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

Percentage Accurate: 95.8% → 97.8%

Time: 8.0s

Alternatives: 14

Speedup: 0.5×

• 41.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (+ (* a b) (+ (* z t) (* x y))) 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) + ((z * t) + (x * y))) <= ((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(z * t) + Float64(x * y))) <= 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[(z * t), $MachinePrecision] + N[(x * y), $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 96.3%

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

      1. +-commutative 96.3%

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

      2. fma-def 98.8%

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

      3. associate-+l+ 98.8%

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

      4. fma-def 98.8%

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

      5. fma-def 98.8%

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

   3. Simplified 98.8%

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

   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. Taylor expanded in x around inf 56.2%

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

4. Final simplification 97.3%

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

Alternative 2: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) + ((a * b) + ((z * t) + (x * y)))) <= ((double) INFINITY)) {
		tmp = (z * t) + ((x * y) + fma(a, b, (c * i)));
	} else {
		tmp = fma(y, x, (z * t));
	}
	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(z * t) + Float64(x * y)))) <= Inf)
		tmp = Float64(Float64(z * t) + Float64(Float64(x * y) + fma(a, b, Float64(c * i))));
	else
		tmp = fma(y, x, Float64(z * t));
	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[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(z * t), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(z * t), $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. +-commutative 100.0%

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

      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%

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

      2. fma-udef 100.0%

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

      3. fma-udef 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-+r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-+r+ 100.0%

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

      9. fma-def 100.0%

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

   5. Applied egg-rr 100.0%

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

   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 5.6%

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

      4. fma-def 22.2%

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

      5. fma-def 27.8%

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

   3. Simplified 27.8%

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

   4. Taylor expanded in a around 0 27.8%

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

   5. Taylor expanded in c around 0 44.7%

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

      1. fma-def 50.2%

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

   7. Simplified 50.2%

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

4. Final simplification 96.5%

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

Alternative 3: 97.8% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (+ (* a b) (+ (* z t) (* x y))) 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) + ((z * t) + (x * y))) <= ((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(z * t) + Float64(x * y))) <= 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[(z * t), $MachinePrecision] + N[(x * y), $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 96.3%

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

      1. +-commutative 96.3%

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

      2. fma-def 98.8%

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

      3. associate-+l+ 98.8%

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

      4. fma-def 98.8%

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

      5. fma-def 98.8%

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

   3. Simplified 98.8%

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

      1. fma-udef 98.8%

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

      2. fma-udef 98.8%

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

      3. associate-+l+ 98.8%

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

      4. +-commutative 98.8%

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

      5. associate-+r+ 98.8%

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

   5. Applied egg-rr 98.8%

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

   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. Taylor expanded in x around inf 56.2%

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

4. Final simplification 97.3%

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

Alternative 4: 97.8% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* z t) (* x y))))))
   (if (<= t_1 INFINITY) 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 = (c * i) + ((a * b) + ((z * t) + (x * y)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = 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(c * i) + Float64(Float64(a * b) + Float64(Float64(z * t) + Float64(x * y))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = 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[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, 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%

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

   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 38.9%

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

      1. fma-def 44.4%

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

   4. Simplified 44.4%

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

   5. Taylor expanded in c around 0 39.7%

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

      1. fma-def 45.3%

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

   7. Simplified 45.3%

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

4. Final simplification 96.1%

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

Alternative 5: 97.8% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* z t) (* x y))))))
   (if (<= t_1 INFINITY) t_1 (fma y x (* 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) + ((z * t) + (x * y)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(y, x, (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(Float64(z * t) + Float64(x * y))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(y, x, Float64(z * t));
	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[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * x + N[(z * t), $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. 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 5.6%

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

      4. fma-def 22.2%

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

      5. fma-def 27.8%

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

   3. Simplified 27.8%

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

   4. Taylor expanded in a around 0 27.8%

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

   5. Taylor expanded in c around 0 44.7%

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

      1. fma-def 50.2%

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

   7. Simplified 50.2%

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

4. Final simplification 96.5%

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

Alternative 6: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + x \cdot y\\ t_2 := c \cdot i + \left(a \cdot b + t_1\right)\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* x y))) (t_2 (+ (* c i) (+ (* a b) t_1))))
   (if (<= t_2 INFINITY) t_2 t_1)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (x * y);
	double t_2 = (c * i) + ((a * b) + t_1);
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} 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 = (z * t) + (x * y);
	double t_2 = (c * i) + ((a * b) + t_1);
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (x * y)
	t_2 = (c * i) + ((a * b) + t_1)
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(x * y))
	t_2 = Float64(Float64(c * i) + Float64(Float64(a * b) + t_1))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z * t) + (x * y);
	t_2 = (c * i) + ((a * b) + t_1);
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	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[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, 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%

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

   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 5.6%

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

      4. fma-def 22.2%

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

      5. fma-def 27.8%

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

   3. Simplified 27.8%

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

   4. Taylor expanded in a around 0 27.8%

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

   5. Taylor expanded in c around 0 44.7%

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

4. Final simplification 96.1%

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

Alternative 7: 43.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.2 \cdot 10^{+59}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-294}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{-241}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.85 \cdot 10^{-23}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.12 \cdot 10^{+64}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.2e+59)
   (* a b)
   (if (<= (* a b) 2e-294)
     (* x y)
     (if (<= (* a b) 3.8e-241)
       (* z t)
       (if (<= (* a b) 1.85e-23)
         (* x y)
         (if (<= (* a b) 1.12e+64)
           (* c i)
           (if (<= (* a b) 3.2e+72) (* x y) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.2e+59) {
		tmp = a * b;
	} else if ((a * b) <= 2e-294) {
		tmp = x * y;
	} else if ((a * b) <= 3.8e-241) {
		tmp = z * t;
	} else if ((a * b) <= 1.85e-23) {
		tmp = x * y;
	} else if ((a * b) <= 1.12e+64) {
		tmp = c * i;
	} else if ((a * b) <= 3.2e+72) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-1.2d+59)) then
        tmp = a * b
    else if ((a * b) <= 2d-294) then
        tmp = x * y
    else if ((a * b) <= 3.8d-241) then
        tmp = z * t
    else if ((a * b) <= 1.85d-23) then
        tmp = x * y
    else if ((a * b) <= 1.12d+64) then
        tmp = c * i
    else if ((a * b) <= 3.2d+72) then
        tmp = x * y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.2e+59) {
		tmp = a * b;
	} else if ((a * b) <= 2e-294) {
		tmp = x * y;
	} else if ((a * b) <= 3.8e-241) {
		tmp = z * t;
	} else if ((a * b) <= 1.85e-23) {
		tmp = x * y;
	} else if ((a * b) <= 1.12e+64) {
		tmp = c * i;
	} else if ((a * b) <= 3.2e+72) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.2e+59:
		tmp = a * b
	elif (a * b) <= 2e-294:
		tmp = x * y
	elif (a * b) <= 3.8e-241:
		tmp = z * t
	elif (a * b) <= 1.85e-23:
		tmp = x * y
	elif (a * b) <= 1.12e+64:
		tmp = c * i
	elif (a * b) <= 3.2e+72:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.2e+59)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 2e-294)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 3.8e-241)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.85e-23)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.12e+64)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 3.2e+72)
		tmp = Float64(x * y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.2e+59)
		tmp = a * b;
	elseif ((a * b) <= 2e-294)
		tmp = x * y;
	elseif ((a * b) <= 3.8e-241)
		tmp = z * t;
	elseif ((a * b) <= 1.85e-23)
		tmp = x * y;
	elseif ((a * b) <= 1.12e+64)
		tmp = c * i;
	elseif ((a * b) <= 3.2e+72)
		tmp = x * y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.2e+59], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e-294], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.8e-241], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.85e-23], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.12e+64], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.2e+72], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.2000000000000001e59 or 3.2000000000000001e72 < (*.f64 a b)

   1. Initial program 92.7%

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

   2. Taylor expanded in a around inf 62.0%

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

   if -1.2000000000000001e59 < (*.f64 a b) < 2.00000000000000003e-294 or 3.7999999999999999e-241 < (*.f64 a b) < 1.8500000000000001e-23 or 1.11999999999999995e64 < (*.f64 a b) < 3.2000000000000001e72

   1. Initial program 94.1%

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

   2. Taylor expanded in x around inf 48.5%

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

   if 2.00000000000000003e-294 < (*.f64 a b) < 3.7999999999999999e-241

   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 55.9%

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

   if 1.8500000000000001e-23 < (*.f64 a b) < 1.11999999999999995e64

   1. Initial program 85.7%

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

   2. Taylor expanded in c around inf 42.9%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.2 \cdot 10^{+59}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-294}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{-241}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.85 \cdot 10^{-23}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.12 \cdot 10^{+64}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 8: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.6 \cdot 10^{+139} \lor \neg \left(c \cdot i \leq 1.25 \cdot 10^{+218}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -5.6e+139) (not (<= (* c i) 1.25e+218)))
   (+ (* a b) (* c i))
   (+ (* 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 (((c * i) <= -5.6e+139) || !((c * i) <= 1.25e+218)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + ((z * t) + (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) <= (-5.6d+139)) .or. (.not. ((c * i) <= 1.25d+218))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (a * b) + ((z * t) + (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) <= -5.6e+139) || !((c * i) <= 1.25e+218)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + ((z * t) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -5.6e+139) or not ((c * i) <= 1.25e+218):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + ((z * t) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -5.6e+139) || !(Float64(c * i) <= 1.25e+218))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(z * t) + 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) <= -5.6e+139) || ~(((c * i) <= 1.25e+218)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + ((z * t) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -5.6e+139], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.25e+218]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -5.5999999999999997e139 or 1.24999999999999996e218 < (*.f64 c i)

   1. Initial program 82.2%

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

   2. Taylor expanded in x around 0 77.0%

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

      1. fma-def 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in t around 0 75.7%

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

   if -5.5999999999999997e139 < (*.f64 c i) < 1.24999999999999996e218

   1. Initial program 97.2%

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

   2. Taylor expanded in c around 0 88.3%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.6 \cdot 10^{+139} \lor \neg \left(c \cdot i \leq 1.25 \cdot 10^{+218}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 9: 62.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+204}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3 \cdot 10^{+217}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.7e+204)
   (* c i)
   (if (<= (* c i) 3e+217) (+ (* 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) <= -3.7e+204) {
		tmp = c * i;
	} else if ((c * i) <= 3e+217) {
		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) <= (-3.7d+204)) then
        tmp = c * i
    else if ((c * i) <= 3d+217) 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) <= -3.7e+204) {
		tmp = c * i;
	} else if ((c * i) <= 3e+217) {
		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) <= -3.7e+204:
		tmp = c * i
	elif (c * i) <= 3e+217:
		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) <= -3.7e+204)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 3e+217)
		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) <= -3.7e+204)
		tmp = c * i;
	elseif ((c * i) <= 3e+217)
		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], -3.7e+204], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3e+217], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.7e204 or 2.99999999999999976e217 < (*.f64 c i)

   1. Initial program 79.3%

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

   2. Taylor expanded in c around inf 65.0%

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

   if -3.7e204 < (*.f64 c i) < 2.99999999999999976e217

   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 0 78.2%

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

      1. fma-def 78.2%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in c around 0 69.0%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+204}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3 \cdot 10^{+217}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 10: 61.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+107}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+36} \lor \neg \left(x \leq 7800000\right):\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -4.2e+107)
   (+ (* a b) (* x y))
   (if (or (<= x -4.8e+36) (not (<= x 7800000.0)))
     (+ (* z t) (* x y))
     (+ (* a b) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -4.2e+107) {
		tmp = (a * b) + (x * y);
	} else if ((x <= -4.8e+36) || !(x <= 7800000.0)) {
		tmp = (z * t) + (x * y);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-4.2d+107)) then
        tmp = (a * b) + (x * y)
    else if ((x <= (-4.8d+36)) .or. (.not. (x <= 7800000.0d0))) then
        tmp = (z * t) + (x * y)
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -4.2e+107) {
		tmp = (a * b) + (x * y);
	} else if ((x <= -4.8e+36) || !(x <= 7800000.0)) {
		tmp = (z * t) + (x * y);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -4.2e+107:
		tmp = (a * b) + (x * y)
	elif (x <= -4.8e+36) or not (x <= 7800000.0):
		tmp = (z * t) + (x * y)
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -4.2e+107)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif ((x <= -4.8e+36) || !(x <= 7800000.0))
		tmp = Float64(Float64(z * t) + Float64(x * y));
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -4.2e+107)
		tmp = (a * b) + (x * y);
	elseif ((x <= -4.8e+36) || ~((x <= 7800000.0)))
		tmp = (z * t) + (x * y);
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -4.2e+107], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -4.8e+36], N[Not[LessEqual[x, 7800000.0]], $MachinePrecision]], N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1999999999999999e107

   1. Initial program 89.1%

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

   2. Taylor expanded in z around 0 89.1%

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

      1. fma-def 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in c around 0 84.5%

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

   if -4.1999999999999999e107 < x < -4.79999999999999985e36 or 7.8e6 < x

   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 93.1%

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

      4. fma-def 93.1%

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

      5. fma-def 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in a around 0 70.3%

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

   5. Taylor expanded in c around 0 53.9%

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

   if -4.79999999999999985e36 < x < 7.8e6

   1. Initial program 94.8%

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

   2. Taylor expanded in x around 0 85.1%

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

      1. fma-def 86.6%

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

   4. Simplified 86.6%

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

   5. Taylor expanded in t around 0 62.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+107}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+36} \lor \neg \left(x \leq 7800000\right):\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 11: 78.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+42}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -4.8e+42)
   (+ (* a b) (+ (* z t) (* x y)))
   (+ (* c i) (+ (* z t) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -4.8e+42) {
		tmp = (a * b) + ((z * t) + (x * y));
	} else {
		tmp = (c * i) + ((z * t) + (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 (x <= (-4.8d+42)) then
        tmp = (a * b) + ((z * t) + (x * y))
    else
        tmp = (c * i) + ((z * t) + (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 (x <= -4.8e+42) {
		tmp = (a * b) + ((z * t) + (x * y));
	} else {
		tmp = (c * i) + ((z * t) + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -4.8e+42:
		tmp = (a * b) + ((z * t) + (x * y))
	else:
		tmp = (c * i) + ((z * t) + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -4.8e+42)
		tmp = Float64(Float64(a * b) + Float64(Float64(z * t) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(z * t) + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -4.8e+42)
		tmp = (a * b) + ((z * t) + (x * y));
	else
		tmp = (c * i) + ((z * t) + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -4.8e+42], N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7999999999999997e42

   1. Initial program 90.1%

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

   2. Taylor expanded in c around 0 85.0%

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

   if -4.7999999999999997e42 < x

   1. Initial program 93.8%

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

   2. Taylor expanded in x around 0 77.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+42}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \end{array} \]

Alternative 12: 43.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.6 \cdot 10^{+23}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 3.1 \cdot 10^{+74}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -6.6e+23) (* a b) (if (<= (* a b) 3.1e+74) (* 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) <= -6.6e+23) {
		tmp = a * b;
	} else if ((a * b) <= 3.1e+74) {
		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) <= (-6.6d+23)) then
        tmp = a * b
    else if ((a * b) <= 3.1d+74) 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) <= -6.6e+23) {
		tmp = a * b;
	} else if ((a * b) <= 3.1e+74) {
		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) <= -6.6e+23:
		tmp = a * b
	elif (a * b) <= 3.1e+74:
		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) <= -6.6e+23)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 3.1e+74)
		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) <= -6.6e+23)
		tmp = a * b;
	elseif ((a * b) <= 3.1e+74)
		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], -6.6e+23], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.1e+74], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -6.60000000000000059e23 or 3.10000000000000021e74 < (*.f64 a b)

   1. Initial program 93.1%

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

   2. Taylor expanded in a around inf 60.3%

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

   if -6.60000000000000059e23 < (*.f64 a b) < 3.10000000000000021e74

   1. Initial program 92.8%

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

   2. Taylor expanded in c around inf 34.4%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.6 \cdot 10^{+23}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 3.1 \cdot 10^{+74}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 13: 56.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+22}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -5e+22) (+ (* a b) (* x y)) (+ (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -5e+22) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-5d+22)) then
        tmp = (a * b) + (x * y)
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -5e+22) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -5e+22:
		tmp = (a * b) + (x * y)
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -5e+22)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -5e+22)
		tmp = (a * b) + (x * y);
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -5e+22], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9999999999999996e22

   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 z around 0 85.2%

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

      1. fma-def 86.7%

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

   4. Simplified 86.7%

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

   5. Taylor expanded in c around 0 79.2%

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

   if -4.9999999999999996e22 < x

   1. Initial program 94.1%

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

   2. Taylor expanded in x around 0 77.3%

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

      1. fma-def 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in t around 0 59.5%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+22}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 14: 28.1% 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 92.9%

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

2. Taylor expanded in a around inf 33.2%

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

3. Final simplification 33.2%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023196 
(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)))