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

Percentage Accurate: 96.1% → 97.5%

Time: 11.9s

Alternatives: 13

Speedup: 0.4×

• 41.4% 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: 96.1% 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: 97.5% accurate, 0.4× speedup

Math

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

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 (+ (* c i) (* y (+ x (/ (* a b) y)))))))

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 = (c * i) + (y * (x + ((a * b) / 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 = ((a * b) + ((x * y) + (z * t))) + (c * i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (y * (x + ((a * b) / y)));
	}
	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 = (c * i) + (y * (x + ((a * b) / y)))
	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(Float64(c * i) + Float64(y * Float64(x + Float64(Float64(a * b) / y))));
	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 = (c * i) + (y * (x + ((a * b) / y)));
	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[(N[(c * i), $MachinePrecision] + N[(y * N[(x + N[(N[(a * b), $MachinePrecision] / y), $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 t around inf 25.0%

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

      1. associate-/l* 25.0%

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

   5. Simplified 25.0%

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

   6. Taylor expanded in t around 0 37.5%

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

   7. Taylor expanded in y around inf 62.5%

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

4. Final simplification 98.8%

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

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

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 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-define 96.9%

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

   3. associate-+l+ 96.9%

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

   4. fma-define 97.3%

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

   5. fma-define 97.7%

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

3. Simplified 97.7%

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

Alternative 3: 98.1% 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 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-define 96.9%

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

   3. +-commutative 96.9%

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

   4. fma-define 97.6%

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

   5. fma-define 97.6%

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

3. Simplified 97.6%

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

Alternative 4: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-304}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+144}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -4e+123)
   (+ (* x y) (* c i))
   (if (<= (* x y) 2e-304)
     (+ (* a b) (* c i))
     (if (<= (* x y) 2e+144) (+ (* c i) (* z t)) (* y (+ x (/ (* a b) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 2e-304) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2e+144) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = y * (x + ((a * b) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-4d+123)) then
        tmp = (x * y) + (c * i)
    else if ((x * y) <= 2d-304) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 2d+144) then
        tmp = (c * i) + (z * t)
    else
        tmp = y * (x + ((a * b) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 2e-304) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2e+144) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = y * (x + ((a * b) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -4e+123:
		tmp = (x * y) + (c * i)
	elif (x * y) <= 2e-304:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 2e+144:
		tmp = (c * i) + (z * t)
	else:
		tmp = y * (x + ((a * b) / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -4e+123)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(x * y) <= 2e-304)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 2e+144)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = Float64(y * Float64(x + Float64(Float64(a * b) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -4e+123)
		tmp = (x * y) + (c * i);
	elseif ((x * y) <= 2e-304)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 2e+144)
		tmp = (c * i) + (z * t);
	else
		tmp = y * (x + ((a * b) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+123], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-304], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+144], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.99999999999999991e123

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 83.9%

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

   if -3.99999999999999991e123 < (*.f64 x y) < 1.99999999999999994e-304

   1. Initial program 99.0%

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

   3. Taylor expanded in a around inf 73.9%

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

   if 1.99999999999999994e-304 < (*.f64 x y) < 2.00000000000000005e144

   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 z around inf 69.3%

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

   if 2.00000000000000005e144 < (*.f64 x y)

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf 82.3%

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

      1. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around 0 89.7%

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

   7. Taylor expanded in y around inf 92.8%

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

   8. Taylor expanded in c around 0 91.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-304}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+144}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-304}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+149}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* c i))))
   (if (<= (* x y) -4e+123)
     t_1
     (if (<= (* x y) 2e-304)
       (+ (* a b) (* c i))
       (if (<= (* x y) 4e+149) (+ (* c i) (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = t_1;
	} else if ((x * y) <= 2e-304) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 4e+149) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (c * i)
    if ((x * y) <= (-4d+123)) then
        tmp = t_1
    else if ((x * y) <= 2d-304) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 4d+149) then
        tmp = (c * i) + (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = t_1;
	} else if ((x * y) <= 2e-304) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 4e+149) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (c * i)
	tmp = 0
	if (x * y) <= -4e+123:
		tmp = t_1
	elif (x * y) <= 2e-304:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 4e+149:
		tmp = (c * i) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -4e+123)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-304)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 4e+149)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -4e+123)
		tmp = t_1;
	elseif ((x * y) <= 2e-304)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 4e+149)
		tmp = (c * i) + (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e+123], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-304], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+149], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999991e123 or 4.0000000000000002e149 < (*.f64 x y)

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf 82.7%

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

   if -3.99999999999999991e123 < (*.f64 x y) < 1.99999999999999994e-304

   1. Initial program 99.0%

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

   3. Taylor expanded in a around inf 73.9%

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

   if 1.99999999999999994e-304 < (*.f64 x y) < 4.0000000000000002e149

   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 z around inf 68.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-304}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+149}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-304}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+149}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -4e+123)
   (* x y)
   (if (<= (* x y) 2e-304)
     (+ (* a b) (* c i))
     (if (<= (* x y) 4e+149) (+ (* c i) (* z t)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = x * y;
	} else if ((x * y) <= 2e-304) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 4e+149) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-4d+123)) then
        tmp = x * y
    else if ((x * y) <= 2d-304) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 4d+149) then
        tmp = (c * i) + (z * t)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = x * y;
	} else if ((x * y) <= 2e-304) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 4e+149) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -4e+123:
		tmp = x * y
	elif (x * y) <= 2e-304:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 4e+149:
		tmp = (c * i) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -4e+123)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 2e-304)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 4e+149)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -4e+123)
		tmp = x * y;
	elseif ((x * y) <= 2e-304)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 4e+149)
		tmp = (c * i) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+123], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-304], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+149], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999991e123 or 4.0000000000000002e149 < (*.f64 x y)

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf 82.7%

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

   4. Taylor expanded in i around inf 73.5%

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

   5. Taylor expanded in i around 0 75.3%

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

   if -3.99999999999999991e123 < (*.f64 x y) < 1.99999999999999994e-304

   1. Initial program 99.0%

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

   3. Taylor expanded in a around inf 73.9%

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

   if 1.99999999999999994e-304 < (*.f64 x y) < 4.0000000000000002e149

   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 z around inf 68.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-304}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+149}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+105} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+136}\right):\\ \;\;\;\;c \cdot i + y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1e+105) (not (<= (* x y) 4e+136)))
   (+ (* c i) (* y (+ x (/ (* a b) 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 (((x * y) <= -1e+105) || !((x * y) <= 4e+136)) {
		tmp = (c * i) + (y * (x + ((a * b) / 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 (((x * y) <= (-1d+105)) .or. (.not. ((x * y) <= 4d+136))) then
        tmp = (c * i) + (y * (x + ((a * b) / 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 (((x * y) <= -1e+105) || !((x * y) <= 4e+136)) {
		tmp = (c * i) + (y * (x + ((a * b) / 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 ((x * y) <= -1e+105) or not ((x * y) <= 4e+136):
		tmp = (c * i) + (y * (x + ((a * b) / 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 ((Float64(x * y) <= -1e+105) || !(Float64(x * y) <= 4e+136))
		tmp = Float64(Float64(c * i) + Float64(y * Float64(x + Float64(Float64(a * b) / 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 (((x * y) <= -1e+105) || ~(((x * y) <= 4e+136)))
		tmp = (c * i) + (y * (x + ((a * b) / 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[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+105], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+136]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(y * N[(x + N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $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) < -9.9999999999999994e104 or 4.00000000000000023e136 < (*.f64 x y)

   1. Initial program 93.0%

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

   3. Taylor expanded in t around inf 77.7%

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

      1. associate-/l* 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in t around 0 89.2%

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

   7. Taylor expanded in y around inf 91.6%

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

   if -9.9999999999999994e104 < (*.f64 x y) < 4.00000000000000023e136

   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 x around 0 93.8%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+105} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+136}\right):\\ \;\;\;\;c \cdot i + y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+144}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -4e+123)
   (+ (* c i) (+ (* x y) (* z t)))
   (if (<= (* x y) 2e+144)
     (+ (* c i) (+ (* a b) (* z t)))
     (* y (+ x (/ (* a b) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else if ((x * y) <= 2e+144) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = y * (x + ((a * b) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-4d+123)) then
        tmp = (c * i) + ((x * y) + (z * t))
    else if ((x * y) <= 2d+144) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = y * (x + ((a * b) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else if ((x * y) <= 2e+144) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = y * (x + ((a * b) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -4e+123:
		tmp = (c * i) + ((x * y) + (z * t))
	elif (x * y) <= 2e+144:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = y * (x + ((a * b) / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -4e+123)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	elseif (Float64(x * y) <= 2e+144)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(y * Float64(x + Float64(Float64(a * b) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -4e+123)
		tmp = (c * i) + ((x * y) + (z * t));
	elseif ((x * y) <= 2e+144)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = y * (x + ((a * b) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+123], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+144], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999991e123

   1. Initial program 95.9%

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

   3. Taylor expanded in a around 0 91.5%

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

   if -3.99999999999999991e123 < (*.f64 x y) < 2.00000000000000005e144

   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 x around 0 93.4%

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

   if 2.00000000000000005e144 < (*.f64 x y)

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf 82.3%

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

      1. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around 0 89.7%

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

   7. Taylor expanded in y around inf 92.8%

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

   8. Taylor expanded in c around 0 91.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+144}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+105}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+144}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e+105)
   (+ (* c i) (+ (* a b) (* x y)))
   (if (<= (* x y) 2e+144)
     (+ (* c i) (+ (* a b) (* z t)))
     (* y (+ x (/ (* a b) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+105) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if ((x * y) <= 2e+144) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = y * (x + ((a * b) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1d+105)) then
        tmp = (c * i) + ((a * b) + (x * y))
    else if ((x * y) <= 2d+144) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = y * (x + ((a * b) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+105) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if ((x * y) <= 2e+144) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = y * (x + ((a * b) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e+105:
		tmp = (c * i) + ((a * b) + (x * y))
	elif (x * y) <= 2e+144:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = y * (x + ((a * b) / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e+105)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	elseif (Float64(x * y) <= 2e+144)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(y * Float64(x + Float64(Float64(a * b) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e+105)
		tmp = (c * i) + ((a * b) + (x * y));
	elseif ((x * y) <= 2e+144)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = y * (x + ((a * b) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+105], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+144], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.9999999999999994e104

   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 0 88.7%

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

   if -9.9999999999999994e104 < (*.f64 x y) < 2.00000000000000005e144

   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 x around 0 93.9%

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

   if 2.00000000000000005e144 < (*.f64 x y)

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf 82.3%

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

      1. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around 0 89.7%

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

   7. Taylor expanded in y around inf 92.8%

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

   8. Taylor expanded in c around 0 91.2%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+105}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+144}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+144}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -4e+123)
   (+ (* x y) (* c i))
   (if (<= (* x y) 2e+144)
     (+ (* c i) (+ (* a b) (* z t)))
     (* y (+ x (/ (* a b) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 2e+144) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = y * (x + ((a * b) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-4d+123)) then
        tmp = (x * y) + (c * i)
    else if ((x * y) <= 2d+144) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = y * (x + ((a * b) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -4e+123) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 2e+144) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = y * (x + ((a * b) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -4e+123:
		tmp = (x * y) + (c * i)
	elif (x * y) <= 2e+144:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = y * (x + ((a * b) / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -4e+123)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(x * y) <= 2e+144)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(y * Float64(x + Float64(Float64(a * b) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -4e+123)
		tmp = (x * y) + (c * i);
	elseif ((x * y) <= 2e+144)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = y * (x + ((a * b) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+123], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+144], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999991e123

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 83.9%

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

   if -3.99999999999999991e123 < (*.f64 x y) < 2.00000000000000005e144

   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 x around 0 93.4%

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

   if 2.00000000000000005e144 < (*.f64 x y)

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf 82.3%

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

      1. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around 0 89.7%

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

   7. Taylor expanded in y around inf 92.8%

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

   8. Taylor expanded in c around 0 91.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+144}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+149}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -4e+123) (not (<= (* x y) 4e+149)))
   (* 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) <= -4e+123) || !((x * y) <= 4e+149)) {
		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) <= (-4d+123)) .or. (.not. ((x * y) <= 4d+149))) 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) <= -4e+123) || !((x * y) <= 4e+149)) {
		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) <= -4e+123) or not ((x * y) <= 4e+149):
		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) <= -4e+123) || !(Float64(x * y) <= 4e+149))
		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) <= -4e+123) || ~(((x * y) <= 4e+149)))
		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], -4e+123], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+149]], $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) < -3.99999999999999991e123 or 4.0000000000000002e149 < (*.f64 x y)

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf 82.7%

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

   4. Taylor expanded in i around inf 73.5%

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

   5. Taylor expanded in i around 0 75.3%

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

   if -3.99999999999999991e123 < (*.f64 x y) < 4.0000000000000002e149

   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 a around inf 67.6%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+123} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+149}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+110} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+149}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2e+110) (not (<= (* x y) 4e+149))) (* x y) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+110) || !((x * y) <= 4e+149)) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2d+110)) .or. (.not. ((x * y) <= 4d+149))) then
        tmp = x * y
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+110) || !((x * y) <= 4e+149)) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2e+110) or not ((x * y) <= 4e+149):
		tmp = x * y
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+110) || !(Float64(x * y) <= 4e+149))
		tmp = Float64(x * y);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2e+110) || ~(((x * y) <= 4e+149)))
		tmp = x * y;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+110], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+149]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2e110 or 4.0000000000000002e149 < (*.f64 x y)

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf 81.7%

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

   4. Taylor expanded in i around inf 72.7%

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

   5. Taylor expanded in i around 0 74.5%

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

   if -2e110 < (*.f64 x y) < 4.0000000000000002e149

   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 37.0%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+110} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+149}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.3% 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 96.9%

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

3. Taylor expanded in c around inf 28.9%

   \[\leadsto \color{blue}{c \cdot i} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024087 
(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)))