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

Percentage Accurate: 95.6% → 97.7%

Time: 12.0s

Alternatives: 12

Speedup: 0.5×

• 42.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. associate-+l+ 93.7%

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

   3. fma-def 95.3%

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

   4. associate-+r+ 95.3%

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

   5. +-commutative 95.3%

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

   6. associate-+l+ 95.3%

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

   7. fma-def 96.1%

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

   8. +-commutative 96.1%

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

   9. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 2: 97.7% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

   1. +-commutative 93.7%

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

   2. fma-def 95.7%

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

   3. +-commutative 95.7%

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

   4. fma-def 96.9%

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

   5. fma-def 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 3: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   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. fma-def 0.0%

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

      2. add-cube-cbrt 0.0%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}} + a \cdot b\right) + c \cdot i \]

      3. pow3 0.0%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   3. Applied egg-rr 0.0%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   4. Taylor expanded in x around 0 25.0%

      \[\leadsto \left(\color{blue}{{1}^{0.3333333333333333} \cdot \left(t \cdot z\right)} + a \cdot b\right) + c \cdot i \]
   5. Step-by-step derivation

      1. associate-*r* 25.0%

         \[\leadsto \left(\color{blue}{\left({1}^{0.3333333333333333} \cdot t\right) \cdot z} + a \cdot b\right) + c \cdot i \]

      2. pow-base-1 25.0%

         \[\leadsto \left(\left(\color{blue}{1} \cdot t\right) \cdot z + a \cdot b\right) + c \cdot i \]

      3. *-lft-identity 25.0%

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

   6. Simplified 25.0%

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

      1. associate-+l+ 25.0%

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

      2. *-commutative 25.0%

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

      3. fma-def 43.8%

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

      4. fma-def 50.0%

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

   8. Applied egg-rr 50.0%

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

4. Final simplification 96.9%

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

Alternative 4: 96.8% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

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

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

      2. add-cube-cbrt 0.0%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}} + a \cdot b\right) + c \cdot i \]

      3. pow3 0.0%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   3. Applied egg-rr 0.0%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   4. Taylor expanded in x around 0 25.0%

      \[\leadsto \left(\color{blue}{{1}^{0.3333333333333333} \cdot \left(t \cdot z\right)} + a \cdot b\right) + c \cdot i \]
   5. Step-by-step derivation

      1. associate-*r* 25.0%

         \[\leadsto \left(\color{blue}{\left({1}^{0.3333333333333333} \cdot t\right) \cdot z} + a \cdot b\right) + c \cdot i \]

      2. pow-base-1 25.0%

         \[\leadsto \left(\left(\color{blue}{1} \cdot t\right) \cdot z + a \cdot b\right) + c \cdot i \]

      3. *-lft-identity 25.0%

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

   6. Simplified 25.0%

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

   7. Taylor expanded in c around 0 44.2%

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

4. Final simplification 96.5%

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

Alternative 5: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -2.15 \cdot 10^{+238}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.4 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -2.2 \cdot 10^{+106} \lor \neg \left(x \cdot y \leq 7.2 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* x y) -2.15e+238)
     (* x y)
     (if (<= (* x y) -3.4e+199)
       t_1
       (if (or (<= (* x y) -2.2e+106) (not (<= (* x y) 7.2e+133)))
         (* x y)
         (+ (* c i) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -2.15e+238) {
		tmp = x * y;
	} else if ((x * y) <= -3.4e+199) {
		tmp = t_1;
	} else if (((x * y) <= -2.2e+106) || !((x * y) <= 7.2e+133)) {
		tmp = x * y;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((x * y) <= (-2.15d+238)) then
        tmp = x * y
    else if ((x * y) <= (-3.4d+199)) then
        tmp = t_1
    else if (((x * y) <= (-2.2d+106)) .or. (.not. ((x * y) <= 7.2d+133))) then
        tmp = x * y
    else
        tmp = (c * i) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -2.15e+238) {
		tmp = x * y;
	} else if ((x * y) <= -3.4e+199) {
		tmp = t_1;
	} else if (((x * y) <= -2.2e+106) || !((x * y) <= 7.2e+133)) {
		tmp = x * y;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -2.15e+238:
		tmp = x * y
	elif (x * y) <= -3.4e+199:
		tmp = t_1
	elif ((x * y) <= -2.2e+106) or not ((x * y) <= 7.2e+133):
		tmp = x * y
	else:
		tmp = (c * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -2.15e+238)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.4e+199)
		tmp = t_1;
	elseif ((Float64(x * y) <= -2.2e+106) || !(Float64(x * y) <= 7.2e+133))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(c * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -2.15e+238)
		tmp = x * y;
	elseif ((x * y) <= -3.4e+199)
		tmp = t_1;
	elseif (((x * y) <= -2.2e+106) || ~(((x * y) <= 7.2e+133)))
		tmp = x * y;
	else
		tmp = (c * i) + t_1;
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.15e+238], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.4e+199], t$95$1, If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.2e+106], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.2e+133]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.14999999999999992e238 or -3.4e199 < (*.f64 x y) < -2.19999999999999992e106 or 7.19999999999999956e133 < (*.f64 x y)

   1. Initial program 88.6%

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

   2. Taylor expanded in x around inf 77.7%

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

   if -2.14999999999999992e238 < (*.f64 x y) < -3.4e199

   1. Initial program 83.3%

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

      1. fma-def 83.3%

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

      2. add-cube-cbrt 83.3%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}} + a \cdot b\right) + c \cdot i \]

      3. pow3 83.3%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   3. Applied egg-rr 83.3%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   4. Taylor expanded in x around 0 68.0%

      \[\leadsto \left(\color{blue}{{1}^{0.3333333333333333} \cdot \left(t \cdot z\right)} + a \cdot b\right) + c \cdot i \]
   5. Step-by-step derivation

      1. associate-*r* 68.0%

         \[\leadsto \left(\color{blue}{\left({1}^{0.3333333333333333} \cdot t\right) \cdot z} + a \cdot b\right) + c \cdot i \]

      2. pow-base-1 68.0%

         \[\leadsto \left(\left(\color{blue}{1} \cdot t\right) \cdot z + a \cdot b\right) + c \cdot i \]

      3. *-lft-identity 68.0%

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

   6. Simplified 68.0%

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

   7. Taylor expanded in c around 0 84.7%

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

   if -2.19999999999999992e106 < (*.f64 x y) < 7.19999999999999956e133

   1. Initial program 96.1%

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

   2. Taylor expanded in x around 0 89.7%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.15 \cdot 10^{+238}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.4 \cdot 10^{+199}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2.2 \cdot 10^{+106} \lor \neg \left(x \cdot y \leq 7.2 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 6: 42.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.4 \cdot 10^{+112}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -9.2 \cdot 10^{+86}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.3 \cdot 10^{-27}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -4.4 \cdot 10^{-264}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.66 \cdot 10^{+121}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5.4e+112)
   (* a b)
   (if (<= (* a b) -9.2e+86)
     (* x y)
     (if (<= (* a b) -1.3e-27)
       (* z t)
       (if (<= (* a b) -4.4e-264)
         (* c i)
         (if (<= (* a b) 1.66e+121) (* 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) <= -5.4e+112) {
		tmp = a * b;
	} else if ((a * b) <= -9.2e+86) {
		tmp = x * y;
	} else if ((a * b) <= -1.3e-27) {
		tmp = z * t;
	} else if ((a * b) <= -4.4e-264) {
		tmp = c * i;
	} else if ((a * b) <= 1.66e+121) {
		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) <= (-5.4d+112)) then
        tmp = a * b
    else if ((a * b) <= (-9.2d+86)) then
        tmp = x * y
    else if ((a * b) <= (-1.3d-27)) then
        tmp = z * t
    else if ((a * b) <= (-4.4d-264)) then
        tmp = c * i
    else if ((a * b) <= 1.66d+121) 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) <= -5.4e+112) {
		tmp = a * b;
	} else if ((a * b) <= -9.2e+86) {
		tmp = x * y;
	} else if ((a * b) <= -1.3e-27) {
		tmp = z * t;
	} else if ((a * b) <= -4.4e-264) {
		tmp = c * i;
	} else if ((a * b) <= 1.66e+121) {
		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) <= -5.4e+112:
		tmp = a * b
	elif (a * b) <= -9.2e+86:
		tmp = x * y
	elif (a * b) <= -1.3e-27:
		tmp = z * t
	elif (a * b) <= -4.4e-264:
		tmp = c * i
	elif (a * b) <= 1.66e+121:
		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) <= -5.4e+112)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -9.2e+86)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -1.3e-27)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -4.4e-264)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 1.66e+121)
		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) <= -5.4e+112)
		tmp = a * b;
	elseif ((a * b) <= -9.2e+86)
		tmp = x * y;
	elseif ((a * b) <= -1.3e-27)
		tmp = z * t;
	elseif ((a * b) <= -4.4e-264)
		tmp = c * i;
	elseif ((a * b) <= 1.66e+121)
		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], -5.4e+112], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -9.2e+86], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.3e-27], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4.4e-264], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.66e+121], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -5.4000000000000002e112 or 1.66000000000000002e121 < (*.f64 a b)

   1. Initial program 87.8%

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

   2. Taylor expanded in a around inf 63.3%

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

   if -5.4000000000000002e112 < (*.f64 a b) < -9.19999999999999958e86 or -4.39999999999999988e-264 < (*.f64 a b) < 1.66000000000000002e121

   1. Initial program 98.2%

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

   2. Taylor expanded in x around inf 42.1%

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

   if -9.19999999999999958e86 < (*.f64 a b) < -1.30000000000000009e-27

   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 inf 54.3%

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

   if -1.30000000000000009e-27 < (*.f64 a b) < -4.39999999999999988e-264

   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 c around inf 56.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.4 \cdot 10^{+112}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -9.2 \cdot 10^{+86}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.3 \cdot 10^{-27}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -4.4 \cdot 10^{-264}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.66 \cdot 10^{+121}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 7: 63.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -2.4 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 7.6 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 5.6 \cdot 10^{-40}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -2.4e+143)
     t_2
     (if (<= (* c i) 7.6e-87)
       t_1
       (if (<= (* c i) 5.6e-40) (* x y) (if (<= (* c i) 2e+206) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -2.4e+143) {
		tmp = t_2;
	} else if ((c * i) <= 7.6e-87) {
		tmp = t_1;
	} else if ((c * i) <= 5.6e-40) {
		tmp = x * y;
	} else if ((c * i) <= 2e+206) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-2.4d+143)) then
        tmp = t_2
    else if ((c * i) <= 7.6d-87) then
        tmp = t_1
    else if ((c * i) <= 5.6d-40) then
        tmp = x * y
    else if ((c * i) <= 2d+206) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -2.4e+143) {
		tmp = t_2;
	} else if ((c * i) <= 7.6e-87) {
		tmp = t_1;
	} else if ((c * i) <= 5.6e-40) {
		tmp = x * y;
	} else if ((c * i) <= 2e+206) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -2.4e+143:
		tmp = t_2
	elif (c * i) <= 7.6e-87:
		tmp = t_1
	elif (c * i) <= 5.6e-40:
		tmp = x * y
	elif (c * i) <= 2e+206:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -2.4e+143)
		tmp = t_2;
	elseif (Float64(c * i) <= 7.6e-87)
		tmp = t_1;
	elseif (Float64(c * i) <= 5.6e-40)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 2e+206)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -2.4e+143)
		tmp = t_2;
	elseif ((c * i) <= 7.6e-87)
		tmp = t_1;
	elseif ((c * i) <= 5.6e-40)
		tmp = x * y;
	elseif ((c * i) <= 2e+206)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.4e+143], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 7.6e-87], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 5.6e-40], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2e+206], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.3999999999999998e143 or 2.0000000000000001e206 < (*.f64 c i)

   1. Initial program 85.1%

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

      1. fma-def 85.1%

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

      2. add-cube-cbrt 85.1%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}} + a \cdot b\right) + c \cdot i \]

      3. pow3 85.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   3. Applied egg-rr 85.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   4. Taylor expanded in x around inf 77.0%

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

   if -2.3999999999999998e143 < (*.f64 c i) < 7.6e-87 or 5.5999999999999999e-40 < (*.f64 c i) < 2.0000000000000001e206

   1. Initial program 96.7%

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

      1. fma-def 96.7%

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

      2. add-cube-cbrt 95.8%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}} + a \cdot b\right) + c \cdot i \]

      3. pow3 95.8%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   3. Applied egg-rr 95.8%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   4. Taylor expanded in x around 0 71.8%

      \[\leadsto \left(\color{blue}{{1}^{0.3333333333333333} \cdot \left(t \cdot z\right)} + a \cdot b\right) + c \cdot i \]
   5. Step-by-step derivation

      1. associate-*r* 71.8%

         \[\leadsto \left(\color{blue}{\left({1}^{0.3333333333333333} \cdot t\right) \cdot z} + a \cdot b\right) + c \cdot i \]

      2. pow-base-1 71.8%

         \[\leadsto \left(\left(\color{blue}{1} \cdot t\right) \cdot z + a \cdot b\right) + c \cdot i \]

      3. *-lft-identity 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in c around 0 64.8%

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

   if 7.6e-87 < (*.f64 c i) < 5.5999999999999999e-40

   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 inf 85.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.4 \cdot 10^{+143}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 7.6 \cdot 10^{-87}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5.6 \cdot 10^{-40}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+206}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 8: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -9.2 \cdot 10^{+86}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4200000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 1.65 \cdot 10^{+56}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.04 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* a b) -9.2e+86)
     (+ (* a b) (* c i))
     (if (<= (* a b) 4200000000.0)
       t_1
       (if (<= (* a b) 1.65e+56)
         (* x y)
         (if (<= (* a b) 1.04e+77) t_1 (+ (* 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) + (z * t);
	double tmp;
	if ((a * b) <= -9.2e+86) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= 4200000000.0) {
		tmp = t_1;
	} else if ((a * b) <= 1.65e+56) {
		tmp = x * y;
	} else if ((a * b) <= 1.04e+77) {
		tmp = t_1;
	} else {
		tmp = (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) + (z * t)
    if ((a * b) <= (-9.2d+86)) then
        tmp = (a * b) + (c * i)
    else if ((a * b) <= 4200000000.0d0) then
        tmp = t_1
    else if ((a * b) <= 1.65d+56) then
        tmp = x * y
    else if ((a * b) <= 1.04d+77) then
        tmp = t_1
    else
        tmp = (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) + (z * t);
	double tmp;
	if ((a * b) <= -9.2e+86) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= 4200000000.0) {
		tmp = t_1;
	} else if ((a * b) <= 1.65e+56) {
		tmp = x * y;
	} else if ((a * b) <= 1.04e+77) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (a * b) <= -9.2e+86:
		tmp = (a * b) + (c * i)
	elif (a * b) <= 4200000000.0:
		tmp = t_1
	elif (a * b) <= 1.65e+56:
		tmp = x * y
	elif (a * b) <= 1.04e+77:
		tmp = t_1
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -9.2e+86)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(a * b) <= 4200000000.0)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.65e+56)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.04e+77)
		tmp = t_1;
	else
		tmp = 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) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -9.2e+86)
		tmp = (a * b) + (c * i);
	elseif ((a * b) <= 4200000000.0)
		tmp = t_1;
	elseif ((a * b) <= 1.65e+56)
		tmp = x * y;
	elseif ((a * b) <= 1.04e+77)
		tmp = t_1;
	else
		tmp = (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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -9.2e+86], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4200000000.0], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.65e+56], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.04e+77], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -9.19999999999999958e86

   1. Initial program 85.5%

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

      1. fma-def 85.5%

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

      2. add-cube-cbrt 85.3%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}} + a \cdot b\right) + c \cdot i \]

      3. pow3 85.2%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   3. Applied egg-rr 85.2%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   4. Taylor expanded in x around inf 68.0%

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

   if -9.19999999999999958e86 < (*.f64 a b) < 4.2e9 or 1.65000000000000001e56 < (*.f64 a b) < 1.04e77

   1. Initial program 97.2%

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

      1. fma-def 97.2%

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

      2. add-cube-cbrt 96.3%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}} + a \cdot b\right) + c \cdot i \]

      3. pow3 96.4%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   3. Applied egg-rr 96.4%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   4. Taylor expanded in x around 0 72.7%

      \[\leadsto \left(\color{blue}{{1}^{0.3333333333333333} \cdot \left(t \cdot z\right)} + a \cdot b\right) + c \cdot i \]
   5. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto \left(\color{blue}{\left({1}^{0.3333333333333333} \cdot t\right) \cdot z} + a \cdot b\right) + c \cdot i \]

      2. pow-base-1 72.7%

         \[\leadsto \left(\left(\color{blue}{1} \cdot t\right) \cdot z + a \cdot b\right) + c \cdot i \]

      3. *-lft-identity 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in a around 0 67.5%

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

   if 4.2e9 < (*.f64 a b) < 1.65000000000000001e56

   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 x around inf 86.5%

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

   if 1.04e77 < (*.f64 a b)

   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. fma-def 93.9%

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

      2. add-cube-cbrt 93.6%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}} + a \cdot b\right) + c \cdot i \]

      3. pow3 93.6%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   3. Applied egg-rr 93.6%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   4. Taylor expanded in x around 0 90.0%

      \[\leadsto \left(\color{blue}{{1}^{0.3333333333333333} \cdot \left(t \cdot z\right)} + a \cdot b\right) + c \cdot i \]
   5. Step-by-step derivation

      1. associate-*r* 90.0%

         \[\leadsto \left(\color{blue}{\left({1}^{0.3333333333333333} \cdot t\right) \cdot z} + a \cdot b\right) + c \cdot i \]

      2. pow-base-1 90.0%

         \[\leadsto \left(\left(\color{blue}{1} \cdot t\right) \cdot z + a \cdot b\right) + c \cdot i \]

      3. *-lft-identity 90.0%

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

   6. Simplified 90.0%

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

   7. Taylor expanded in c around 0 82.1%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.2 \cdot 10^{+86}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4200000000:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.65 \cdot 10^{+56}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.04 \cdot 10^{+77}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 9: 42.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.9 \cdot 10^{+194}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.75 \cdot 10^{-263}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.4 \cdot 10^{+148}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -4.9e+194)
   (* a b)
   (if (<= (* a b) -2.75e-263)
     (* c i)
     (if (<= (* a b) 3.4e+148) (* 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 ((a * b) <= -4.9e+194) {
		tmp = a * b;
	} else if ((a * b) <= -2.75e-263) {
		tmp = c * i;
	} else if ((a * b) <= 3.4e+148) {
		tmp = z * t;
	} 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) <= (-4.9d+194)) then
        tmp = a * b
    else if ((a * b) <= (-2.75d-263)) then
        tmp = c * i
    else if ((a * b) <= 3.4d+148) then
        tmp = z * t
    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) <= -4.9e+194) {
		tmp = a * b;
	} else if ((a * b) <= -2.75e-263) {
		tmp = c * i;
	} else if ((a * b) <= 3.4e+148) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -4.9e+194:
		tmp = a * b
	elif (a * b) <= -2.75e-263:
		tmp = c * i
	elif (a * b) <= 3.4e+148:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -4.9e+194)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -2.75e-263)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 3.4e+148)
		tmp = Float64(z * t);
	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) <= -4.9e+194)
		tmp = a * b;
	elseif ((a * b) <= -2.75e-263)
		tmp = c * i;
	elseif ((a * b) <= 3.4e+148)
		tmp = z * t;
	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], -4.9e+194], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.75e-263], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.4e+148], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.90000000000000026e194 or 3.4000000000000003e148 < (*.f64 a b)

   1. Initial program 87.8%

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

   2. Taylor expanded in a around inf 69.9%

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

   if -4.90000000000000026e194 < (*.f64 a b) < -2.74999999999999986e-263

   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 c around inf 41.7%

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

   if -2.74999999999999986e-263 < (*.f64 a b) < 3.4000000000000003e148

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 38.5%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.9 \cdot 10^{+194}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.75 \cdot 10^{-263}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.4 \cdot 10^{+148}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 10: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.38 \cdot 10^{+79} \lor \neg \left(x \cdot y \leq 3.7 \cdot 10^{+119}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.38e+79) (not (<= (* x y) 3.7e+119)))
   (* x y)
   (+ (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.38e+79) || !((x * y) <= 3.7e+119)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1.38d+79)) .or. (.not. ((x * y) <= 3.7d+119))) then
        tmp = x * y
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.38e+79) || !((x * y) <= 3.7e+119)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.38e+79) or not ((x * y) <= 3.7e+119):
		tmp = x * y
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.38e+79) || !(Float64(x * y) <= 3.7e+119))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.38e+79) || ~(((x * y) <= 3.7e+119)))
		tmp = x * y;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.38e+79], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.7e+119]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.38e79 or 3.7e119 < (*.f64 x y)

   1. Initial program 89.0%

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

   2. Taylor expanded in x around inf 70.3%

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

   if -1.38e79 < (*.f64 x y) < 3.7e119

   1. Initial program 96.0%

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

      1. fma-def 96.0%

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

      2. add-cube-cbrt 95.5%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}} + a \cdot b\right) + c \cdot i \]

      3. pow3 95.5%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   3. Applied egg-rr 95.5%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)}^{3}} + a \cdot b\right) + c \cdot i \]

   4. Taylor expanded in x around inf 62.9%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.38 \cdot 10^{+79} \lor \neg \left(x \cdot y \leq 3.7 \cdot 10^{+119}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 11: 43.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.9 \cdot 10^{+194} \lor \neg \left(a \cdot b \leq 1.08 \cdot 10^{+76}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -4.9e+194) (not (<= (* a b) 1.08e+76))) (* 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 (((a * b) <= -4.9e+194) || !((a * b) <= 1.08e+76)) {
		tmp = a * b;
	} 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 (((a * b) <= (-4.9d+194)) .or. (.not. ((a * b) <= 1.08d+76))) then
        tmp = a * b
    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 (((a * b) <= -4.9e+194) || !((a * b) <= 1.08e+76)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -4.9e+194) or not ((a * b) <= 1.08e+76):
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -4.9e+194) || !(Float64(a * b) <= 1.08e+76))
		tmp = Float64(a * b);
	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 (((a * b) <= -4.9e+194) || ~(((a * b) <= 1.08e+76)))
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -4.9e+194], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.08e+76]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.90000000000000026e194 or 1.07999999999999999e76 < (*.f64 a b)

   1. Initial program 89.7%

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

   2. Taylor expanded in a around inf 63.2%

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

   if -4.90000000000000026e194 < (*.f64 a b) < 1.07999999999999999e76

   1. Initial program 95.8%

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

   2. Taylor expanded in c around inf 32.8%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.9 \cdot 10^{+194} \lor \neg \left(a \cdot b \leq 1.08 \cdot 10^{+76}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 12: 27.0% 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 93.7%

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

2. Taylor expanded in a around inf 26.9%

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

3. Final simplification 26.9%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023301 
(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)))