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

Percentage Accurate: 95.6% → 98.0%

Time: 9.9s

Alternatives: 19

Speedup: 0.5×

• 41.5% 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: 95.6% 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: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-+l+ 91.8%

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

   2. associate-+l+ 91.8%

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

   3. fma-def 93.3%

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

   4. fma-def 96.1%

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

   5. fma-def 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 2: 97.8% 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 91.8%

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

   1. +-commutative 91.8%

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

   2. fma-def 92.9%

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

   3. associate-+l+ 92.9%

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

   4. fma-def 93.7%

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

   5. fma-def 95.7%

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

3. Simplified 95.7%

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

4. Final simplification 95.7%

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

Alternative 3: 97.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 63.2%

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

   2. Taylor expanded in x around inf 84.2%

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

   if -inf.0 < (*.f64 x y)

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. fma-def 95.3%

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

      3. associate-+l+ 95.3%

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

      4. fma-def 95.3%

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

      5. fma-def 97.0%

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

   3. Simplified 97.0%

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

      1. fma-udef 95.8%

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

      2. fma-udef 95.8%

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

      3. fma-udef 94.1%

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

      4. associate-+l+ 94.1%

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

      5. +-commutative 94.1%

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

      6. associate-+r+ 94.1%

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

      7. associate-+r+ 94.1%

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

      8. fma-udef 97.0%

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

      9. fma-def 97.9%

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

      10. +-commutative 97.9%

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

   5. Applied egg-rr 97.9%

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

4. Final simplification 96.9%

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

Alternative 4: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(c * i), $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. Step-by-step derivation

      1. associate-+l+ 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   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. Taylor expanded in a around 0 19.0%

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

   3. Taylor expanded in t around 0 47.9%

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

      1. +-commutative 47.9%

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

      2. fma-def 57.4%

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

   5. Applied egg-rr 57.4%

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

4. Final simplification 96.5%

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

Alternative 5: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   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. Taylor expanded in z around 0 42.9%

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

   3. Taylor expanded in y around 0 47.8%

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

      1. *-commutative 47.8%

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

      2. fma-def 57.3%

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

   5. Applied egg-rr 57.3%

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

4. Final simplification 96.5%

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

Alternative 6: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   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. Taylor expanded in a around 0 19.0%

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

   3. Taylor expanded in t around 0 47.9%

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

      1. +-commutative 47.9%

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

      2. fma-def 57.4%

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

   5. Applied egg-rr 57.4%

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

4. Final simplification 96.5%

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

Alternative 7: 97.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   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. Taylor expanded in a around 0 19.0%

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

   3. Taylor expanded in t around 0 47.9%

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

4. Final simplification 95.7%

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

Alternative 8: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ t_3 := c \cdot i + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -1.16 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq 9.8 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 4.5 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t)))
        (t_2 (+ (* a b) (* x y)))
        (t_3 (+ (* c i) (* x y))))
   (if (<= (* a b) -1.16e+33)
     t_2
     (if (<= (* a b) -1.35e-5)
       t_1
       (if (<= (* a b) -8.2e-151)
         t_3
         (if (<= (* a b) 9.8e-163) t_1 (if (<= (* a b) 4.5e+85) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double t_3 = (c * i) + (x * y);
	double tmp;
	if ((a * b) <= -1.16e+33) {
		tmp = t_2;
	} else if ((a * b) <= -1.35e-5) {
		tmp = t_1;
	} else if ((a * b) <= -8.2e-151) {
		tmp = t_3;
	} else if ((a * b) <= 9.8e-163) {
		tmp = t_1;
	} else if ((a * b) <= 4.5e+85) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (a * b) + (x * y)
    t_3 = (c * i) + (x * y)
    if ((a * b) <= (-1.16d+33)) then
        tmp = t_2
    else if ((a * b) <= (-1.35d-5)) then
        tmp = t_1
    else if ((a * b) <= (-8.2d-151)) then
        tmp = t_3
    else if ((a * b) <= 9.8d-163) then
        tmp = t_1
    else if ((a * b) <= 4.5d+85) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double t_3 = (c * i) + (x * y);
	double tmp;
	if ((a * b) <= -1.16e+33) {
		tmp = t_2;
	} else if ((a * b) <= -1.35e-5) {
		tmp = t_1;
	} else if ((a * b) <= -8.2e-151) {
		tmp = t_3;
	} else if ((a * b) <= 9.8e-163) {
		tmp = t_1;
	} else if ((a * b) <= 4.5e+85) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (x * y)
	t_3 = (c * i) + (x * y)
	tmp = 0
	if (a * b) <= -1.16e+33:
		tmp = t_2
	elif (a * b) <= -1.35e-5:
		tmp = t_1
	elif (a * b) <= -8.2e-151:
		tmp = t_3
	elif (a * b) <= 9.8e-163:
		tmp = t_1
	elif (a * b) <= 4.5e+85:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	t_3 = Float64(Float64(c * i) + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -1.16e+33)
		tmp = t_2;
	elseif (Float64(a * b) <= -1.35e-5)
		tmp = t_1;
	elseif (Float64(a * b) <= -8.2e-151)
		tmp = t_3;
	elseif (Float64(a * b) <= 9.8e-163)
		tmp = t_1;
	elseif (Float64(a * b) <= 4.5e+85)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (a * b) + (x * y);
	t_3 = (c * i) + (x * y);
	tmp = 0.0;
	if ((a * b) <= -1.16e+33)
		tmp = t_2;
	elseif ((a * b) <= -1.35e-5)
		tmp = t_1;
	elseif ((a * b) <= -8.2e-151)
		tmp = t_3;
	elseif ((a * b) <= 9.8e-163)
		tmp = t_1;
	elseif ((a * b) <= 4.5e+85)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.16e+33], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1.35e-5], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -8.2e-151], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 9.8e-163], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 4.5e+85], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.16000000000000001e33 or 4.50000000000000007e85 < (*.f64 a b)

   1. Initial program 86.9%

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

   2. Taylor expanded in z around 0 86.2%

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

   3. Taylor expanded in c around 0 79.7%

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

   if -1.16000000000000001e33 < (*.f64 a b) < -1.3499999999999999e-5 or -8.2000000000000002e-151 < (*.f64 a b) < 9.8000000000000005e-163

   1. Initial program 94.7%

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

   2. Taylor expanded in x around 0 78.8%

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

   3. Taylor expanded in a around 0 77.7%

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

   if -1.3499999999999999e-5 < (*.f64 a b) < -8.2000000000000002e-151 or 9.8000000000000005e-163 < (*.f64 a b) < 4.50000000000000007e85

   1. Initial program 94.2%

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

   2. Taylor expanded in a around 0 87.5%

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

   3. Taylor expanded in t around 0 76.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.16 \cdot 10^{+33}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{-151}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 9.8 \cdot 10^{-163}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.5 \cdot 10^{+85}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 9: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.25 \cdot 10^{+33} \lor \neg \left(a \cdot b \leq 1.95 \cdot 10^{-150}\right) \land \left(a \cdot b \leq 6.5 \cdot 10^{-96} \lor \neg \left(a \cdot b \leq 4.75 \cdot 10^{+61}\right)\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -2.25e+33)
         (and (not (<= (* a b) 1.95e-150))
              (or (<= (* a b) 6.5e-96) (not (<= (* a b) 4.75e+61)))))
   (+ (* a b) (* x y))
   (+ (* 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) <= -2.25e+33) || (!((a * b) <= 1.95e-150) && (((a * b) <= 6.5e-96) || !((a * b) <= 4.75e+61)))) {
		tmp = (a * b) + (x * y);
	} 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) <= (-2.25d+33)) .or. (.not. ((a * b) <= 1.95d-150)) .and. ((a * b) <= 6.5d-96) .or. (.not. ((a * b) <= 4.75d+61))) then
        tmp = (a * b) + (x * y)
    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) <= -2.25e+33) || (!((a * b) <= 1.95e-150) && (((a * b) <= 6.5e-96) || !((a * b) <= 4.75e+61)))) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -2.25e+33) or (not ((a * b) <= 1.95e-150) and (((a * b) <= 6.5e-96) or not ((a * b) <= 4.75e+61))):
		tmp = (a * b) + (x * y)
	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) <= -2.25e+33) || (!(Float64(a * b) <= 1.95e-150) && ((Float64(a * b) <= 6.5e-96) || !(Float64(a * b) <= 4.75e+61))))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	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) <= -2.25e+33) || (~(((a * b) <= 1.95e-150)) && (((a * b) <= 6.5e-96) || ~(((a * b) <= 4.75e+61)))))
		tmp = (a * b) + (x * y);
	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], -2.25e+33], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.95e-150]], $MachinePrecision], Or[LessEqual[N[(a * b), $MachinePrecision], 6.5e-96], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.75e+61]], $MachinePrecision]]]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.25e33 or 1.9500000000000001e-150 < (*.f64 a b) < 6.50000000000000001e-96 or 4.7499999999999998e61 < (*.f64 a b)

   1. Initial program 88.4%

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

   2. Taylor expanded in z around 0 86.7%

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

   3. Taylor expanded in c around 0 77.8%

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

   if -2.25e33 < (*.f64 a b) < 1.9500000000000001e-150 or 6.50000000000000001e-96 < (*.f64 a b) < 4.7499999999999998e61

   1. Initial program 94.4%

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

   2. Taylor expanded in x around 0 72.0%

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

   3. Taylor expanded in a around 0 69.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.25 \cdot 10^{+33} \lor \neg \left(a \cdot b \leq 1.95 \cdot 10^{-150}\right) \land \left(a \cdot b \leq 6.5 \cdot 10^{-96} \lor \neg \left(a \cdot b \leq 4.75 \cdot 10^{+61}\right)\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 10: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + \left(a \cdot b + z \cdot t\right)\\ t_2 := c \cdot i + x \cdot y\\ \mathbf{if}\;x \leq -7 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{+103}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (* z t)))) (t_2 (+ (* c i) (* x y))))
   (if (<= x -7e+157)
     t_2
     (if (<= x -1.05e+136)
       t_1
       (if (<= x -1.65e+103)
         (+ (* x y) (* z t))
         (if (<= x -2.2e+95)
           (+ (* c i) (* a b))
           (if (<= x 2.4e-114) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((a * b) + (z * t));
	double t_2 = (c * i) + (x * y);
	double tmp;
	if (x <= -7e+157) {
		tmp = t_2;
	} else if (x <= -1.05e+136) {
		tmp = t_1;
	} else if (x <= -1.65e+103) {
		tmp = (x * y) + (z * t);
	} else if (x <= -2.2e+95) {
		tmp = (c * i) + (a * b);
	} else if (x <= 2.4e-114) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + ((a * b) + (z * t))
    t_2 = (c * i) + (x * y)
    if (x <= (-7d+157)) then
        tmp = t_2
    else if (x <= (-1.05d+136)) then
        tmp = t_1
    else if (x <= (-1.65d+103)) then
        tmp = (x * y) + (z * t)
    else if (x <= (-2.2d+95)) then
        tmp = (c * i) + (a * b)
    else if (x <= 2.4d-114) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((a * b) + (z * t));
	double t_2 = (c * i) + (x * y);
	double tmp;
	if (x <= -7e+157) {
		tmp = t_2;
	} else if (x <= -1.05e+136) {
		tmp = t_1;
	} else if (x <= -1.65e+103) {
		tmp = (x * y) + (z * t);
	} else if (x <= -2.2e+95) {
		tmp = (c * i) + (a * b);
	} else if (x <= 2.4e-114) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + ((a * b) + (z * t))
	t_2 = (c * i) + (x * y)
	tmp = 0
	if x <= -7e+157:
		tmp = t_2
	elif x <= -1.05e+136:
		tmp = t_1
	elif x <= -1.65e+103:
		tmp = (x * y) + (z * t)
	elif x <= -2.2e+95:
		tmp = (c * i) + (a * b)
	elif x <= 2.4e-114:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)))
	t_2 = Float64(Float64(c * i) + Float64(x * y))
	tmp = 0.0
	if (x <= -7e+157)
		tmp = t_2;
	elseif (x <= -1.05e+136)
		tmp = t_1;
	elseif (x <= -1.65e+103)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (x <= -2.2e+95)
		tmp = Float64(Float64(c * i) + Float64(a * b));
	elseif (x <= 2.4e-114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((a * b) + (z * t));
	t_2 = (c * i) + (x * y);
	tmp = 0.0;
	if (x <= -7e+157)
		tmp = t_2;
	elseif (x <= -1.05e+136)
		tmp = t_1;
	elseif (x <= -1.65e+103)
		tmp = (x * y) + (z * t);
	elseif (x <= -2.2e+95)
		tmp = (c * i) + (a * b);
	elseif (x <= 2.4e-114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+157], t$95$2, If[LessEqual[x, -1.05e+136], t$95$1, If[LessEqual[x, -1.65e+103], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.2e+95], N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-114], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.00000000000000004e157 or 2.4000000000000001e-114 < x

   1. Initial program 90.3%

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

   2. Taylor expanded in a around 0 78.5%

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

   3. Taylor expanded in t around 0 64.0%

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

   if -7.00000000000000004e157 < x < -1.05e136 or -2.1999999999999999e95 < x < 2.4000000000000001e-114

   1. Initial program 93.2%

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

   2. Taylor expanded in x around 0 82.9%

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

   if -1.05e136 < x < -1.65000000000000004e103

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 86.6%

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

   3. Taylor expanded in c around 0 86.6%

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

   if -1.65000000000000004e103 < x < -2.1999999999999999e95

   1. Initial program 50.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+157}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+136}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{+103}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-114}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \]

Alternative 11: 43.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.62 \cdot 10^{+50}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.55 \cdot 10^{-58}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -9.5 \cdot 10^{-183}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+53}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.62e+50)
   (* c i)
   (if (<= (* c i) -2.55e-58)
     (* a b)
     (if (<= (* c i) -9.5e-183)
       (* z t)
       (if (<= (* c i) 1.05e+53) (* x y) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.62e+50) {
		tmp = c * i;
	} else if ((c * i) <= -2.55e-58) {
		tmp = a * b;
	} else if ((c * i) <= -9.5e-183) {
		tmp = z * t;
	} else if ((c * i) <= 1.05e+53) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1.62d+50)) then
        tmp = c * i
    else if ((c * i) <= (-2.55d-58)) then
        tmp = a * b
    else if ((c * i) <= (-9.5d-183)) then
        tmp = z * t
    else if ((c * i) <= 1.05d+53) then
        tmp = x * y
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.62e+50) {
		tmp = c * i;
	} else if ((c * i) <= -2.55e-58) {
		tmp = a * b;
	} else if ((c * i) <= -9.5e-183) {
		tmp = z * t;
	} else if ((c * i) <= 1.05e+53) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.62e+50:
		tmp = c * i
	elif (c * i) <= -2.55e-58:
		tmp = a * b
	elif (c * i) <= -9.5e-183:
		tmp = z * t
	elif (c * i) <= 1.05e+53:
		tmp = x * y
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.62e+50)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2.55e-58)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= -9.5e-183)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.05e+53)
		tmp = Float64(x * y);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1.62e+50)
		tmp = c * i;
	elseif ((c * i) <= -2.55e-58)
		tmp = a * b;
	elseif ((c * i) <= -9.5e-183)
		tmp = z * t;
	elseif ((c * i) <= 1.05e+53)
		tmp = x * y;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.62e+50], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.55e-58], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -9.5e-183], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.05e+53], N[(x * y), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -1.61999999999999996e50 or 1.0500000000000001e53 < (*.f64 c i)

   1. Initial program 86.3%

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

   2. Taylor expanded in c around inf 61.9%

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

   if -1.61999999999999996e50 < (*.f64 c i) < -2.55e-58

   1. Initial program 89.5%

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

   2. Taylor expanded in a around inf 42.9%

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

   if -2.55e-58 < (*.f64 c i) < -9.5000000000000008e-183

   1. Initial program 95.8%

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

   2. Taylor expanded in z around inf 59.3%

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

   if -9.5000000000000008e-183 < (*.f64 c i) < 1.0500000000000001e53

   1. Initial program 97.0%

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

   2. Taylor expanded in x around inf 45.1%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.62 \cdot 10^{+50}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.55 \cdot 10^{-58}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -9.5 \cdot 10^{-183}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+53}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 12: 61.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.65 \cdot 10^{+50}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.08 \cdot 10^{-182}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7.2 \cdot 10^{+172}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.65e+50)
   (* c i)
   (if (<= (* c i) -1.08e-182)
     (+ (* a b) (* z t))
     (if (<= (* c i) 7.2e+172) (+ (* a b) (* 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) <= -2.65e+50) {
		tmp = c * i;
	} else if ((c * i) <= -1.08e-182) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 7.2e+172) {
		tmp = (a * b) + (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) <= (-2.65d+50)) then
        tmp = c * i
    else if ((c * i) <= (-1.08d-182)) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 7.2d+172) then
        tmp = (a * b) + (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) <= -2.65e+50) {
		tmp = c * i;
	} else if ((c * i) <= -1.08e-182) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 7.2e+172) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.65e+50:
		tmp = c * i
	elif (c * i) <= -1.08e-182:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 7.2e+172:
		tmp = (a * b) + (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) <= -2.65e+50)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.08e-182)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 7.2e+172)
		tmp = Float64(Float64(a * b) + 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) <= -2.65e+50)
		tmp = c * i;
	elseif ((c * i) <= -1.08e-182)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 7.2e+172)
		tmp = (a * b) + (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], -2.65e+50], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.08e-182], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7.2e+172], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.6500000000000001e50 or 7.1999999999999995e172 < (*.f64 c i)

   1. Initial program 84.5%

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

   2. Taylor expanded in c around inf 68.7%

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

   if -2.6500000000000001e50 < (*.f64 c i) < -1.08000000000000003e-182

   1. Initial program 92.4%

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

   2. Taylor expanded in x around 0 73.3%

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

   3. Taylor expanded in c around 0 65.3%

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

   if -1.08000000000000003e-182 < (*.f64 c i) < 7.1999999999999995e172

   1. Initial program 96.6%

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

   2. Taylor expanded in z around 0 71.4%

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

   3. Taylor expanded in c around 0 64.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.65 \cdot 10^{+50}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.08 \cdot 10^{-182}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7.2 \cdot 10^{+172}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 13: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -4:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -4.2 \cdot 10^{-183}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* a b))))
   (if (<= (* c i) -4.0)
     t_1
     (if (<= (* c i) -4.2e-183)
       (+ (* a b) (* z t))
       (if (<= (* c i) 8.2e+67) (+ (* a b) (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (a * b);
	double tmp;
	if ((c * i) <= -4.0) {
		tmp = t_1;
	} else if ((c * i) <= -4.2e-183) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 8.2e+67) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (a * b)
    if ((c * i) <= (-4.0d0)) then
        tmp = t_1
    else if ((c * i) <= (-4.2d-183)) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 8.2d+67) then
        tmp = (a * b) + (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (a * b);
	double tmp;
	if ((c * i) <= -4.0) {
		tmp = t_1;
	} else if ((c * i) <= -4.2e-183) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 8.2e+67) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (a * b)
	tmp = 0
	if (c * i) <= -4.0:
		tmp = t_1
	elif (c * i) <= -4.2e-183:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 8.2e+67:
		tmp = (a * b) + (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(a * b))
	tmp = 0.0
	if (Float64(c * i) <= -4.0)
		tmp = t_1;
	elseif (Float64(c * i) <= -4.2e-183)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 8.2e+67)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (a * b);
	tmp = 0.0;
	if ((c * i) <= -4.0)
		tmp = t_1;
	elseif ((c * i) <= -4.2e-183)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 8.2e+67)
		tmp = (a * b) + (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -4.0], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -4.2e-183], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.2e+67], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -4 or 8.19999999999999959e67 < (*.f64 c i)

   1. Initial program 86.8%

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

   2. Taylor expanded in z around 0 79.3%

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

   3. Taylor expanded in y around 0 71.4%

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

   if -4 < (*.f64 c i) < -4.2000000000000004e-183

   1. Initial program 94.7%

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

   2. Taylor expanded in x around 0 75.8%

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

   3. Taylor expanded in c around 0 72.1%

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

   if -4.2000000000000004e-183 < (*.f64 c i) < 8.19999999999999959e67

   1. Initial program 96.1%

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

   2. Taylor expanded in z around 0 72.9%

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

   3. Taylor expanded in c around 0 69.2%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -4.2 \cdot 10^{-183}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 14: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.65 \cdot 10^{+62} \lor \neg \left(a \cdot b \leq 1.9 \cdot 10^{+48}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.65e+62) (not (<= (* a b) 1.9e+48)))
   (+ (* c i) (+ (* a b) (* x y)))
   (+ (* 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) <= -1.65e+62) || !((a * b) <= 1.9e+48)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} 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) <= (-1.65d+62)) .or. (.not. ((a * b) <= 1.9d+48))) then
        tmp = (c * i) + ((a * b) + (x * y))
    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) <= -1.65e+62) || !((a * b) <= 1.9e+48)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} 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) <= -1.65e+62) or not ((a * b) <= 1.9e+48):
		tmp = (c * i) + ((a * b) + (x * y))
	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) <= -1.65e+62) || !(Float64(a * b) <= 1.9e+48))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	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) <= -1.65e+62) || ~(((a * b) <= 1.9e+48)))
		tmp = (c * i) + ((a * b) + (x * y));
	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], -1.65e+62], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.9e+48]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $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) < -1.65e62 or 1.9e48 < (*.f64 a b)

   1. Initial program 87.2%

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

   2. Taylor expanded in z around 0 87.1%

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

   if -1.65e62 < (*.f64 a b) < 1.9e48

   1. Initial program 94.4%

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

   2. Taylor expanded in a around 0 90.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.65 \cdot 10^{+62} \lor \neg \left(a \cdot b \leq 1.9 \cdot 10^{+48}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 15: 43.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.22 \cdot 10^{-160}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.8 \cdot 10^{+85}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.7e+62)
   (* a b)
   (if (<= (* a b) 1.22e-160)
     (* z t)
     (if (<= (* a b) 5.8e+85) (* c i) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.7e+62) {
		tmp = a * b;
	} else if ((a * b) <= 1.22e-160) {
		tmp = z * t;
	} else if ((a * b) <= 5.8e+85) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-1.7d+62)) then
        tmp = a * b
    else if ((a * b) <= 1.22d-160) then
        tmp = z * t
    else if ((a * b) <= 5.8d+85) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.7e+62) {
		tmp = a * b;
	} else if ((a * b) <= 1.22e-160) {
		tmp = z * t;
	} else if ((a * b) <= 5.8e+85) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.7e+62:
		tmp = a * b
	elif (a * b) <= 1.22e-160:
		tmp = z * t
	elif (a * b) <= 5.8e+85:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.7e+62)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 1.22e-160)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 5.8e+85)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.7e+62)
		tmp = a * b;
	elseif ((a * b) <= 1.22e-160)
		tmp = z * t;
	elseif ((a * b) <= 5.8e+85)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.7e+62], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.22e-160], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.8e+85], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.70000000000000007e62 or 5.79999999999999995e85 < (*.f64 a b)

   1. Initial program 86.2%

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

   2. Taylor expanded in a around inf 67.5%

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

   if -1.70000000000000007e62 < (*.f64 a b) < 1.22000000000000003e-160

   1. Initial program 95.2%

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

   2. Taylor expanded in z around inf 41.1%

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

   if 1.22000000000000003e-160 < (*.f64 a b) < 5.79999999999999995e85

   1. Initial program 93.0%

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

   2. Taylor expanded in c around inf 33.9%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.22 \cdot 10^{-160}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.8 \cdot 10^{+85}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 16: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+85}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-114}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -9.8e+85)
   (+ (* c i) (+ (* a b) (* x y)))
   (if (<= x 2.4e-114) (+ (* c i) (+ (* a b) (* z t))) (+ (* c i) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -9.8e+85) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if (x <= 2.4e-114) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + (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 <= (-9.8d+85)) then
        tmp = (c * i) + ((a * b) + (x * y))
    else if (x <= 2.4d-114) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + (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 <= -9.8e+85) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if (x <= 2.4e-114) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -9.8e+85:
		tmp = (c * i) + ((a * b) + (x * y))
	elif x <= 2.4e-114:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -9.8e+85)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	elseif (x <= 2.4e-114)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + 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 <= -9.8e+85)
		tmp = (c * i) + ((a * b) + (x * y));
	elseif (x <= 2.4e-114)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -9.8e+85], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-114], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.7999999999999993e85

   1. Initial program 90.2%

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

   2. Taylor expanded in z around 0 78.2%

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

   if -9.7999999999999993e85 < x < 2.4000000000000001e-114

   1. Initial program 93.4%

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

   2. Taylor expanded in x around 0 84.0%

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

   if 2.4000000000000001e-114 < x

   1. Initial program 90.3%

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

   2. Taylor expanded in a around 0 76.4%

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

   3. Taylor expanded in t around 0 59.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+85}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-114}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \]

Alternative 17: 44.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.2 \cdot 10^{+85}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5.8e+64) (* a b) (if (<= (* a b) 1.2e+85) (* c i) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5.8e+64) {
		tmp = a * b;
	} else if ((a * b) <= 1.2e+85) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-5.8d+64)) then
        tmp = a * b
    else if ((a * b) <= 1.2d+85) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5.8e+64) {
		tmp = a * b;
	} else if ((a * b) <= 1.2e+85) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -5.8e+64:
		tmp = a * b
	elif (a * b) <= 1.2e+85:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -5.8e+64)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 1.2e+85)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -5.8e+64)
		tmp = a * b;
	elseif ((a * b) <= 1.2e+85)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -5.8e+64], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.2e+85], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.79999999999999986e64 or 1.19999999999999998e85 < (*.f64 a b)

   1. Initial program 86.2%

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

   2. Taylor expanded in a around inf 67.5%

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

   if -5.79999999999999986e64 < (*.f64 a b) < 1.19999999999999998e85

   1. Initial program 94.6%

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

   2. Taylor expanded in c around inf 32.9%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.2 \cdot 10^{+85}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 18: 51.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+156}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-114}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.15e+156)
   (* x y)
   (if (<= x 2.4e-114) (+ (* a b) (* 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 <= -2.15e+156) {
		tmp = x * y;
	} else if (x <= 2.4e-114) {
		tmp = (a * b) + (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 <= (-2.15d+156)) then
        tmp = x * y
    else if (x <= 2.4d-114) then
        tmp = (a * b) + (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 <= -2.15e+156) {
		tmp = x * y;
	} else if (x <= 2.4e-114) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -2.15e+156:
		tmp = x * y
	elif x <= 2.4e-114:
		tmp = (a * b) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.15e+156)
		tmp = Float64(x * y);
	elseif (x <= 2.4e-114)
		tmp = Float64(Float64(a * b) + 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 <= -2.15e+156)
		tmp = x * y;
	elseif (x <= 2.4e-114)
		tmp = (a * b) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.15e+156], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.4e-114], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.14999999999999993e156 or 2.4000000000000001e-114 < x

   1. Initial program 90.3%

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

   2. Taylor expanded in x around inf 44.9%

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

   if -2.14999999999999993e156 < x < 2.4000000000000001e-114

   1. Initial program 92.9%

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

   2. Taylor expanded in x around 0 80.5%

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

   3. Taylor expanded in c around 0 55.2%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+156}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-114}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 19: 27.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

2. Taylor expanded in a around inf 25.9%

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

3. Final simplification 25.9%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023229 
(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)))