)
		tmp = z * (t + ((a * b) / z));
	elseif (t <= 1.65e+79)
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[t, -31000000.0], N[(z * N[(t + N[(N[(a * b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+79], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.1e7

   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 82.6%

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

   4. Taylor expanded in z around inf 76.5%

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

   5. Taylor expanded in c around 0 63.8%

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

   if -3.1e7 < t < 1.6500000000000001e79

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 88.2%

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

   if 1.6500000000000001e79 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 81.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -31000000:\\ \;\;\;\;z \cdot \left(t + \frac{a \cdot b}{z}\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+79}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-64} \lor \neg \left(t \leq 1.3 \cdot 10^{+79}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -7e-64) (not (<= t 1.3e+79))) (* 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 ((t <= -7e-64) || !(t <= 1.3e+79)) {
		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 ((t <= (-7d-64)) .or. (.not. (t <= 1.3d+79))) 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 ((t <= -7e-64) || !(t <= 1.3e+79)) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -7e-64) or not (t <= 1.3e+79):
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -7e-64) || !(t <= 1.3e+79))
		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 ((t <= -7e-64) || ~((t <= 1.3e+79)))
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -7e-64], N[Not[LessEqual[t, 1.3e+79]], $MachinePrecision]], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.0000000000000006e-64 or 1.30000000000000007e79 < t

   1. Initial program 92.9%

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

   3. Taylor expanded in z around inf 82.7%

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

   4. Taylor expanded in a around 0 72.4%

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

   5. Taylor expanded in z around inf 47.6%

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

   if -7.0000000000000006e-64 < t < 1.30000000000000007e79

   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 c around inf 37.7%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-64} \lor \neg \left(t \leq 1.3 \cdot 10^{+79}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ c \cdot i \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

3. Taylor expanded in c around inf 28.0%

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

4. Final simplification 28.0%

   \[\leadsto c \cdot i \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(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)))