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

Percentage Accurate: 96.0% → 97.9%

Time: 9.4s

Alternatives: 17

Speedup: 0.5×

• 40.4% 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: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. fma-def 0.0%

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

   3. Simplified 0.0%

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

      1. fma-def 0.0%

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

      2. +-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

   6. Taylor expanded in x around inf 80.0%

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

4. Final simplification 99.6%

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

Alternative 2: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. 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 z around 0 11.1%

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

   3. Taylor expanded in c around 0 45.0%

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

      1. fma-def 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 99.2%

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

Alternative 3: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

   5. Applied egg-rr 100.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. fma-def 0.0%

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

   3. Simplified 0.0%

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

      1. fma-def 0.0%

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

      2. +-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

   6. Taylor expanded in x around inf 80.0%

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

4. Final simplification 99.6%

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

Alternative 4: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

   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 z around 0 11.1%

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

   3. Taylor expanded in c around 0 45.0%

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

      1. fma-def 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 99.2%

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

Alternative 5: 97.3% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

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

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%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

   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. Step-by-step derivation

      1. associate-+l+ 0.0%

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

      2. associate-+l+ 0.0%

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

      3. fma-def 0.0%

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

      4. fma-def 0.0%

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

      5. fma-def 11.1%

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

   3. Simplified 11.1%

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

   4. Taylor expanded in a around 0 44.4%

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

   5. Taylor expanded in c around 0 77.8%

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

4. Final simplification 99.2%

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

Alternative 6: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -3.2 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 9.4 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* a b) -1e+151)
     t_2
     (if (<= (* a b) -3.2e+104)
       t_1
       (if (<= (* a b) -1.5e+47)
         t_2
         (if (<= (* a b) 9.4e+38) t_1 (+ (* a b) (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -1e+151) {
		tmp = t_2;
	} else if ((a * b) <= -3.2e+104) {
		tmp = t_1;
	} else if ((a * b) <= -1.5e+47) {
		tmp = t_2;
	} else if ((a * b) <= 9.4e+38) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (a * b) + (x * y)
    if ((a * b) <= (-1d+151)) then
        tmp = t_2
    else if ((a * b) <= (-3.2d+104)) then
        tmp = t_1
    else if ((a * b) <= (-1.5d+47)) then
        tmp = t_2
    else if ((a * b) <= 9.4d+38) then
        tmp = t_1
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -1e+151) {
		tmp = t_2;
	} else if ((a * b) <= -3.2e+104) {
		tmp = t_1;
	} else if ((a * b) <= -1.5e+47) {
		tmp = t_2;
	} else if ((a * b) <= 9.4e+38) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	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)
	tmp = 0
	if (a * b) <= -1e+151:
		tmp = t_2
	elif (a * b) <= -3.2e+104:
		tmp = t_1
	elif (a * b) <= -1.5e+47:
		tmp = t_2
	elif (a * b) <= 9.4e+38:
		tmp = t_1
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -1e+151)
		tmp = t_2;
	elseif (Float64(a * b) <= -3.2e+104)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.5e+47)
		tmp = t_2;
	elseif (Float64(a * b) <= 9.4e+38)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((a * b) <= -1e+151)
		tmp = t_2;
	elseif ((a * b) <= -3.2e+104)
		tmp = t_1;
	elseif ((a * b) <= -1.5e+47)
		tmp = t_2;
	elseif ((a * b) <= 9.4e+38)
		tmp = t_1;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+151], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -3.2e+104], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.5e+47], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 9.4e+38], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.00000000000000002e151 or -3.2e104 < (*.f64 a b) < -1.5000000000000001e47

   1. Initial program 98.1%

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

   2. Taylor expanded in z around 0 87.4%

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

   3. Taylor expanded in c around 0 78.2%

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

   if -1.00000000000000002e151 < (*.f64 a b) < -3.2e104 or -1.5000000000000001e47 < (*.f64 a b) < 9.3999999999999998e38

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf 67.1%

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

   if 9.3999999999999998e38 < (*.f64 a b)

   1. Initial program 92.6%

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

   2. Taylor expanded in a around inf 75.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+151}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -3.2 \cdot 10^{+104}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 9.4 \cdot 10^{+38}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 7: 65.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.46 \cdot 10^{-25}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -6.2 \cdot 10^{-105}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+29}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.9e+73)
   (+ (* x y) (* c i))
   (if (<= (* c i) -1.46e-25)
     (+ (* c i) (* z t))
     (if (<= (* c i) -6.2e-105)
       (+ (* a b) (* x y))
       (if (<= (* c i) 1.05e+29) (+ (* 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) {
	double tmp;
	if ((c * i) <= -4.9e+73) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= -1.46e-25) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= -6.2e-105) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 1.05e+29) {
		tmp = (x * y) + (z * t);
	} 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 ((c * i) <= (-4.9d+73)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= (-1.46d-25)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= (-6.2d-105)) then
        tmp = (a * b) + (x * y)
    else if ((c * i) <= 1.05d+29) then
        tmp = (x * y) + (z * t)
    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 ((c * i) <= -4.9e+73) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= -1.46e-25) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= -6.2e-105) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 1.05e+29) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4.9e+73:
		tmp = (x * y) + (c * i)
	elif (c * i) <= -1.46e-25:
		tmp = (c * i) + (z * t)
	elif (c * i) <= -6.2e-105:
		tmp = (a * b) + (x * y)
	elif (c * i) <= 1.05e+29:
		tmp = (x * y) + (z * t)
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4.9e+73)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= -1.46e-25)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= -6.2e-105)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(c * i) <= 1.05e+29)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	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 ((c * i) <= -4.9e+73)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= -1.46e-25)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= -6.2e-105)
		tmp = (a * b) + (x * y);
	elseif ((c * i) <= 1.05e+29)
		tmp = (x * y) + (z * t);
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4.9e+73], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.46e-25], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -6.2e-105], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.05e+29], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 c i) < -4.8999999999999999e73

   1. Initial program 93.3%

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

   2. Taylor expanded in x around inf 82.9%

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

   if -4.8999999999999999e73 < (*.f64 c i) < -1.46e-25

   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 z around inf 67.4%

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

   if -1.46e-25 < (*.f64 c i) < -6.20000000000000029e-105

   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 z around 0 80.8%

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

   3. Taylor expanded in c around 0 75.0%

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

   if -6.20000000000000029e-105 < (*.f64 c i) < 1.0500000000000001e29

   1. Initial program 97.5%

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

      1. associate-+l+ 97.5%

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

      2. associate-+l+ 97.5%

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

      3. fma-def 97.5%

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

      4. fma-def 97.5%

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

      5. fma-def 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around 0 72.4%

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

   5. Taylor expanded in c around 0 69.0%

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

   if 1.0500000000000001e29 < (*.f64 c i)

   1. Initial program 94.9%

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

   2. Taylor expanded in a around inf 75.5%

      \[\leadsto \color{blue}{a \cdot b} + c \cdot i \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.46 \cdot 10^{-25}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -6.2 \cdot 10^{-105}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+29}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 8: 56.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := c \cdot i + z \cdot t\\ \mathbf{if}\;a \leq -6 \cdot 10^{+128}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -0.065:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-34}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))) (t_2 (+ (* c i) (* z t))))
   (if (<= a -6e+128)
     (+ (* a b) (* c i))
     (if (<= a -2.3e+65)
       t_1
       (if (<= a -0.065)
         t_2
         (if (<= a -1.26e-19)
           t_1
           (if (<= a -2e-151)
             t_2
             (if (<= a 6e-34) (+ (* x y) (* c i)) (* a b)))))))))

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);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if (a <= -6e+128) {
		tmp = (a * b) + (c * i);
	} else if (a <= -2.3e+65) {
		tmp = t_1;
	} else if (a <= -0.065) {
		tmp = t_2;
	} else if (a <= -1.26e-19) {
		tmp = t_1;
	} else if (a <= -2e-151) {
		tmp = t_2;
	} else if (a <= 6e-34) {
		tmp = (x * y) + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    t_2 = (c * i) + (z * t)
    if (a <= (-6d+128)) then
        tmp = (a * b) + (c * i)
    else if (a <= (-2.3d+65)) then
        tmp = t_1
    else if (a <= (-0.065d0)) then
        tmp = t_2
    else if (a <= (-1.26d-19)) then
        tmp = t_1
    else if (a <= (-2d-151)) then
        tmp = t_2
    else if (a <= 6d-34) then
        tmp = (x * y) + (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 t_1 = (a * b) + (x * y);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if (a <= -6e+128) {
		tmp = (a * b) + (c * i);
	} else if (a <= -2.3e+65) {
		tmp = t_1;
	} else if (a <= -0.065) {
		tmp = t_2;
	} else if (a <= -1.26e-19) {
		tmp = t_1;
	} else if (a <= -2e-151) {
		tmp = t_2;
	} else if (a <= 6e-34) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (c * i) + (z * t)
	tmp = 0
	if a <= -6e+128:
		tmp = (a * b) + (c * i)
	elif a <= -2.3e+65:
		tmp = t_1
	elif a <= -0.065:
		tmp = t_2
	elif a <= -1.26e-19:
		tmp = t_1
	elif a <= -2e-151:
		tmp = t_2
	elif a <= 6e-34:
		tmp = (x * y) + (c * i)
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (a <= -6e+128)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (a <= -2.3e+65)
		tmp = t_1;
	elseif (a <= -0.065)
		tmp = t_2;
	elseif (a <= -1.26e-19)
		tmp = t_1;
	elseif (a <= -2e-151)
		tmp = t_2;
	elseif (a <= 6e-34)
		tmp = Float64(Float64(x * y) + 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)
	t_1 = (a * b) + (x * y);
	t_2 = (c * i) + (z * t);
	tmp = 0.0;
	if (a <= -6e+128)
		tmp = (a * b) + (c * i);
	elseif (a <= -2.3e+65)
		tmp = t_1;
	elseif (a <= -0.065)
		tmp = t_2;
	elseif (a <= -1.26e-19)
		tmp = t_1;
	elseif (a <= -2e-151)
		tmp = t_2;
	elseif (a <= 6e-34)
		tmp = (x * y) + (c * i);
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+128], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.3e+65], t$95$1, If[LessEqual[a, -0.065], t$95$2, If[LessEqual[a, -1.26e-19], t$95$1, If[LessEqual[a, -2e-151], t$95$2, If[LessEqual[a, 6e-34], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.9999999999999997e128

   1. Initial program 93.9%

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

   2. Taylor expanded in a around inf 81.0%

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

   if -5.9999999999999997e128 < a < -2.3e65 or -0.065000000000000002 < a < -1.2599999999999999e-19

   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 z around 0 65.8%

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

   3. Taylor expanded in c around 0 72.7%

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

   if -2.3e65 < a < -0.065000000000000002 or -1.2599999999999999e-19 < a < -1.9999999999999999e-151

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 64.3%

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

   if -1.9999999999999999e-151 < a < 6e-34

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 66.7%

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

   if 6e-34 < a

   1. Initial program 93.7%

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

      1. associate-+l+ 93.7%

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

      2. fma-def 93.7%

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

   3. Simplified 93.7%

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

      1. fma-def 93.7%

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

      2. +-commutative 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in a around inf 42.3%

      \[\leadsto \color{blue}{a \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+128}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{+65}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \leq -0.065:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-19}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-151}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-34}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 9: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+185}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+76} \lor \neg \left(x \leq 5.8 \cdot 10^{-94}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (* x y)))))
   (if (<= x -7e+231)
     t_1
     (if (<= x -1.75e+185)
       (+ (* x y) (* z t))
       (if (or (<= x -5e+76) (not (<= x 5.8e-94)))
         t_1
         (+ (* 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 t_1 = (c * i) + ((a * b) + (x * y));
	double tmp;
	if (x <= -7e+231) {
		tmp = t_1;
	} else if (x <= -1.75e+185) {
		tmp = (x * y) + (z * t);
	} else if ((x <= -5e+76) || !(x <= 5.8e-94)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + ((a * b) + (x * y))
    if (x <= (-7d+231)) then
        tmp = t_1
    else if (x <= (-1.75d+185)) then
        tmp = (x * y) + (z * t)
    else if ((x <= (-5d+76)) .or. (.not. (x <= 5.8d-94))) then
        tmp = t_1
    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 t_1 = (c * i) + ((a * b) + (x * y));
	double tmp;
	if (x <= -7e+231) {
		tmp = t_1;
	} else if (x <= -1.75e+185) {
		tmp = (x * y) + (z * t);
	} else if ((x <= -5e+76) || !(x <= 5.8e-94)) {
		tmp = t_1;
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + ((a * b) + (x * y))
	tmp = 0
	if x <= -7e+231:
		tmp = t_1
	elif x <= -1.75e+185:
		tmp = (x * y) + (z * t)
	elif (x <= -5e+76) or not (x <= 5.8e-94):
		tmp = t_1
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)))
	tmp = 0.0
	if (x <= -7e+231)
		tmp = t_1;
	elseif (x <= -1.75e+185)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif ((x <= -5e+76) || !(x <= 5.8e-94))
		tmp = t_1;
	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)
	t_1 = (c * i) + ((a * b) + (x * y));
	tmp = 0.0;
	if (x <= -7e+231)
		tmp = t_1;
	elseif (x <= -1.75e+185)
		tmp = (x * y) + (z * t);
	elseif ((x <= -5e+76) || ~((x <= 5.8e-94)))
		tmp = t_1;
	else
		tmp = (c * i) + ((a * b) + (z * t));
	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[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+231], t$95$1, If[LessEqual[x, -1.75e+185], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5e+76], N[Not[LessEqual[x, 5.8e-94]], $MachinePrecision]], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.9999999999999997e231 or -1.75000000000000012e185 < x < -4.99999999999999991e76 or 5.79999999999999991e-94 < x

   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 0 82.0%

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

   if -6.9999999999999997e231 < x < -1.75000000000000012e185

   1. Initial program 72.7%

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

      1. associate-+l+ 72.7%

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

      2. associate-+l+ 72.7%

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

      3. fma-def 72.7%

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

      4. fma-def 72.7%

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

      5. fma-def 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in a around 0 65.0%

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

   5. Taylor expanded in c around 0 82.7%

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

   if -4.99999999999999991e76 < x < 5.79999999999999991e-94

   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 x around 0 91.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+231}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+185}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+76} \lor \neg \left(x \leq 5.8 \cdot 10^{-94}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 10: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.2 \cdot 10^{+64}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+38}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -8.2e+64)
   (+ (* c i) (+ (* a b) (* z t)))
   (if (<= (* a b) 1e+38)
     (+ (* c i) (+ (* x y) (* z t)))
     (+ (* c i) (+ (* a b) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -8.2e+64) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((a * b) <= 1e+38) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (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 ((a * b) <= (-8.2d+64)) then
        tmp = (c * i) + ((a * b) + (z * t))
    else if ((a * b) <= 1d+38) then
        tmp = (c * i) + ((x * y) + (z * t))
    else
        tmp = (c * i) + ((a * b) + (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 ((a * b) <= -8.2e+64) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((a * b) <= 1e+38) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -8.2e+64:
		tmp = (c * i) + ((a * b) + (z * t))
	elif (a * b) <= 1e+38:
		tmp = (c * i) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -8.2e+64)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	elseif (Float64(a * b) <= 1e+38)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -8.2e+64)
		tmp = (c * i) + ((a * b) + (z * t));
	elseif ((a * b) <= 1e+38)
		tmp = (c * i) + ((x * y) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -8.2e+64], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+38], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -8.19999999999999956e64

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0 82.7%

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

   if -8.19999999999999956e64 < (*.f64 a b) < 9.99999999999999977e37

   1. Initial program 97.9%

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

   2. Taylor expanded in a around 0 95.7%

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

   if 9.99999999999999977e37 < (*.f64 a b)

   1. Initial program 92.6%

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

   2. Taylor expanded in z around 0 85.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.2 \cdot 10^{+64}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+38}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]

Alternative 11: 36.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+97}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{+38}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-75}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-241}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-304}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-155}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -3.1e+97)
   (* x y)
   (if (<= x -1.42e+38)
     (* a b)
     (if (<= x -2.9e-75)
       (* z t)
       (if (<= x -2e-241)
         (* c i)
         (if (<= x -1.9e-304)
           (* a b)
           (if (<= x 1.35e-155) (* 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 <= -3.1e+97) {
		tmp = x * y;
	} else if (x <= -1.42e+38) {
		tmp = a * b;
	} else if (x <= -2.9e-75) {
		tmp = z * t;
	} else if (x <= -2e-241) {
		tmp = c * i;
	} else if (x <= -1.9e-304) {
		tmp = a * b;
	} else if (x <= 1.35e-155) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-3.1d+97)) then
        tmp = x * y
    else if (x <= (-1.42d+38)) then
        tmp = a * b
    else if (x <= (-2.9d-75)) then
        tmp = z * t
    else if (x <= (-2d-241)) then
        tmp = c * i
    else if (x <= (-1.9d-304)) then
        tmp = a * b
    else if (x <= 1.35d-155) then
        tmp = c * i
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -3.1e+97) {
		tmp = x * y;
	} else if (x <= -1.42e+38) {
		tmp = a * b;
	} else if (x <= -2.9e-75) {
		tmp = z * t;
	} else if (x <= -2e-241) {
		tmp = c * i;
	} else if (x <= -1.9e-304) {
		tmp = a * b;
	} else if (x <= 1.35e-155) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -3.1e+97:
		tmp = x * y
	elif x <= -1.42e+38:
		tmp = a * b
	elif x <= -2.9e-75:
		tmp = z * t
	elif x <= -2e-241:
		tmp = c * i
	elif x <= -1.9e-304:
		tmp = a * b
	elif x <= 1.35e-155:
		tmp = c * i
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -3.1e+97)
		tmp = Float64(x * y);
	elseif (x <= -1.42e+38)
		tmp = Float64(a * b);
	elseif (x <= -2.9e-75)
		tmp = Float64(z * t);
	elseif (x <= -2e-241)
		tmp = Float64(c * i);
	elseif (x <= -1.9e-304)
		tmp = Float64(a * b);
	elseif (x <= 1.35e-155)
		tmp = Float64(c * i);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -3.1e+97)
		tmp = x * y;
	elseif (x <= -1.42e+38)
		tmp = a * b;
	elseif (x <= -2.9e-75)
		tmp = z * t;
	elseif (x <= -2e-241)
		tmp = c * i;
	elseif (x <= -1.9e-304)
		tmp = a * b;
	elseif (x <= 1.35e-155)
		tmp = c * i;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -3.1e+97], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.42e+38], N[(a * b), $MachinePrecision], If[LessEqual[x, -2.9e-75], N[(z * t), $MachinePrecision], If[LessEqual[x, -2e-241], N[(c * i), $MachinePrecision], If[LessEqual[x, -1.9e-304], N[(a * b), $MachinePrecision], If[LessEqual[x, 1.35e-155], N[(c * i), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.09999999999999981e97 or 1.34999999999999991e-155 < x

   1. Initial program 93.9%

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

      1. associate-+l+ 93.9%

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

      2. fma-def 93.9%

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

   3. Simplified 93.9%

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

      1. fma-def 93.9%

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

      2. +-commutative 93.9%

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

   5. Applied egg-rr 93.9%

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

   6. Taylor expanded in x around inf 41.4%

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

   if -3.09999999999999981e97 < x < -1.4200000000000001e38 or -1.9999999999999999e-241 < x < -1.8999999999999998e-304

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-def 99.9%

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

      2. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around inf 33.9%

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

   if -1.4200000000000001e38 < x < -2.9000000000000002e-75

   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%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around inf 41.9%

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

   if -2.9000000000000002e-75 < x < -1.9999999999999999e-241 or -1.8999999999999998e-304 < x < 1.34999999999999991e-155

   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 c around inf 38.9%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+97}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{+38}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-75}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-241}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-304}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-155}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 12: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.75 \cdot 10^{-25} \lor \neg \left(c \cdot i \leq 4.4 \cdot 10^{+22}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.75e-25) (not (<= (* c i) 4.4e+22)))
   (+ (* a b) (* c i))
   (+ (* a b) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.75e-25) || !((c * i) <= 4.4e+22)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (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 (((c * i) <= (-1.75d-25)) .or. (.not. ((c * i) <= 4.4d+22))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (a * b) + (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 (((c * i) <= -1.75e-25) || !((c * i) <= 4.4e+22)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.75e-25) or not ((c * i) <= 4.4e+22):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.75e-25) || !(Float64(c * i) <= 4.4e+22))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -1.75e-25) || ~(((c * i) <= 4.4e+22)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.75e-25], N[Not[LessEqual[N[(c * i), $MachinePrecision], 4.4e+22]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.7500000000000001e-25 or 4.4e22 < (*.f64 c i)

   1. Initial program 95.0%

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

   2. Taylor expanded in a around inf 70.1%

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

   if -1.7500000000000001e-25 < (*.f64 c i) < 4.4e22

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 65.2%

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

   3. Taylor expanded in c around 0 61.8%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.75 \cdot 10^{-25} \lor \neg \left(c \cdot i \leq 4.4 \cdot 10^{+22}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 13: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -64000000:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+190}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -64000000.0)
   (+ (* x y) (* z t))
   (if (<= y 7.5e+190) (+ (* c i) (+ (* a b) (* z t))) (+ (* 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 (y <= -64000000.0) {
		tmp = (x * y) + (z * t);
	} else if (y <= 7.5e+190) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (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 (y <= (-64000000.0d0)) then
        tmp = (x * y) + (z * t)
    else if (y <= 7.5d+190) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (x * y) + (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 (y <= -64000000.0) {
		tmp = (x * y) + (z * t);
	} else if (y <= 7.5e+190) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -64000000.0:
		tmp = (x * y) + (z * t)
	elif y <= 7.5e+190:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -64000000.0)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (y <= 7.5e+190)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -64000000.0)
		tmp = (x * y) + (z * t);
	elseif (y <= 7.5e+190)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -64000000.0], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+190], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4e7

   1. Initial program 96.4%

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

      1. associate-+l+ 96.4%

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

      2. associate-+l+ 96.4%

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

      3. fma-def 96.4%

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

      4. fma-def 96.4%

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

      5. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in a around 0 80.6%

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

   5. Taylor expanded in c around 0 71.8%

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

   if -6.4e7 < y < 7.4999999999999994e190

   1. Initial program 98.8%

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

   2. Taylor expanded in x around 0 89.5%

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

   if 7.4999999999999994e190 < y

   1. Initial program 86.1%

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

   2. Taylor expanded in x around inf 78.3%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -64000000:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+190}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]

Alternative 14: 42.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.7 \cdot 10^{+145}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+187}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -4.7e+145) (* a b) (if (<= (* a b) 5e+187) (* 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) <= -4.7e+145) {
		tmp = a * b;
	} else if ((a * b) <= 5e+187) {
		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) <= (-4.7d+145)) then
        tmp = a * b
    else if ((a * b) <= 5d+187) 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) <= -4.7e+145) {
		tmp = a * b;
	} else if ((a * b) <= 5e+187) {
		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) <= -4.7e+145:
		tmp = a * b
	elif (a * b) <= 5e+187:
		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) <= -4.7e+145)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 5e+187)
		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) <= -4.7e+145)
		tmp = a * b;
	elseif ((a * b) <= 5e+187)
		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], -4.7e+145], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+187], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.7000000000000002e145 or 5.0000000000000001e187 < (*.f64 a b)

   1. Initial program 90.9%

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

      1. associate-+l+ 90.9%

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

      2. fma-def 90.9%

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

   3. Simplified 90.9%

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

      1. fma-def 90.9%

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

      2. +-commutative 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in a around inf 71.5%

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

   if -4.7000000000000002e145 < (*.f64 a b) < 5.0000000000000001e187

   1. Initial program 98.4%

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

   2. Taylor expanded in c around inf 34.8%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.7 \cdot 10^{+145}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+187}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 15: 53.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -82000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+174}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -82000000.0)
   (* x y)
   (if (<= y 5.2e+174) (+ (* 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 (y <= -82000000.0) {
		tmp = x * y;
	} else if (y <= 5.2e+174) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-82000000.0d0)) then
        tmp = x * y
    else if (y <= 5.2d+174) then
        tmp = (a * b) + (c * i)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -82000000.0) {
		tmp = x * y;
	} else if (y <= 5.2e+174) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -82000000.0:
		tmp = x * y
	elif y <= 5.2e+174:
		tmp = (a * b) + (c * i)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -82000000.0)
		tmp = Float64(x * y);
	elseif (y <= 5.2e+174)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -82000000.0)
		tmp = x * y;
	elseif (y <= 5.2e+174)
		tmp = (a * b) + (c * i);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -82000000.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 5.2e+174], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2e7 or 5.1999999999999997e174 < y

   1. Initial program 92.6%

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

      1. associate-+l+ 92.6%

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

      2. fma-def 92.6%

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

   3. Simplified 92.6%

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

      1. fma-def 92.6%

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

      2. +-commutative 92.6%

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

   5. Applied egg-rr 92.6%

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

   6. Taylor expanded in x around inf 61.0%

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

   if -8.2e7 < y < 5.1999999999999997e174

   1. Initial program 98.7%

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

   2. Taylor expanded in a around inf 61.5%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -82000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+174}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 16: 37.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+123}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-176}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -1.02e+123)
   (* a b)
   (if (<= a -4.9e-176) (* z t) (if (<= a 1.35e-36) (* 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 <= -1.02e+123) {
		tmp = a * b;
	} else if (a <= -4.9e-176) {
		tmp = z * t;
	} else if (a <= 1.35e-36) {
		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 <= (-1.02d+123)) then
        tmp = a * b
    else if (a <= (-4.9d-176)) then
        tmp = z * t
    else if (a <= 1.35d-36) 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 <= -1.02e+123) {
		tmp = a * b;
	} else if (a <= -4.9e-176) {
		tmp = z * t;
	} else if (a <= 1.35e-36) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -1.02e+123:
		tmp = a * b
	elif a <= -4.9e-176:
		tmp = z * t
	elif a <= 1.35e-36:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -1.02e+123)
		tmp = Float64(a * b);
	elseif (a <= -4.9e-176)
		tmp = Float64(z * t);
	elseif (a <= 1.35e-36)
		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 <= -1.02e+123)
		tmp = a * b;
	elseif (a <= -4.9e-176)
		tmp = z * t;
	elseif (a <= 1.35e-36)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -1.02e+123], N[(a * b), $MachinePrecision], If[LessEqual[a, -4.9e-176], N[(z * t), $MachinePrecision], If[LessEqual[a, 1.35e-36], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.02e123 or 1.35000000000000004e-36 < a

   1. Initial program 93.9%

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

      1. associate-+l+ 93.9%

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

      2. fma-def 93.9%

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

   3. Simplified 93.9%

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

      1. fma-def 93.9%

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

      2. +-commutative 93.9%

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

   5. Applied egg-rr 93.9%

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

   6. Taylor expanded in a around inf 47.4%

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

   if -1.02e123 < a < -4.8999999999999997e-176

   1. Initial program 96.6%

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

      1. associate-+l+ 96.6%

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

      2. fma-def 96.6%

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

   3. Simplified 96.6%

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

      1. fma-def 96.6%

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

      2. +-commutative 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in z around inf 36.5%

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

   if -4.8999999999999997e-176 < a < 1.35000000000000004e-36

   1. Initial program 99.0%

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

   2. Taylor expanded in c around inf 34.5%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+123}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-176}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 17: 27.4% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l+ 96.5%

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

   2. fma-def 96.5%

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

3. Simplified 96.5%

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

   1. fma-def 96.5%

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

   2. +-commutative 96.5%

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

5. Applied egg-rr 96.5%

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

6. Taylor expanded in a around inf 25.9%

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

7. Final simplification 25.9%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023240 
(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)))